CN113393064A - Method for predicting service life of cadmium-nickel storage battery of motor train unit and terminal equipment - Google Patents

Method for predicting service life of cadmium-nickel storage battery of motor train unit and terminal equipment Download PDF

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CN113393064A
CN113393064A CN202110942159.5A CN202110942159A CN113393064A CN 113393064 A CN113393064 A CN 113393064A CN 202110942159 A CN202110942159 A CN 202110942159A CN 113393064 A CN113393064 A CN 113393064A
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于天剑
代毅
刘嘉文
成庶
伍珣
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Abstract

本发明公开了一种动车组镉镍蓄电池的寿命预测方法及终端设备，方法包括：对待测动车组镉镍蓄电池进行循环寿命试验，获得待测动车组镉镍蓄电池随循环次数变换的循环容量；将循环容量输入至粒子滤波算法中训练，得到容量估计值；将容量估计值作为扩展卡尔曼滤波算法的实际测量值，利用扩展卡尔曼滤波算法预测动车组镉镍蓄电池的寿命。本发明提出了使用数据拟合的方法建立动车组镉镍蓄电池的退化模型，该方法能够精确地描述蓄电池退化的主体趋势。在此基础上，进一步提出了一种将粒子滤波算法与扩展卡尔曼滤波算法相结合的新的融合算法，该算法可精确预测动车组镉镍蓄电池的寿命，预测精度高。

Figure 202110942159

The invention discloses a life prediction method and terminal equipment for a cadmium-nickel battery of an EMU. The method includes: performing a cycle life test on the cadmium-nickel battery of the EMU to be tested, and obtaining the cycle capacity of the cadmium-nickel battery of the EMU to be tested that changes with the number of cycles; The cycle capacity is input into the particle filter algorithm for training, and the capacity estimate is obtained; the capacity estimate is used as the actual measurement value of the extended Kalman filter algorithm, and the extended Kalman filter algorithm is used to predict the life of the EMU's cadmium-nickel battery. The present invention proposes to use a data fitting method to establish a degradation model of a cadmium-nickel battery of an EMU, and the method can accurately describe the main trend of battery degradation. On this basis, a new fusion algorithm combining the particle filter algorithm and the extended Kalman filter algorithm is further proposed. The algorithm can accurately predict the life of the EMU's cadmium-nickel battery with high prediction accuracy.

Figure 202110942159

Description

一种动车组镉镍蓄电池的寿命预测方法及终端设备A life prediction method and terminal equipment of a cadmium-nickel battery for an EMU

技术领域technical field

本发明属于电池寿命预测技术领域，具体是涉及到一种动车组镉镍蓄电池的寿命预测方法及终端设备。The invention belongs to the technical field of battery life prediction, and in particular relates to a life prediction method and terminal equipment of a cadmium-nickel battery for an EMU.

背景技术Background technique

根据《2013-2017年中国铁路行业市场前瞻与投资战略规划分析报告》可知，我国铁路的发展趋势主要表现在以下两个方面：一是客运列车的高速化；二是货运列车的重载化。而其中客运列车的高速化与动车组息息相关。蓄电池组是动车组关键设备之一，其作为动车组中直流辅助回路的电源，在动车组架线停电或辅助电源装置（APU）出现故障时，将为照明、通信及紧急换气等系统提供电源。蓄电池的可靠性涉及到了动车组的行车安全，所以其检修十分严格。目前，一节动车组检修费用约为六万元，而且检修过程耗时耗力。实际运用检修中，蓄电池更换返厂检修的依据为运营里程数或使用年限。在这个过程中，一旦检测到蓄电池性能指标不符合相应标准，则会立即更换。而往往此时镉镍电池体还有较大的余量可用，如果提前更换，毫无疑问会提高动车组的运营成本。因此，对动车组蓄电池寿命研究具有非常重要的意义。According to the "2013-2017 China Railway Industry Market Prospects and Investment Strategic Planning Analysis Report", the development trend of my country's railways is mainly reflected in the following two aspects: one is the high-speed passenger trains; the other is the heavy load of freight trains. Among them, the high speed of passenger trains is closely related to the EMU. The battery pack is one of the key equipment of the EMU. It acts as the power supply of the DC auxiliary circuit in the EMU. When the EMU is powered off or the auxiliary power supply unit (APU) fails, it will provide lighting, communication and emergency ventilation systems. power supply. The reliability of the battery involves the driving safety of the EMU, so its maintenance is very strict. At present, the maintenance cost of an EMU is about 60,000 yuan, and the maintenance process is time-consuming and labor-intensive. In the actual operation and maintenance, the basis for the battery replacement and returning to the factory for maintenance is the operating mileage or service life. In this process, once it is detected that the battery performance index does not meet the corresponding standards, it will be replaced immediately. At this time, the nickel-cadmium battery often has a large margin available. If it is replaced in advance, it will undoubtedly increase the operating cost of the EMU. Therefore, it is very important to study the battery life of EMUs.

蓄电池寿命预测技术在国内还处于研究阶段，尤其是碱性蓄电池的寿命预测技术更是缺乏。国内外相关的蓄电池预测算法大致可以分为模型驱动、数据驱动和混合方法三种，其中模型驱动是根据工作条件、制造材料和退化机理来建立退化模型，从而实现对蓄电池寿命的预测。JOUIN等提出基于PF的质子交换膜燃料电池(PEMFC)剩余使用寿命预测方法，并分别对线性、指数和对数-线性模型三种退化模型进行对比分析，结果表明三种模型中的对数-线性模型对PEMFC的预测精确度更高。ZHANG等提出利用无迹卡尔曼滤波(UKF)来对PEMFC进行损伤追踪并对寿命进行预测，其预测结果表明该方法具有较高的预测精度。丁劲涛忽略蓄电池大倍率放电时的温升与放电深度等因素的影响，采用EKF算法预测蓄电池的RUL，结果证明该方法不仅非常精简而且准确性也较好。许参等通过建立变化负载和常数负载两种不同的模型，使模型与实际运行情况更加符合。The battery life prediction technology is still in the research stage in China, especially the life prediction technology of alkaline batteries is lacking. Relevant battery prediction algorithms at home and abroad can be roughly divided into three types: model-driven, data-driven and hybrid methods. Model-driven is to establish a degradation model according to working conditions, manufacturing materials and degradation mechanisms, so as to predict battery life. JOUIN et al. proposed a method for predicting the remaining service life of proton exchange membrane fuel cells (PEMFC) based on PF, and compared and analyzed three degradation models of linear, exponential and log-linear models respectively. The results showed that the log- The linear model was more accurate in predicting PEMFC. ZHANG et al. proposed to use unscented Kalman filter (UKF) to track damage to PEMFC and predict its lifespan. The prediction results show that this method has high prediction accuracy. Ding Jintao ignores the influence of factors such as temperature rise and depth of discharge when the battery is discharged at a high rate, and uses the EKF algorithm to predict the RUL of the battery. The results show that the method is not only very simple but also accurate. Xu et al. established two different models of variable load and constant load to make the model more consistent with the actual operation.

数据驱动不需要建立先验退化模型，而是通过对原始数据进行处理得到其相应的的行为模型。王莉等人提出基于最小二乘的支持向量机(SVM)的阀控式铅酸蓄电池寿命预测方法，其通过对线性微分方程求最优解，提高了算法运行速度。杨传凯等人将铅酸蓄电池的健康状态和端电压作为变量，通过Grid-Search法来确定LIBSVM的最优参数，结果表明其精确度较高。吴海洋等人提出一种基于遗传算法的反向传播(BP)神经网络预测模型，其通过对不同温度和型号下的蓄电池的剩余容量预测，从而实时监控工况和预测寿命。LIU等提出了一种基于间接健康指标和多重高斯过程回归(GPR)模型的锂离子电池寿命预测方法，从而实现了单点预测和多步预测。ZHAO等提出了一种基于转换算法的非等距灰色预测模型，解决了电池实际老化与电池加速老化不等同的问题。Data-driven does not need to establish a priori degradation model, but obtains its corresponding behavioral model by processing the original data. Wang Li et al. proposed a valve-regulated lead-acid battery life prediction method based on the least squares support vector machine (SVM), which improved the running speed of the algorithm by finding the optimal solution to the linear differential equation. Yang Chuankai et al. used the health state and terminal voltage of lead-acid batteries as variables, and used the Grid-Search method to determine the optimal parameters of LIBSVM, and the results showed that the accuracy was high. Wu Haiyang et al. proposed a back-propagation (BP) neural network prediction model based on genetic algorithm, which can monitor the working conditions and predict the life in real time by predicting the remaining capacity of batteries under different temperatures and models. LIU et al. proposed a lithium-ion battery life prediction method based on indirect health indicators and a multiple Gaussian process regression (GPR) model, thereby realizing single-point prediction and multi-step prediction. ZHAO et al. proposed a non-isometric gray prediction model based on a conversion algorithm, which solved the problem that the actual aging of the battery is not equal to the accelerated aging of the battery.

混合方法则是通过将多种预测算法融合或结合，从而消除单一算法的缺陷，并保留组成算法的优势。刘嘉蔚等提出一种基于核超限学习机和局部加权回归散点平滑法(LOWESS)融合的PEMFC剩余寿命预测方法，其通过等间隔采样法和LOWESS来实现数据的重构和平滑处理。ZHOU等分别利用稀疏贝叶斯方法实现长期寿命预测和灰色模型实现短期寿命预。胡天中等将多尺度分解与深度神经网络（DNN）融合来预测锂电池寿命，其通过相关性分析与集合经验模态将退化数据分解为主趋势数据和波动数据。陈通等将BP神经网络和深层感知器相融合，提高了原始数据的精度，从而使预测更加精确。Hybrid methods eliminate the shortcomings of a single algorithm and retain the advantages of the constituent algorithms by fusing or combining multiple prediction algorithms. Liu Jiawei et al. proposed a PEMFC residual life prediction method based on the fusion of kernel extreme learning machine and local weighted regression scatter smoothing method (LOWESS). ZHOU et al. used sparse Bayesian method to realize long-term life prediction and grey model to realize short-term life prediction respectively. Hu Tianzhong integrated multi-scale decomposition and deep neural network (DNN) to predict the life of lithium batteries, and decomposed the degradation data into main trend data and fluctuation data through correlation analysis and ensemble empirical mode. Chen Tong et al. integrated the BP neural network and the deep perceptron to improve the accuracy of the original data, thus making the prediction more accurate.

然而，现有技术中并未公开动车组镉镍蓄电池的寿命预测方法，致使在电池还有较大余量的情况下进行更换，使动车组的运营成本大幅提高。However, the prior art does not disclose the life prediction method of the nickel-cadmium battery of the EMU, so that the battery is replaced when there is still a large margin, and the operating cost of the EMU is greatly increased.

发明内容SUMMARY OF THE INVENTION

本发明提供了一种动车组镉镍蓄电池的寿命预测方法及终端设备，从而解决现有技术中存在的难以准确预测动车组镉镍蓄电池寿命的技术问题。The invention provides a life prediction method and terminal equipment of a cadmium-nickel battery for an EMU, thereby solving the technical problem in the prior art that it is difficult to accurately predict the life of an EMU's cadmium-nickel battery.

本发明内容的第一方面公开了一种动车组镉镍蓄电池的寿命预测方法，包括：A first aspect of the content of the present invention discloses a life prediction method for a cadmium-nickel battery of an EMU, including:

对待测动车组镉镍蓄电池进行循环寿命试验，获得所述待测动车组镉镍蓄电池随循环次数变换的循环容量；Carry out a cycle life test on the cadmium-nickel battery of the EMU to be tested, and obtain the cycle capacity of the cadmium-nickel battery of the EMU to be tested that changes with the number of cycles;

将所述循环容量输入至粒子滤波算法中训练，得到容量估计值

Figure DEST_PATH_IMAGE001
；Input the loop capacity into the particle filter algorithm for training to obtain the capacity estimate
Figure DEST_PATH_IMAGE001
;

将所述容量估计值

Figure 509232DEST_PATH_IMAGE001
作为扩展卡尔曼滤波算法的实际测量值
Figure 443690DEST_PATH_IMAGE002
，利用所述扩展卡尔曼滤波算法预测所述动车组镉镍蓄电池的寿命。the capacity estimate
Figure 509232DEST_PATH_IMAGE001
Actual measurement as an extended Kalman filter algorithm
Figure 443690DEST_PATH_IMAGE002
, using the extended Kalman filter algorithm to predict the life of the nickel-cadmium battery of the EMU.

优选地，所述将所述容量估计值

Figure 233791DEST_PATH_IMAGE001
作为扩展卡尔曼滤波算法的实际测量值
Figure 519279DEST_PATH_IMAGE002
，利用所述扩展卡尔曼滤波算法预测所述动车组镉镍蓄电池的寿命，具体为：Preferably, the said capacity estimate is
Figure 233791DEST_PATH_IMAGE001
Actual measurement as an extended Kalman filter algorithm
Figure 519279DEST_PATH_IMAGE002
, using the extended Kalman filter algorithm to predict the life of the nickel-cadmium battery of the EMU, specifically:

根据所述循环容量确定所述待测动车组镉镍蓄电池容量的递推关系式；Determine the recursive relationship formula of the capacity of the cadmium-nickel battery of the EMU to be tested according to the cycle capacity;

根据所述递推关系式确定所述待测动车组镉镍蓄电池状态转移方程和状态测量方程；其中，待测动车组镉镍蓄电池状态转移方程为所述容量递推关系式加上过程噪声

Figure DEST_PATH_IMAGE003
，而所述待测动车组镉镍蓄电池状态测量方程等于所述状态转移方程的状态值加上测量噪声
Figure 380925DEST_PATH_IMAGE004
；Determine the state transition equation and state measurement equation of the nickel-cadmium battery of the EMU to be tested according to the recurrence relation; wherein, the state transition equation of the nickel-cadmium battery of the EMU to be tested is the capacity recurrence relation plus process noise
Figure DEST_PATH_IMAGE003
, and the state measurement equation of the nickel-cadmium battery of the EMU to be tested is equal to the state value of the state transition equation plus the measurement noise
Figure 380925DEST_PATH_IMAGE004
;

将所述容量估计值

Figure 205442DEST_PATH_IMAGE001
作为扩展卡尔曼滤波算法中所述待测动车组镉镍蓄电池状态测量方程的实际测量值
Figure DEST_PATH_IMAGE005
；the capacity estimate
Figure 205442DEST_PATH_IMAGE001
As the actual measurement value of the state measurement equation of the EMU under test described in the extended Kalman filter algorithm
Figure DEST_PATH_IMAGE005
;

利用所述扩展卡尔曼滤波算法预测所述动车组镉镍蓄电池的寿命。The extended Kalman filter algorithm is used to predict the lifetime of the nickel-cadmium battery of the EMU.

优选地，根据所述循环容量确定所述待测动车组镉镍蓄电池容量的递推关系式，具体为：Preferably, according to the cycle capacity, determine the recursive relationship formula of the capacity of the cadmium-nickel battery of the EMU to be tested, specifically:

根据所述循环容量，利用数据拟合的方法确定所述待测动车组镉镍蓄电池容量的递推关系式。According to the cycle capacity, the recursive relationship formula of the capacity of the cadmium-nickel battery of the EMU to be tested is determined by the method of data fitting.

优选地，所述待测动车组镉镍蓄电池状态转移方程为：Preferably, the state transition equation of the nickel-cadmium battery of the EMU to be tested is:

Figure 25500DEST_PATH_IMAGE006
Figure 25500DEST_PATH_IMAGE006

式中，

Figure DEST_PATH_IMAGE007
为
Figure 798284DEST_PATH_IMAGE008
时刻所述待测动车组镉镍蓄电池的循环容量，
Figure 371610DEST_PATH_IMAGE009
为
Figure 608556DEST_PATH_IMAGE008
时刻所述待测动车组镉镍蓄电池的循环容量，
Figure DEST_PATH_IMAGE010
为
Figure 802777DEST_PATH_IMAGE008
时刻所述待测动车组镉镍蓄电池的过程噪声，
Figure 62857DEST_PATH_IMAGE011
为状态转移函数。In the formula,
Figure DEST_PATH_IMAGE007
for
Figure 798284DEST_PATH_IMAGE008
The cycle capacity of the nickel-cadmium battery of the EMU to be tested at the time,
Figure 371610DEST_PATH_IMAGE009
for
Figure 608556DEST_PATH_IMAGE008
The cycle capacity of the nickel-cadmium battery of the EMU to be tested at the time,
Figure DEST_PATH_IMAGE010
for
Figure 802777DEST_PATH_IMAGE008
the process noise of the nickel-cadmium battery of the EMU to be tested at the time,
Figure 62857DEST_PATH_IMAGE011
is the state transition function.

优选地，所述待测动车组镉镍蓄电池状态测量方程为：Preferably, the state measurement equation of the nickel-cadmium battery of the EMU to be tested is:

Figure DEST_PATH_IMAGE012
Figure DEST_PATH_IMAGE012

式中，

Figure 499261DEST_PATH_IMAGE013
为
Figure 262818DEST_PATH_IMAGE008
时刻待测动车组镉镍蓄电池的后验状态估计值，
Figure DEST_PATH_IMAGE014
为
Figure 627940DEST_PATH_IMAGE008
时刻所述待测动车组镉镍蓄电池的循环容量，
Figure 876781DEST_PATH_IMAGE010
为
Figure 821603DEST_PATH_IMAGE008
时刻的测量噪声，
Figure 705246DEST_PATH_IMAGE015
为状态测量函数。In the formula,
Figure 499261DEST_PATH_IMAGE013
for
Figure 262818DEST_PATH_IMAGE008
The posterior state estimate of the nickel-cadmium battery of the EMU to be tested at all times,
Figure DEST_PATH_IMAGE014
for
Figure 627940DEST_PATH_IMAGE008
The cycle capacity of the nickel-cadmium battery of the EMU to be tested at the time,
Figure 876781DEST_PATH_IMAGE010
for
Figure 821603DEST_PATH_IMAGE008
measurement noise at time,
Figure 705246DEST_PATH_IMAGE015
is a state measurement function.

优选地，所述扩展卡尔曼滤波算法的时间更新方程包括先验状态更新方程和先验协方差矩阵更新方程；Preferably, the time update equation of the extended Kalman filter algorithm includes a priori state update equation and a priori covariance matrix update equation;

所述先验状态更新方程为：The prior state update equation is:

Figure DEST_PATH_IMAGE016
Figure DEST_PATH_IMAGE016

式中，

Figure 710111DEST_PATH_IMAGE017
为
Figure 475941DEST_PATH_IMAGE018
时刻所述待测动车组镉镍蓄电池的循环容量的后验状态估计值；
Figure DEST_PATH_IMAGE019
为
Figure 451551DEST_PATH_IMAGE020
时刻所述待测动车组镉镍蓄电池的循环容量的先验状态估计值；In the formula,
Figure 710111DEST_PATH_IMAGE017
for
Figure 475941DEST_PATH_IMAGE018
The posterior state estimate value of the cycle capacity of the nickel-cadmium battery of the EMU to be tested at the moment;
Figure DEST_PATH_IMAGE019
for
Figure 451551DEST_PATH_IMAGE020
a priori state estimate value of the cycle capacity of the nickel-cadmium battery of the EMU to be tested at time;

所述先验协方差矩阵更新方程为：The prior covariance matrix update equation is:

Figure DEST_PATH_IMAGE021
Figure DEST_PATH_IMAGE021

式中，

Figure 252017DEST_PATH_IMAGE022
为
Figure DEST_PATH_IMAGE023
对
Figure 896625DEST_PATH_IMAGE024
的偏导，
Figure 353014DEST_PATH_IMAGE025
为
Figure 609945DEST_PATH_IMAGE023
对q的偏导，
Figure DEST_PATH_IMAGE026
为
Figure 828699DEST_PATH_IMAGE018
时刻后验预测误差协方差矩阵，
Figure 644209DEST_PATH_IMAGE027
为
Figure 166324DEST_PATH_IMAGE008
时刻的先验预测误差协方差矩阵，
Figure DEST_PATH_IMAGE028
为
Figure 725481DEST_PATH_IMAGE018
时刻过程误差协方差矩阵。In the formula,
Figure 252017DEST_PATH_IMAGE022
for
Figure DEST_PATH_IMAGE023
right
Figure 896625DEST_PATH_IMAGE024
's bias,
Figure 353014DEST_PATH_IMAGE025
for
Figure 609945DEST_PATH_IMAGE023
The partial derivative with respect to q,
Figure DEST_PATH_IMAGE026
for
Figure 828699DEST_PATH_IMAGE018
time posterior prediction error covariance matrix,
Figure 644209DEST_PATH_IMAGE027
for
Figure 166324DEST_PATH_IMAGE008
a priori prediction error covariance matrix at time,
Figure DEST_PATH_IMAGE028
for
Figure 725481DEST_PATH_IMAGE018
Time process error covariance matrix.

优选地，所述扩展卡尔曼滤波算法的滤波更新方程包括卡尔曼增益更新方程、后验状态更新方程和后验协方差矩阵更新方程；Preferably, the filter update equation of the extended Kalman filter algorithm includes a Kalman gain update equation, a posterior state update equation and a posterior covariance matrix update equation;

所述卡尔曼增益更新方程为：The Kalman gain update equation is:

Figure 703802DEST_PATH_IMAGE029
Figure 703802DEST_PATH_IMAGE029

式中，

Figure DEST_PATH_IMAGE030
为
Figure 221371DEST_PATH_IMAGE008
时刻的测量误差协方差矩阵，
Figure 917931DEST_PATH_IMAGE031
为
Figure DEST_PATH_IMAGE032
对
Figure 47823DEST_PATH_IMAGE024
的偏导，
Figure 615071DEST_PATH_IMAGE033
为
Figure DEST_PATH_IMAGE034
对
Figure 897017DEST_PATH_IMAGE035
的偏导，
Figure 815294DEST_PATH_IMAGE036
为卡尔曼增益；In the formula,
Figure DEST_PATH_IMAGE030
for
Figure 221371DEST_PATH_IMAGE008
the measurement error covariance matrix at time,
Figure 917931DEST_PATH_IMAGE031
for
Figure DEST_PATH_IMAGE032
right
Figure 47823DEST_PATH_IMAGE024
's bias,
Figure 615071DEST_PATH_IMAGE033
for
Figure DEST_PATH_IMAGE034
right
Figure 897017DEST_PATH_IMAGE035
's bias,
Figure 815294DEST_PATH_IMAGE036
is the Kalman gain;

所述后验状态更新方程为：The posterior state update equation is:

Figure DEST_PATH_IMAGE037
Figure DEST_PATH_IMAGE037

所述后验协方差矩阵更新方程为：The posterior covariance matrix update equation is:

Figure 214789DEST_PATH_IMAGE038
Figure 214789DEST_PATH_IMAGE038

式中，

Figure DEST_PATH_IMAGE039
为单位对角矩阵。In the formula,
Figure DEST_PATH_IMAGE039
is a unit diagonal matrix.

优选地，将所述循环容量输入至粒子滤波算法中训练，得到容量估计值

Figure 167702DEST_PATH_IMAGE040
，具体为：Preferably, the loop capacity is input into the particle filter algorithm for training to obtain a capacity estimate
Figure 167702DEST_PATH_IMAGE040
,Specifically:

Figure 495915DEST_PATH_IMAGE041
Figure 495915DEST_PATH_IMAGE041

式中，N为采样粒子数目，

Figure DEST_PATH_IMAGE042
为
Figure 901488DEST_PATH_IMAGE008
时刻第
Figure 606139DEST_PATH_IMAGE043
个采样粒子的已归一化的状态值，
Figure DEST_PATH_IMAGE044
为
Figure 413558DEST_PATH_IMAGE008
时刻第
Figure 148558DEST_PATH_IMAGE043
个采样粒子所对应的已归一化的权值。where N is the number of sampled particles,
Figure DEST_PATH_IMAGE042
for
Figure 901488DEST_PATH_IMAGE008
the moment
Figure 606139DEST_PATH_IMAGE043
the normalized state values of each sampled particle,
Figure DEST_PATH_IMAGE044
for
Figure 413558DEST_PATH_IMAGE008
the moment
Figure 148558DEST_PATH_IMAGE043
The normalized weights corresponding to each sampled particle.

优选地，所述

Figure 775849DEST_PATH_IMAGE008
时刻第
Figure 487453DEST_PATH_IMAGE043
个采样粒子的已归一化的状态值
Figure 149378DEST_PATH_IMAGE042
是通过蒙特卡罗重要性采样获得的，具体为：Preferably, the
Figure 775849DEST_PATH_IMAGE008
the moment
Figure 487453DEST_PATH_IMAGE043
the normalized state values of the sampled particles
Figure 149378DEST_PATH_IMAGE042
is obtained by Monte Carlo importance sampling, specifically:

Figure 819394DEST_PATH_IMAGE045
Figure 819394DEST_PATH_IMAGE045

式中，q()为重要性概率密度分布，

Figure DEST_PATH_IMAGE046
为
Figure 199560DEST_PATH_IMAGE008
时刻的测量值；In the formula, q() is the importance probability density distribution,
Figure DEST_PATH_IMAGE046
for
Figure 199560DEST_PATH_IMAGE008
the measured value of the moment;

所述

Figure 714855DEST_PATH_IMAGE008
时刻第
Figure 231287DEST_PATH_IMAGE043
个采样粒子所对应的已归一化的权值
Figure 806625DEST_PATH_IMAGE044
为said
Figure 714855DEST_PATH_IMAGE008
the moment
Figure 231287DEST_PATH_IMAGE043
The normalized weights corresponding to the sampled particles
Figure 806625DEST_PATH_IMAGE044
for

Figure 912902DEST_PATH_IMAGE047
Figure 912902DEST_PATH_IMAGE047

式中，

Figure DEST_PATH_IMAGE048
为
Figure 763046DEST_PATH_IMAGE020
时刻第
Figure 133985DEST_PATH_IMAGE043
个采样粒子的未归一化的状态值，
Figure 145803DEST_PATH_IMAGE049
为
Figure 703823DEST_PATH_IMAGE020
时刻第
Figure 92079DEST_PATH_IMAGE043
个采样粒子所对应的未归一化的权值。In the formula,
Figure DEST_PATH_IMAGE048
for
Figure 763046DEST_PATH_IMAGE020
the moment
Figure 133985DEST_PATH_IMAGE043
the unnormalized state values of each sampled particle,
Figure 145803DEST_PATH_IMAGE049
for
Figure 703823DEST_PATH_IMAGE020
the moment
Figure 92079DEST_PATH_IMAGE043
The unnormalized weights corresponding to each sampled particle.

优选地，所述

Figure 317524DEST_PATH_IMAGE020
时刻第
Figure 234665DEST_PATH_IMAGE043
个采样粒子所对应的未归一化的权值
Figure 811139DEST_PATH_IMAGE049
与
Figure DEST_PATH_IMAGE050
时刻的权值
Figure 504551DEST_PATH_IMAGE051
之间的递推关系，具体为：Preferably, the
Figure 317524DEST_PATH_IMAGE020
the moment
Figure 234665DEST_PATH_IMAGE043
The unnormalized weights corresponding to each sampled particle
Figure 811139DEST_PATH_IMAGE049
and
Figure DEST_PATH_IMAGE050
moment weight
Figure 504551DEST_PATH_IMAGE051
The recursive relationship between , specifically:

Figure DEST_PATH_IMAGE052
Figure DEST_PATH_IMAGE052

式中，

Figure 850082DEST_PATH_IMAGE053
为第
Figure 469282DEST_PATH_IMAGE043
个粒子
Figure 1895DEST_PATH_IMAGE008
时刻的先验概率分布，由所述蓄电池状态转移方程决定，其概率分布形状和系统的过程噪声
Figure DEST_PATH_IMAGE054
形状一致，
Figure 731953DEST_PATH_IMAGE055
为测量的似然概率分布，由所述蓄电池状态测量方程决定，其概率分布形状和系统的测量噪声
Figure DEST_PATH_IMAGE056
形状一致，q()为重要性概率密度分布。In the formula,
Figure 850082DEST_PATH_IMAGE053
for the first
Figure 469282DEST_PATH_IMAGE043
particles
Figure 1895DEST_PATH_IMAGE008
The prior probability distribution of time is determined by the battery state transition equation, its probability distribution shape and the process noise of the system
Figure DEST_PATH_IMAGE054
same shape,
Figure 731953DEST_PATH_IMAGE055
The likelihood probability distribution for the measurement is determined by the battery state measurement equation, its probability distribution shape and the measurement noise of the system
Figure DEST_PATH_IMAGE056
The shape is the same, and q() is the importance probability density distribution.

本发明内容的第二方面公开了一种终端设备，包括存储器、处理器以及存储在所述存储器中并可在所述处理器上运行的计算机程序，所述处理器执行所述计算机程序时实现上述方法的步骤。A second aspect of the content of the present invention discloses a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the computer program when the processor executes the computer program. steps of the above method.

本发明提出了使用数据拟合的方法建立动车组镉镍蓄电池的退化模型，该方法能够精确地描述蓄电池退化的主体趋势。在此基础上，进一步提出了一种将粒子滤波算法与扩展卡尔曼滤波算法相结合的新的融合算法，该算法可精确预测动车组镉镍蓄电池的寿命，预测精度高。The present invention proposes to use a data fitting method to establish a degradation model of a cadmium-nickel battery of an EMU, and the method can accurately describe the main trend of battery degradation. On this basis, a new fusion algorithm combining the particle filter algorithm and the extended Kalman filter algorithm is further proposed. The algorithm can accurately predict the life of the EMU's cadmium-nickel battery with high prediction accuracy.

附图说明Description of drawings

附图1为本发明的动车组镉镍蓄电池的寿命预测方法的流程图；Accompanying drawing 1 is the flow chart of the life prediction method of EMU cadmium-nickel battery of the present invention;

附图2为本发明的动车组镉镍蓄电池的寿命预测方法中粒子滤波算法的重要性重采样的示意图；Accompanying drawing 2 is the schematic diagram of the importance resampling of particle filter algorithm in the life prediction method of EMU of nickel-cadmium battery of the present invention;

附图3为本发明实施例中动车组镉镍蓄电池2900次循环的放电容量曲线；Fig. 3 is the discharge capacity curve of 2900 cycles of nickel-cadmium battery of EMU in the embodiment of the present invention;

附图4为本发明实施例中Ck-1和Ck的拟合结果示意图；Accompanying drawing 4 is the fitting result schematic diagram of Ck-1 and Ck in the embodiment of the present invention;

附图5为本发明实施例中基于PF的动车组镉镍蓄电池的寿命预测结果图；Accompanying drawing 5 is the life prediction result diagram of PF-based EMU cadmium-nickel battery in the embodiment of the present invention;

附图6为本发明实施例中基于EKF的动车组镉镍蓄电池的寿命预测结果图；Accompanying drawing 6 is the life prediction result diagram of EMU-based nickel-cadmium battery of EMU in the embodiment of the present invention;

附图7为本发明实施例中基于本发明方法（PF-EKF方法）的动车组镉镍蓄电池的寿命预测结果图；7 is a graph showing the life prediction result of the nickel-cadmium battery of the EMU based on the method of the present invention (PF-EKF method) in the embodiment of the present invention;

附图8为本发明实施例中PF、EKF和PF-EKF方法的寿命预测结果对比图。8 is a comparison diagram of the life prediction results of the PF, EKF and PF-EKF methods in the embodiment of the present invention.

具体实施方式Detailed ways

下文将结合附图以及具体实施案例对本发明的技术方案做更进一步的详细说明。应当了解，下列实施例仅为示例性地说明和解释本发明，而不应被解释为对本发明保护范围的限制。凡基于本发明上述内容所实现的技术均涵盖在本发明旨在保护的范围内。The technical solutions of the present invention will be described in further detail below with reference to the accompanying drawings and specific implementation cases. It should be understood that the following examples are only for illustrating and explaining the present invention, and should not be construed as limiting the protection scope of the present invention. All technologies implemented based on the above content of the present invention are covered within the intended protection scope of the present invention.

本发明内容的第一方面公开了一种动车组镉镍蓄电池的寿命预测方法，其流程图如图1，包括：The first aspect of the content of the present invention discloses a life prediction method for a cadmium-nickel battery of an EMU, the flowchart of which is shown in Figure 1, including:

步骤1、对待测动车组镉镍蓄电池进行循环寿命试验，获得待测动车组镉镍蓄电池随循环次数变换的循环容量。Step 1. Perform a cycle life test on the cadmium-nickel battery of the EMU to be tested, and obtain the cycle capacity of the cadmium-nickel battery of the EMU to be tested that changes with the number of cycles.

步骤2、将循环容量输入至粒子滤波算法中训练，得到容量估计值

Figure 463149DEST_PATH_IMAGE057
。Step 2. Input the loop capacity into the particle filter algorithm for training to obtain the estimated capacity
Figure 463149DEST_PATH_IMAGE057
.

动车组镉镍蓄电池的寿命变化是非线性过程，而粒子滤波算法（简称PF）在对非线性、非高斯系统进行预测时具有非常高的优越性，并且能比较准确地表示基于测量值和控制量的后验概率分布情况。PF的本质思想是采用一组粒子近似等于所研究系统的后验概率分布情况，并用这组粒子的平均值近似作为粒子滤波的预测期望值。The life change of nickel-cadmium batteries in EMUs is a nonlinear process, and the particle filter algorithm (PF for short) has very high advantages in predicting nonlinear and non-Gaussian systems, and can more accurately represent measured values and control variables. The posterior probability distribution of . The essential idea of PF is to use a set of particles approximately equal to the posterior probability distribution of the system under study, and use the average value of this set of particles as the predicted expected value of particle filtering.

PF算法的基本思想是贝叶斯估计、蒙特卡罗采样和重要性采样。贝叶斯估计是一种通过贝叶斯理论来对所研究系统的概率分布情况进行状态更新的方法，但是更新过程中必须知道先验概率分布和实际测量值才能得到系统的后验概率分布。The basic idea of PF algorithm is Bayesian estimation, Monte Carlo sampling and importance sampling. Bayesian estimation is a method to update the state of the probability distribution of the studied system through Bayesian theory, but in the update process, the prior probability distribution and the actual measurement value must be known to obtain the posterior probability distribution of the system.

贝叶斯估计需要运行积分运算，为了避免产生积分运算，粒子滤波算法引入蒙特卡洛采样来解决这个问题。蒙特卡洛采样的核心思想就是利用一组粒子的平均值来代替积分运算，所以蒙特卡洛可以避免贝叶斯估计中的积分运算简化算法，提高了算法的运行速度。重要性采样通过对每个粒子引入重要性权值来大幅度减少蒙特卡洛采样所需要的粒子数量，从而提高的算法的精确度和运算速度。Bayesian estimation needs to run the integral operation. In order to avoid the integral operation, the particle filter algorithm introduces Monte Carlo sampling to solve this problem. The core idea of Monte Carlo sampling is to use the average value of a group of particles to replace the integral operation, so Monte Carlo can avoid the simplified algorithm of integral operation in Bayesian estimation and improve the running speed of the algorithm. Importance sampling greatly reduces the number of particles required for Monte Carlo sampling by introducing importance weights to each particle, thereby improving the accuracy and speed of the algorithm.

PF可以分为序贯重要性采样(SIS)部分和重要性重采样(SIR)部分。SIS是用来寻找

Figure 751785DEST_PATH_IMAGE058
时刻的粒子权值
Figure DEST_PATH_IMAGE059
和
Figure 37273DEST_PATH_IMAGE060
时刻的粒子权值
Figure 571023DEST_PATH_IMAGE061
之间的递推关系，从而避免重要性采样中需要利用已知的全部测量值来求粒子权值的问题。假设
Figure 625566DEST_PATH_IMAGE058
时刻的状态
Figure DEST_PATH_IMAGE062
只受初始时刻到
Figure 117728DEST_PATH_IMAGE058
时刻的测量值
Figure 624932DEST_PATH_IMAGE063
影响，那么可以得到：PF can be divided into Sequential Importance Sampling (SIS) part and Importance Resampling (SIR) part. SIS is used to find
Figure 751785DEST_PATH_IMAGE058
Particle weights at moments
Figure DEST_PATH_IMAGE059
and
Figure 37273DEST_PATH_IMAGE060
Particle weights at moments
Figure 571023DEST_PATH_IMAGE061
The recursive relationship between them, so as to avoid the problem of needing to use all known measurement values to calculate particle weights in importance sampling. Assumption
Figure 625566DEST_PATH_IMAGE058
state of the moment
Figure DEST_PATH_IMAGE062
only limited by the initial time
Figure 117728DEST_PATH_IMAGE058
measurement at time
Figure 624932DEST_PATH_IMAGE063
effect, then you can get:

Figure DEST_PATH_IMAGE064
(1)
Figure DEST_PATH_IMAGE064
(1)

Figure 994996DEST_PATH_IMAGE065
(2)
Figure 994996DEST_PATH_IMAGE065
(2)

Figure DEST_PATH_IMAGE066
(3)
Figure DEST_PATH_IMAGE066
(3)

式中：

Figure 435205DEST_PATH_IMAGE067
表示重要性概率密度分布，
Figure DEST_PATH_IMAGE068
为
Figure 98267DEST_PATH_IMAGE069
时刻的先验概率分布；
Figure DEST_PATH_IMAGE070
为
Figure 623926DEST_PATH_IMAGE071
时刻测量的似然概率分布。where:
Figure 435205DEST_PATH_IMAGE067
represents the importance probability density distribution,
Figure DEST_PATH_IMAGE068
for
Figure 98267DEST_PATH_IMAGE069
The prior probability distribution of the moment;
Figure DEST_PATH_IMAGE070
for
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Likelihood probability distribution measured at time instants.

而：and:

Figure 992154DEST_PATH_IMAGE072
(4)
Figure 992154DEST_PATH_IMAGE072
(4)

将式(1)、(2)与(3)代入到式(4)中，经过化简可得到：Substitute equations (1), (2) and (3) into equation (4), and after simplification, we can get:

Figure DEST_PATH_IMAGE073
（5）
Figure DEST_PATH_IMAGE073
(5)

若 时刻系统状态只受 时刻系统状态与 时刻的测量值影响，那么递推关系可以写成：If the system state at time is only affected by the system state at time and the measured value at time , then the recurrence relation can be written as:

Figure 552449DEST_PATH_IMAGE074
（6）
Figure 552449DEST_PATH_IMAGE074
(6)

以上就是粒子滤波的SIS部分。The above is the SIS part of the particle filter.

SIR是用来解决SIS出现的粒子退化问题，其核心思想是将小权值的粒子忽略掉，并增加大权值的粒子数量，从而保持粒子总数不变。粒子数量分配与权值大小有关，也就是说权值越大，分配的粒子数量就越多，反之亦然。其具体示意图如图2所示。SIR is used to solve the problem of particle degradation in SIS. Its core idea is to ignore particles with small weights and increase the number of particles with large weights, so as to keep the total number of particles unchanged. The distribution of the number of particles is related to the size of the weight, that is, the larger the weight, the more particles are allocated, and vice versa. Its specific schematic diagram is shown in Figure 2.

假设当前状态共有

Figure DEST_PATH_IMAGE075
个粒子，
Figure 855254DEST_PATH_IMAGE076
表示
Figure 602630DEST_PATH_IMAGE075
个粒子中第
Figure DEST_PATH_IMAGE077
个粒子被复制的数目，则有：Assuming that the current state has a total of
Figure DEST_PATH_IMAGE075
particles,
Figure 855254DEST_PATH_IMAGE076
express
Figure 602630DEST_PATH_IMAGE075
of particles
Figure DEST_PATH_IMAGE077
The number of particles copied, then:

Figure 547452DEST_PATH_IMAGE078
（7）
Figure 547452DEST_PATH_IMAGE078
(7)

Figure DEST_PATH_IMAGE079
（8）
Figure DEST_PATH_IMAGE079
(8)

Figure 463718DEST_PATH_IMAGE080
（9）
Figure 463718DEST_PATH_IMAGE080
(9)

重采样的粒子必须满足上述条件。The resampled particles must satisfy the above conditions.

将上述粒子滤波算法应用于本申请的实施例中，用以获得容量估计值

Figure DEST_PATH_IMAGE081
，具体为：The above-mentioned particle filter algorithm is applied to the embodiments of the present application to obtain a capacity estimate
Figure DEST_PATH_IMAGE081
,Specifically:

根据第一公式确定容量估计值

Figure 203004DEST_PATH_IMAGE081
，第一公式为：Determine the capacity estimate according to the first formula
Figure 203004DEST_PATH_IMAGE081
, the first formula is:

Figure 906518DEST_PATH_IMAGE082
（10）
Figure 906518DEST_PATH_IMAGE082
(10)

式中，N为采样粒子数目，

Figure DEST_PATH_IMAGE083
为
Figure 655031DEST_PATH_IMAGE084
时刻第
Figure DEST_PATH_IMAGE085
个采样粒子的已归一化的状态值，
Figure 658759DEST_PATH_IMAGE086
为
Figure 801902DEST_PATH_IMAGE084
时刻第
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个采样粒子所对应的已归一化的权值。where N is the number of sampled particles,
Figure DEST_PATH_IMAGE083
for
Figure 655031DEST_PATH_IMAGE084
the moment
Figure DEST_PATH_IMAGE085
the normalized state values of each sampled particle,
Figure 658759DEST_PATH_IMAGE086
for
Figure 801902DEST_PATH_IMAGE084
the moment
Figure 523871DEST_PATH_IMAGE085
The normalized weights corresponding to each sampled particle.

其中，

Figure 13758DEST_PATH_IMAGE084
时刻第
Figure 137572DEST_PATH_IMAGE085
个采样粒子的已归一化的状态值
Figure 953081DEST_PATH_IMAGE083
是通过蒙特卡罗重要性采样获得的，具体为：in,
Figure 13758DEST_PATH_IMAGE084
the moment
Figure 137572DEST_PATH_IMAGE085
the normalized state values of the sampled particles
Figure 953081DEST_PATH_IMAGE083
is obtained by Monte Carlo importance sampling, specifically:

Figure DEST_PATH_IMAGE087
（11）
Figure DEST_PATH_IMAGE087
(11)

式中，q()为重要性概率密度分布，

Figure 896766DEST_PATH_IMAGE088
为
Figure 455923DEST_PATH_IMAGE084
时刻的测量值；In the formula, q() is the importance probability density distribution,
Figure 896766DEST_PATH_IMAGE088
for
Figure 455923DEST_PATH_IMAGE084
the measured value of the moment;

所述

Figure 670129DEST_PATH_IMAGE084
时刻第
Figure 656540DEST_PATH_IMAGE085
个采样粒子所对应的已归一化的权值
Figure DEST_PATH_IMAGE089
为said
Figure 670129DEST_PATH_IMAGE084
the moment
Figure 656540DEST_PATH_IMAGE085
The normalized weights corresponding to the sampled particles
Figure DEST_PATH_IMAGE089
for

Figure 618680DEST_PATH_IMAGE090
（12）
Figure 618680DEST_PATH_IMAGE090
(12)

式中，

Figure 715949DEST_PATH_IMAGE091
为
Figure DEST_PATH_IMAGE092
时刻第
Figure 548775DEST_PATH_IMAGE085
个采样粒子的未归一化的状态值，
Figure 706087DEST_PATH_IMAGE093
为
Figure 358785DEST_PATH_IMAGE092
时刻第
Figure 498561DEST_PATH_IMAGE085
个采样粒子所对应的未归一化的权值。In the formula,
Figure 715949DEST_PATH_IMAGE091
for
Figure DEST_PATH_IMAGE092
the moment
Figure 548775DEST_PATH_IMAGE085
the unnormalized state values of each sampled particle,
Figure 706087DEST_PATH_IMAGE093
for
Figure 358785DEST_PATH_IMAGE092
the moment
Figure 498561DEST_PATH_IMAGE085
The unnormalized weights corresponding to each sampled particle.

Figure 185894DEST_PATH_IMAGE092
时刻第
Figure 514107DEST_PATH_IMAGE085
个采样粒子所对应的未归一化的权值
Figure 654101DEST_PATH_IMAGE093
与
Figure DEST_PATH_IMAGE094
时刻的权值
Figure 358752DEST_PATH_IMAGE095
之间的递推关系，具体为：
Figure 185894DEST_PATH_IMAGE092
the moment
Figure 514107DEST_PATH_IMAGE085
The unnormalized weights corresponding to each sampled particle
Figure 654101DEST_PATH_IMAGE093
and
Figure DEST_PATH_IMAGE094
moment weight
Figure 358752DEST_PATH_IMAGE095
The recursive relationship between , specifically:

Figure DEST_PATH_IMAGE096
（13）
Figure DEST_PATH_IMAGE096
(13)

式中，

Figure 697330DEST_PATH_IMAGE097
为第
Figure 930865DEST_PATH_IMAGE085
个粒子
Figure 59620DEST_PATH_IMAGE092
时刻的先验概率分布，由所述蓄电池状态转移方程决定，其概率分布形状和系统的过程噪声
Figure 302383DEST_PATH_IMAGE098
形状一致，
Figure DEST_PATH_IMAGE099
为测量的似然概率分布，由所述蓄电池状态测量方程决定，其概率分布形状和系统的测量噪声
Figure 495467DEST_PATH_IMAGE056
形状一致，q()为重要性概率密度分布。In the formula,
Figure 697330DEST_PATH_IMAGE097
for the first
Figure 930865DEST_PATH_IMAGE085
particles
Figure 59620DEST_PATH_IMAGE092
The prior probability distribution of time is determined by the battery state transition equation, its probability distribution shape and the process noise of the system
Figure 302383DEST_PATH_IMAGE098
same shape,
Figure DEST_PATH_IMAGE099
The likelihood probability distribution for the measurement is determined by the battery state measurement equation, its probability distribution shape and the measurement noise of the system
Figure 495467DEST_PATH_IMAGE056
The shape is the same, and q() is the importance probability density distribution.

步骤3、将容量估计值

Figure 899903DEST_PATH_IMAGE100
作为扩展卡尔曼滤波算法的实际测量值
Figure 748910DEST_PATH_IMAGE101
，利用扩展卡尔曼滤波算法预测动车组镉镍蓄电池的寿命。Step 3. Estimate the capacity
Figure 899903DEST_PATH_IMAGE100
Actual measurement as an extended Kalman filter algorithm
Figure 748910DEST_PATH_IMAGE101
, using the extended Kalman filter algorithm to predict the life of EMU cadmium-nickel battery.

扩展卡尔曼滤波（简称EKF）的本质思想就是将非线性系统的状态转移函数用泰勒级数展开，然后忽略展开的泰勒级数中的高次项，这时得到一个近似的线性系统，最后使用卡尔曼滤波对该系统的状态进行估计。EKF的关键在于非线性系统的线性化和卡尔曼滤波的实现，其中KF的基本思想将状态转移函数的得到预测值与测量值通过权值分配相加得到后验状态估计值，而这个权值叫做卡尔曼增益。The essential idea of Extended Kalman Filtering (EKF for short) is to expand the state transfer function of the nonlinear system with Taylor series, and then ignore the high-order terms in the expanded Taylor series, then obtain an approximate linear system, and finally use The Kalman filter estimates the state of the system. The key to EKF lies in the linearization of nonlinear systems and the realization of Kalman filtering. The basic idea of KF is to add the predicted value and measured value of the state transfer function to obtain the posterior state estimate value through weight distribution, and this weight value It's called the Kalman gain.

上述步骤3具体为：The above step 3 is specifically:

步骤3.1、根据循环容量确定所述待测动车组镉镍蓄电池容量的递推关系式，具体为：根据循环容量，利用数据拟合的方法确定待测动车组镉镍蓄电池容量的递推关系式。Step 3.1. Determine the recursive relationship formula of the capacity of the EMU to be tested according to the cycle capacity, specifically: according to the cycle capacity, use the method of data fitting to determine the recurrence relationship of the capacity of the EMU to be tested. .

步骤3.2、根据递推关系式确定待测动车组镉镍蓄电池状态转移方程和状态测量方程，其中待测动车组镉镍蓄电池状态转移方程为容量递推关系式加上过程噪声

Figure 795364DEST_PATH_IMAGE102
，待测动车组镉镍蓄电池状态测量方程等于状态转移方程的状态值加上测量噪声
Figure 311796DEST_PATH_IMAGE103
，具体地：Step 3.2. Determine the state transition equation and state measurement equation of the Ni-Cd battery for the EMU to be tested according to the recursive relationship, wherein the state transfer equation for the Ni-Cd battery for the EMU to be tested is the capacity recurrence relationship plus process noise
Figure 795364DEST_PATH_IMAGE102
, the state measurement equation of the nickel-cadmium battery of the EMU to be tested is equal to the state value of the state transition equation plus the measurement noise
Figure 311796DEST_PATH_IMAGE103
,specifically:

待测动车组镉镍蓄电池状态转移方程为：The state transition equation of the cadmium-nickel battery to be tested is:

Figure DEST_PATH_IMAGE104
（14）
Figure DEST_PATH_IMAGE104
(14)

式中，

Figure 447986DEST_PATH_IMAGE105
为
Figure 518710DEST_PATH_IMAGE084
时刻待测动车组镉镍蓄电池的循环容量，
Figure 103275DEST_PATH_IMAGE106
为
Figure DEST_PATH_IMAGE107
时刻待测动车组镉镍蓄电池的循环容量，
Figure 5372DEST_PATH_IMAGE108
为
Figure 17190DEST_PATH_IMAGE084
时刻待测动车组镉镍蓄电池的过程噪声，
Figure DEST_PATH_IMAGE109
为状态转移函数。In the formula,
Figure 447986DEST_PATH_IMAGE105
for
Figure 518710DEST_PATH_IMAGE084
The cycle capacity of the nickel-cadmium battery of the EMU to be measured at all times,
Figure 103275DEST_PATH_IMAGE106
for
Figure DEST_PATH_IMAGE107
The cycle capacity of the nickel-cadmium battery of the EMU to be measured at all times,
Figure 5372DEST_PATH_IMAGE108
for
Figure 17190DEST_PATH_IMAGE084
The process noise of the nickel-cadmium battery of the EMU to be tested at all times,
Figure DEST_PATH_IMAGE109
is the state transition function.

待测动车组镉镍蓄电池状态测量方程为：The state measurement equation of the nickel-cadmium battery of the EMU to be tested is:

Figure 371948DEST_PATH_IMAGE110
（15）
Figure 371948DEST_PATH_IMAGE110
(15)

式中，

Figure DEST_PATH_IMAGE111
为
Figure 527248DEST_PATH_IMAGE084
时刻待测动车组镉镍蓄电池的后验状态估计值，
Figure 18273DEST_PATH_IMAGE105
为
Figure 200992DEST_PATH_IMAGE084
时刻待测动车组镉镍蓄电池的循环容量，
Figure 246309DEST_PATH_IMAGE112
为
Figure 172676DEST_PATH_IMAGE084
时刻的测量噪声，
Figure DEST_PATH_IMAGE113
为状态测量函数。In the formula,
Figure DEST_PATH_IMAGE111
for
Figure 527248DEST_PATH_IMAGE084
The posterior state estimate of the nickel-cadmium battery of the EMU to be tested at all times,
Figure 18273DEST_PATH_IMAGE105
for
Figure 200992DEST_PATH_IMAGE084
The cycle capacity of the nickel-cadmium battery of the EMU to be measured at all times,
Figure 246309DEST_PATH_IMAGE112
for
Figure 172676DEST_PATH_IMAGE084
measurement noise at time,
Figure DEST_PATH_IMAGE113
is a state measurement function.

EKF的基本算法中最为重要的五个核心方程可以分为时间更新方程和滤波更新方程。其中的时间更新方程又可以分为先验状态更新方程和先验协方差矩阵更新方程；The five most important core equations in the basic algorithm of EKF can be divided into time update equation and filter update equation. The time update equation can be divided into a priori state update equation and a priori covariance matrix update equation;

先验状态更新方程为：The prior state update equation is:

Figure 49365DEST_PATH_IMAGE114
（16）
Figure 49365DEST_PATH_IMAGE114
(16)

式中，

Figure DEST_PATH_IMAGE115
为
Figure 450258DEST_PATH_IMAGE116
时刻待测动车组镉镍蓄电池的循环容量的后验状态估计值；
Figure DEST_PATH_IMAGE117
为
Figure 514029DEST_PATH_IMAGE092
时刻待测动车组镉镍蓄电池的循环容量的先验状态估计值；In the formula,
Figure DEST_PATH_IMAGE115
for
Figure 450258DEST_PATH_IMAGE116
The posterior state estimate of the cycle capacity of the nickel-cadmium battery of the EMU to be tested at all times;
Figure DEST_PATH_IMAGE117
for
Figure 514029DEST_PATH_IMAGE092
The prior state estimate of the cycle capacity of the nickel-cadmium battery of the EMU to be tested at all times;

先验协方差矩阵更新方程为：The prior covariance matrix update equation is:

Figure 244088DEST_PATH_IMAGE118
（17）
Figure 244088DEST_PATH_IMAGE118
(17)

式中，

Figure DEST_PATH_IMAGE119
为
Figure 709704DEST_PATH_IMAGE120
对
Figure DEST_PATH_IMAGE121
的偏导，
Figure 765385DEST_PATH_IMAGE122
为
Figure 552337DEST_PATH_IMAGE120
对
Figure DEST_PATH_IMAGE123
的偏导，
Figure 617245DEST_PATH_IMAGE124
为
Figure DEST_PATH_IMAGE125
时刻后验预测误差协方差矩阵，
Figure 202948DEST_PATH_IMAGE126
为
Figure 632792DEST_PATH_IMAGE092
时刻的先验预测误差协方差矩阵，
Figure 405576DEST_PATH_IMAGE127
为
Figure 477437DEST_PATH_IMAGE116
时刻过程误差协方差矩阵。In the formula,
Figure DEST_PATH_IMAGE119
for
Figure 709704DEST_PATH_IMAGE120
right
Figure DEST_PATH_IMAGE121
's bias,
Figure 765385DEST_PATH_IMAGE122
for
Figure 552337DEST_PATH_IMAGE120
right
Figure DEST_PATH_IMAGE123
's bias,
Figure 617245DEST_PATH_IMAGE124
for
Figure DEST_PATH_IMAGE125
time posterior prediction error covariance matrix,
Figure 202948DEST_PATH_IMAGE126
for
Figure 632792DEST_PATH_IMAGE092
a priori prediction error covariance matrix at time,
Figure 405576DEST_PATH_IMAGE127
for
Figure 477437DEST_PATH_IMAGE116
Time process error covariance matrix.

扩展卡尔曼滤波算法的滤波更新方程包括卡尔曼增益更新方程、后验状态更新方程和后验协方差矩阵更新方程；The filter update equation of the extended Kalman filter algorithm includes the Kalman gain update equation, the posterior state update equation and the posterior covariance matrix update equation;

其中卡尔曼增益更新方程为：where the Kalman gain update equation is:

Figure DEST_PATH_IMAGE128
（18）
Figure DEST_PATH_IMAGE128
(18)

式中，

Figure 150602DEST_PATH_IMAGE129
为
Figure DEST_PATH_IMAGE130
时刻的测量误差协方差矩阵，
Figure 548085DEST_PATH_IMAGE131
为
Figure DEST_PATH_IMAGE132
对
Figure 73744DEST_PATH_IMAGE121
的偏导，
Figure 949296DEST_PATH_IMAGE133
为
Figure 447274DEST_PATH_IMAGE132
对
Figure 750079DEST_PATH_IMAGE035
的偏导，
Figure DEST_PATH_IMAGE134
为卡尔曼增益；In the formula,
Figure 150602DEST_PATH_IMAGE129
for
Figure DEST_PATH_IMAGE130
the measurement error covariance matrix at time,
Figure 548085DEST_PATH_IMAGE131
for
Figure DEST_PATH_IMAGE132
right
Figure 73744DEST_PATH_IMAGE121
's bias,
Figure 949296DEST_PATH_IMAGE133
for
Figure 447274DEST_PATH_IMAGE132
right
Figure 750079DEST_PATH_IMAGE035
's bias,
Figure DEST_PATH_IMAGE134
is the Kalman gain;

后验状态更新方程为：The posterior state update equation is:

Figure 264499DEST_PATH_IMAGE135
（19）
Figure 264499DEST_PATH_IMAGE135
(19)

后验协方差矩阵更新方程为：The posterior covariance matrix update equation is:

Figure DEST_PATH_IMAGE136
（20）
Figure DEST_PATH_IMAGE136
(20)

式中，

Figure 943742DEST_PATH_IMAGE039
为单位对角矩阵。In the formula,
Figure 943742DEST_PATH_IMAGE039
is a unit diagonal matrix.

步骤3.3、将容量估计值

Figure 561805DEST_PATH_IMAGE137
作为扩展卡尔曼滤波算法中待测动车组镉镍蓄电池状态测量方程的实际测量值
Figure 35512DEST_PATH_IMAGE138
；Step 3.3. Estimate the capacity
Figure 561805DEST_PATH_IMAGE137
As the actual measurement value of the state measurement equation of the EMU under test in the extended Kalman filter algorithm
Figure 35512DEST_PATH_IMAGE138
;

步骤3.4、利用上述扩展卡尔曼滤波算法预测动车组镉镍蓄电池的寿命，即：Step 3.4, using the above-mentioned extended Kalman filter algorithm to predict the life of the EMU's cadmium-nickel battery, namely:

将实际测量值

Figure DEST_PATH_IMAGE139
代入至公式(16)至公式(20)中，即可得到动车组镉镍蓄电池的寿命预测结果。the actual measured value
Figure DEST_PATH_IMAGE139
Substitute into formula (16) to formula (20), the life prediction result of nickel-cadmium battery of EMU can be obtained.

综上，本发明实施例的预测方法具体为：To sum up, the prediction method in the embodiment of the present invention is specifically:

EKF对某个系统进行预测时，其实际是通过权衡实际测量值与状态预测值得到一个最优估计值。通常测量函数的系数都是1，但是预测时实际测量值一般是未知的。若是将PF得到的预测结果作为EKF的实际测量值，就可以通过卡尔曼增益来权衡PF得到的后验状态估计值与EKF的先验状态预测值，从而使PF的预测精度得到提高。PF-EKF融合的核心思想就是将PF的k时刻的后验状态估计值作为EKF的k时刻的实际测量值输入到算法中，最后利用EKF得到后验状态估计值。该融合算法是属于预测结果融合，并没有涉及到参数融合。When EKF predicts a system, it actually obtains an optimal estimated value by weighing the actual measured value and the state predicted value. Usually the coefficients of the measurement function are all 1, but the actual measurement value is generally unknown at the time of prediction. If the prediction result obtained by PF is used as the actual measurement value of EKF, the posterior state estimate value obtained by PF and the prior state prediction value of EKF can be weighed by Kalman gain, so that the prediction accuracy of PF can be improved. The core idea of PF-EKF fusion is to input the posterior state estimate value of PF at time k as the actual measurement value of EKF at time k into the algorithm, and finally use EKF to obtain the posterior state estimate value. The fusion algorithm belongs to prediction result fusion, and does not involve parameter fusion.

假设非线性系统的系统方程如式(14)和(15)，首先利用PF中的第一公式得到其容量估计值 ，对该系统的状态转移方程和状态测量方程进行线性化处理。PF-EKF算法将PF的容量估计值

Figure 270184DEST_PATH_IMAGE140
作为EKF中的实际测量值
Figure 487539DEST_PATH_IMAGE138
。根据式(15)，先验状态测量值为：Assuming that the system equations of the nonlinear system are as shown in equations (14) and (15), the first equation in PF is used to obtain the estimated capacity, and the state transition equation and state measurement equation of the system are linearized. The PF-EKF algorithm converts the capacity estimate of the PF
Figure 270184DEST_PATH_IMAGE140
as actual measurement in EKF
Figure 487539DEST_PATH_IMAGE138
. According to equation (15), the prior state measurement value is:

Figure DEST_PATH_IMAGE141
(21)
Figure DEST_PATH_IMAGE141
(twenty one)

然后根据式(16)、(17)、(18)、(19)和(20)，可以得到最终的后验状态估计值，即为预测值。Then according to equations (16), (17), (18), (19) and (20), the final a posteriori state estimation value, which is the predicted value, can be obtained.

本发明内容的第二方面公开了一种终端设备，包括存储器、处理器以及存储在存储器中并可在处理器上运行的计算机程序，处理器执行计算机程序时实现上述方法的步骤。A second aspect of the content of the present invention discloses a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the above method when executing the computer program.

下面，将以更为具体的实施例验证本发明的方法。In the following, the method of the present invention will be verified with more specific examples.

该具体实施例的研究对象为亚通达的LPH160A型镉镍蓄电池，该蓄电池的标称电压为1.2V，额定容量C为160A•h。试验设备包括蓄电池组测试系统、大电流放电测试系统、高低温试验箱等。The research object of this specific embodiment is the LPH160A NiCd battery of Yatongda, the nominal voltage of the battery is 1.2V, and the rated capacity C is 160A•h. The test equipment includes battery pack test system, high current discharge test system, high and low temperature test chamber, etc.

对LPH160A型镉镍蓄电池进行循环寿命试验，该试验在25°C±5°C环境下进行，然后以50次循环为一组，每组循环中的第一次循环以0.25C充电6h，以0.25C放电2.5h，2~50次循环以0.2C充电7h~8h，以0.2C放电至1.0V/节，直至任一50次循环的放电时间少于3.5h为止，以0.2C再进行一组循环，若连续两组的第50次循环放电时间都少于3.5h，说明容量下降到额定容量的70%以下，则寿命试验终止。试验结果如图3所示。The cycle life test is carried out on LPH160A type cadmium-nickel battery, the test is carried out in the environment of 25 ° C ± 5 ° C, and then 50 cycles are taken as a group, the first cycle in each group of cycles is charged at 0.25C for 6h, with Discharge at 0.25C for 2.5h, charge at 0.2C for 7h~8h for 2~50 cycles, discharge at 0.2C to 1.0V/cell, until the discharge time of any 50 cycles is less than 3.5h, then carry out another cycle at 0.2C. If the discharge time of the 50th cycle of the two consecutive groups is less than 3.5h, it means that the capacity drops below 70% of the rated capacity, and the life test is terminated. The test results are shown in Figure 3.

将LPH160A型镉镍蓄电池2900次循环的容量划分为训练集和测试集，前2300次循环容量作为训练集，后600次循环容量作为测试集。The capacity of LPH160A-type nickel-cadmium battery for 2900 cycles is divided into training set and test set, the first 2300 cycle capacity is used as training set, and the last 600 cycle capacity is used as test set.

训练集表示为C1,C2,C3...C2300，蓄电池状态转移方程实际上等于第k-1次循环的容量Ck-1和第k次循环的容量Ck的递推关系式加上过程噪声

Figure 491267DEST_PATH_IMAGE142
。当k=2,3,...2300时，Ck-1为训练集中的C1,C2,C3... C2299，Ck为训练集中的C2,C3,C4...C2300。利用MATLAB的拟合工具箱，将Ck-1输入到x中，将Ck输入到y中，然后运行求y关于x的拟合函数，就可以得到Ck-1和Ck的递推关系式，从而得到状态转移方程。其拟合函数图如图4所示。The training set is denoted as C1,C2,C3...C2300, the battery state transition equation is actually equal to the recursive relationship between the capacity Ck-1 of the k-1th cycle and the capacity Ck of the kth cycle plus the process noise
Figure 491267DEST_PATH_IMAGE142
. When k=2,3,...2300, Ck-1 is C1,C2,C3...C2299 in the training set, and Ck is C2,C3,C4...C2300 in the training set. Using the fitting toolbox of MATLAB, input Ck-1 into x, input Ck into y, and then run the fitting function of y with respect to x to obtain the recurrence relation between Ck-1 and Ck, thus Get the state transition equation. Its fitting function diagram is shown in Figure 4.

故可得该型蓄电池的状态转移方程和状态测量方程分别为：Therefore, the state transition equation and state measurement equation of this type of battery can be obtained as:

Figure DEST_PATH_IMAGE143
(22)
Figure DEST_PATH_IMAGE143
(twenty two)

Figure 437007DEST_PATH_IMAGE144
(23)
Figure 437007DEST_PATH_IMAGE144
(twenty three)

为表明本发明实施例方法的有效性，规定镉镍蓄电池的容量衰减到初始容量的70%时，该镉镍蓄电池失效。经过多次运行调整算法的相关参数，得到了相对最佳预测效果。为验证本发明方法的有效性，将本发明的方法的预测结果与基于PF的蓄电池寿命预测结果和基于EKF的蓄电池寿命预测结果进行比较。其中图5为基于PF的动车组镉镍蓄电池寿命预测结果，图6为基于EKF的动车组镉镍蓄电池寿命预测结果，图7为基于PF-EKF算法的动车组镉镍蓄电池寿命预测结果，图8为上述三种算法预测结果对比图。In order to demonstrate the effectiveness of the method of the embodiment of the present invention, it is stipulated that the nickel-cadmium battery will fail when the capacity of the nickel-cadmium battery decays to 70% of the initial capacity. After several runs to adjust the relevant parameters of the algorithm, the relative best prediction effect is obtained. To verify the effectiveness of the method of the present invention, the prediction results of the method of the present invention are compared with the battery life prediction results based on PF and the battery life prediction results based on EKF. Among them, Figure 5 is the life prediction result of EMU based on PF, Figure 6 is the life prediction result of EMU based on EKF, and Figure 7 is the life prediction result of EMU based on PF-EKF algorithm. 8 is the comparison chart of the prediction results of the above three algorithms.

从图5、6、7和8可知，PF、EKF和PF-EKF三种算法大致上能够预测蓄电池退化的主体趋势，虽然由于镉镍蓄电池存在记忆效应等，导致该模型不能准确的描述退化的详细过程，但是还是能够得到较为精确的剩余使用寿命（Remaining Useful Life，简称RUL）预测结果。从图中能够得到这三种算法RUL预测值分别为574、568和563次循环，而蓄电池的实际RUL为544次循环。具体评价指标如表1：It can be seen from Figures 5, 6, 7 and 8 that the three algorithms of PF, EKF and PF-EKF can roughly predict the main trend of battery degradation, although due to the memory effect of nickel-cadmium batteries, the model cannot accurately describe the degradation Detailed process, but still can get more accurate remaining useful life (Remaining Useful Life, RUL) prediction results. It can be obtained from the figure that the predicted RUL values of these three algorithms are 574, 568 and 563 cycles respectively, while the actual RUL of the battery is 544 cycles. The specific evaluation indicators are shown in Table 1:

表1 三种算法的预测结果分析Table 1 Analysis of the prediction results of the three algorithms

Figure 893396DEST_PATH_IMAGE145
Figure 893396DEST_PATH_IMAGE145

从表1的三种算法预测结果分析可知，对于LPH160A型镉镍蓄电池的寿命预测，PF、EKF和PF-EKF三种算法的预测结果都落后于实际值，这是由于任何系统具有滞后性。三种算法的预测误差皆在可接受范围内，而其中PF-EKF融合算法的寿命预测误差最小(3.493%)，准确率最高(96.507%)。故本发明提出的PF-EKF算法对动车组蓄电池寿命预测最为精确，对后续动车组蓄电池的电池管理系统（BatteryManagementSystem,即BMS）的建立具有一定的指导意义。From the analysis of the prediction results of the three algorithms in Table 1, it can be seen that for the life prediction of the LPH160A-type nickel-cadmium battery, the prediction results of the three algorithms of PF, EKF and PF-EKF all lag behind the actual value, which is due to the hysteresis of any system. The prediction errors of the three algorithms are all within the acceptable range, and the PF-EKF fusion algorithm has the smallest life prediction error (3.493%) and the highest accuracy (96.507%). Therefore, the PF-EKF algorithm proposed by the present invention is the most accurate in predicting the life of the EMU battery, and has certain guiding significance for the establishment of the battery management system (Battery Management System, ie BMS) of the subsequent EMU battery.

本发明提出了使用数据拟合的方法建立动车组镉镍蓄电池的退化模型，该方法能够精确地描述蓄电池退化的主体趋势。在此基础上，进一步提出了一种将粒子滤波算法与扩展卡尔曼滤波算法相结合的新的融合算法，该算法可精确预测动车组镉镍蓄电池的寿命，预测精度高。The present invention proposes to use a data fitting method to establish a degradation model of a cadmium-nickel battery of an EMU, and the method can accurately describe the main trend of battery degradation. On this basis, a new fusion algorithm combining the particle filter algorithm and the extended Kalman filter algorithm is further proposed. The algorithm can accurately predict the life of the EMU's cadmium-nickel battery with high prediction accuracy.

Claims (9)

1.一种动车组镉镍蓄电池的寿命预测方法，其特征是，包括：1. the life-span prediction method of a kind of EMU cadmium-nickel storage battery, is characterized in that, comprises: 对待测动车组镉镍蓄电池进行循环寿命试验，获得所述待测动车组镉镍蓄电池随循环次数变换的循环容量；Carry out a cycle life test on the cadmium-nickel battery of the EMU to be tested, and obtain the cycle capacity of the cadmium-nickel battery of the EMU to be tested that changes with the number of cycles; 将所述循环容量输入至粒子滤波算法中训练，得到容量估计值
Figure 207792DEST_PATH_IMAGE001
；Input the loop capacity into the particle filter algorithm for training to obtain the capacity estimate
Figure 207792DEST_PATH_IMAGE001
; 将所述容量估计值
Figure 74116DEST_PATH_IMAGE001
作为扩展卡尔曼滤波算法的实际测量值
Figure 114622DEST_PATH_IMAGE002
，利用所述扩展卡尔曼滤波算法预测所述动车组镉镍蓄电池的寿命，具体为：the capacity estimate
Figure 74116DEST_PATH_IMAGE001
Actual measurement as an extended Kalman filter algorithm
Figure 114622DEST_PATH_IMAGE002
, using the extended Kalman filter algorithm to predict the life of the nickel-cadmium battery of the EMU, specifically: 根据所述循环容量确定所述待测动车组镉镍蓄电池容量的递推关系式；Determine the recursive relationship formula of the capacity of the cadmium-nickel battery of the EMU to be tested according to the cycle capacity; 根据所述递推关系式确定所述待测动车组镉镍蓄电池状态转移方程和状态测量方程；Determine the state transition equation and state measurement equation of the cadmium-nickel battery of the EMU to be tested according to the recurrence relation; 将所述容量估计值
Figure 724595DEST_PATH_IMAGE001
作为扩展卡尔曼滤波算法中所述待测动车组镉镍蓄电池状态测量方程的实际测量值
Figure 160256DEST_PATH_IMAGE002
；the capacity estimate
Figure 724595DEST_PATH_IMAGE001
As the actual measurement value of the state measurement equation of the EMU under test described in the extended Kalman filter algorithm
Figure 160256DEST_PATH_IMAGE002
; 利用所述扩展卡尔曼滤波算法预测所述动车组镉镍蓄电池的寿命。The extended Kalman filter algorithm is used to predict the lifetime of the nickel-cadmium battery of the EMU. 2.如权利要求1所述的方法，其特征是，所述待测动车组镉镍蓄电池状态转移方程为：2. method as claimed in claim 1, is characterized in that, described cadmium-nickel accumulator state transition equation of described EMU to be measured is:
Figure 197482DEST_PATH_IMAGE003
Figure 197482DEST_PATH_IMAGE003
 式中，
Figure 476017DEST_PATH_IMAGE004
为
Figure 624101DEST_PATH_IMAGE005
时刻所述待测动车组镉镍蓄电池的循环容量，
Figure 179847DEST_PATH_IMAGE006
为
Figure 387975DEST_PATH_IMAGE007
时刻所述待测动车组镉镍蓄电池的循环容量，
Figure 904538DEST_PATH_IMAGE008
为
Figure 856313DEST_PATH_IMAGE005
时刻所述待测动车组镉镍蓄电池的过程噪声，
Figure 266566DEST_PATH_IMAGE009
为状态转移函数。In the formula,
Figure 476017DEST_PATH_IMAGE004
for
Figure 624101DEST_PATH_IMAGE005
The cycle capacity of the nickel-cadmium battery of the EMU to be tested at the time,
Figure 179847DEST_PATH_IMAGE006
for
Figure 387975DEST_PATH_IMAGE007
The cycle capacity of the nickel-cadmium battery of the EMU to be tested at the time,
Figure 904538DEST_PATH_IMAGE008
for
Figure 856313DEST_PATH_IMAGE005
the process noise of the nickel-cadmium battery of the EMU to be tested at the time,
Figure 266566DEST_PATH_IMAGE009
is the state transition function. 3.如权利要求2所述的方法，其特征是，所述待测动车组镉镍蓄电池状态测量方程为：3. method as claimed in claim 2 is characterized in that, described cadmium-nickel battery state measurement equation of described EMU to be measured is:
Figure 645595DEST_PATH_IMAGE010
Figure 645595DEST_PATH_IMAGE010
 式中，
Figure 898722DEST_PATH_IMAGE011
为
Figure 388609DEST_PATH_IMAGE005
时刻待测动车组镉镍蓄电池的后验状态估计值，
Figure 918947DEST_PATH_IMAGE004
为
Figure 203298DEST_PATH_IMAGE005
时刻所述待测动车组镉镍蓄电池的循环容量，
Figure 204707DEST_PATH_IMAGE012
为
Figure 498286DEST_PATH_IMAGE005
时刻的测量噪声，
Figure 883130DEST_PATH_IMAGE013
为状态测量函数。In the formula,
Figure 898722DEST_PATH_IMAGE011
for
Figure 388609DEST_PATH_IMAGE005
The posterior state estimate of the nickel-cadmium battery of the EMU to be tested at all times,
Figure 918947DEST_PATH_IMAGE004
for
Figure 203298DEST_PATH_IMAGE005
The cycle capacity of the nickel-cadmium battery of the EMU to be tested at the time,
Figure 204707DEST_PATH_IMAGE012
for
Figure 498286DEST_PATH_IMAGE005
measurement noise at time,
Figure 883130DEST_PATH_IMAGE013
is a state measurement function. 4.如权利要求3所述的方法，其特征是，所述扩展卡尔曼滤波算法的时间更新方程包括先验状态更新方程和先验协方差矩阵更新方程；4. The method of claim 3, wherein the time update equation of the extended Kalman filter algorithm comprises a priori state update equation and a priori covariance matrix update equation; 所述先验状态更新方程为：The prior state update equation is:
Figure 603962DEST_PATH_IMAGE014
Figure 603962DEST_PATH_IMAGE014
 式中，
Figure 566102DEST_PATH_IMAGE015
为
Figure 132212DEST_PATH_IMAGE007
时刻所述待测动车组镉镍蓄电池的循环容量的后验状态估计值；
Figure 699460DEST_PATH_IMAGE016
为
Figure 528875DEST_PATH_IMAGE005
时刻所述待测动车组镉镍蓄电池的循环容量的先验状态估计值；In the formula,
Figure 566102DEST_PATH_IMAGE015
for
Figure 132212DEST_PATH_IMAGE007
The posterior state estimate value of the cycle capacity of the nickel-cadmium battery of the EMU to be tested at the moment;
Figure 699460DEST_PATH_IMAGE016
for
Figure 528875DEST_PATH_IMAGE005
a priori state estimate value of the cycle capacity of the nickel-cadmium battery of the EMU to be tested at time; 所述先验协方差矩阵更新方程为：The prior covariance matrix update equation is:
Figure 915994DEST_PATH_IMAGE017
Figure 915994DEST_PATH_IMAGE017
 式中，
Figure 364424DEST_PATH_IMAGE018
为
Figure 786179DEST_PATH_IMAGE019
对
Figure 786496DEST_PATH_IMAGE020
的偏导，
Figure 660911DEST_PATH_IMAGE021
为
Figure 896720DEST_PATH_IMAGE022
对q的偏导，
Figure 172980DEST_PATH_IMAGE023
为
Figure 344199DEST_PATH_IMAGE007
时刻后验预测误差协方差矩阵，
Figure 705910DEST_PATH_IMAGE024
为
Figure 994678DEST_PATH_IMAGE025
时刻的先验预测误差协方差矩阵，
Figure 125445DEST_PATH_IMAGE026
为
Figure 467564DEST_PATH_IMAGE007
时刻过程误差协方差矩阵。In the formula,
Figure 364424DEST_PATH_IMAGE018
for
Figure 786179DEST_PATH_IMAGE019
right
Figure 786496DEST_PATH_IMAGE020
's bias,
Figure 660911DEST_PATH_IMAGE021
for
Figure 896720DEST_PATH_IMAGE022
The partial derivative with respect to q ,
Figure 172980DEST_PATH_IMAGE023
for
Figure 344199DEST_PATH_IMAGE007
time posterior prediction error covariance matrix,
Figure 705910DEST_PATH_IMAGE024
for
Figure 994678DEST_PATH_IMAGE025
a priori prediction error covariance matrix at time,
Figure 125445DEST_PATH_IMAGE026
for
Figure 467564DEST_PATH_IMAGE007
Time process error covariance matrix. 5.如权利要求4所述的方法，其特征是，所述扩展卡尔曼滤波算法的滤波更新方程包括卡尔曼增益更新方程、后验状态更新方程和后验协方差矩阵更新方程；5. method as claimed in claim 4 is characterized in that, the filter update equation of described extended Kalman filter algorithm comprises Kalman gain update equation, posterior state update equation and posterior covariance matrix update equation; 所述卡尔曼增益更新方程为：The Kalman gain update equation is:
Figure 316572DEST_PATH_IMAGE027
Figure 316572DEST_PATH_IMAGE027
 式中，
Figure 159763DEST_PATH_IMAGE028
为
Figure 145036DEST_PATH_IMAGE025
时刻的测量误差协方差矩阵，
Figure 658057DEST_PATH_IMAGE029
为
Figure 994361DEST_PATH_IMAGE030
对
Figure 126396DEST_PATH_IMAGE020
的偏导，
Figure 231755DEST_PATH_IMAGE031
为
Figure 915677DEST_PATH_IMAGE030
对
Figure 739277DEST_PATH_IMAGE032
的偏导，
Figure 658691DEST_PATH_IMAGE033
为卡尔曼增益；In the formula,
Figure 159763DEST_PATH_IMAGE028
for
Figure 145036DEST_PATH_IMAGE025
the measurement error covariance matrix at time,
Figure 658057DEST_PATH_IMAGE029
for
Figure 994361DEST_PATH_IMAGE030
right
Figure 126396DEST_PATH_IMAGE020
's bias,
Figure 231755DEST_PATH_IMAGE031
for
Figure 915677DEST_PATH_IMAGE030
right
Figure 739277DEST_PATH_IMAGE032
's bias,
Figure 658691DEST_PATH_IMAGE033
is the Kalman gain; 所述后验状态更新方程为：The posterior state update equation is:
Figure 618557DEST_PATH_IMAGE034
Figure 618557DEST_PATH_IMAGE034
 所述后验协方差矩阵更新方程为：The posterior covariance matrix update equation is:
Figure 738960DEST_PATH_IMAGE035
Figure 738960DEST_PATH_IMAGE035
 式中，
Figure 784276DEST_PATH_IMAGE036
位对角矩阵。In the formula,
Figure 784276DEST_PATH_IMAGE036
Bit-diagonal matrix. 6.如权利要求1-5任一项所述的方法，其特征是，将所述循环容量输入至粒子滤波算法中训练，得到容量估计值
Figure 756649DEST_PATH_IMAGE001
，具体为：6. The method according to any one of claims 1-5, wherein the circulation capacity is input into a particle filter algorithm for training to obtain an estimated capacity value
Figure 756649DEST_PATH_IMAGE001
,Specifically:
Figure 836601DEST_PATH_IMAGE037
Figure 836601DEST_PATH_IMAGE037
 式中，N为采样粒子数目，
Figure 862326DEST_PATH_IMAGE038
为
Figure 394938DEST_PATH_IMAGE039
时刻第
Figure 921734DEST_PATH_IMAGE040
个采样粒子的已归一化的状态值，
Figure 856192DEST_PATH_IMAGE041
为
Figure 52818DEST_PATH_IMAGE039
时刻第
Figure 72727DEST_PATH_IMAGE040
个采样粒子所对应的已归一化的权值。where N is the number of sampled particles,
Figure 862326DEST_PATH_IMAGE038
for
Figure 394938DEST_PATH_IMAGE039
the moment
Figure 921734DEST_PATH_IMAGE040
the normalized state values of each sampled particle,
Figure 856192DEST_PATH_IMAGE041
for
Figure 52818DEST_PATH_IMAGE039
the moment
Figure 72727DEST_PATH_IMAGE040
The normalized weights corresponding to each sampled particle. 7.如权利要求6所述的方法，其特征是，所述
Figure 888367DEST_PATH_IMAGE039
时刻第
Figure 411753DEST_PATH_IMAGE040
个采样粒子的已归一化的状态值
Figure 107176DEST_PATH_IMAGE038
是通过蒙特卡罗重要性采样获得的，具体为：7. The method of claim 6, wherein the
Figure 888367DEST_PATH_IMAGE039
the moment
Figure 411753DEST_PATH_IMAGE040
the normalized state values of the sampled particles
Figure 107176DEST_PATH_IMAGE038
is obtained by Monte Carlo importance sampling, specifically:
Figure 552064DEST_PATH_IMAGE042
Figure 552064DEST_PATH_IMAGE042
 式中，q()为重要性概率密度分布，
Figure 686242DEST_PATH_IMAGE043
为
Figure 532975DEST_PATH_IMAGE039
时刻的测量值；In the formula, q() is the importance probability density distribution,
Figure 686242DEST_PATH_IMAGE043
for
Figure 532975DEST_PATH_IMAGE039
the measured value of the moment; 所述
Figure 133721DEST_PATH_IMAGE039
时刻第
Figure 439806DEST_PATH_IMAGE044
个采样粒子所对应的已归一化的权值
Figure 784200DEST_PATH_IMAGE045
为said
Figure 133721DEST_PATH_IMAGE039
the moment
Figure 439806DEST_PATH_IMAGE044
The normalized weights corresponding to the sampled particles
Figure 784200DEST_PATH_IMAGE045
for
Figure 485440DEST_PATH_IMAGE046
Figure 485440DEST_PATH_IMAGE046
 式中，
Figure 522666DEST_PATH_IMAGE047
为
Figure 801200DEST_PATH_IMAGE048
时刻第
Figure 949285DEST_PATH_IMAGE049
个采样粒子的未归一化的状态值，
Figure 505031DEST_PATH_IMAGE050
为
Figure 713159DEST_PATH_IMAGE048
时刻第
Figure 229722DEST_PATH_IMAGE051
个采样粒子所对应的未归一化的权值。In the formula,
Figure 522666DEST_PATH_IMAGE047
for
Figure 801200DEST_PATH_IMAGE048
the moment
Figure 949285DEST_PATH_IMAGE049
the unnormalized state values of each sampled particle,
Figure 505031DEST_PATH_IMAGE050
for
Figure 713159DEST_PATH_IMAGE048
the moment
Figure 229722DEST_PATH_IMAGE051
The unnormalized weights corresponding to each sampled particle. 8.如权利要求7所述的方法，所述
Figure 915918DEST_PATH_IMAGE039
时刻第
Figure 591750DEST_PATH_IMAGE049
个采样粒子所对应的未归一化的权值
Figure 705200DEST_PATH_IMAGE050
与
Figure 223906DEST_PATH_IMAGE052
时刻的权值
Figure 448214DEST_PATH_IMAGE053
之间的递推关系，具体为：8. The method of claim 7, the
Figure 915918DEST_PATH_IMAGE039
the moment
Figure 591750DEST_PATH_IMAGE049
The unnormalized weights corresponding to each sampled particle
Figure 705200DEST_PATH_IMAGE050
and
Figure 223906DEST_PATH_IMAGE052
moment weight
Figure 448214DEST_PATH_IMAGE053
The recursive relationship between , specifically:
Figure 775290DEST_PATH_IMAGE054
Figure 775290DEST_PATH_IMAGE054
 式中，
Figure 262903DEST_PATH_IMAGE055
为第
Figure 941009DEST_PATH_IMAGE049
个粒子
Figure 546171DEST_PATH_IMAGE039
时刻的先验概率分布，由所述蓄电池状态转移方程决定，其概率分布形状和系统的过程噪声
Figure 993333DEST_PATH_IMAGE056
形状一致，
Figure 386268DEST_PATH_IMAGE057
为测量的似然概率分布，由所述蓄电池状态测量方程决定，其概率分布形状和系统的测量噪声
Figure 551671DEST_PATH_IMAGE058
形状一致，q()为重要性概率密度分布。In the formula,
Figure 262903DEST_PATH_IMAGE055
for the first
Figure 941009DEST_PATH_IMAGE049
particles
Figure 546171DEST_PATH_IMAGE039
The prior probability distribution of time is determined by the battery state transition equation, its probability distribution shape and the process noise of the system
Figure 993333DEST_PATH_IMAGE056
same shape,
Figure 386268DEST_PATH_IMAGE057
The likelihood probability distribution for the measurement is determined by the battery state measurement equation, its probability distribution shape and the measurement noise of the system
Figure 551671DEST_PATH_IMAGE058
The shape is the same, and q() is the importance probability density distribution. 9.一种终端设备，包括存储器、处理器以及存储在所述存储器中并可在所述处理器上运行的计算机程序，其特征是，所述处理器执行所述计算机程序时实现如权利要求1至8任一项所述方法的步骤。9. A terminal device, comprising a memory, a processor and a computer program stored in the memory and running on the processor, wherein the processor implements the computer program as claimed in the claims when executing the computer program The steps of any one of 1 to 8.
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