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

The invention discloses a life prediction method of a cadmium-nickel storage battery of a motor train unit and terminal equipment, wherein the method comprises the following steps: carrying out a cycle life test on the cadmium-nickel storage battery of the motor train unit to be tested to obtain the cycle capacity of the cadmium-nickel storage battery of the motor train unit to be tested along with the cycle frequency conversion; inputting the circulating capacity into a particle filter algorithm for training to obtain a capacity estimation value; and taking the capacity estimation value as an actual measurement value of an extended Kalman filtering algorithm, and predicting the service life of the cadmium-nickel storage battery of the motor train unit by using the extended Kalman filtering algorithm. The invention provides a method for establishing a degradation model of a cadmium-nickel storage battery of a motor train unit by using data fitting, and the method can accurately describe the main trend of the degradation of the storage battery. On the basis, a new fusion algorithm combining the particle filter algorithm and the extended Kalman filter algorithm is further provided, the algorithm can accurately predict the service life of the cadmium-nickel storage battery of the motor train unit, and the prediction precision is high.

Description

Method for predicting service life of cadmium-nickel storage battery of motor train unit and terminal equipment
Technical Field
The invention belongs to the technical field of battery life prediction, and particularly relates to a life prediction method of a cadmium-nickel storage battery of a motor train unit and terminal equipment.
Background
According to the market prospect and investment strategy planning analysis report of the Chinese railway industry in 2013-2017, the development trend of the Chinese railway is mainly shown in the following two aspects: firstly, the passenger train is speeded up; secondly, the freight train is overloaded. The speeding of passenger trains is closely related to motor trains. The storage battery pack is one of key equipment of the motor train unit, is used as a power supply of a direct current auxiliary loop in the motor train unit, and provides power for systems such as illumination, communication and emergency ventilation when the motor train unit is in power failure in an overhead line or an Auxiliary Power Unit (APU) fails. The reliability of the storage battery relates to the driving safety of the motor train unit, so the maintenance is very strict. At present, the maintenance cost of one motor train unit is about sixty thousand yuan, and the maintenance process is time-consuming and labor-consuming. In actual application maintenance, the basis of replacement and return of the storage battery to the factory for maintenance is the number of miles in operation or the service life. In the process, the storage battery can be replaced immediately once the performance index of the storage battery is detected to be not in accordance with the corresponding standard. At this time, the cadmium-nickel battery body still has a large margin available, and if the cadmium-nickel battery body is replaced in advance, the operation cost of the motor train unit is undoubtedly increased. Therefore, the method has very important significance for the research on the service life of the storage battery of the motor train unit.
The technology for predicting the service life of the storage battery is still in the research stage at home, and especially the technology for predicting the service life of the alkaline storage battery is lacked. At home and abroad, related storage battery prediction algorithms can be roughly divided into three methods, namely model driving, data driving and mixing, wherein the model driving is to establish a degradation model according to working conditions, manufacturing materials and a degradation mechanism so as to realize the prediction of the service life of the storage battery. Juuin et al propose a PF-based Proton Exchange Membrane Fuel Cell (PEMFC) remaining service life prediction method, and respectively perform comparative analysis on three degradation models, namely a linear model, an exponential model and a log-linear model, and the result shows that the log-linear model of the three models has higher prediction accuracy on the PEMFC. ZHANG and the like propose that Unscented Kalman Filtering (UKF) is used for carrying out damage tracking on the PEMFC and predicting the service life, and the prediction result shows that the method has higher prediction precision. The influence of factors such as temperature rise and discharge depth of the storage battery during high-rate discharge is ignored in Dingjintao, the RUL of the storage battery is predicted by adopting an EKF algorithm, and the result proves that the method is very simple and has good accuracy. The allowable parameters and the like enable the model to be more consistent with the actual operation condition by establishing two different models of the variable load and the constant load.
The data driving does not need to establish an a priori degradation model, and a corresponding behavior model is obtained by processing the original data. Wanli et al propose a least square based method for predicting the life of a valve-regulated lead-acid battery by a Support Vector Machine (SVM), which improves the operation speed of the algorithm by solving an optimal solution to a linear differential equation. Yang Kyva et al determined the optimum parameters of LIBSVM by Grid-Search method using the health status and terminal voltage of lead-acid battery as variables, and the results showed that it had higher accuracy. Wu ocean et al propose a Back Propagation (BP) neural network prediction model based on a genetic algorithm, which monitors the working condition and predicts the service life in real time by predicting the residual capacity of storage batteries under different temperatures and models. LIU and the like provide a lithium ion battery life prediction method based on indirect health indexes and a multiple Gaussian Process Regression (GPR) model, so that single-point prediction and multi-step prediction are realized. ZHAO et al propose a non-equidistant gray prediction model based on a conversion algorithm, which solves the problem that the actual aging of the battery is not equivalent to the accelerated aging of the battery.
The hybrid method is to eliminate the defects of a single algorithm and to retain the advantages of the constituent algorithms by fusing or combining multiple prediction algorithms. Liujia weizi et al propose a PEMFC (proton exchange membrane fuel cell) residual life prediction method based on fusion of a nuclear ultralimit learning machine and a local weighted regression scatter point smoothing method (LOWESS), and the method realizes reconstruction and smoothing processing of data through an equidistant sampling method and the LOWESS. And the ZHOU and the like respectively utilize a sparse Bayesian method to realize long-term life prediction and a gray model to realize short-term life prediction. The multi-scale decomposition and a Deep Neural Network (DNN) are fused in Hutian and the like to predict the service life of the lithium battery, and degradation data are decomposed into main trend data and fluctuation data through correlation analysis and an ensemble empirical mode. Chentong and the like fuse the BP neural network and the deep sensor, so that the accuracy of original data is improved, and the prediction is more accurate.
However, the prior art does not disclose a method for predicting the service life of the cadmium-nickel storage battery of the motor train unit, so that the cadmium-nickel storage battery of the motor train unit is replaced under the condition that the battery has a larger margin, and the operation cost of the motor train unit is greatly increased.
Disclosure of Invention
The invention provides a method for predicting the service life of a cadmium-nickel storage battery of a motor train unit and terminal equipment, and aims to solve the technical problem that the service life of the cadmium-nickel storage battery of the motor train unit is difficult to accurately predict in the prior art.
The invention discloses a life prediction method of a cadmium-nickel storage battery of a motor train unit, which comprises the following steps:
carrying out a cycle life test on the cadmium-nickel storage battery of the motor train unit to be tested to obtain the cycle capacity of the cadmium-nickel storage battery of the motor train unit to be tested along with the cycle frequency conversion;
inputting the circulation capacity into a particle filter algorithm for training to obtain a capacity estimation value
Figure DEST_PATH_IMAGE001
；
Estimating the capacity
Figure 509232DEST_PATH_IMAGE001
Actual measurement as extended Kalman Filter Algorithm
Figure 443690DEST_PATH_IMAGE002
And predicting the service life of the cadmium-nickel storage battery of the motor train unit by using the extended Kalman filtering algorithm.
Preferably, said estimating said capacity
Figure 233791DEST_PATH_IMAGE001
Actual measurement as extended Kalman Filter Algorithm
Figure 519279DEST_PATH_IMAGE002
And predicting the service life of the cadmium-nickel storage battery of the motor train unit by using the extended Kalman filter algorithm, which specifically comprises the following steps:
determining a recurrence relation of the capacity of the cadmium-nickel storage battery of the motor train unit to be tested according to the circulating capacity;
determining a state transition equation and a state measurement equation of the cadmium-nickel storage battery of the motor train unit to be tested according to the recursion relational expression; wherein the state transition equation of the cadmium-nickel storage battery of the motor train unit to be tested is the capacity recurrence relation plus process noise
Figure DEST_PATH_IMAGE003
The state measurement equation of the cadmium-nickel storage battery of the motor train unit to be measured is equal to the state value of the state transition equation plus the measurement noise
Figure 380925DEST_PATH_IMAGE004
；
Estimating the capacity
Figure 205442DEST_PATH_IMAGE001
As the actual measurement value of the cadmium-nickel storage battery state measurement equation of the motor train unit to be measured in the extended Kalman filtering algorithm
Figure DEST_PATH_IMAGE005
；
And predicting the service life of the cadmium-nickel storage battery of the motor train unit by using the extended Kalman filtering algorithm.
Preferably, determining a recursion relational expression of the capacity of the cadmium-nickel storage battery of the motor train unit to be tested according to the circulating capacity, specifically:
and determining a recurrence relation of the capacity of the cadmium-nickel storage battery of the motor train unit to be tested by using a data fitting method according to the circulating capacity.
Preferably, the state transition equation of the cadmium-nickel storage battery of the motor train unit to be tested is as follows:
Figure 25500DEST_PATH_IMAGE006
in the formula,
Figure DEST_PATH_IMAGE007
is composed of
Figure 798284DEST_PATH_IMAGE008
The circulating capacity of the cadmium-nickel storage battery of the motor train unit to be tested is measured,
Figure 371610DEST_PATH_IMAGE009
is composed of
Figure 608556DEST_PATH_IMAGE008
The circulating capacity of the cadmium-nickel storage battery of the motor train unit to be tested is measured,
Figure DEST_PATH_IMAGE010
is composed of
Figure 802777DEST_PATH_IMAGE008
The process noise of the cadmium-nickel storage battery of the motor train unit to be tested is measured,
Figure 62857DEST_PATH_IMAGE011
is a state transfer function.
Preferably, the state measurement equation of the cadmium-nickel storage battery of the motor train unit to be measured is as follows:
Figure DEST_PATH_IMAGE012
in the formula,
Figure 499261DEST_PATH_IMAGE013
is composed of
Figure 262818DEST_PATH_IMAGE008
Movement to be measured at any momentThe posterior state estimated value of the cadmium-nickel accumulator in the train set,
Figure DEST_PATH_IMAGE014
is composed of
Figure 627940DEST_PATH_IMAGE008
The circulating capacity of the cadmium-nickel storage battery of the motor train unit to be tested is measured,
Figure 876781DEST_PATH_IMAGE010
is composed of
Figure 821603DEST_PATH_IMAGE008
The noise of the measurement at the time of day,
Figure 705246DEST_PATH_IMAGE015
is a state measurement function.
Preferably, the time update equation of the extended kalman filter algorithm includes an a priori state update equation and an a priori covariance matrix update equation;
the prior state update equation is:
Figure DEST_PATH_IMAGE016
in the formula,
Figure 710111DEST_PATH_IMAGE017
is composed of
Figure 475941DEST_PATH_IMAGE018
The posterior state estimation value of the cycle capacity of the cadmium-nickel storage battery of the motor train unit to be tested is obtained at the moment;
Figure DEST_PATH_IMAGE019
is composed of
Figure 451551DEST_PATH_IMAGE020
Estimating the prior state of the circulating capacity of the cadmium-nickel storage battery of the motor train unit to be tested at the moment;
the prior covariance matrix update equation is:
Figure DEST_PATH_IMAGE021
in the formula,
Figure 252017DEST_PATH_IMAGE022
is composed of
Figure DEST_PATH_IMAGE023
To pair
Figure 896625DEST_PATH_IMAGE024
The partial derivatives of (a) are,
Figure 353014DEST_PATH_IMAGE025
is composed of
Figure 609945DEST_PATH_IMAGE023
For the partial derivatives of q, the partial derivatives,
Figure DEST_PATH_IMAGE026
is composed of
Figure 828699DEST_PATH_IMAGE018
The time of day a posteriori prediction error covariance matrix,
Figure 644209DEST_PATH_IMAGE027
is composed of
Figure 166324DEST_PATH_IMAGE008
The prior prediction error covariance matrix for the time instance,
Figure DEST_PATH_IMAGE028
is composed of
Figure 725481DEST_PATH_IMAGE018
Time of day process error covariance matrix.
Preferably, the filter update equations of the extended kalman filter algorithm include a kalman gain update equation, an a posteriori state update equation, and an a posteriori covariance matrix update equation;
the kalman gain update equation is:
Figure 703802DEST_PATH_IMAGE029
in the formula,
Figure DEST_PATH_IMAGE030
is composed of
Figure 221371DEST_PATH_IMAGE008
The covariance matrix of the measurement errors at a time instant,
Figure 917931DEST_PATH_IMAGE031
is composed of
Figure DEST_PATH_IMAGE032
To pair
Figure 47823DEST_PATH_IMAGE024
The partial derivatives of (a) are,
Figure 615071DEST_PATH_IMAGE033
is composed of
Figure DEST_PATH_IMAGE034
To pair
Figure 897017DEST_PATH_IMAGE035
The partial derivatives of (a) are,
Figure 815294DEST_PATH_IMAGE036
is the Kalman gain;
the posterior state update equation is:
Figure DEST_PATH_IMAGE037
the posterior covariance matrix updating equation is as follows:
Figure 214789DEST_PATH_IMAGE038
in the formula,
Figure DEST_PATH_IMAGE039
is an identity diagonal matrix.
Preferably, the cyclic capacity is input into a particle filter algorithm for training to obtain a capacity estimation value
Figure 167702DEST_PATH_IMAGE040
The method specifically comprises the following steps:
Figure 495915DEST_PATH_IMAGE041
wherein N is the number of sampling particles,
Figure DEST_PATH_IMAGE042
is composed of
Figure 901488DEST_PATH_IMAGE008
At the first moment
Figure 606139DEST_PATH_IMAGE043
The normalized state values of the individual sample particles,
Figure DEST_PATH_IMAGE044
is composed of
Figure 413558DEST_PATH_IMAGE008
At the first moment
Figure 148558DEST_PATH_IMAGE043
The normalized weight value corresponding to each sampling particle.
Preferably, the
Figure 775849DEST_PATH_IMAGE008
At the first moment
Figure 487453DEST_PATH_IMAGE043
Normalized state value of individual sample particles
Figure 149378DEST_PATH_IMAGE042
The method is obtained by Monte Carlo importance sampling, and specifically comprises the following steps:
Figure 819394DEST_PATH_IMAGE045
wherein q () is an importance probability density distribution,
Figure DEST_PATH_IMAGE046
is composed of
Figure 199560DEST_PATH_IMAGE008
A measured value of time of day;
the above-mentioned
Figure 714855DEST_PATH_IMAGE008
At the first moment
Figure 231287DEST_PATH_IMAGE043
Normalized weight value corresponding to each sampling particle
Figure 806625DEST_PATH_IMAGE044
Is composed of
Figure 912902DEST_PATH_IMAGE047
In the formula,
Figure DEST_PATH_IMAGE048
is composed of
Figure 763046DEST_PATH_IMAGE020
At the first moment
Figure 133985DEST_PATH_IMAGE043
The unnormalized state values of the individual sample particles,
Figure 145803DEST_PATH_IMAGE049
is composed of
Figure 703823DEST_PATH_IMAGE020
At the first moment
Figure 92079DEST_PATH_IMAGE043
The non-normalized weight value corresponding to each sampling particle.
Preferably, the
Figure 317524DEST_PATH_IMAGE020
At the first moment
Figure 234665DEST_PATH_IMAGE043
Non-normalized weight corresponding to each sampling particle
Figure 811139DEST_PATH_IMAGE049
And
Figure DEST_PATH_IMAGE050
weight of time
Figure 504551DEST_PATH_IMAGE051
The recurrence relation between the two is specifically as follows:
Figure DEST_PATH_IMAGE052
in the formula,
Figure 850082DEST_PATH_IMAGE053
is as follows
Figure 469282DEST_PATH_IMAGE043
Particles of
Figure 1895DEST_PATH_IMAGE008
The prior probability distribution of the moment is determined by the battery state transition equation, the shape of the probability distribution and the process noise of the system
Figure DEST_PATH_IMAGE054
Are uniform in shape，
Figure 731953DEST_PATH_IMAGE055
For the likelihood probability distribution of the measurement, determined by the battery state measurement equation, its probability distribution shape and the measurement noise of the system
Figure DEST_PATH_IMAGE056
The shapes are uniform, and q () is the importance probability density distribution.
A second aspect of the present disclosure discloses a terminal device, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.
The invention provides a method for establishing a degradation model of a cadmium-nickel storage battery of a motor train unit by using data fitting, and the method can accurately describe the main trend of the degradation of the storage battery. On the basis, a new fusion algorithm combining the particle filter algorithm and the extended Kalman filter algorithm is further provided, the algorithm can accurately predict the service life of the cadmium-nickel storage battery of the motor train unit, and the prediction precision is high.
Drawings
FIG. 1 is a flow chart of a life prediction method of a cadmium-nickel storage battery of a motor train unit;
FIG. 2 is a schematic diagram of importance resampling of a particle filter algorithm in the life prediction method of the cadmium-nickel storage battery of the motor train unit;
FIG. 3 is a discharge capacity curve of 2900 cycles of a cadmium-nickel storage battery of the motor train unit in the embodiment of the invention;
FIG. 4 is a diagram showing the fitting results of Ck-1 and Ck in an embodiment of the present invention;
FIG. 5 is a life prediction result diagram of a motor train unit cadmium-nickel storage battery based on PF in an embodiment of the invention;
FIG. 6 is a life prediction result diagram of a motor train unit cadmium-nickel storage battery based on EKF in an embodiment of the invention;
FIG. 7 is a life prediction result diagram of a cadmium-nickel storage battery of a motor train unit based on the method (PF-EKF method) in the embodiment of the invention;
FIG. 8 is a comparison of life prediction results for PF, EKF, and PF-EKF methods in accordance with an embodiment of the present invention.
Detailed Description
The technical solution of the present invention will be described in further detail with reference to the accompanying drawings and specific embodiments. It is to be understood that the following examples are only illustrative and explanatory of the present invention and should not be construed as limiting the scope of the present invention. All the technologies realized based on the above-mentioned contents of the present invention are covered in the protection scope of the present invention.
The first aspect of the invention discloses a life prediction method for a cadmium-nickel storage battery of a motor train unit, and a flow chart is shown in fig. 1, and the method comprises the following steps:
step 1, carrying out a cycle life test on the cadmium-nickel storage battery of the motor train unit to be tested to obtain the cycle capacity of the cadmium-nickel storage battery of the motor train unit to be tested along with the cycle frequency conversion.
Step 2, inputting the circulation capacity into a particle filter algorithm for training to obtain a capacity estimation value
Figure 463149DEST_PATH_IMAGE057
。
The service life change of the cadmium-nickel storage battery of the motor train unit is a nonlinear process, and a particle filter algorithm (PF for short) has very high superiority when a nonlinear and non-Gaussian system is predicted, and can accurately represent the posterior probability distribution condition based on measured values and control quantities. The essential idea of the PF is to use a set of particles approximately equal to the posterior probability distribution of the system under study and use the average approximation of this set of particles as the predicted expectation of the particle filtering.
The basic ideas of the PF algorithm are bayesian estimation, monte carlo sampling, and importance sampling. Bayesian estimation is a method for updating the state of the probability distribution of the system under study by Bayesian theory, but the posterior probability distribution of the system can be obtained only by knowing prior probability distribution and actual measurement value in the updating process.
Bayesian estimation needs to operate integral operation, and in order to avoid integral operation, Monte Carlo sampling is introduced into a particle filter algorithm to solve the problem. The core idea of Monte Carlo sampling is to replace integral operation with the average value of a group of particles, so Monte Carlo can avoid integral operation in Bayes estimation and simplify algorithm, and improve the operation speed of the algorithm. The importance sampling greatly reduces the number of particles required by Monte Carlo sampling by introducing an importance weight to each particle, thereby improving the accuracy and the operation speed of the algorithm.
The PF can be divided into a Sequential Importance Sampling (SIS) section and an importance resampling (SIR) section. SIS is used to find
Figure 751785DEST_PATH_IMAGE058
Particle weight of time
Figure DEST_PATH_IMAGE059
And
Figure 37273DEST_PATH_IMAGE060
particle weight of time
Figure 571023DEST_PATH_IMAGE061
The recurrence relation between the two is avoided, thereby avoiding the problem that all known measurement values are required to be used for solving the weight value of the particle in the importance sampling. Suppose that
Figure 625566DEST_PATH_IMAGE058
State of the moment
Figure DEST_PATH_IMAGE062
Only subject to the initial time
Figure 117728DEST_PATH_IMAGE058
Measured value of time of day
Figure 624932DEST_PATH_IMAGE063
The influence then yields:
Figure DEST_PATH_IMAGE064
(1)
Figure 994996DEST_PATH_IMAGE065
(2)
Figure DEST_PATH_IMAGE066
(3)
in the formula:
Figure 435205DEST_PATH_IMAGE067
a probability density distribution of importance is represented,
Figure DEST_PATH_IMAGE068
is composed of
Figure 98267DEST_PATH_IMAGE069
Prior probability distribution of time;
Figure DEST_PATH_IMAGE070
is composed of
Figure 623926DEST_PATH_IMAGE071
Likelihood probability distribution of time of day measurements.
And:
Figure 992154DEST_PATH_IMAGE072
(4)
substituting the formulas (1), (2) and (3) into the formula (4) to obtain the compound through simplification:
Figure DEST_PATH_IMAGE073
（5）
if the system state at a time is only affected by the system state at a time and the measured value at that time, the recurrence relation can be written as:
Figure 552449DEST_PATH_IMAGE074
（6）
the above is the SIS part of the particle filter.
SIR is used to solve the problem of particle degradation of SIS, and its core idea is to omit particles with small weight and increase the number of particles with large weight, thereby keeping the total number of particles unchanged. The distribution of the number of particles is related to the weight value, that is, the larger the weight value is, the larger the number of particles distributed is, and vice versa. The specific schematic diagram is shown in fig. 2.
Assuming that the current state is common
Figure DEST_PATH_IMAGE075
The number of the particles is one,
Figure 855254DEST_PATH_IMAGE076
to represent
Figure 602630DEST_PATH_IMAGE075
In the particles of
Figure DEST_PATH_IMAGE077
The number of particles that are replicated is:
Figure 547452DEST_PATH_IMAGE078
（7）
Figure DEST_PATH_IMAGE079
（8）
Figure 463718DEST_PATH_IMAGE080
（9）
the resampled particles must satisfy the above conditions.
The particle filter algorithm is applied to the embodiment of the present application to obtain the capacity estimation value
Figure DEST_PATH_IMAGE081
The method specifically comprises the following steps:
determining a capacity estimation value according to a first formula
Figure 203004DEST_PATH_IMAGE081
The first formula is:
Figure 906518DEST_PATH_IMAGE082
（10）
wherein N is the number of sampling particles,
Figure DEST_PATH_IMAGE083
is composed of
Figure 655031DEST_PATH_IMAGE084
At the first moment
Figure DEST_PATH_IMAGE085
The normalized state values of the individual sample particles,
Figure 658759DEST_PATH_IMAGE086
is composed of
Figure 801902DEST_PATH_IMAGE084
At the first moment
Figure 523871DEST_PATH_IMAGE085
The normalized weight value corresponding to each sampling particle.
Wherein,
Figure 13758DEST_PATH_IMAGE084
at the first moment
Figure 137572DEST_PATH_IMAGE085
Normalized state value of individual sample particles
Figure 953081DEST_PATH_IMAGE083
Is obtained by Monte CarloThe importance sampling is obtained by:
Figure DEST_PATH_IMAGE087
（11）
wherein q () is an importance probability density distribution,
Figure 896766DEST_PATH_IMAGE088
is composed of
Figure 455923DEST_PATH_IMAGE084
A measured value of time of day;
the above-mentioned
Figure 670129DEST_PATH_IMAGE084
At the first moment
Figure 656540DEST_PATH_IMAGE085
Normalized weight value corresponding to each sampling particle
Figure DEST_PATH_IMAGE089
Is composed of
Figure 618680DEST_PATH_IMAGE090
（12）
In the formula,
Figure 715949DEST_PATH_IMAGE091
is composed of
Figure DEST_PATH_IMAGE092
At the first moment
Figure 548775DEST_PATH_IMAGE085
The unnormalized state values of the individual sample particles,
Figure 706087DEST_PATH_IMAGE093
is composed of
Figure 358785DEST_PATH_IMAGE092
At the first moment
Figure 498561DEST_PATH_IMAGE085
The non-normalized weight value corresponding to each sampling particle.
Figure 185894DEST_PATH_IMAGE092
At the first moment
Figure 514107DEST_PATH_IMAGE085
Non-normalized weight corresponding to each sampling particle
Figure 654101DEST_PATH_IMAGE093
And
Figure DEST_PATH_IMAGE094
weight of time
Figure 358752DEST_PATH_IMAGE095
The recurrence relation between the two is specifically as follows:
Figure DEST_PATH_IMAGE096
（13）
in the formula,
Figure 697330DEST_PATH_IMAGE097
is as follows
Figure 930865DEST_PATH_IMAGE085
Particles of
Figure 59620DEST_PATH_IMAGE092
The prior probability distribution of the moment is determined by the battery state transition equation, the shape of the probability distribution and the process noise of the system
Figure 302383DEST_PATH_IMAGE098
The shapes of the two-dimensional spherical graphite are consistent,
Figure DEST_PATH_IMAGE099
for the likelihood probability distribution of the measurement, determined by the battery state measurement equation, its probability distribution shape and the measurement noise of the system
Figure 495467DEST_PATH_IMAGE056
The shapes are uniform, and q () is the importance probability density distribution.
Step 3, estimating the capacity
Figure 899903DEST_PATH_IMAGE100
Actual measurement as extended Kalman Filter Algorithm
Figure 748910DEST_PATH_IMAGE101
And predicting the service life of the cadmium-nickel storage battery of the motor train unit by utilizing an extended Kalman filtering algorithm.
The essential idea of extended kalman filtering (EKF for short) is to expand the state transfer function of a nonlinear system by taylor series, then ignore the high-order terms in the expanded taylor series, at this time, obtain an approximate linear system, and finally estimate the state of the system by using kalman filtering. The key point of the EKF lies in the linearization of a nonlinear system and the realization of Kalman filtering, wherein the basic idea of KF is to obtain a posterior state estimation value by distributing and adding a predicted value and a measured value of a state transfer function through a weight, and the weight is called as Kalman gain.
The step 3 is specifically:
step 3.1, determining a recursion relational expression of the capacity of the cadmium-nickel storage battery of the motor train unit to be tested according to the circulating capacity, specifically comprising the following steps: and determining a recurrence relation of the capacity of the cadmium-nickel storage battery of the motor train unit to be tested by using a data fitting method according to the circulating capacity.
Step 3.2, determining a cadmium-nickel storage battery state transition equation and a state measurement equation of the motor train unit to be tested according to the recursion relational expression, wherein the cadmium-nickel storage battery state transition equation of the motor train unit to be tested is the capacity recursion relational expression plus process noise
Figure 795364DEST_PATH_IMAGE102
The state measurement equation of the cadmium-nickel storage battery of the motor train unit to be measured is equal to the state value of the state transition equation plus the measurement noise
Figure 311796DEST_PATH_IMAGE103
Specifically:
the state transition equation of the cadmium-nickel storage battery of the motor train unit to be tested is as follows:
Figure DEST_PATH_IMAGE104
（14）
in the formula,
Figure 447986DEST_PATH_IMAGE105
is composed of
Figure 518710DEST_PATH_IMAGE084
The circulating capacity of the cadmium-nickel storage battery of the motor train unit to be tested at any moment,
Figure 103275DEST_PATH_IMAGE106
is composed of
Figure DEST_PATH_IMAGE107
The circulating capacity of the cadmium-nickel storage battery of the motor train unit to be tested at any moment,
Figure 5372DEST_PATH_IMAGE108
is composed of
Figure 17190DEST_PATH_IMAGE084
The process noise of the cadmium-nickel storage battery of the motor train unit to be tested at any time,
Figure DEST_PATH_IMAGE109
is a state transfer function.
The state measurement equation of the cadmium-nickel storage battery of the motor train unit to be measured is as follows:
Figure 371948DEST_PATH_IMAGE110
（15）
in the formula,
Figure DEST_PATH_IMAGE111
is composed of
Figure 527248DEST_PATH_IMAGE084
The posterior state estimation value of the cadmium-nickel storage battery of the motor train unit to be tested at any moment,
Figure 18273DEST_PATH_IMAGE105
is composed of
Figure 200992DEST_PATH_IMAGE084
The circulating capacity of the cadmium-nickel storage battery of the motor train unit to be tested at any moment,
Figure 246309DEST_PATH_IMAGE112
is composed of
Figure 172676DEST_PATH_IMAGE084
The noise of the measurement at the time of day,
Figure DEST_PATH_IMAGE113
is a state measurement function.
The five most important core equations in the basic algorithm of EKF can be divided into a time update equation and a filter update equation. The time updating equation can be divided into a prior state updating equation and a prior covariance matrix updating equation;
the prior state update equation is:
Figure 49365DEST_PATH_IMAGE114
（16）
in the formula,
Figure DEST_PATH_IMAGE115
is composed of
Figure 450258DEST_PATH_IMAGE116
The posterior state estimation value of the cycle capacity of the cadmium-nickel storage battery of the motor train unit to be tested at any moment;
Figure DEST_PATH_IMAGE117
is composed of
Figure 514029DEST_PATH_IMAGE092
The priori state estimation value of the circulating capacity of the cadmium-nickel storage battery of the motor train unit to be tested at any moment;
the prior covariance matrix update equation is:
Figure 244088DEST_PATH_IMAGE118
（17）
in the formula,
Figure DEST_PATH_IMAGE119
is composed of
Figure 709704DEST_PATH_IMAGE120
To pair
Figure DEST_PATH_IMAGE121
The partial derivatives of (a) are,
Figure 765385DEST_PATH_IMAGE122
is composed of
Figure 552337DEST_PATH_IMAGE120
To pair
Figure DEST_PATH_IMAGE123
The partial derivatives of (a) are,
Figure 617245DEST_PATH_IMAGE124
is composed of
Figure DEST_PATH_IMAGE125
The time of day a posteriori prediction error covariance matrix,
Figure 202948DEST_PATH_IMAGE126
is composed of
Figure 632792DEST_PATH_IMAGE092
The prior prediction error covariance matrix for the time instance,
Figure 405576DEST_PATH_IMAGE127
is composed of
Figure 477437DEST_PATH_IMAGE116
Time of day process error covariance matrix.
The filtering updating equation of the extended Kalman filtering algorithm comprises a Kalman gain updating equation, an a posteriori state updating equation and an a posteriori covariance matrix updating equation;
wherein the kalman gain update equation is:
Figure DEST_PATH_IMAGE128
（18）
in the formula,
Figure 150602DEST_PATH_IMAGE129
is composed of
Figure DEST_PATH_IMAGE130
The covariance matrix of the measurement errors at a time instant,
Figure 548085DEST_PATH_IMAGE131
is composed of
Figure DEST_PATH_IMAGE132
To pair
Figure 73744DEST_PATH_IMAGE121
The partial derivatives of (a) are,
Figure 949296DEST_PATH_IMAGE133
is composed of
Figure 447274DEST_PATH_IMAGE132
To pair
Figure 750079DEST_PATH_IMAGE035
The partial derivatives of (a) are,
Figure DEST_PATH_IMAGE134
is the Kalman gain;
the posterior state update equation is:
Figure 264499DEST_PATH_IMAGE135
（19）
the posterior covariance matrix update equation is:
Figure DEST_PATH_IMAGE136
（20）
in the formula,
Figure 943742DEST_PATH_IMAGE039
is an identity diagonal matrix.
Step 3.3, estimating the capacity
Figure 561805DEST_PATH_IMAGE137
Actual measurement value used as state measurement equation of cadmium-nickel storage battery of motor train unit to be measured in extended Kalman filtering algorithm
Figure 35512DEST_PATH_IMAGE138
；
Step 3.4, predicting the service life of the cadmium-nickel storage battery of the motor train unit by using the extended Kalman filtering algorithm, namely:
the actual measured value
Figure DEST_PATH_IMAGE139
And substituting the predicted life into the formulas (16) to (20) to obtain the life prediction result of the cadmium-nickel storage battery of the motor train unit.
To sum up, the prediction method of the embodiment of the present invention specifically includes:
when the EKF predicts a certain system, it actually obtains an optimal estimation value by balancing the actual measurement value and the state prediction value. Usually the coefficients of the measurement function are all 1, but the actual measurement values are generally unknown at the time of prediction. If the prediction result obtained by the PF is used as the actual measurement value of the EKF, the posterior state estimation value obtained by the PF and the prior state prediction value of the EKF can be balanced through the Kalman gain, so that the prediction precision of the PF is improved. The core idea of PF-EKF fusion is to input the posterior state estimated value of PF at k time as the actual measurement value of EKF at k time into the algorithm, and finally obtain the posterior state estimated value by using EKF. The fusion algorithm belongs to prediction result fusion and does not involve parameter fusion.
Assuming the system equation of the nonlinear system as the equations (14) and (15), the capacity estimation value is obtained by using the first equation in the PF, and the state transition equation and the state measurement equation of the system are linearized. PF-EKF algorithm estimates the capacity of the PF
Figure 270184DEST_PATH_IMAGE140
As actual measurement in EKF
Figure 487539DEST_PATH_IMAGE138
. From equation (15), the prior state measurements are:
Figure DEST_PATH_IMAGE141
(21)
then, according to the expressions (16), (17), (18), (19) and (20), a final posterior state estimation value, that is, a prediction value, can be obtained.
A second aspect of the present disclosure discloses a terminal device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, the processor implementing the steps of the above method when executing the computer program.
In the following, the method of the invention will be verified with more specific examples.
The subject of this particular example is a sub-reach model LPH160A cadmium-nickel battery with a nominal voltage of 1.2V and a rated capacity C of 160 A.h. The test equipment comprises a storage battery pack test system, a large-current discharge test system, a high-low temperature test box and the like.
The method comprises the steps of carrying out a cycle life test on an LPH160A type cadmium-nickel storage battery, wherein the test is carried out under the environment of 25 +/-5 ℃, then 50 cycles are taken as one group, the first cycle in each group of cycles is charged for 6 hours at 0.25 ℃, discharged for 2.5 hours at 0.25 ℃, and charged for 7 to 8 hours at 0.2 ℃ in 2 to 50 cycles, and discharged to 1.0V/node at 0.2C until the discharge time of any 50 cycles is less than 3.5 hours, and then another group of cycles is carried out at 0.2C, and if the discharge time of the 50 th cycle in two groups is less than 3.5 hours, the capacity is reduced to be less than 70% of the rated capacity, the life test is terminated. The test results are shown in FIG. 3.
The capacity of 2900 cycles of LPH160A type cadmium-nickel accumulator is divided into training set and test set, the capacity of the first 2300 cycles is used as training set, and the capacity of the last 600 cycles is used as test set.
The training set is denoted C1, C2, C3... C2300, and the battery state transition equation is effectively equal to the recursion of the capacity Ck-1 of the k-1 th cycle and the capacity Ck of the k-th cycle plus 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. And inputting Ck-1 into x and Ck into y by using a fitting tool box of MATLAB, and then running to solve a fitting function of y relative to x to obtain a recursion relational expression of Ck-1 and Ck so as to obtain a state transition equation. The fitting function graph is shown in fig. 4.
Therefore, the state transition equation and the state measurement equation of the storage battery are respectively obtained as follows:
Figure DEST_PATH_IMAGE143
(22)
Figure 437007DEST_PATH_IMAGE144
(23)
to demonstrate the effectiveness of the method of an embodiment of the present invention, a cadmium-nickel battery was specified to fail when its capacity decayed to 70% of its initial capacity. And obtaining the relatively optimal prediction effect by running the relevant parameters of the adjustment algorithm for multiple times. To verify the effectiveness of the method of the present invention, the prediction results of the method of the present invention are compared to PF-based battery life prediction results and EKF-based battery life prediction results. Wherein, fig. 5 is a life prediction result of a cadmium-nickel storage battery of a motor train unit based on PF, fig. 6 is a life prediction result of a cadmium-nickel storage battery of a motor train unit based on EKF, fig. 7 is a life prediction result of a cadmium-nickel storage battery of a motor train unit based on PF-EKF algorithm, and fig. 8 is a comparison graph of the prediction results of the three algorithms.
As can be seen from fig. 5, 6, 7 and 8, the three algorithms PF, EKF and PF-EKF can substantially predict the main trend of battery degradation, and although the detailed process of degradation cannot be accurately described by the model due to the memory effect of the cadmium-nickel battery, a more accurate prediction result of Remaining Useful Life (RUL) can be obtained. From the figure, it can be seen that the predicted values of the three algorithms RUL are 574, 568 and 563 cycles, respectively, while the actual RUL of the battery is 544 cycles. Specific evaluation indexes are shown in table 1:
TABLE 1 analysis of predicted results for three algorithms
Figure 893396DEST_PATH_IMAGE145
From the analysis of the prediction results of the three algorithms in table 1, it can be seen that the prediction results of the three algorithms PF, EKF and PF-EKF for the life prediction of the LPH160A type cadmium nickel battery fall behind the actual values due to the hysteresis of any system. The prediction errors of the three algorithms are within an acceptable range, and the life prediction error of the PF-EKF fusion algorithm is the smallest (3.493%) and the accuracy is the highest (96.507%). Therefore, the PF-EKF algorithm provided by the invention is most accurate in the life prediction of the storage battery of the motor train unit, and has certain guiding significance for the establishment of a Battery Management System (BMS) of the storage battery of the subsequent motor train unit.
The invention provides a method for establishing a degradation model of a cadmium-nickel storage battery of a motor train unit by using data fitting, and the method can accurately describe the main trend of the degradation of the storage battery. On the basis, a new fusion algorithm combining the particle filter algorithm and the extended Kalman filter algorithm is further provided, the algorithm can accurately predict the service life of the cadmium-nickel storage battery of the motor train unit, and the prediction precision is high.

Claims (9)

1. A life prediction method for a cadmium-nickel storage battery of a motor train unit is characterized by comprising the following steps:
carrying out a cycle life test on the cadmium-nickel storage battery of the motor train unit to be tested to obtain the cycle capacity of the cadmium-nickel storage battery of the motor train unit to be tested along with the cycle frequency conversion;
inputting the circulation capacity into a particle filter algorithm for training to obtain a capacity estimation value
Figure 207792DEST_PATH_IMAGE001
；
Estimating the capacity
Figure 74116DEST_PATH_IMAGE001
Actual measurement as extended Kalman Filter Algorithm
Figure 114622DEST_PATH_IMAGE002
And predicting the service life of the cadmium-nickel storage battery of the motor train unit by using the extended Kalman filter algorithm, which specifically comprises the following steps:
determining a recurrence relation of the capacity of the cadmium-nickel storage battery of the motor train unit to be tested according to the circulating capacity;
determining a state transition equation and a state measurement equation of the cadmium-nickel storage battery of the motor train unit to be tested according to the recursion relational expression;
estimating the capacity
Figure 724595DEST_PATH_IMAGE001
As the actual measurement value of the cadmium-nickel storage battery state measurement equation of the motor train unit to be measured in the extended Kalman filtering algorithm
Figure 160256DEST_PATH_IMAGE002
；
And predicting the service life of the cadmium-nickel storage battery of the motor train unit by using the extended Kalman filtering algorithm.
2. The method as claimed in claim 1, wherein the state transition equation of the cadmium-nickel storage battery of the motor train unit to be tested is as follows:
Figure 197482DEST_PATH_IMAGE003
in the formula,
Figure 476017DEST_PATH_IMAGE004
is composed of
Figure 624101DEST_PATH_IMAGE005
The circulating capacity of the cadmium-nickel storage battery of the motor train unit to be tested is measured,
Figure 179847DEST_PATH_IMAGE006
is composed of
Figure 387975DEST_PATH_IMAGE007
The circulating capacity of the cadmium-nickel storage battery of the motor train unit to be tested is measured,
Figure 904538DEST_PATH_IMAGE008
is composed of
Figure 856313DEST_PATH_IMAGE005
The process noise of the cadmium-nickel storage battery of the motor train unit to be tested is measured,
Figure 266566DEST_PATH_IMAGE009
is a state transfer function.
3. The method as claimed in claim 2, wherein the state measurement equation of the cadmium-nickel storage battery of the motor train unit to be measured is as follows:
Figure 645595DEST_PATH_IMAGE010
in the formula,
Figure 898722DEST_PATH_IMAGE011
is composed of
Figure 388609DEST_PATH_IMAGE005
The posterior state estimation value of the cadmium-nickel storage battery of the motor train unit to be tested at any moment,
Figure 918947DEST_PATH_IMAGE004
is composed of
Figure 203298DEST_PATH_IMAGE005
The circulating capacity of the cadmium-nickel storage battery of the motor train unit to be tested is measured,
Figure 204707DEST_PATH_IMAGE012
is composed of
Figure 498286DEST_PATH_IMAGE005
The noise of the measurement at the time of day,
Figure 883130DEST_PATH_IMAGE013
is a state measurement function.
4. The method of claim 3, wherein the time update equations of the extended Kalman filter algorithm comprise a priori state update equations and a priori covariance matrix update equations;
the prior state update equation is:
Figure 603962DEST_PATH_IMAGE014
in the formula,
Figure 566102DEST_PATH_IMAGE015
is composed of
Figure 132212DEST_PATH_IMAGE007
The posterior state estimation value of the cycle capacity of the cadmium-nickel storage battery of the motor train unit to be tested is obtained at the moment;
Figure 699460DEST_PATH_IMAGE016
is composed of
Figure 528875DEST_PATH_IMAGE005
Estimating the prior state of the circulating capacity of the cadmium-nickel storage battery of the motor train unit to be tested at the moment;
the prior covariance matrix update equation is:
Figure 915994DEST_PATH_IMAGE017
in the formula,
Figure 364424DEST_PATH_IMAGE018
is composed of
Figure 786179DEST_PATH_IMAGE019
To pair
Figure 786496DEST_PATH_IMAGE020
The partial derivatives of (a) are,
Figure 660911DEST_PATH_IMAGE021
is composed of
Figure 896720DEST_PATH_IMAGE022
To pairqThe partial derivatives of (a) are,
Figure 172980DEST_PATH_IMAGE023
is composed of
Figure 344199DEST_PATH_IMAGE007
The time of day a posteriori prediction error covariance matrix,
Figure 705910DEST_PATH_IMAGE024
is composed of
Figure 994678DEST_PATH_IMAGE025
The prior prediction error covariance matrix for the time instance,
Figure 125445DEST_PATH_IMAGE026
is composed of
Figure 467564DEST_PATH_IMAGE007
Time of day process error covariance matrix.
5. The method of claim 4, wherein the filter update equations of the extended Kalman filter algorithm include a Kalman gain update equation, an a posteriori state update equation, and an a posteriori covariance matrix update equation;
the kalman gain update equation is:
Figure 316572DEST_PATH_IMAGE027
in the formula,
Figure 159763DEST_PATH_IMAGE028
is composed of
Figure 145036DEST_PATH_IMAGE025
The covariance matrix of the measurement errors at a time instant,
Figure 658057DEST_PATH_IMAGE029
is composed of
Figure 994361DEST_PATH_IMAGE030
To pair
Figure 126396DEST_PATH_IMAGE020
The partial derivatives of (a) are,
Figure 231755DEST_PATH_IMAGE031
is composed of
Figure 915677DEST_PATH_IMAGE030
To pair
Figure 739277DEST_PATH_IMAGE032
The partial derivatives of (a) are,
Figure 658691DEST_PATH_IMAGE033
is the Kalman gain;
the posterior state update equation is:
Figure 618557DEST_PATH_IMAGE034
the posterior covariance matrix updating equation is as follows:
Figure 738960DEST_PATH_IMAGE035
in the formula,
Figure 784276DEST_PATH_IMAGE036
a bit diagonal matrix.
6. A method according to any of claims 1 to 5, wherein the cyclic capacity is trained by inputting the cyclic capacity into a particle filter algorithm to obtain a capacity estimate
Figure 756649DEST_PATH_IMAGE001
The method specifically comprises the following steps:
Figure 836601DEST_PATH_IMAGE037
wherein N is the number of sampling particles,
Figure 862326DEST_PATH_IMAGE038
is composed of
Figure 394938DEST_PATH_IMAGE039
At the first moment
Figure 921734DEST_PATH_IMAGE040
The normalized state values of the individual sample particles,
Figure 856192DEST_PATH_IMAGE041
is composed of
Figure 52818DEST_PATH_IMAGE039
At the first moment
Figure 72727DEST_PATH_IMAGE040
The normalized weight value corresponding to each sampling particle.
7. The method of claim 6, wherein said step of determining is performed by a computer
Figure 888367DEST_PATH_IMAGE039
At the first moment
Figure 411753DEST_PATH_IMAGE040
Normalized state value of individual sample particles
Figure 107176DEST_PATH_IMAGE038
The method is obtained by Monte Carlo importance sampling, and specifically comprises the following steps:
Figure 552064DEST_PATH_IMAGE042
wherein q () is an importance probability density distribution,
Figure 686242DEST_PATH_IMAGE043
is composed of
Figure 532975DEST_PATH_IMAGE039
A measured value of time of day;
the above-mentioned
Figure 133721DEST_PATH_IMAGE039
At the first moment
Figure 439806DEST_PATH_IMAGE044
Normalized weight value corresponding to each sampling particle
Figure 784200DEST_PATH_IMAGE045
Is composed of
Figure 485440DEST_PATH_IMAGE046
In the formula,
Figure 522666DEST_PATH_IMAGE047
is composed of
Figure 801200DEST_PATH_IMAGE048
At the first moment
Figure 949285DEST_PATH_IMAGE049
The unnormalized state values of the individual sample particles,
Figure 505031DEST_PATH_IMAGE050
is composed of
Figure 713159DEST_PATH_IMAGE048
At the first moment
Figure 229722DEST_PATH_IMAGE051
The non-normalized weight value corresponding to each sampling particle.
8. The method of claim 7, said
Figure 915918DEST_PATH_IMAGE039
At the first moment
Figure 591750DEST_PATH_IMAGE049
Non-normalized weight corresponding to each sampling particle
Figure 705200DEST_PATH_IMAGE050
And
Figure 223906DEST_PATH_IMAGE052
weight of time
Figure 448214DEST_PATH_IMAGE053
The recurrence relation between the two is specifically as follows:
Figure 775290DEST_PATH_IMAGE054
in the formula,
Figure 262903DEST_PATH_IMAGE055
is as follows
Figure 941009DEST_PATH_IMAGE049
Particles of
Figure 546171DEST_PATH_IMAGE039
The prior probability distribution of the moment is determined by the battery state transition equation, the shape of the probability distribution and the process noise of the system
Figure 993333DEST_PATH_IMAGE056
The shapes of the two-dimensional spherical graphite are consistent,
Figure 386268DEST_PATH_IMAGE057
for the likelihood probability distribution of the measurement, determined by the battery state measurement equation, its probability distribution shape and the measurement noise of the system
Figure 551671DEST_PATH_IMAGE058
The shapes are uniform, and q () is the importance probability density distribution.
9. A terminal device comprising a memory, a processor and a computer program stored in said memory and executable on said processor, characterized in that said processor implements the steps of the method according to any of claims 1 to 8 when executing said computer program.
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Application publication date: 20210914