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AI+电芯 | 基于时间和温度的动力电池剩余寿命RUL预测

AI+电芯

RUL

中文

AI+电芯RUL中文

JiaweiMiao

发布于 2023-09-08

推荐镜像 :Basic Image:bohrium-notebook:2023-04-07

推荐机型 :c32_m128_cpu

数据集

NASA_B5-7_pkl(v1)

基于时间和温度的动力电池剩余寿命RUL预测

快速开始：点击上方的 开始连接 按钮，选择 bohrium-notebook:2023-04-07镜像 和尽可能高的CPU配置机型即可开始。

背景

全球汽车数量的快速增长引发了人们对空气污染、全球变暖和自然资源枯竭的严重担忧。这些担忧促使了开发更安全、高效和环保的交通方式。随着电动汽车在全世界的兴起，锂离子电池产业快速发展。在所有最先进的存储技术中，锂离子电池具有最高水平的能量存储密度以及低自放电、超长寿命和循环性能等其他优点。

出于这些原因，我们必须拥有一种有效的算法，利用几个周期内测量的电压、电流和温度等特征来高精度预测电动汽车电池的剩余使用寿命 (RUL)。一个充电周期是指从充满电到放电再充满电的使用周期。平均锂离子电池通常可持续 300-500 个充电周期，每个充电周期都会导致电池容量的减少。当电池的容量下降到总容量的一定百分比以下时，电池实际上变得无法使用，具体取决于制造商和给定电池的使用情况。本案例的研究以70%作为阈值。

在这个项目中，我们应用数据分析和机器学习技术来预测电动汽车电池的剩余使用寿命（RUL），主要方法为使用一些特别的时间序列点和温度，在不同的机器学习算法下进行研究。我们使用了NASA公共数据集提供的电池退化数据集。

本Notebook搬运自github/aweditya/ev-battery-degradation

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!pip install seaborn==0.11.0 simple_colors==0.1.5 keras==2.7.0

Looking in indexes: https://pypi.tuna.tsinghua.edu.cn/simple
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WARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv

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加载一些必要的工具包

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# Basic libraries

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

import cmath

import seaborn as sns

from simple_colors import *

sns.set()

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数据描述

本数据集由四块锂离子电池在三种不同工况下的数据组成：充电、放电和室温下的阻抗测试

充电曲线 - 每个电池均以 1.5A 的恒流 (CC) 充电，直至电池电压达到 4.2V。然后以恒压（CV）模式充电，直至充电电流降至20mA
放电曲线 - 以 2A CC 进行放电，直至每个电池的电池电压分别降至 2.7V、2.5V、2.2V 和 2.5V
阻抗曲线 - 使用电化学阻抗谱 (EIS) 扫描范围为 0.1Hz 至 5kHz

每个电池都要经过 168 次充电-放电循环，这会导致加速老化。一旦电池容量减少 30%，即从 2 Ahr 减少到 1.4 Ahr，实验就停止。

数据类型

Charging fields （充电工况）
1. Battery terminal voltage (Volts) 电池终端电压
2. Battery output current (Amps) 电池输出电流
3. Battery temperature (°C) 电池温度
4. Current measured at charger (Amps) 充电器上测量的电流
5. Voltage measured at charger (Volts) 充电器上测量的电压
6. Measurement time stamps (secs) 测试时间戳
Discharging fields （放电工况）
1. Battery terminal voltage (Volts) 电池终端电压
2. Battery output current (Amps) 电池输出电流
3. Battery temperature (°C) 电池温度
4. Current measured at load (Amps) 充电器上测量的电流
5. Voltage measured at load (Volts) 充电器上测量的电压
6. Measurement time stamps (secs) 测试时间戳
7. Battery capacity (Ahr) for discharge till 2.7V 电池容量

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探索性数据分析 (EDA)

可用数据位于 MATLAB 结构中，为了便于分析，我们使用 pymatreader 模块在 Python 中加载数据，然后将数据帧导出为 pickle (.pkl) 文件。如果用户想直接从 .mat 文件加载数据，请使用以下命令从 pymatreader 库导入所需的函数：

from pymatreader import read_mat

并使用以下代码替换所有 pd.read_pickle 调用：

data = read_mat('path_to_file/B0005.mat')

df = pd.DataFrame(data['B0005']['cycle'])

数据分为三个数据帧，分别用于充电、放电和阻抗测量。放电数据将用于 RUL 预测，而阻抗数据将用于解释导致电池退化的内部机制。

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[3]

df = pd.read_pickle('/bohr/nasapkl-1637/v1/datasets/data/B0005.pkl')

	type	ambient_temperature	time	data
0	charge	24	0.000	{'Voltage_measured': [3.873017221300996, 3.479...
1	discharge	24	8243.672	{'Voltage_measured': [4.191491807505295, 4.190...
2	charge	24	12574.063	{'Voltage_measured': [3.3250546568448542, 3.00...
3	discharge	24	23730.485	{'Voltage_measured': [4.189773213846608, 4.188...
4	charge	24	28042.891	{'Voltage_measured': [3.3526036599987754, 3.03...
...	...	...	...	...
611	discharge	24	4761863.438	{'Voltage_measured': [4.18482689434833, 4.1843...
612	charge	24	4769141.844	{'Voltage_measured': [3.7032033475672854, 3.33...
613	discharge	24	4779444.204	{'Voltage_measured': [4.201968615940368, 4.200...
614	impedance	24	4782370.719	{'Sense_current': [(839.7420654296875-31.55541...
615	charge	24	4831284.125	{'Voltage_measured': [0.23635618415267867, 0.0...

616 rows × 4 columns

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显示数据集行列数和其包含的数据类型。

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# Print number of records (rows) and columns in the dataframe

print("Number of records:", len(df.index))

print("Number of columns:", len(df.columns))

print("---------------------")

# Printing the data type of each variable/column

print("Datatype of each column")

df.dtypes

Number of records: 616
Number of columns: 4
---------------------
Datatype of each column

type                    object
ambient_temperature      int64
time                   float64
data                    object
dtype: object

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检查是否有缺失的数据值

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# Checking for missing values in columns type, ambient_temperature and date

# We do not check for data immediately because the entries in data are

# Python dictionaries

df[['type', 'ambient_temperature', 'time']].isna().sum()

type                   0
ambient_temperature    0
time                   0
dtype: int64

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列类型表示当前的工况类型。环境温度列包含进行实验的温度，24度与数据集描述一致。我们可以绘制直方图来检查列类型和环境温度的变化。

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custom_params = {"axes.spines.right": False, "axes.spines.top": False}

sns.set_theme(style="whitegrid", rc=custom_params)

# Function to make a histogram plot for different columns in the data

def change_width(ax, new_value):

'''

Takes in a matplotlib axis object used for plotting a histogram/bar plot

and changes the width of the bars

Arguments:

ax -- matplotlib axis object

new_value -- float, the desired width of the histogram bars

'''

for patch in ax.patches :

current_width = patch.get_width()

diff = current_width - new_value

# Changing the bar width

patch.set_width(new_value)

# Recentering the bar

patch.set_x(patch.get_x() + diff * .5)

def plot_histogram(df, col, width = 0):

'''

Plots a histogram of the specified column of the dataframe

Arguments:

df -- pandas DataFrame object

col -- string, label of a column in the "df" dataframe

width -- float, if not equal to zero, the width of the bars in the histogram are modied

'''

plt.figure(figsize=(10, 5))

ax = sns.countplot(data = df, x = col, dodge = False)

ax.yaxis.tick_left()

ax.xaxis.tick_bottom()

# Change axis labels

plt.ylabel('Count', fontsize=14)

if col == 'ambient_temperature': plt.xlabel(col.capitalize().replace('_', ' ') + ' (°C)', fontsize=14)

else: plt.xlabel(col.capitalize(), fontsize=14)

# Change tick sizes

plt.xticks(fontsize=14)

plt.yticks(fontsize=14)

if width != 0: change_width(ax, width)

plt.show()

plot_histogram(df=df, col='type')

plot_histogram(df=df, col='ambient_temperature', width = 0.25)

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在列类型中，充电和放电是均匀分布的，这与电池先充电后放电的事实是一致的。环境温度列仅包含 24°C，这告诉我们实验条件在多个循环中是一致的。请注意，环境温度与电池温度不同。

时间列包含 MATLAB 日期时间格式 (YYYY-mm-dd-HH-mm-ss.s) 的实验开始时间。很明显，充电和放电循环之间存在一段时间间隔，在此期间电池处于休息状态。尽管我们将重点关注放电数据来预测 RUL，但我们还将绘制充电和阻抗周期中的数据。

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# This function splits the data into three dataframes containing charge, discharge and impedance data

def split_data(cell_number):

'''

Takes cell number as input and return three dataframes containing the different types of data in the

corresponding .pkl datafile

Arguments:

cell_number -- integer, should be one of 5, 6, 7, 18 (.pkl files corresponding to the above mentioned cells are available)

Returns:

charge -- pandas DataFrame object, contains the data of type "charge" pulled from the specified .pkl file

discharge -- pandas DataFrame object, contains data of type "discharge"

impedance -- pandas DataFrame object, contains data of type "impedance"

'''

num = '0' + str(cell_number) if cell_number != 18 else '18'

df = pd.read_pickle('/bohr/nasapkl-1637/v1/datasets/data/B00' + num + '.pkl')

#df = pd.DataFrame(data['B00' + num]['cycle'])

charge = df[df['type'] == 'charge']

discharge = df[df['type'] == 'discharge']

impedance = df[df['type'] == 'impedance']

return charge, discharge, impedance

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charge, discharge, impedance = split_data(cell_number = 5)

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充电周期

我们首先绘制不同周期充电数据的字段。这有助于我们了解电池退化对充电性能的影响。

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# This function returns a dataframe containing the measurements and

# the corresponding datatype stored depending on the "level".

def get_dtypes(df, col2, level = 1, exclusions = []):

'''

Takes a dataframe and a column and returns a dataframe containing data types present in the specified column

of the dataframe subject to conditions.

Arguments:

df -- pandas DataFrame object

col2 -- string, label of a columns in the df dataframe

level -- integer, specifies whether the function should return the data type of

the data in the column (level 1), or in the case that the data type is an array,

return the data type of the data present within the array (level 2).

exclusions -- list, if level is not 1, the function will treat the data in the

column as arrays. This exclusions list will contain those rows

which have non-array entitities so that a level 2 analysis is

skipped for them. (These row labels are obtained after running

a level 1 analysis)

Returns:

pandas DataFrame object containing row names and corresponding data types

'''

col1 = 'Measurements'

dtypes = []

keys = []

if level == 1:

for key in df.iloc[0]['data'].keys():

keys.append(key)

dtypes.append(str(type(df.iloc[0]['data'][key])))

else:

for key in df.iloc[0]['data'].keys():

if not (key in exclusions):

keys.append(key)

dtypes.append(df.iloc[0]['data'][key].dtype)

return pd.DataFrame((keys, dtypes), index = [col1, 'Datatype']).transpose()

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# List the types of measurements made in the charging cycle

print(blue('Measurements made with the type of data stored in it:', 'bold'))

# Printing the type of each key

get_dtypes(charge, 'Datatype', level = 1)

Measurements made with the type of data stored in it:

	Measurements	Datatype
0	Voltage_measured	<class 'numpy.ndarray'>
1	Current_measured	<class 'numpy.ndarray'>
2	Temperature_measured	<class 'numpy.ndarray'>
3	Current_charge	<class 'numpy.ndarray'>
4	Voltage_charge	<class 'numpy.ndarray'>
5	Time	<class 'numpy.ndarray'>

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# All the data is in numpy arrays so we also print the datatype

# of the data in those arrays

get_dtypes(charge, 'Datatype', level = 2)

	Measurements	Datatype
0	Voltage_measured	float64
1	Current_measured	float64
2	Temperature_measured	float64
3	Current_charge	float64
4	Voltage_charge	float64
5	Time	float64

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我们观察到每个字典值都是一个由 float 数据类型的时间序列数据组成的 Python 列表。 Time给出了进行测量的时刻。下图给出了电压电流随之间的变化。

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sns.set()

# Plot voltage and current variation for the charging cycle

time0 = charge.iloc[0]['data']['Time'] # Measurement time samples for each run

voltage0 = charge.iloc[0]['data']['Voltage_measured']

current0 = charge.iloc[0]['data']['Current_measured']

time160 = charge.iloc[160]['data']['Time'] # Measurement time samples for each run

voltage160 = charge.iloc[160]['data']['Voltage_measured']

current160 = charge.iloc[160]['data']['Current_measured']

voltages = {0: voltage0, 1: voltage160}

currents = {0: current0, 1: current160}

times = {0: time0, 1: time160}

cycles = {0: 0, 1: 160}

fig, axes = plt.subplots(2, 1, figsize=(9, 10))

axes_2 = [0,0]

for i in [0,1]:

axes[i].set_xlabel('Time (seconds)', fontsize=14)

axes[i].set_ylabel('Battery Voltage (V)', fontsize=14)

axes[i].plot(times[i], voltages[i], label = 'Voltage')

axes[i].scatter(times[i], voltages[i], s = 4)

axes[i].legend(loc = (0.7,0.23))

axes_2[i] = axes[i].twinx()

axes_2[i].set_ylabel('Measured Current (A)', fontsize=14)

axes_2[i].plot(times[i], currents[i], label = 'Current', color = 'r')

axes_2[i].scatter(times[i], currents[i], s = 4, color = 'r')

axes_2[i].grid(False)

axes_2[i].scatter(np.linspace(0,times[i][-1],150), [0.02 for i in range(150)], s = 0.05, color = 'black')

axes_2[i].legend(title = f'Cycle {cycles[i]}', loc = (0.7,0.3))

fig.tight_layout() # otherwise the right y-label is slightly clipped

plt.show()

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从上图中，我们确认电池以恒流充电至 4.2V，之后随着测量的电流下降而以恒压充电。比较不同周期之间的图，我们观察到电池在老化时需要更长的时间来充电，这通过电池电压达到 4.2V 的时间更长来表明。我们没有明确绘制在充电器上测量的电流和电压，因为我们希望这些图与上面看到的类似。

下面我们来看看温度随时间变化的曲线。

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# Temperature variation during charging cycle

plt.figure(figsize=(10, 5))

cycles = [0, 40, 80, 120, 160]

for cycle in cycles:

time = charge.iloc[cycle]['data']['Time']

data = charge.iloc[cycle]['data']['Temperature_measured']

plt.plot(time, data, label=f'cycle{cycle}', linewidth=1.5)

plt.xlabel('Time (seconds)', fontsize=14)

plt.ylabel('Temperature (°C)', fontsize=14)

plt.legend()

plt.show()

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[14]

# Plotting temperature and voltage on the same plot

measured_voltage = charge.iloc[0]['data']['Voltage_measured']

measured_temperature = charge.iloc[0]['data']['Temperature_measured']

time = charge.iloc[0]['data']['Time']

fig, ax1 = plt.subplots(figsize=(10, 5))

ax1.set_xlabel('Time (seconds)', fontsize=14)

ax1.set_ylabel('Battery Voltage (V)', fontsize=14)

ax1.plot(time, measured_voltage, label='Voltage')

ax1.scatter(time, measured_voltage, s=5)

ax1.legend(loc = (0.8,0.43))

ax2 = ax1.twinx()

ax2.set_ylabel('Battery Temperature (°C)', fontsize=14)

ax2.plot(time, measured_temperature, color='red', label='Temperature')

ax2.scatter(time, measured_temperature, color='red', s=5)

ax2.legend(loc = (0.8,0.5))

ax2.grid(False)

fig.tight_layout()

plt.show()

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充电周期中的温度与电池退化之间似乎没有很强的相关性，尽管总体趋势相似：在恒流阶段温度升高，在恒压阶段温度降低。

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阻抗周期

背景

通过在宽频率范围内向电池施加小交流电压并测量通过它的电流来测量电化学阻抗。信号保持较小，以确保细胞表现出伪线性。阻抗是一个复数，由其大小和相位指定。

根据数据集描述，应用频率在 0.1Hz 到 5kHz 之间的交流电流来估计电池阻抗。然后用它来获得不同降解阶段的电解和电荷转移电阻。

电解电阻是电解质的电阻
电荷转移阻力是离子在电池中不同化合物之间转移时所面临的阻力

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[15]

# List the types of measurements made in the charging cycle

print(blue('Measurements made with the type of data stored in it:', 'bold'))

# Printing the type of each key

get_dtypes(impedance, 'Type', level = 1)

Measurements made with the type of data stored in it:

	Measurements	Datatype
0	Sense_current	<class 'numpy.ndarray'>
1	Battery_current	<class 'numpy.ndarray'>
2	Current_ratio	<class 'numpy.ndarray'>
3	Battery_impedance	<class 'numpy.ndarray'>
4	Rectified_Impedance	<class 'numpy.ndarray'>
5	Re	<class 'float'>
6	Rct	<class 'float'>

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Sense_current、Battery_current、Current_ratio、Battery_impedance、Rectified_Impedance 是 numpy 数组，而 Re（电解电阻）、Rct（电荷转移电阻）是浮点值。我们还打印 numpy 数组的数据类型，以确认这些数量是复数。

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[16]

# Printing the datatype of each key which is an array.

# Re and Rct are of type float so they will be excluded

get_dtypes(impedance, 'Datatype', level = 2, exclusions = ['Re', 'Rct'])

	Measurements	Datatype
0	Sense_current	complex128
1	Battery_current	complex128
2	Current_ratio	complex128
3	Battery_impedance	complex128
4	Rectified_Impedance	complex128

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我们继续绘制不同运行的 Sense_current、Battery_current、Current_ratio、Battery_impedance、Rectified_Impedance，而 Re、Rct 则绘制为运行的函数，因为它们是浮点数。

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[17]

# Helper function for plotting impedance characteristics

def plot_impedance_characteristics(df, feature, runs=[0, 80, 160, 240], log_scale=False):

'''

Takes dataframe (containing impedance data), feature, and a list of runs as input and plots

the data stored in it. Since the function is specifically for impedance data, and that has

data stored in complex format, the graph of the magnitudes is plotted.

Arguments:

df -- pandas DataFrame object, should contain impedance data conforming to the required format

feature -- string, the data corresponding to this feature will be plotted

runs -- list, plots of the specified feature will be made for all the runs specified in this list

log_scale -- bool, specifies whether the axes should be log-scaled

'''

fig, axes = plt.subplots(1, 2, figsize=(20, 5))

if log_scale:

axes[0].set_xscale('log')

axes[0].set_yscale('log')

axes[1].set_xscale('log')

# Plotting the magnitude for different runs

for run in runs:

data = df.iloc[run]['data'][feature]

data_magnitude = np.abs(data)[5:]

axes[0].plot(data_magnitude, label=f'run{run}')

axes[0].legend()

axes[0].set_title(f'{feature.replace("_", " ").title()} Magnitude plot', fontsize=16)

# Plotting the phase for different runs

for run in runs:

data = df.iloc[run]['data'][feature]

data_phase = [cmath.phase(data[i]) for i in range(len(data))][5:]

axes[1].plot(data_phase, label=f'run{run}')

axes[1].legend()

axes[1].set_title(f'{feature.replace("_", " ").title()} Phase plot', fontsize=16)

plt.show()

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[18]

plot_impedance_characteristics(impedance, 'Sense_current')

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从感测电流幅值图中可以看出，不同频率下施加的电流幅值在不同的运行中几乎是恒定的，这是预期的，因为测量必须在相似的条件下进行。我们对电池电流重复上述过程。

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[19]

plot_impedance_characteristics(impedance, 'Battery_current')

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[20]

plot_impedance_characteristics(impedance, 'Current_ratio')

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到目前为止，随着电池随时间的推移而退化，电池内部参数似乎没有任何明显的趋势。

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[21]

plot_impedance_characteristics(impedance, 'Battery_impedance')

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从电池阻抗图中，我们观察到随着时间的推移，阻抗稳定并且不会振荡。

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[22]

plot_impedance_characteristics(impedance, 'Rectified_Impedance')

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尽管相位图没有任何相关特征，但幅度图显示随着电池老化，整流阻抗会增加。

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[23]

# Helper function to plot resistances as a function of runs

def plot_resistance(df, key):

'''

Takes a dataframe (containing impedance data) and key as input and plots the data corresponding

to the key.

Arguments:

df -- pandas DataFrame object, should contain impedance data conforming to the required format

key -- string, should be one of "Re" or "Rct". The function scans the complete dataframe for

the required key (each row in the dataframe corresponds to one run, and each run contains

one value for "Re" and "Rct")

'''

resistance = [impedance.iloc[i]['data'][key] for i in range(len(impedance))]

labels = {

'Re': 'Electrolytic Resistance',

'Rct': 'Charge-transfer Resistance'

}

plt.figure(figsize=(10, 5))

plt.title(f'{labels[key]} for different runs', fontsize=16)

plt.ylabel('Resistance (Ohms)', fontsize=14)

plt.plot(resistance)

plt.show()

# Plot the electrolytic and charge-transfer resistance for different runs

plot_resistance(impedance, 'Re')

plot_resistance(impedance, 'Rct')

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我们没有直接尝试分析阻抗，而是采用不同的方法，尝试了解这些数据何时被收集（到目前为止，我们一直将不同的循环称为runs，但让我们尝试了解这意味着什么）

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[24]

impedance.index # Print indices for impedance measurements in the original data

Int64Index([ 40,  42,  44,  46,  48,  50,  52,  54,  56,  58,
            ...
            594, 596, 598, 600, 602, 604, 606, 608, 610, 614],
           dtype='int64', length=278)

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我们“Zoom in”到数据组中围绕阻抗测量的不同位置。

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[25]

df[35:50]

	type	ambient_temperature	time	data
35	charge	24	268433.610	{'Voltage_measured': [3.3967166797066484, 3.09...
36	discharge	24	279067.297	{'Voltage_measured': [4.188779799856791, 4.188...
37	charge	24	283098.204	{'Voltage_measured': [3.3869430085009946, 3.08...
38	discharge	24	293897.563	{'Voltage_measured': [4.189272591516219, 4.188...
39	charge	24	1398364.969	{'Voltage_measured': [3.5795499179382677, 3.23...
40	impedance	24	1410431.938	{'Sense_current': [(-1+1j), (820.6094970703125...
41	discharge	24	1411321.875	{'Voltage_measured': [4.187614060563439, 4.186...
42	impedance	24	1416658.391	{'Sense_current': [(-1+1j), (656.5957641601562...
43	charge	24	1417540.422	{'Voltage_measured': [3.389085680145772, 3.068...
44	impedance	24	1429569.094	{'Sense_current': [(-1+1j), (809.5048217773438...
45	discharge	24	1430451.079	{'Voltage_measured': [4.1876287811083985, 4.18...
46	impedance	24	1435746.266	{'Sense_current': [(-1+1j), (684.2487182617188...
47	charge	24	1436628.422	{'Voltage_measured': [3.380743064766377, 3.062...
48	impedance	24	1448655.735	{'Sense_current': [(-1+1j), (812.7781982421875...
49	discharge	24	1449537.782	{'Voltage_measured': [4.187447226312926, 4.186...

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我们观察到，在电池充电和放电后会进行单独的阻抗测量。现在让我们比较一下电池在特定点充电和放电后的阻抗特性。

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# 40 is an impedance measurement after charging

# 42 is an impedance measurement after discharging

runs = [40, 42]

keys = ['Sense_current', 'Battery_current', 'Current_ratio',

'Battery_impedance', 'Rectified_Impedance']

for key in keys:

plot_impedance_characteristics(df, key, runs, log_scale=False) # Plotting the parameters in keys

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尽管放电后电解电阻和电荷转移电阻有所降低，但图中似乎没有什么特别的地方。

我们还对电池阻抗和整流阻抗的奈奎斯特图进行了实验。在奈奎斯特图中，复数的实部和虚部沿着不同的轴绘制。

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def plot_nyquist(df, feature, runs=[0, 80, 160, 240]):

'''

Function to make a Nyquist plot for battery and rectified impedance. In a

Nyquist plot, the real and imaginary parts are plotted against each other.

Arguments:

df -- pandas DataFrame object, should contain impedance data conforming to the required format

feature -- string, the data corresponding to this feature will be plotted

runs -- list, plots of the specified feature will be made for all the runs specified in this list

'''

plt.figure(figsize=(10, 5))

# Plotting the magnitude for different runs

for run in runs:

data = df.iloc[run]['data'][feature]

data_real = [data[i].real for i in range(len(data))]

data_imag = [-data[i].imag for i in range(len(data))]

plt.scatter(data_real, data_imag, label=f'run{run}')

plt.legend()

plt.title(f'{feature.replace("_", " ").title()} Nyquist plot', fontsize=16)

plt.xlabel('Re(Z) Ω', fontsize=14)

plt.ylabel('-Im(Z) Ω', fontsize=14)

plt.show()

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plot_nyquist(impedance, feature='Battery_impedance', runs=[80, 160, 240]) # Plotting the parameters in keys

plot_nyquist(impedance, feature='Rectified_Impedance', runs=[80, 160, 240]) # Plotting the parameters in keys

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从上述内容可以看出，电池电阻似乎随着放电而增加。

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放电周期

我们首先绘制放电周期的特征，以了解电池退化的影响。我们不会绘制负载处的电压和电流，因为在电池处测量的电压和电流可以让我们了解总体趋势。

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# List the types of measurements made in the charging cycle

print(blue('Measurements made with the type of data stored in it:', 'bold'))

# Printing the type of each key

get_dtypes(discharge, 'Datatype', level = 1)

Measurements made with the type of data stored in it:

	Measurements	Datatype
0	Voltage_measured	<class 'numpy.ndarray'>
1	Current_measured	<class 'numpy.ndarray'>
2	Temperature_measured	<class 'numpy.ndarray'>
3	Current_load	<class 'numpy.ndarray'>
4	Voltage_load	<class 'numpy.ndarray'>
5	Time	<class 'numpy.ndarray'>
6	Capacity	<class 'float'>

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除容量外，所有特征都是时间序列数据，并将针对不同的放电周期进行绘制。我们还将容量绘制为放电周期的函数。请注意，电池容量是在该特定循环放电结束时提供的。

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# Printing the datatype of each key which is an array.

# Capacity is of type float so it will be excluded

get_dtypes(discharge, 'Datatype', level = 2, exclusions = ['Capacity'])

	Measurements	Datatype
0	Voltage_measured	float64
1	Current_measured	float64
2	Temperature_measured	float64
3	Current_load	float64
4	Voltage_load	float64
5	Time	float64

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from matplotlib.patches import Rectangle

# This function plots the data of specified type (voltage, current or temperature)

# for the cycle numbers specified by "cycle_list" argument

sns.set()

def dc_cycle_plots(cell_number, cycle_list, type, figsize = (10,5), only_scatter = False, zoom_beginning_range = None):

'''

Creates plots of the specified type of data for the specified number of cycles for the specified cell number.

Arguments:

cell_number -- integer, should be one of 5, 6, 7, 18

cycle_list -- list, contains the required cycle numbers for which the plots should be made

type -- string, can be one of "voltage", "current", "temperature". The plots for the

corresponding type will be created after the discharge data is extracted for the

specified cell number.

figsize -- tuple, specifies the size of the plot

only_scatter -- bool, set to True if only the scatter plot is desired

zoom_beggining_range -- integer, if this argument is not "None", a small subplot will be

created for the data sliced from the first value to the value specified.

In addition to the subplot, a rectangle will also be created around

the initial part of the graph.

!! for type = "voltage" only !!

'''

_, discharge, _= split_data(cell_number)

labels = {'voltage': 'Battery terminal voltage (V)',

'current': 'Battery output current (A)',

'temperature': 'Battery temperature (°C)'}

type_ = type.capitalize() + '_measured'

fig, ax0 = plt.subplots(1, 1, figsize = figsize)

for cycle in cycle_list:

time_data = discharge.iloc[cycle]['data']['Time'] # List of times obtained from the "discharge" dataframe

type_data = discharge.iloc[cycle]['data'][type_] # Data of the type specified, obtained from the "discharge" dataframe

if not only_scatter: ax0.plot(time_data, type_data, label = f"cycle {cycle}")

ax0.scatter(time_data, type_data, s = 5)

plt.title(f"{type.capitalize()} Measured for cell number {cell_number}", fontsize = 16)

plt.xlabel("Time (seconds)", fontsize = 14)

plt.ylabel(labels[type], fontsize = 14)

plt.legend()

if zoom_beginning_range != None and type == 'voltage':

ax0.add_patch(Rectangle((-50,3.9), 200, 0.4, edgecolor = "black", facecolor = "none"))

ax0.text(200, 4.1, "Initial Sharp Decrease")

sns.reset_orig()

ax = fig.add_axes([0.17, 0.3, 0.2, 0.2])

for cycle in cycle_list:

time_data = discharge.iloc[cycle]['data']['Time'][:zoom_beginning_range] # List of times obtained from the "discharge" dataframe

type_data = discharge.iloc[cycle]['data'][type_][:zoom_beginning_range] # Data of the type specified, obtained from the "discharge" dataframe

ax.plot(time_data, type_data)

ax.scatter(time_data, type_data, s = 1)

ax.set_xlabel("Magnified portion")

ax.grid(False)

sns.set()

plt.show()

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[32]

cycles = [0, 40, 80, 120, 160]

figsize = (10,5)

# Observing that voltage has an initial drop, we magnify the initial sharp decrease in voltage measured

dc_cycle_plots(5, cycles, 'voltage', figsize = figsize, only_scatter = False, zoom_beginning_range = 5)

dc_cycle_plots(5, cycles, 'current', figsize = figsize, only_scatter = False)

dc_cycle_plots(5, cycles, 'temperature', figsize = figsize, only_scatter = False)

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[33]

# Plotting temperature and discharge on the same plot

measured_voltage = discharge.iloc[0]['data']['Voltage_measured']

measured_temperature = discharge.iloc[0]['data']['Temperature_measured']

time = discharge.iloc[0]['data']['Time']

fig, ax1 = plt.subplots(figsize=(10, 5))

ax1.set_xlabel('Time (seconds)', fontsize=14)

ax1.set_ylabel('Battery Voltage (V)', fontsize=14)

ax1.plot(time, measured_voltage, label='Voltage')

ax1.scatter(time, measured_voltage, s=5)

ax1.legend(loc = (0.45,0.13))

ax2 = ax1.twinx()

ax2.set_ylabel('Battery Temperature (°C)', fontsize=14)

ax2.plot(time, measured_temperature, color='red', label='Temperature')

ax2.scatter(time, measured_temperature, color='red', s=5)

ax2.grid(False)

ax2.legend(loc = (0.45,0.2))

fig.tight_layout()

plt.show()

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[34]

# Plotting capacity as a function of discharge cycles

capacity = [discharge.iloc[i]['data']['Capacity'] for i in range(len(discharge))]

plt.figure(figsize=(10, 5))

plt.title('Variation of Capacity with Discharge Cycle', fontsize=16)

plt.xlabel('Cycle', fontsize=14)

plt.ylabel('Battery Capacity (Ahr)', fontsize=14)

plt.plot(capacity, linewidth=0.5)

plt.scatter(np.arange(0, len(capacity)), capacity, s=5)

plt.show()

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我们强调了放电特性中的一些重要特征。

电压

我们可以将图分为 4 个部分：开始处急剧下降，看起来呈线性，然后是一个直到拐点斜率减小的区域。随后出现指数式下降，然后实验停止。由于酸从电解质扩散到极板，电池电压在此之后开始上升。最初的急剧下降是由于施加负载电流时的内部电池阻抗造成的。该部分的斜率可用于估计该阻抗，并且与电池阻抗随着电池退化而增加的事实相一致。

温度

我们可以将该图分为 3 个部分：温度急剧上升至拐点，温度以较小的斜率上升直至峰值温度，最后下降。下降是由于负载的移除使电池恢复到环境温度所致。第一部分可归因于突然施加负载电流。

我们观察到，随着电池的老化，电池放电所需的时间会减少。我们还观察到，电池达到的最高温度随着电池放电而单调增加。随着电池性能的下降，电池达到最高温度所需的时间会减少。

我们观察到，一旦电池电压下降到2.6-2.7V，放电就停止了。这是因为 18650 锂离子电池的放电截止电压为 3.0V。正如数据集描述中提到的，该实验使电池超出了这个范围，加速了退化效应。

剩余寿命（RUL）预测

我们使用间接方法来估计 RUL。电池容量是使用放电周期中进行的测量来估计的。虽然可以用测量容量来预测，但在电动汽车运行时这是不可行的。另一方面，电压和电流测量则很容易进行。

我们首先预处理数据以进行特征提取。提取的特征：

电池电压达到 2.7V 至 4V 之间指定电压值的时刻
电池放电且负载电流停止的时间
电池放电时达到的最高温度
电池达到最高温度的时间

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[35]

# This function splits the data into three dataframes containing charge, discharge and impedance data

def split_data(cell_number):

'''

Takes cell number as input and return three dataframes containing the different types of data in the

corresponding .pkl datafile

Arguments:

cell_number -- integer, should be one of 5, 6, 7, 18 (.pkl files corresponding to the above mentioned cells are available)

Returns:

charge -- pandas DataFrame object, contains the data of type "charge" pulled from the specified .pkl file

discharge -- pandas DataFrame object, contains data of type "discharge"

impedance -- pandas DataFrame object, contains data of type "impedance"

'''

num = '0' + str(cell_number) if cell_number != 18 else '18'

df = pd.read_pickle('/bohr/nasapkl-1637/v1/datasets/data/B00' + num + '.pkl')

charge = df[df['type'] == 'charge']

discharge = df[df['type'] == 'discharge']

impedance = df[df['type'] == 'impedance']

return charge, discharge, impedance

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[36]

# This function performs the major preprocessing of the data, by picking out the data values

# which will be used for training out of the complete available data

def preprocessing(cell_number, voltage_splits = 16):

'''

Extracts features and labels from the data from the specified cell number

and returns them as numpy arrays

Arguments:

cell_number -- integer, should be one of 5, 6, 7, 18

voltage_splits -- integer, specifies number of values the interval of voltages

[2.7, 4] should be split into

Returns:

x -- numpy array, contains the feature data. The required features are extracted

from the discharge data of the specified cell number.

y -- numpy array, contains the labels corresponding to the features in "x"

'''

_, discharge, _ = split_data(cell_number)

# Default split is 16 which gives the following voltages:

# [2.7, 2.787, 2.873, 2.96, 3.047,3.13333333, 3.22, 3.307, 3.393,

# 3.48, 3.567, 3.653, 3.74, 3.827, 3.913, 4.]

voltages = np.linspace(2.7, 4, voltage_splits)

# features0 stores the Times at which terminal voltage is 2.7, ..., 4

# features1 stores the Time to reach minimum terminal voltage

# feature2 stores the Maximum temperature

# feature3 stores the Time to reach maximum temperature

feature0, feature1, feature2, feature3 = [], [], [], []

for i in range(len(discharge)):

time_data = discharge.iloc[i]['data']['Time'] # Getting time data from the discharge dataframe

voltage_data = discharge.iloc[i]['data']['Voltage_measured'] # Getting voltage data

temp_data = discharge.iloc[i]['data']['Temperature_measured'] # Getting temperature data

times = []

for j in range(voltage_splits):

time_for_closest_voltage = time_data[np.argmin(np.abs(voltage_data - voltages[j]))] # time at which the reading stored in "voltage_data" is closest

times.append(time_for_closest_voltage) # to one of the values in the "voltages" array

feature0 = feature0 + [times]

feature1.append(time_data[np.argmin(voltage_data)])

feature2.append(np.max(temp_data))

time_for_max_temp = time_data[np.argmax(temp_data)] # time at which temperature reaches its maximum value

feature3.append(time_for_max_temp)

# Using list comprehension:

# feature0 = [[discharge.iloc[i]['data']['Time'][np.argmin(np.abs(discharge.iloc[i]['data']['Voltage_measured'] - voltages[j]))] for j in range(len(voltages))] for i in range(len(discharge))]

# feature1 = [discharge.iloc[i]['data']['Time'][np.argmin(discharge.iloc[i]['data']['Voltage_measured'])] for i in range(len(discharge))]

# feature2 = [np.max(discharge.iloc[j]['data']['Temperature_measured']) for j in range(len(discharge))]

# feature3 = [discharge.iloc[j]['data']['Time'][np.argmax(discharge.iloc[j]['data']['Temperature_measured'])] for j in range(len(discharge))]

x = np.array(feature0)

feature1 = np.array(feature1)

feature1 = feature1[:, np.newaxis]

feature2 = np.array(feature2)

feature2 = feature2[:, np.newaxis]

feature3 = np.array(feature3)

feature3 = feature3[:, np.newaxis]

x = np.hstack((x, feature1, feature2, feature3))

y = np.array([discharge.iloc[i]['data']['Capacity'] for i in range(len(discharge))])

return x, y

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提取的特征并不都是唯一的。它们之间存在高度相关性，我们通过相关性热图来说明。

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[37]

x, y = preprocessing(5, 16)

# Plot a correlation matrix to determine if there are any redundancies

corr = pd.DataFrame(x).corr()

# Plotting a heatmap between continuous variables

plt.figure(figsize=(20,10))

ax = sns.heatmap(corr,

xticklabels=corr.columns,

yticklabels=corr.columns,

annot=True)

plt.show()

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机器学习框架

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!pip install scikit-learn xgboost==1.5.1 catboost==1.0.3 lightgbm==3.3.1

Looking in indexes: https://pypi.tuna.tsinghua.edu.cn/simple
Requirement already satisfied: scikit-learn in /opt/conda/lib/python3.8/site-packages (1.0.2)
Collecting xgboost==1.5.1
  Downloading https://pypi.tuna.tsinghua.edu.cn/packages/36/16/3a81d29dea691882bc95151879217a0c21c07740d0355dc90fe11836e10d/xgboost-1.5.1-py3-none-manylinux2014_x86_64.whl (173.5 MB)
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Collecting catboost==1.0.3
  Downloading https://pypi.tuna.tsinghua.edu.cn/packages/2f/f3/b432b0f2472fe62bd47d5ed653ffd022f49d242ac7c8017b853951c36726/catboost-1.0.3-cp38-none-manylinux1_x86_64.whl (76.3 MB)
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Collecting lightgbm==3.3.1
  Downloading https://pypi.tuna.tsinghua.edu.cn/packages/6a/69/b5e23ed4c6ce40f820440b776fdc0401fa4531eab73c38d228d9d59236b1/lightgbm-3.3.1-py3-none-manylinux1_x86_64.whl (2.0 MB)
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Installing collected packages: xgboost, lightgbm, catboost
  Attempting uninstall: xgboost
    Found existing installation: xgboost 0.90
    Uninstalling xgboost-0.90:
      Successfully uninstalled xgboost-0.90
  Attempting uninstall: lightgbm
    Found existing installation: lightgbm 2.2.3
    Uninstalling lightgbm-2.2.3:
      Successfully uninstalled lightgbm-2.2.3
Successfully installed catboost-1.0.3 lightgbm-3.3.1 xgboost-1.5.1
WARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv

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# Import some additional libraries for ML tasks

from sklearn.model_selection import train_test_split

from sklearn.preprocessing import StandardScaler

from sklearn.svm import SVR

from sklearn.ensemble import RandomForestRegressor, AdaBoostRegressor

from sklearn.neural_network import MLPRegressor

from xgboost import XGBRegressor

from catboost import CatBoostRegressor

from lightgbm import LGBMRegressor

from sklearn.metrics import mean_squared_error, r2_score

/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index

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# This function prepares the x and y data for training by performing the test-train split,

# and applying StandardScaler to normalize the values. The scaler is saved as a global

# variable so that it can be used to obtain the original data by performing inverse_transform

# (if needed)

def prep_for_training(x, y, scale_config = True):

'''

Prepares the features and labels for applying to machine learning models.

Features are split into testing and training subsets and then scaled using

StandardScaler.

Arguments:

x -- numpy array, contains features

y -- numpy array, contains labels

scale_config -- bool, if True, redefines the scaler and fits it to the training data,

which is a subset of "x" created by the train_test_split function.

Returns:

train -- list, contains the training data consisting of features and corresponding labels

test -- list, contains the testing data consisting of features and corresponding labels

Additional:

scaler is a global variable and can be used in later steps in case the original data

needs to be extracted, by running scaler.inverse_transform()

'''

global scaler

# Split the data in the ratio 80:20 for training, testing respectively

train_x, test_x, train_y, test_y = train_test_split(x, y, train_size = 0.8)

if scale_config:

# Standardize the training data

scaler = StandardScaler()

# Fit the scaler to X_train

scaler.fit(train_x)

# Transform the entire data using the computed mean and variance

train_x = scaler.transform(train_x)

test_x = scaler.transform(test_x)

train = [train_x, train_y]

test = [test_x, test_y]

return train, test

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我们使用主成分分析（PCA）来减少特征的维度，保留尽可能多的可变性。我们使用保留 1% 标准偏差所需的最少组件数量。

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x, y = preprocessing(5, 16) # using cell 5 for training

[train_x, train_y], [test_x, test_y] = prep_for_training(x, y)

# Import the module for PCA

from sklearn.decomposition import PCA

# Re-centre the data to have zero mean

X_for_pca = train_x - np.mean(train_x, axis=0)[np.newaxis, :]

# Compute std. deviation of L2 norm input vectors

l2_norm = np.sum(X_for_pca ** 2, axis=-1)

std_dev = np.std(l2_norm)

# Threshold for dimensionality reduction set to 1% of std. deviation

threshold = 0.01 * std_dev

rmse_vs_components = [] # List of RMSE vs n_components for plotting

desired_components = 19 # Start by assuming all components are necessary

# Iterate over number of retained dimensions

for n_components in range(1, 20):

pca = PCA(n_components=n_components)

# Fit PCA onto the input data

pca.fit(X_for_pca)

# Apply dimensionality reduction on X

X_transformed = pca.transform(X_for_pca)

# Transform back to the starting space to compute reconstruction error

X_projected = pca.inverse_transform(X_transformed)

# Compute RMSE reconstruction error

rmse = np.sum((X_for_pca - X_projected) ** 2, axis=-1).mean()

if rmse < threshold:

if n_components <= desired_components:

desired_components = n_components

#desired_components = min(n_components, desired_components)

rmse_vs_components.append(rmse)

# Plot RMSE vs Components Retained

plt.figure(figsize=(15, 8))

plt.xlabel('Components Retained', fontsize=14)

plt.ylabel('RMSE Reconstruction Error', fontsize=14)

plt.plot(np.arange(1, 20), rmse_vs_components, lw=3)

plt.scatter(np.arange(1, 20), rmse_vs_components, lw=3, s = 10)

plt.scatter(np.linspace(0,19,500),[threshold for i in range(500)], s = 0.05, color = 'r')

plt.text(14, threshold + 0.05, "Threshold", fontsize = 14)

plt.xticks(np.arange(0, 20, 1))

plt.yticks(np.arange(0,2.75,0.25))

print(red(f"{desired_components}", 'bold'), "components are sufficient to satisfy the RMSE reconstruction criterion")

plt.show()

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我们使用经过PCA降维后获得的特征来转换训练数据和测试数据。

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n_components = desired_components # Sufficient dimensions after compression

# PCA with 8 retained dimensions

pca = PCA(n_components=n_components)

pca.fit(X_for_pca)

train_x = pca.transform(train_x)

test_x = pca.transform(test_x)

# Print the shape for confirmation

print(train_x.shape)

print(test_x.shape)

(134, 8)
(34, 8)

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我们将训练如下模型:

1. Support Vector Regressor 支持向量回归 (SVR):

与普通线性回归相反，其中目标函数是： $min i = 1 \sum n (y_{i} - w_{i} x_{i})$ SVR的目标函数是最小化系数向量d $l^{2}$ 范数 — 而不是平方误差。相反，误差项在约束中处理，我们将绝对误差设置为小于或等于指定的裕度（用 $ϵ$ 表示）。目标函数因此变为 $min ∣∣ w ∣ ∣^{2}$ 受约束 $∣ y_{i} - w_{i} x_{i} ∣ < ϵ$

2. Multilayered Perceptron 多层感知器 (MLP):

多层感知器由输入层和输出层以及多个可能的隐藏层组成。应用每个隐藏层的激活函数后，通过计算前一层的输出与当前隐藏层的权重之间的点积来计算隐藏层的输出。这一直持续到到达输出层。在训练期间，输出将用于“反向传播”算法，以根据所选标准减少计算损失。在测试期间，输出按原样使用。

3. Random Forest Regressor 随机森林回归：:

随机森林使用集成学习来实现回归/分类目的。训练几个决策树并将它们各自的预测汇集起来，以获得比单棵树更准确的结果。在回归任务中，模型的输出是所有决策树预测的平均值。

以下四种算法属于Boosting 算法系列。 Boosting 是一种集成建模技术，试图从多个弱分类器中构建一个鲁棒的分类器。它是通过串联使用弱模型来构建模型来完成的。首先，根据训练数据构建模型。然后构建第二个模型，它试图纠正第一个模型中存在的错误。此过程继续进行，并添加模型，直到正确预测完整的训练数据集或添加最大数量的模型。

4. XGBoost Regressor:

XGBoost（或 eXtreme Gradient Boosting）是一种基于决策树的集成机器学习算法，使用梯度提升算法。

5. AdaBoost Regressor:

AdaBoost（或自适应增强）是第一个成功实现增强算法的方法。 AdaBoost 算法涉及使用非常短的（一级）决策树作为弱学习器，并按顺序添加到集成中。

6. LightBGM Regressor:

LightBGM（或 Light Boosted Gradient Machine）通过添加一种自动特征选择以及专注于具有较大梯度的增强示例来扩展梯度增强算法。这会显着加快训练速度并提高预测性能。

7. CatBoost Regressor:

CatBoost 是 Yandex 开发的开源库。它是一个深度梯度提升库，它使用不经意的决策树来生长平衡树。

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# These functions train and evaluate their respective models. Models are saved as

# global variables so they can be used in the later step of evaluating the model.

# Evaluation is carried out on completely different cells which the model has not seen

def eval_svr(train, test, training = True):

'''

If training is enabled, a new instance of a Support Vector Regression model is created

and fit on the training data. The model is then fed with test data and it's performance

is reported. If training is disabled, the model previously defined is simply evaluated

using the test data and it's performance is reported.

Arguments:

train -- list, should be of the form [train features, train labels]

test -- list, should be of the form [test features, test labels]

training -- bool, specifies whether training is enabled or disabled

Additional:

The model created is a global variable and can be used in later steps when evaluating

on different datasets (after setting training to "False").

'''

global svr

if training:

# Define a SVM regressor with a Gaussian kernel

svr = SVR()

# Train the model

svr.fit(train[0], train[1])

# Test the model returning mean accuracy

print(blue(f"Evaluating the Support Vector Regressor...", 'bold'))

print(f"R2 Score = {svr.score(test[0], test[1]):.4f}")

mse = mean_squared_error(svr.predict(test[0]), test[1])

rmse = np.sqrt(mse)

print(f"RMSE = {rmse:.4f}")

def eval_mlp(train, test, training = True, layer_size = 100, max_iter = 100):

'''

If training is enabled, a new instance of a Multi Layered Perceptron model is created

and fit on the training data. The model is then fed with test data and it's performance

is reported. If training is disabled, the model previously defined is simply evaluated

using the test data and it's performance is reported.

Arguments:

train -- list, should be of the form [train features, train labels]

test -- list, should be of the form [test features, test labels]

training -- bool, specifies whether training is enabled or disabled

Additional:

The model created is a global variable and can be used in later steps when evaluating

on different datasets (after setting training to "False").

'''

global mlp

if training:

# Define a regressor with 1 hidden layer

mlp = MLPRegressor(hidden_layer_sizes = (layer_size,), max_iter = max_iter)

# Train the model

mlp.fit(train[0], train[1])

# Test the model returning mean accuracy

print(blue(f"Evaluating the Multi-Layer Perceptron...", 'bold'))

print(f"R2 Score = {mlp.score(test[0], test[1]):.4f}")

mse = mean_squared_error(mlp.predict(test[0]), test[1])

rmse = np.sqrt(mse)

print(f"RMSE = {rmse:.4f}")

def eval_rf(train, test, training = True, n_estimators = 100):

'''

If training is enabled, a new instance of a Random Forest Regression model is created

and fit on the training data. The model is then fed with test data and it's performance

is reported. If training is disabled, the model previously defined is simply evaluated

using the test data and it's performance is reported.

Arguments:

train -- list, should be of the form [train features, train labels]

test -- list, should be of the form [test features, test labels]

training -- bool, specifies whether training is enabled or disabled

Additional:

The model created is a global variable and can be used in later steps when evaluating

on different datasets (after setting training to "False").

'''

global regressor

if training:

# Define a random forest regressor

regressor = RandomForestRegressor(n_estimators = n_estimators)

# Train the model

regressor.fit(train[0], train[1])

# Test the model returning mean accuracy

print(blue(f"Evaluating the Random Forest Regressor...", 'bold'))

print(f"R2 Score = {regressor.score(test[0], test[1]):.4f}")

mse = mean_squared_error(regressor.predict(test[0]), test[1])

rmse = np.sqrt(mse)

print(f"RMSE = {rmse:.4f}")

def eval_xgb(train, test, training = True):

'''

If training is enabled, a new instance of an XGBoost Regression model is created

and fit on the training data. The model is then fed with test data and it's performance

is reported. If training is disabled, the model previously defined is simply evaluated

using the test data and it's performance is reported.

Arguments:

train -- list, should be of the form [train features, train labels]

test -- list, should be of the form [test features, test labels]

training -- bool, specifies whether training is enabled or disabled

Additional:

The model created is a global variable and can be used in later steps when evaluating

on different datasets (after setting training to "False").

'''

global xgbre

if training:

# Define a xgb regressor

xgbre = XGBRegressor()

# Train the model

xgbre.fit(train[0], train[1])

# Test the model returning mean accuracy

y_pred = xgbre.predict(test[0])

print(blue(f"Evaluating the XGBoost Regressor...", 'bold'))

print(f"R2 Score = {r2_score(test[1], y_pred):.4f}")

mse = mean_squared_error(test[1], y_pred)

rmse = np.sqrt(mse)

print(f"RMSE = {rmse:.4f}")

def eval_abr(train, test, training = True):

'''

If training is enabled, a new instance of an AdaBoost Regression model is created

and fit on the training data. The model is then fed with test data and it's performance

is reported. If training is disabled, the model previously defined is simply evaluated

using the test data and it's performance is reported.

Arguments:

train -- list, should be of the form [train features, train labels]

test -- list, should be of the form [test features, test labels]

training -- bool, specifies whether training is enabled or disabled

Additional:

The model created is a global variable and can be used in later steps when evaluating

on different datasets (after setting training to "False").

'''

global abr

if training:

# Define a adaboost regressor

abr = AdaBoostRegressor()

# Train the model

abr.fit(train[0], train[1])

# Test the model returning mean accuracy

y_pred = abr.predict(test[0])

print(blue(f"Evaluating the AdaBoost Regressor...", 'bold'))

print(f"R2 Score = {r2_score(test[1], y_pred):.4f}")

mse = mean_squared_error(test[1], y_pred)

rmse = np.sqrt(mse)

print(f"RMSE = {rmse:.4f}")

def eval_lgbmr(train, test, training = True):

'''

If training is enabled, a new instance of a Light GBM Regression model is created

and fit on the training data. The model is then fed with test data and it's performance

is reported. If training is disabled, the model previously defined is simply evaluated

using the test data and it's performance is reported.

Arguments:

train -- list, should be of the form [train features, train labels]

test -- list, should be of the form [test features, test labels]

training -- bool, specifies whether training is enabled or disabled

Additional:

The model created is a global variable and can be used in later steps when evaluating

on different datasets (after setting training to "False").

'''

global lgbmr

if training:

# Define a LightBGM regressor

lgbmr = LGBMRegressor(force_col_wise=True)

# Train the model

lgbmr.fit(train[0], train[1])

# Test the model returning mean accuracy

y_pred = lgbmr.predict(test[0])

print(blue(f"Evaluating the LightGBM Regressor...", 'bold'))

print(f"R2 Score = {r2_score(test[1], y_pred):.4f}")

mse = mean_squared_error(test[1], y_pred)

rmse = np.sqrt(mse)

print(f"RMSE = {rmse:.4f}")

def eval_cbr(train, test, training = True):

'''

If training is enabled, a new instance of a Cat Boost Regression model is created

and fit on the training data. The model is then fed with test data and it's performance

is reported. If training is disabled, the model previously defined is simply evaluated

using the test data and it's performance is reported.

Arguments:

train -- list, should be of the form [train features, train labels]

test -- list, should be of the form [test features, test labels]

training -- bool, specifies whether training is enabled or disabled

Additional:

The model created is a global variable and can be used in later steps when evaluating

on different datasets (after setting training to "False").

'''

global cbr

if training:

# Define a LightBGM regressor

cbr = CatBoostRegressor()

# Train the model

cbr.fit(train[0], train[1])

# Test the model returning mean accuracy

y_pred = cbr.predict(test[0])

print(blue(f"Evaluating the CatBoost Regressor...", 'bold'))

print(f"R2 Score = {r2_score(test[1], y_pred):.4f}")

mse = mean_squared_error(test[1], y_pred)

rmse = np.sqrt(mse)

print(f"RMSE = {rmse:.4f}")

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train, test = [train_x, train_y], [test_x, test_y]

eval_svr(train, test, training = True)

eval_rf(train, test, training = True)

eval_xgb(train, test, training = True)

eval_abr(train, test, training = True)

eval_lgbmr(train, test, training = True)

eval_cbr(train, test, training = True)

Evaluating the Support Vector Regressor...
R2 Score = 0.9158
RMSE = 0.0577
Evaluating the Random Forest Regressor...
R2 Score = 0.9973
RMSE = 0.0104
Evaluating the XGBoost Regressor...
R2 Score = 0.9962
RMSE = 0.0122
Evaluating the AdaBoost Regressor...
R2 Score = 0.9958
RMSE = 0.0128
Evaluating the LightGBM Regressor...
R2 Score = 0.9975
RMSE = 0.0098
Learning rate set to 0.029803
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Evaluating the CatBoost Regressor...
R2 Score = 0.9943
RMSE = 0.0151

代码

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超参数调优

代码

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[45]

from sklearn.model_selection import GridSearchCV

from sklearn.metrics import mean_squared_error

from sklearn.metrics import mean_absolute_error

import multiprocessing

#XGBoost hyper-parameter tuning

def hyperParameterTuning(X_train, y_train):

param_tuning = {

'learning_rate': [0.01, 0.1],

'max_depth': [3, 5, 7, 10],

'min_child_weight': [1, 3, 5],

'n_estimators' : [100, 200, 500]

}

print(blue('Performing hyperparameter tuning for the XGBoost Regressor', 'bold'))

xgb_model = XGBRegressor()

gsearch = GridSearchCV(estimator = xgb_model,

param_grid = param_tuning,

cv = 2, verbose = 1, n_jobs = -1, error_score = 0.00)

gsearch.fit(X_train,y_train)

print(gsearch.best_params_)

param_tuning = {

'n_estimators':[10, 50, 100, 500, 1000],

'learning_rate':[0.0001, 0.001, 0.01, 0.1, 1]

}

print(blue('Performing hyperparameter tuning for the AdaBoost Regressor', 'bold'))

abr_model = AdaBoostRegressor()

gsearch = GridSearchCV(estimator = abr_model,

param_grid = param_tuning,

cv = 2, n_jobs = -1, verbose = 1, error_score = 0.00)

gsearch.fit(X_train,y_train)

print(gsearch.best_params_)

param_tuning = {

'max_depth': (9, 13),

'min_split_gain': (0.001, 0.1),

'min_child_weight': (10, 30, 50)

}

print(blue('Performing hyperparameter tuning for the LightGBM Regressor', 'bold'))

lgbmr_model = LGBMRegressor()

gsearch = GridSearchCV(estimator = lgbmr_model,

param_grid = param_tuning,

cv = 2, verbose = 1, n_jobs = -1, error_score = 0.00)

gsearch.fit(X_train,y_train)

print(gsearch.best_params_)

param_tuning = {

'iterations': [50, 100, 150, 200],

'learning_rate': [0.01, 0.05, 0.1],

'depth': [2, 4, 6, 8]

}

print(blue('Performing hyperparameter tuning for the CatBoost Regressor', 'bold'))

cbr_model = CatBoostRegressor()

gsearch = GridSearchCV(estimator = cbr_model,

param_grid = param_tuning,

cv = 2, verbose = 1, n_jobs = -1, error_score = 0.00)

gsearch.fit(X_train,y_train)

print(gsearch.best_params_)

代码

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[46]

hyperParameterTuning(train[0], train[1])

Performing hyperparameter tuning for the XGBoost Regressor
Fitting 2 folds for each of 72 candidates, totalling 144 fits
{'learning_rate': 0.1, 'max_depth': 5, 'min_child_weight': 1, 'n_estimators': 200}
Performing hyperparameter tuning for the AdaBoost Regressor
Fitting 2 folds for each of 25 candidates, totalling 50 fits
{'learning_rate': 1, 'n_estimators': 1000}
Performing hyperparameter tuning for the LightGBM Regressor
Fitting 2 folds for each of 12 candidates, totalling 24 fits
{'max_depth': 9, 'min_child_weight': 10, 'min_split_gain': 0.001}
Performing hyperparameter tuning for the CatBoost Regressor
Fitting 2 folds for each of 48 candidates, totalling 96 fits
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{'depth': 2, 'iterations': 200, 'learning_rate': 0.05}

代码

文本

使用具有 LSTM 和密集层的人工神经网络

代码

文本

[47]

!pip install keras-preprocessing

!pip install tensorflow

Looking in indexes: https://pypi.tuna.tsinghua.edu.cn/simple
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  Downloading https://pypi.tuna.tsinghua.edu.cn/packages/79/4c/7c3275a01e12ef9368a892926ab932b33bb13d55794881e3573482b378a7/Keras_Preprocessing-1.1.2-py2.py3-none-any.whl (42 kB)
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Installing collected packages: keras-preprocessing
Successfully installed keras-preprocessing-1.1.2
WARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv
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  Downloading https://pypi.tuna.tsinghua.edu.cn/packages/de/44/bf1b0eef5b13e6201aef076ff34b91bc40aace8591cd273c1c2a94a9cc00/keras-2.11.0-py2.py3-none-any.whl (1.7 MB)
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代码

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[48]

# Using an Artificial Neural Network with LSTM and Dense layers

# Importing required libraries

from keras.models import Model

from keras.layers import Input, Dense, LSTM

from keras.utils.vis_utils import plot_model

from tqdm.keras import TqdmCallback

from keras.callbacks import EarlyStopping

import tqdm.notebook as tq

def create_model(lstm_size = 32, dense_size = 10, plot = False, dpi = 96):

'''

Returns an Artificial Neural Network model made for regression tasks

Arguments:

lstm_size -- integer, specifies number of neurons in the hidden LSTM layer

dense_size -- integer, specifies number of neurons in the hidden Dense layer

plot -- bool, specifies whether the model visualization plot should be

displayed

dpi -- integer, if plot = True, specifies the dots-per-inch for the model

plot image

Returns:

model -- a compiled ANN built for regression tasks.

'''

inputs = Input(shape = (8,1), name = 'Input_features')

lstm = LSTM(lstm_size, input_shape = (8,1))(inputs)

dense2 = Dense(dense_size)(lstm)

output = Dense(1, name = 'Output_Layer')(dense2)

model = Model(inputs = inputs, outputs = output)

model.compile(optimizer = 'adam', loss = 'mean_squared_error')

if plot:

print("Visualizing the model and its layers :")

display(plot_model(model, show_shapes = True, dpi = dpi))

return model

def eval_nn(train, test,

training = True,

lstm_size = 32,

dense_size = 10,

plot = False, dpi = 96,

epochs = 100,

ncols = None,

verbose = 1,

return_results = True):

'''

If training is enabled, a new instance of an Artificial Neural Network model is created

and fit on the training data. The model is then fed with test data and it's performance

is reported. If training is disabled, the model previously defined is simply evaluated

using the test data and it's performance is reported.

Arguments:

train -- list, should be of the form [train features, train labels]

test -- list, should be of the form [test features, test labels]

training -- bool, specifies whether training is enabled or disabled

lstm_size -- integer, specifies number of neurons in the hidden LSTM layer

dense_size -- integer, specifies number of neurons in the hidden Dense layer

plot -- bool, specifies whether the model visualization plot should be displayed

dpi -- integer, if plot = True, specifies the dots-per-inch for the model

plot image (larger number, larger image)

epochs -- integer, specifies number of epochs the model should train for

ncols -- integer, specifies number of columns for the training progress bar

verbose -- integer, when verbosity is set to 1:

model training progress bar is shown

model evaluation progress bar is shown

R2 Score and RMSE Loss are printed

When verbosity is NOT 1, all outputs are silenced

return_results -- bool, when True, returns the value of RMSE. (For use in

hyperprameter tuning)

Additional:

The model created is a global variable and can be used in later steps when evaluating

on different datasets (after setting training to "False").

'''

global nn

if training: train_x = train[0].reshape(-1,8,1)

test_x = test[0].reshape(-1,8,1)

if training:

es_callback = EarlyStopping(monitor = 'loss', patience = 20)

if verbose == 1:

tqdm_callback = TqdmCallback(verbose = 0, ncols = ncols)

callbacks = [tqdm_callback, es_callback]

else: callbacks = [es_callback]

# Define the model

nn = create_model(lstm_size = lstm_size, dense_size = dense_size, plot = plot, dpi = dpi)

# Train the model

nn.fit(train_x, train[1],

epochs = epochs,

batch_size = 1,

verbose = 0,

callbacks = callbacks)

# Test the model returning mean accuracy

y_pred = nn.predict(test[0])

rmse = np.sqrt(nn.evaluate(test_x, test[1], verbose = verbose))

r2 = r2_score(test[1], y_pred)

if verbose == 1:

print(blue(f"Evaluating the Artificial Neural Network...", 'bold'))

print(f"R2 Score = {r2:.4f}")

print(f"RMSE = {rmse:.4f}")

if return_results: return rmse

2023-09-08 09:19:03.636618: I tensorflow/core/platform/cpu_feature_guard.cc:193] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX2 AVX512F FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
2023-09-08 09:19:06.285520: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer.so.7'; dlerror: libnvinfer.so.7: cannot open shared object file: No such file or directory; LD_LIBRARY_PATH: /usr/mpi/gcc/openmpi-4.1.0rc5/lib:/usr/local/nccl-rdma-sharp-plugins/lib:/usr/local/nvidia/lib64:/usr/local/cuda/lib64:/usr/local/nvidia/lib:/usr/local/nvidia/lib64
2023-09-08 09:19:06.286456: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer_plugin.so.7'; dlerror: libnvinfer_plugin.so.7: cannot open shared object file: No such file or directory; LD_LIBRARY_PATH: /usr/mpi/gcc/openmpi-4.1.0rc5/lib:/usr/local/nccl-rdma-sharp-plugins/lib:/usr/local/nvidia/lib64:/usr/local/cuda/lib64:/usr/local/nvidia/lib:/usr/local/nvidia/lib64
2023-09-08 09:19:06.286470: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Cannot dlopen some TensorRT libraries. If you would like to use Nvidia GPU with TensorRT, please make sure the missing libraries mentioned above are installed properly.

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定义一个模型，其中 LSTM 层有 25 个神经元，Dense 层有 10 个神经元

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[49]

# Defining a model with 25 neurons in the LSTM layer and 10 neurons in the Dense layer

eval_nn(train, test,

training = True,

lstm_size = 32,

dense_size = 10,

plot = False,

epochs = 100,

verbose = 1,

return_results = False)

2023-09-08 09:19:08.111321: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcuda.so.1'; dlerror: /usr/lib/x86_64-linux-gnu/libcuda.so.1: file too short; LD_LIBRARY_PATH: /usr/mpi/gcc/openmpi-4.1.0rc5/lib:/usr/local/nccl-rdma-sharp-plugins/lib:/usr/local/nvidia/lib64:/usr/local/cuda/lib64:/usr/local/nvidia/lib:/usr/local/nvidia/lib64
2023-09-08 09:19:08.112118: W tensorflow/compiler/xla/stream_executor/cuda/cuda_driver.cc:265] failed call to cuInit: UNKNOWN ERROR (303)
2/2 [==============================] - 0s 2ms/step
2/2 [==============================] - 0s 3ms/step - loss: 2.6501e-04
Evaluating the Artificial Neural Network...
R2 Score = 0.9933
RMSE = 0.0163

代码

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[50]

import tensorflow as tf

tf.compat.v1.logging.set_verbosity(tf.compat.v1.logging.ERROR)

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人工神经网络的超参数调整

代码

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[51]

# Hyperparameter tuning for the Artificial Neural Network

lstm_sizes = [8, 10, 16, 25, 32]

dense_sizes = [4, 8, 10]

comb_nn = [(lstm_sizes[i], dense_sizes[j]) for i in range(len(lstm_sizes)) for j in range(len(dense_sizes))]

min = 0.1

for i in tq.trange(len(comb_nn)):

lstm_size = comb_nn[i][0]

dense_size = comb_nn[i][1]

results = eval_nn(train, test,

training = True,

lstm_size = lstm_size,

dense_size = dense_size,

plot = False,

verbose = 0,

epochs = 100,

return_results = True)

if results < min:

print(f"Updating minimum loss..... \t Iteration loss = {results:.4f} \t Previous Minimum loss = {min:.4f}")

print(f"Best Params = {comb_nn[i]}")

lstm_best = comb_nn[i][0]

dense_best = comb_nn[i][1]

min = results

print(f"Best results obtained with LSTM layer size = {lstm_best} \t Dense layer size = {dense_best}")

2/2 [==============================] - 0s 2ms/step
Updating minimum loss..... 	 Iteration loss = 0.0221 	 Previous Minimum loss = 0.1000
Best Params = (8, 4)
2/2 [==============================] - 0s 2ms/step
Updating minimum loss..... 	 Iteration loss = 0.0173 	 Previous Minimum loss = 0.0221
Best Params = (8, 8)
2/2 [==============================] - 0s 2ms/step
2/2 [==============================] - 0s 2ms/step
2/2 [==============================] - 0s 2ms/step
Updating minimum loss..... 	 Iteration loss = 0.0116 	 Previous Minimum loss = 0.0173
Best Params = (10, 8)
2/2 [==============================] - 0s 2ms/step
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
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/opt/conda/lib/python3.8/site-packages/xgboost/compat.py:36: FutureWarning: pandas.Int64Index is deprecated and will be removed from pandas in a future version. Use pandas.Index with the appropriate dtype instead.
  from pandas import MultiIndex, Int64Index
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Best results obtained with LSTM layer size = 10 	 Dense layer size = 8

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模型测试

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[52]

eval_nn(train, test,

training = True,

lstm_size = 8,

dense_size = 8,

plot = True, dpi = 80,

epochs = 100,

verbose = 1,

return_results = False)

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模型评估

我们在 5 号电池上训练了模型，通过评估其对其他电池数据的预测来测试其泛化能力。

下面的函数将之前训练的模型应用到尚未用于训练过程的其他单元格的数据上

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[53]

# This function applies the previously trained models to the data of other cells

# which have not been used for the training process

def evaluate_cell(cell_number, model_type, axes, position):

'''

Evaluates the models of specified type on the data corresponding

to the specified cell number. Data is first extracted and processed and then

fed to the model of specified type for evaluation. The results are printed

and a plot of predicted vs true labels is also created.

Arguments:

cell_number -- integer, should be one of 5, 6, 7, 18

model_type -- should be one of "lgbmr", "rf", "nn" or "all"

axes -- matplotlib axes objects, plots will be arranged on these pre-defined axes

position -- tuple, the plot will be arranged in the position specified by this argument.

If model_type = "all" then all models, i.e. lgbmr, rf and nn

are evaluated using the data from the specified cell number and a

single plot containing predicted labels vs true labels is created.

Models are evaluated using the corresponding evaluate functions

after setting training to False.

'''

x, y = preprocessing(cell_number, 16)

x = scaler.transform(x)

x = pca.transform(x)

if model_type == 'xgb' or model_type == 'all':

eval_xgb(_, [x, y], training = False)

axes[position[0], position[1]].plot(xgbre.predict(x), label = "XGBoost Regressor")

if model_type == 'rf' or model_type == 'all':

eval_rf(_, [x, y], training = False)

axes[position[0], position[1]].plot(regressor.predict(x), label = "Random Forest Regressor")

if model_type == 'nn' or model_type == 'all':

eval_nn(_, [x, y], training = False, plot = False)

axes[position[0], position[1]].plot(nn.predict(x.reshape(-1,8,1)), label = "Artificial Neural Network")

axes[position[0], position[1]].plot(y.reshape(-1,1), label = "True labels")

axes[position[0], position[1]].legend()

axes[position[0], position[1]].set_xlabel("Cycles", fontsize = 14)

axes[position[0], position[1]].set_ylabel("Capacity of the battery (Ahr)", fontsize = 14)

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[62]

print(red("Applying the previously trained models to data from cell 7", 'bold'))

fig, axes = plt.subplots(2, 2, figsize = (15, 10))

evaluate_cell(7, 'xgb', axes, (0,0))

evaluate_cell(7, 'nn', axes, (0,1))

evaluate_cell(7, 'rf', axes, (1,0))

print(red("Comparing all models at once", 'bold'))

evaluate_cell(7, 'all', axes, (1,1))

plt.show()

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评估 7 号单元格上的所有模型

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[55]

# Evaluating all the models on cell number 7

x, y = preprocessing(7, 16)

x = scaler.transform(x)

x = pca.transform(x)

eval_svr(_, [x,y], training = False)

eval_rf(_, [x,y], training = False)

eval_xgb(_, [x,y], training = False)

eval_abr(_, [x,y], training = False)

eval_lgbmr(_, [x,y], training = False)

eval_cbr(_, [x,y], training = False)

eval_nn(_, [x,y], training = False, plot = False)

Evaluating the Support Vector Regressor...
R2 Score = 0.8143
RMSE = 0.0692
Evaluating the Random Forest Regressor...
R2 Score = 0.9855
RMSE = 0.0193
Evaluating the XGBoost Regressor...
R2 Score = 0.9731
RMSE = 0.0263
Evaluating the AdaBoost Regressor...
R2 Score = 0.9755
RMSE = 0.0251
Evaluating the LightGBM Regressor...
R2 Score = 0.9832
RMSE = 0.0208
Evaluating the CatBoost Regressor...
R2 Score = 0.9520
RMSE = 0.0352
6/6 [==============================] - 0s 2ms/step
6/6 [==============================] - 0s 2ms/step - loss: 3.9915e-04
Evaluating the Artificial Neural Network...
R2 Score = 0.9845
RMSE = 0.0200

0.019978737555686552

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模型的可解释性

我们想要了解为什么我们的模型会预测它所预测的内容。为此，我们尝试了解每个特征在预测容量方面的重要性。我们首先为每个特征绘制部分依赖图（PDP），假设其他特征保持不变。尽管这些假设特征是独立的（我们正在绘制具有单个输入特征的输出的变化），但我们仍然可以提取有价值的见解。

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[56]

from sklearn.inspection import PartialDependenceDisplay

def partial_dependence_plot(model, feature, ax, data = train[0], line_kw = {}):

'''

Plots a partial dependance plot for the specified feature using the specified model.

Arguments:

model -- regression model, should be one of the models defined in the above cells

feature -- list, contains the features for which the partial dependence plot will

be made

ax -- matplotlib axis object, axis or position where the plot will be made

data -- numpy array, this data will be used to actually prepare the PDP

line_kw -- dict, kwargs for the plot, such as color, linewidth, label, etc.

'''

disp = PartialDependenceDisplay.from_estimator(model,

data,

feature,

kind="average",

n_jobs=3,

grid_resolution=20,

ax=ax,

line_kw=line_kw)

disp.axes_[0][0].set_xlabel(f"Feature {feature}", fontsize=14)

disp.axes_[0][0].set_ylabel("Partial Dependence", fontsize=14)

return disp

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[63]

features = {0: [[i] for i in range(4)],

1: [[i] for i in range(4,8)]}

fig, axes = plt.subplots(4, 2, figsize = (20,20))

fig.suptitle("Partial Dependence Plots for the 8 selected features on the SVR Model \n", fontsize=20)

for (i, j) in zip(features[0], np.arange(4)):

partial_dependence_plot(svr, i, axes[j,0])

for (i, j) in zip(features[1], np.arange(4)):

partial_dependence_plot(svr, i, axes[j,1])

fig.tight_layout(rect=[0, 0, 1, 0.95]) # For removing extra whitespace introduced on using fig.suptitle

plt.show()

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由于我们执行了PCA，因此模型解释性有点复杂。但是，我们可以利用EDA的见解来提出对这些绘图的物理解释。从原始特征中保留直觉。

特征0、4、7具有单调增加的PDP，并且可以与电池电压达到某些指定值的时间相关联。
特征1、2、3、6、5的PDP降低，并且可以与电池在每个放电周期中达到的最高温度相关。

为了验证我们的假设，我们可以用容量来制作原始特征的散点图。为了简洁起见，我们制作了电池电压达到2.8V的容量时间的散点图，以及在放电周期中达到的最高温度的另一个散点图。

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[58]

# Features [0], [4], [7] represent different points in the discharge voltage

# plot (hence the increasing nature since if these relate to times,

# a smaller time corresponds to a smaller capacity)

# Testing our hypothesis by making a scatterplot

# Matrix x below refers to the matrix of features after feature extraction

# Standardizing x

x, y = preprocessing(5, 16)

x_std = (x - np.mean(x, axis=0)) / np.std(x, axis=0)

# Making a scatterplot of capacity vs time at which voltage hits 4 V

# [:, 15] correponds to the 16th column in the dataset i.e. 4V time

plt.figure(figsize=(10, 5))

plt.scatter(x_std[:, 2], y)

plt.xlabel('Feature 3 after normalisation', fontsize=14)

plt.ylabel('Capacity', fontsize=14)

plt.show()

# Making a scatterplot of capacity vs maximum temperature reached

plt.figure(figsize=(10, 5))

plt.scatter(x_std[:, 17], y)

plt.xlabel('Feature 18 after normalisation', fontsize=14)

plt.ylabel('Capacity', fontsize=14)

plt.show()

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我们在上面看到的散点图和 PDP 之间有相当好的一致性。

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[67]

features = {0: [[i] for i in range(4)],

1: [[i] for i in range(4,8)]}

fig, axes = plt.subplots(4, 2, figsize = (20,20))

fig.suptitle("Partial Dependence Plots for the 8 selected features on the trained Random Forest, LightGBM and XGBoost Regression Models \n", fontsize=20)

base_displays = dict() # For storing all PartialDependanceDisplay instances

for (i, j) in zip(features[0], np.arange(4)):

base_disp = partial_dependence_plot(regressor, i, ax = axes[j,0], line_kw = {"label": "Random Forest"})

disp1 = partial_dependence_plot(xgbre, i, ax = base_disp.axes_, line_kw = {"color": "red", "label": "XGBoost"})

disp2 = partial_dependence_plot(lgbmr, i, ax = base_disp.axes_, line_kw = {"color": "green", "label": "LightGBM"})

base_disp.axes_[0][0].legend()

for (i, j) in zip(features[1], np.arange(4)):

base_disp = partial_dependence_plot(regressor, i, ax = axes[j,1], line_kw = {"label": "Random Forest"})

disp1 = partial_dependence_plot(xgbre, i, ax = base_disp.axes_, line_kw = {"color": "red", "label": "XGBoost"})

disp2 = partial_dependence_plot(lgbmr, i, ax = base_disp.axes_, line_kw = {"color": "green", "label": "LightGBM"})

base_disp.axes_[0][0].legend()

fig.tight_layout(rect=[0, 0, 1, 0.95]) # For removing extra whitespace introduced on using fig.suptitle

plt.show()

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[68]

fig, axes = plt.subplots(4, 2, figsize = (20,20))

fig.suptitle("Partial Dependence Plots for the 8 selected features on the Random Forest Model \n", fontsize=20)

for (i, j) in zip(features[0], np.arange(4)):

partial_dependence_plot(regressor, i, axes[j,0])

for (i, j) in zip(features[1], np.arange(4)):

partial_dependence_plot(regressor, i, axes[j,1])

fig.tight_layout(rect=[0, 0, 1, 0.95]) # For removing extra whitespace introduced on using fig.suptitle

plt.show()

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随机森林的 PDP 看起来像平滑的阶梯。这可以通过将随机森林视为决策树的集合来理解，这些决策树根据某些标准做出二元决策。由于 PCA 之后的特征并不纯粹，所以台阶不尖锐。它们是所有原始特征的混合体。

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[72]

fig, axes = plt.subplots(4, 2, figsize = (20,20))

fig.suptitle("Partial Dependence Plots for the 8 selected features on the XGBoost Regression Model \n", fontsize=20)

xgbre.dummy_ = "dummy"

for (i, j) in zip(features[0], np.arange(4)):

partial_dependence_plot(xgbre, i, axes[j,0])

for (i, j) in zip(features[1], np.arange(4)):

partial_dependence_plot(xgbre, i, axes[j,1])

fig.tight_layout(rect=[0, 0, 1, 0.95]) # For removing extra whitespace introduced on using fig.suptitle

plt.show()

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[73]

fig, axes = plt.subplots(4, 2, figsize = (20,20))

fig.suptitle("Partial Dependence Plots for the 8 selected features on the LightGBM Regression Model \n", fontsize=20)

lgbmr.dummy_ = "dummy"

for (i, j) in zip(features[0], np.arange(4)):

partial_dependence_plot(lgbmr, i, axes[j,0])

for (i, j) in zip(features[1], np.arange(4)):

partial_dependence_plot(lgbmr, i, axes[j,1])

fig.tight_layout(rect=[0, 0, 1, 0.95]) # For removing extra whitespace introduced on using fig.suptitle

plt.show()

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附录

在进行PCA的过程中，我们的特征就失去了意义。了解没有 PCA 的 PDP 的性质并与上述 PDP 进行比较和对比将会很有趣。

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[74]

x, y = preprocessing(5, 16) # using cell 5 for training

# Using the original data but not carrying out PCA

train_x1, test_x1, train_y1, test_y1 = train_test_split(x, y, train_size = 0.8)

# Standardize the training data

scaler = StandardScaler()

# Fit the scaler to X_train

scaler.fit(train_x1)

# Transform the entire data using the computed mean and variance

train_x1 = scaler.transform(train_x1)

test_x1 = scaler.transform(test_x1)

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对数据进行归一化后，我们可以训练模型并绘制 PDP。

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[75]

s = SVR()

s.fit(train_x1, train_y1)

print(blue(f"Evaluating the Support Vector Regressor...", 'bold'))

print(f"R2 Score = {s.score(test_x1, test_y1):.4f}")

mse = mean_squared_error(s.predict(test_x1), test_y1)

rmse = np.sqrt(mse)

print(f"RMSE = {rmse:.4f}")

Evaluating the Support Vector Regressor...
R2 Score = 0.8963
RMSE = 0.0594

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[76]

fig, (ax1, ax2) = plt.subplots(1, 2, figsize = (15,5))

# PDP for time at which battery voltage hits 2.7V

disp_s0 = PartialDependenceDisplay.from_estimator(s, train_x1, features=[0], ax=ax1)

# PDP for maximum temperature

disp_s17 = PartialDependenceDisplay.from_estimator(s, train_x1, features=[17], ax=ax2)

plt.show()

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该图看起来与 PCA 的图非常相似。这与我们的分析相符，因为我们预计达到 2.7V 所需的时间越长且最高电池温度越低，容量就会越高。

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[77]

# Using the pre-built sklearn RF regressor without tuning

rf = RandomForestRegressor(n_estimators = 100)

rf.fit(train_x1, train_y1)

print(blue(f"Evaluating the Random Forest Regressor...", 'bold'))

print(f"R2 Score = {rf.score(test_x1, test_y1):.4f}")

mse = mean_squared_error(rf.predict(test_x1), test_y1)

rmse = np.sqrt(mse)

print(f"RMSE = {rmse:.4f}")

Evaluating the Random Forest Regressor...
R2 Score = 0.9994
RMSE = 0.0044

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[78]

fig, (ax1, ax2) = plt.subplots(1, 2, figsize = (15,5))

# PDP for time at which battery voltage hits 2.7V

disp_rf0 = PartialDependenceDisplay.from_estimator(rf, train_x1, features=[0], ax=ax1)

# PDP for maximum temperature

disp_rf17 = PartialDependenceDisplay.from_estimator(rf, train_x1, features=[17], ax=ax2)

plt.show()

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该图看起来与使用 PCA 的图非常相似，只是步骤更加明显。同样有趣的是，尽管我们开始使用的特征高度相关，但即使没有 PCA，模型也取得了类似的结果。

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