CN116502541B - Method for predicting service life of proton exchange membrane fuel cell - Google Patents
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Abstract
The invention discloses a method for predicting the service life of a proton exchange membrane fuel cell, which adopts an improved snake optimization algorithm to respectively optimize a convolutional neural network model CSO-CNN and a random vector network model CSO-RVFL for degradation trend prediction; adopting a particle filter nesting semi-empirical model, firstly carrying out loop iteration through a physical model of a fuel cell to obtain a parameter range of a state equation and an observation equation, and carrying out parameter optimization on the physical model by utilizing a particle swarm optimization algorithm; and finally, performing integrated learning on the data driving model and the physical model prediction result by adopting a Blending algorithm to obtain the performance degradation trend of the fuel cell, and predicting the residual life of the proton exchange membrane fuel cell by using the performance degradation trend prediction result. According to the invention, the improved snake algorithm is utilized to synchronously optimize the CNN and RVFL models, so that the performance degradation trend of the fuel cell can be better obtained, and the accurate and rapid prediction of the residual life of the proton exchange membrane fuel cell is realized.
Description
Technical Field
The invention belongs to the field of fuel cell life prediction, and particularly relates to a proton exchange membrane fuel cell life prediction method.
Background
Global oil and gas production will now reach a top, global warming and environmental pollution have made the task of controlling greenhouse gases and pollutants more serious. In order to solve the problem of energy shortage and better energy conservation and emission reduction, the hydrogen energy is a clean secondary energy source and has good development trend. The hydrogen fuel cell (PEMFC) is used as an important tool for utilizing hydrogen energy, and is different from the traditional storage battery which provides electric energy in an energy storage mode, and the hydrogen fuel cell converts chemical energy into electric energy through electrochemical reaction of hydrogen and oxygen, so long as the hydrogen fuel cell has sufficient hydrogen source and oxygen source, the conversion process can be continued all the time, and zero pollution emission is achieved. The hydrogen fuel cell has the characteristics of high energy conversion rate, low noise, zero emission and the like, and has a very high application prospect. However, the operational lifetime, long-term performance and maintenance costs of PEMFCs are major factors restricting their further commercial development. The method comprises the steps of carrying out accurate prediction on the residual service life, and ensuring the timely maintenance of the hydrogen fuel cell so as to prolong the service life, thereby promoting the development of an industrial chain of the hydrogen energy cell. The prediction of the remaining service life of a hydrogen fuel cell is of great practical significance.
The main idea of the PEMFC is to estimate a degraded state according to a past working profile and a current operation, and then maintain to minimize a maintenance cost and extend a remaining service life according to the state. Due to its nature, hydrogen fuel cells are susceptible to irreversible degradation during storage and operation, resulting in accelerated performance loss and shortened life. The phenomenon of cell degradation will lead to a decrease in the capacity of the hydrogen fuel cell, so it is desirable to predict and quantify this degradation, more precisely the time required for the hydrogen fuel cell to reach a different degree of stack voltage drop. The potential safety hazard can be found before the service life of the battery is ended by accurate and effective prediction, related devices are maintained in advance, and safety accidents caused by the battery problem are avoided. Meanwhile, the use cost can be reduced, the economic loss is reduced for enterprises, and the method has certain reference significance and value for exploring how to prolong the real service life of the enterprises.
The existing model-driven prediction method starts from the structure of the fuel cell to analyze the decay mechanism of the membrane electrode, combines the electrochemical, equivalent circuit, proton exchange membrane and catalyst layer to establish the relationship between the membrane electrode decay index and the output performance, so the model-driven prediction method based on the mechanism has the advantages of high prediction precision, low experimental data requirements and the like, but for a complex system with multiple physics and multiple dimensions such as the fuel cell, a perfect mathematical mechanism model is difficult to establish. The model establishment and prediction of the black box system can be realized based on data driving, and the method has the characteristic of rapid convergence. However, a large amount of data is required for establishing the model, and the prediction accuracy of the model is not simply dependent on the advantages and disadvantages of the algorithm, and is more dependent on the experimental data. Therefore, how to further improve the prediction accuracy is to be explored.
Disclosure of Invention
The invention aims to: aiming at the problems pointed out in the background art, the invention discloses a method for predicting the service life of a proton exchange membrane fuel cell, which can accurately and rapidly predict the residual service life of the proton exchange membrane fuel cell.
The technical scheme is as follows: the invention discloses a method for predicting the service life of a proton exchange membrane fuel cell, which comprises the following steps:
(1) Acquiring monitoring data of a proton exchange membrane fuel cell in advance; and preprocessing the data;
(2) Processing the data acquired in the step (1) based on a principal component analysis method of mutual information, filtering noise peaks through a Gaussian kernel function method, acquiring an input variable set, and dividing the input variable set into a training set and a testing set;
(3) Establishing an improved snake algorithm optimized convolutional neural network model CSO-CNN, inputting the training set obtained in the step (2) into the CSO-CNN model for training, and obtaining a degradation trend DT1 of stack output voltage and fuel cell service time through a test set;
(4) Establishing an improved snake algorithm optimized random vector function connection network model CSO-RVFL, inputting the training set obtained in the step (2) into the CSO-RVFL model for training, and obtaining a degradation trend DT2 of stack output voltage and fuel cell service time through a test set;
(5) Establishing a semi-empirical model of PEMFC voltage attenuation according to a polarization curve and a polarization equation of the fuel cell;
(6) Firstly, training and iterating experimental voltage data to obtain a parameter range of a state equation and an observation equation in a physical model by utilizing a particle filter nesting semi-empirical model, then carrying out parameter optimization by utilizing a particle swarm optimization algorithm, and finally obtaining a degradation trend DT3 of fuel cell voltage and fuel cell service time by utilizing a parameter back-push voltage in the physical model;
(7) And (3) combining the fuel cell degradation trend results obtained in the steps (3), (4) and (6) through Blending integrated learning, and predicting the residual life of the proton exchange membrane cell.
Further, the proton exchange membrane fuel cell monitoring data in step (1) includes aging time, cell and stack voltage, current density, hydrogen inlet and outlet temperatures, air inlet and outlet temperatures, cooling water inlet and outlet temperatures, hydrogen inlet and outlet pressures, air inlet and outlet pressures, hydrogen inlet and outlet flow rates, air inlet and outlet flow rates, cooling water flow rates, and cooling water flow rates.
Further, the implementation process of the step (2) is as follows:
(21) The raw data matrix is as follows:
wherein X is a sample data set of the fuel cell, and i is the number of original data; j is the number of monitoring parameters of the fuel cell;
(22) Given two random variables X and Y, if their respective edge probability distributions and joint probability distributions are p (X), p (Y) and p (X, Y), respectively, then the mutual information I (X; Y) between them is defined as:
(23) The replacement of covariance matrix with mutual information in principal component analysis is as follows:
A T ∑I X,Y A＝Λ (3)
wherein: Σi X,Y Is the mutual information matrix of the data set, A is the characteristic vector beta n Matrix of composition, Λ is eigenvalue v n A diagonal matrix formed;
(24) The principal component matrix z based on mutual information is:
z＝A T x (4)
principal component vectorAnd are orthogonal to each other, beta n Is the principal component vector z n Is a conversion coefficient of (a);
(25) Determining the dimension j of the principal component, and defining the principal component contribution rate sigma of MIPCA n The ratio of the single principal component to the total principal component information amount is:
wherein v n Is a mutual information matrix Sigma I X,Y The nth eigenvalue represents the principal component vector z n Is an information amount of (a); definition of principal component cumulative contribution Rate δ of MIPCA n The sum of the contribution rates of the first n principal components is:
selecting parameters represented by the first W main components with the sum of the contribution rates being more than 90% as an input variable set;
(26) The data is filtered and smoothed, and a Gaussian kernel function formula is adopted as follows:
the filtered data is f (t), as follows:
wherein s is i ＝K[(t j -t i )/h]H is the bandwidth and controls the warp range of the function.
Further, the implementation process of the step (3) is as follows:
the improved snake optimization algorithm CSO is characterized in that Chebyshev mapping initialization is introduced in the process of initializing the snake population, so that the snake population can be searched more widely, and the searching efficiency of the algorithm is improved:
X i ＝cos(karccosx n ),x n ∈[-1,1](10)
wherein X is i Is the position of the ith individual in the whole population, namely the position of the fuel cell input variable, k is the dimension of the fuel cell input variable, x n Is [ -1,1]Random numbers of (a);
simulating different behavior modes of the snakes under different temperatures and different food conditions, and optimizing the input variables of the fuel cell; the fuel cell input variables are sent to CSO and then exist in the form of groups, which are the optimized real content, and the group scale and the iteration number are selected by experience;
the snake population was divided into two groups, female and male, each group accounting for 50%:
N m ≈N/2(11)
N f ＝N-N m (12)
n is the population size of the snake, which is generally set according to the data size and experience of the fuel cell sample, N m And N f The number of males and the number of females, respectively;
the individual finding the best position in the male, female and whole population is to update the input variable position of the fuel cell, X best,m ，X best,f ，X food The method comprises the steps of carrying out a first treatment on the surface of the Calculating the fitness f of the fuel cell input variables best,m ，f best,f ，f food The method comprises the steps of carrying out a first treatment on the surface of the Temperature Temp and food quantity Q are defined:
c 1 set to a constant of 0.5, t 0 The current iteration number is T, and the maximum iteration number is T;
according to the mating model of the snakes, mating behaviors of the snakes can be generated under the conditions of low temperature and sufficient food; otherwise the snake would look for food or eat stored food;
the search process is divided into two phases, exploration and development: the exploration mode occurs in the case of insufficient food, i.e. Q <0.25, where each individual of the snake population explores around looking for food and updates their position; the following is shown:
X i,m ＝X rand,m ±c 2 ×A m ×(Limits×rand+X min ) (15)
X i,f ＝X rand,f ±c 2 ×A f ×(Limits×rand+X min ) (16)
wherein X is i,m And X i,f The position of the ith individual, i.e. the position of the fuel cell input variable, X rand,m And X rand,f Representing random male and female positions, c 2 Constant is 0.05, limits isThe difference between the upper and lower boundaries of the hyper-parameters of the model, rand is a random number of (0, 1), X min Is the lower boundary of the fuel cell input variable, A m And A f The ability to find the optimal location of the fuel cell input variables;
if food is abundant, Q >0.25, will be in development mode; at higher temperatures, temperature >0.6, the snake will only look for food and the location update formula is as follows:
X i ＝X food ±c 3 ×Temp×rand×(X food -X i ) (17)
X food representing the best individual position in the whole population, namely the optimal value of fuel cell degradation trend prediction; c 3 Is a constant; temp is the current temperature;
while in case of lower temperature of <0.6, combat mode or mating process will occur; the combat pattern is as follows:
X i,m ＝X i,m +c 3 ×FM×rand×(Q×X best,f -X i,m ) (18)
X i,f ＝X i,f +c 3 ×FF×rand×(Q×X best,m -X i,f ) (19)
rand is a random number of (0, 1), X best,m And X best,f The best individual position in males and females represents the optimal value of the fuel cell output variable; FM and FF are the ability of the fuel cell to predict the optimal position;
mating patterns are as follows:
X i,m ＝X i,m +c 3 ×M m ×rand×(Q×X i,f -X i,m ) (20)
X i,f ＝X i,f +c 3 ×M f ×rand×(Q×X i,m -X i,f ) (21)
c 3 is set to be constant of 2, M m And M f Optimizing capacity of fuel cell performance degradation trend;
after mating is completed, the female population will spawn and choose whether to hatch to replace the worst male and female individuals in the current population as follows:
X worst,m ＝X min +rand×(X max -X min ) (22)
X worst,f ＝X min +rand×(X max -X min ) (23)
X worst,m and X worst,f Representing worst male and female individuals, X max ，X min Upper and lower boundaries of the fuel cell performance degradation input variables;
optimizing the super parameters of the CNN by adopting a CSO algorithm, and establishing a CSO-CNN prediction model: initializing parameters of a CNN model, and randomly setting weights, thresholds and learning rates of CNNs; performing super-parameter optimization on the model by using a training set through a CSO-CNN prediction model; initializing a snake population, initializing the current food quantity Q and the temperature T, and dividing the population into a female population and a male population; calculating fitness values of male and female, and updating the optimal position and fitness value of the snake, namely the optimal value of the parameter; after the maximum iteration times are reached, decoding the optimal position of the snake to obtain the optimal super-parameters; and inputting the test set into an optimized CSO-CNN prediction model to obtain the degradation trend DT1 of the stack output voltage and time of the fuel cell.
Further, the implementation process of the step (5) is as follows:
the cell voltage of the fuel cell is:
V cell ＝E o -△V act -△V ohm -△V conc (24)
eo is open circuit voltage, deltaV act And DeltaV c o nc Activated polarization and concentration polarization of battery anode and cathode sounds respectively, deltaVo hm Is ohm polarized;
with analysis of the fuel cell and polarization curve, the polarization equation semi-empirical equation is as follows:
wherein V is st And i are respectivelyN is the number of cells in the stack, T is the temperature, and a and b are Tafel constant and concentration constant; the parameter to be identified is the open circuit voltage E 0 Total resistance of battery R, exchange current density i 0 And limiting current density i L ；
Total resistance and exchange current density i according to polarization equation and polarization curve 0 As a time-varying parameter, establishing a semi-empirical model of PEMFC voltage attenuation; r and i in steady state operation 0 The time variation follows a linear equation, which is firstly coupled with each other, and a single variable parameter is adopted to connect R and i in a semi-empirical model 0 The formula is as follows:
α (t) =β·t, β being the degradation rate; r (0) and i 0 (0) Initial values of total resistance and exchange current density, respectively; as the PEMFC degrades, the total resistance R increases and the exchange current density i 0 A reduction; the semi-empirical degradation model of a hydrogen fuel cell is as follows:
where i (t) is the exchange current density of the hydrogen fuel cell at the present moment, and α (t) is the total resistance R and current density i of the fuel cell in the steady state 0 Is a relationship of (3).
Further, the implementation process of the step (6) is as follows:
according to a semi-empirical model of PEMFC voltage attenuation, determining a state equation and an observation equation of the PF model, and redefining x for the state equation and the observation equation k ＝[α k ,β k ] T ，z k ＝V st,k The state space model of the PEMFC is:
wherein z is k I is the observed voltage of the fuel cell k Alpha is the observed current of the fuel cell k For resistors R and i 0 Is the sampling period of data, R 0 N is the number of cells in the stack, T is the temperature, and a and b are Tafel constant and concentration constant; n is n k The parameter to be identified is the open circuit voltage E 0 Total resistance R of battery 0 Initial time current density i 0,k And limiting current density i L ；
PSO optimization algorithm is combined with a semi-empirical model of PF model nested hydrogen fuel cell, and the service life prediction step of the fuel cell is as follows: the voltage data of the fuel cell is transmitted to a semi-empirical model of the PF nested hydrogen fuel cell for cyclic iteration, and the maximum iteration number is reached to output the parameter open-circuit voltage E of the PEMFC model 0 Total resistance R of battery 0 Initial time current density i 0,k And limiting current density i L The method comprises the steps of carrying out a first treatment on the surface of the The value of the output PEMFC model parameter is obtained by iterative optimization of particle swarm 0 Total resistance R of battery 0 Initial time current density i 0,k And limiting current density i L An optimal value; putting the obtained parameter optimal value into a state space model transfer particle of a semi-empirical model system of the PF nested hydrogen fuel cell for cyclic iteration; and outputting a degradation trend DT3 of the mechanism model PEMFC stack voltage and time after the maximum iteration number is reached.
The beneficial effects are that: compared with the prior art, the invention has the beneficial effects that: 1. the invention adopts a mutual information improved principal component analysis method, replaces covariance or a correlation coefficient matrix in the principal component analysis method with a mutual information matrix of a data set to obtain an input variable set with optimal stack output voltage, and removes the influence of noise on model precision by combining a Gaussian kernel function; 2. based on the limitation of the model and the data, the respective advantages of different models can be fully exerted by combining or fusing multiple models so as to obtain better prediction precision; 3. according to the invention, the improved SO algorithm is utilized to synchronously optimize the CNN and RVFL models, SO that the performance degradation trend of the fuel cell can be better obtained; 4. and performing integrated learning on the model results of the fuel cell performance degradation trend obtained by using the data driving and physical model through Blending integration to obtain final fuel cell performance degradation trend prediction results, and calculating the observed residual service life and the predicted residual service life under different failure thresholds to realize the prediction of the residual service life of the proton exchange membrane fuel cell.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a flow chart of data preprocessing;
FIG. 3 is a flow chart of CSO optimization CNN;
FIG. 4 is a flow chart of a CSO algorithm;
figure 5 is a CSO optimized RVFL flow chart;
FIG. 6 is a flow chart of a PSO combined particle filter nested PEMFC semi-empirical model;
FIG. 7 is a flowchart of the Blending ensemble learning prediction final RUL.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
The invention provides a method for predicting the service life of a proton exchange membrane fuel cell, which is mainly divided into two parts: semi-empirical model (physical model) combining data-driven model and mechanism process with experience, final prediction of fuel cell performance degradation trend results by ensemble learning of Blending algorithm combined with calculation of observed remaining useful life under different failure thresholds (M RUL ) And predicted remaining useful life (F RUL ) The method comprises the following steps of realizing prediction of the residual life of the proton exchange membrane fuel cell; as shown in fig. 1, the method specifically comprises the following steps:
step 1: and collecting monitoring data of the proton exchange membrane fuel cell.
Proton exchange membrane fuel cell monitoring parameter information is shown in table 1:
table 1 monitoring parameters for proton exchange membrane fuel cells
Step 2: as shown in fig. 2, the data acquired in step 1 is subjected to principal component analysis (MIPCA) based on mutual information to obtain an optimal input variable set, and noise peaks are filtered by a gaussian kernel function method.
Feature selection is performed based on principal component analysis of Mutual Information (MIPCA), and covariance or a correlation coefficient matrix in a principal component analysis method is replaced by a mutual information matrix of a data set in the mutual information, so that the realization process is as follows:
the raw data matrix is as follows:
wherein X is a sample data set of the fuel cell, and i is the number of original data; j is the number of monitoring parameters of the fuel cell.
Mutual information measures the degree of mutual dependence between the variables, which means the content of mutual possession information between the two variables, given two random variables X and Y, if their respective edge probability distributions and joint probability distributions are p (X), p (Y) and p (X, Y), respectively, then the mutual information I (X; Y) between them is defined as:
the replacement of covariance matrix with mutual information in principal component analysis is as follows:
A T ∑I X,Y A＝Λ (3)
wherein: Σi X,Y Is a mutual information matrix of the dataset, A is a feature vector (beta n N=1, 2, …), Λ being the eigenvalue (v) n N=1, 2, …).
The principal component matrix based on mutual information is:
z＝A T x (4)
main componentAnd are orthogonal to each other, beta n Is the principal component z n Is used for the conversion coefficient of (a).
Determining the dimension j of the principal component, and defining the principal component contribution rate sigma of MIPCA n The ratio of the single principal component to the total principal component information amount is:
wherein v n Is a mutual information matrix Sigma I X,Y The nth eigenvalue represents the principal component z n Is used for the information amount of the (a). Definition of principal component cumulative contribution Rate δ of MIPCA n The sum of the contribution rates of the first n principal components is:
and selecting parameters represented by the first W main components with the sum of the contribution rates being more than 90% as an input variable set.
Because the input variable set contains a large amount of noise and partial peaks, the deviation of the abnormal values can influence the capturing of the true values by the model and generate larger errors on the calculation result, the data is filtered and smoothed, and a Gaussian kernel function formula is adopted as follows:
the filtered data is f (t), as follows:
wherein s is i ＝K[(t j -t i )/h]H is bandwidth, and the warp range of the control functionAnd (5) enclosing to obtain a processed input variable set.
Step 3: and (3) establishing an improved snake algorithm optimized convolutional neural network model (CSO-CNN), dividing the data of the optimal input variable set obtained in the step (2) into a training set and a test set, and inputting the training set and the test set into the (CSO-CNN) model to obtain a degradation trend DT1 of stack output voltage and fuel cell service time, wherein the degradation trend DT1 is shown in FIG. 3.
CNN is one of the models commonly used in deep learning, and consists of one input layer, several hidden layers, and one output layer. The hidden layers of the CNN include a convolutional layer, a pooling layer, and a fully-connected layer. The data is transmitted into the convolution layer through the input layer, then the data characteristics are extracted through convolution calculation, the characteristics obtained by the convolution layer are transmitted to the pooling layer for further extraction, the network complexity is reduced while the main characteristics after convolution are maintained, and the effect of model characteristic extraction is improved.
The convolution calculation is the convolution sum of the input data and the convolution kernel, and the feature set of the input data is obtained through a convolution layer. The calculation process of the convolution layer is as follows:
wherein,representing convolution operation, F representing input data of a convolution layer, w representing weight parameters of a convolution kernel, C, H f ,W f The number of channels, height and width of the convolution kernel, respectively.
The introduced pooling layer is used for reducing dimensions of the visual input object by simulating a human visual system, and the pooling is equivalent to dimension reduction in a space range, so that the model can extract a wider range of features. Meanwhile, the input size of the next layer is reduced, and the calculated amount and the parameter number are further reduced. In general, data features are compressed by taking the maximum or average value of the target region.
CNN can make the input variable data set training speed that characterizes the performance degradation of fuel cell fast and difficult to take place the problem of fitting excessively, but CNN is ambiguous to fuel cell data physical meaning, need to transfer the parameter constantly, to this defect, adopt improved SO algorithm to carry out the optimization to CNN super parameter learning rate, weight and threshold value.
Optimizing the super parameters of the CNN model by using an improved SO algorithm, and establishing the CSO-CNN, wherein the method comprises the following specific steps of:
(1) initializing parameters of a CNN model, and randomly setting weights, thresholds and learning rates of CNNs.
(2) And performing super-parameter optimization on the model by using a training set of the fuel cell performance degradation input variable data set through the improved CSO-CNN model.
(3) The snake population is initialized, the current food quantity Q and the temperature T are initialized, and the populations are divided into female populations and male populations.
(4) And calculating fitness values of the male and female, and updating the optimal position and fitness value of the snake, namely the optimal value of the parameter.
(5) And after the maximum iteration times are reached, decoding the optimal position of the snake to obtain the optimal super-parameters.
(6) Dividing an input variable data set into a training set and a testing set, and training a CNN model to obtain a fuel cell performance degradation trend result DT1.
As shown in fig. 4, the modified snake optimization algorithm (CSO) flow is as follows: in the original snake optimization algorithm, the initialization is randomly generated according to the dimension and the number of input parameters, but in order to obtain the relation between the input variable set and the output variable stack voltage, global searching of the population is needed, so that Chebyshev mapping initialization is introduced in the snake population initialization process, the snake population can be searched more widely, the searching efficiency of the algorithm is improved, and the formula is as follows:
x n+1 ＝cos(karccosx n ),x n ∈[-1,1] (10)
wherein X is i Is the position of the ith individual in the whole population, namely the position of the fuel cell input variable, k is the dimension of the fuel cell input variable, x n Is [ -1,1]Is a random number of (a) in the memory.
And simulating different behavior modes of the snake under different temperatures and different food conditions, and optimizing the input variables of the fuel cell. The fuel cell input variables are fed into the CSO and then exist in the form of a population, which is the real content of optimization, and the population scale and the iteration number are selected empirically.
The snake population was divided into two groups, female and male, each group accounting for 50%:
N m ≈N/2 (11)
N f ＝N-N m (12)
wherein N is the size of the snake population, which is generally set according to the data size and experience of the fuel cell sample, N m And N f The number of males and the number of females, respectively.
The individual finding the best position in the male, female and whole population is to update the input variable position of the fuel cell, X best,m ，X best,f ，X food . Calculating the fitness f of the fuel cell input variables best,m ，f best,f ，f food . Temperature Temp and food quantity Q are defined:
c 1 set to a constant of 0.5, t 0 And T is the maximum iteration number for the current iteration number. The number of iterations is typically set empirically.
According to the mating model of the snakes, mating behavior of the snakes can only occur under the conditions that the temperature is low and food is available; otherwise the snake would only look for food. The search process is divided into two phases, exploration and development.
The exploration mode occurs in the case of insufficient food, i.e. Q <0.25, where each individual of the snake population explores around looking for food and updates their position. The following is shown:
X i,m ＝X rand,m ±c 2 ×A m ×(Limits×rand+X min ) (15)
X i,f ＝X rand,f ±c 2 ×A f ×(Limits×rand+X min ) (16)
wherein X is i,m And X i,f The position of the ith individual, male and female, is the position at which the variable is entered for the fuel cell, X rand,m And X rand,f Representing random male and female positions, c 2 Is constant 0.05, limits is the difference between the upper and lower boundaries of the hyper-parameters of the model, rand is a random number of (0, 1), X min Is the lower boundary of the fuel cell input variable, A m And A f To find the optimal location of the fuel cell input variables.
If the food is full of Q >0.25, it will be in development mode. At higher temperatures, temperature >0.6, the snake will only look for food and the location update formula is as follows:
X i ＝X food ±c 3 ×Temp×rand×(X food -X i ) (17)
X food representing the best individual position in the whole population, namely the optimal value of fuel cell degradation trend prediction; c 3 Set to a constant of 2; temp is the current temperature.
Whereas in case of lower temperatures temperature <0.6, a combat mode or mating process occurs. The combat pattern is as follows:
X i,m ＝X i,m +c 3 ×FM×rand×(Q×X best,f -X i,m ) (18)
X i,f ＝X i,f +c 3 ×FF×rand×(Q×X best,m -X i,f ) (19)
c 3 set to a constant of 2, rand is a random number of (0, 1), X best,m And X best,f The best individual position in males and females represents the optimal value of the fuel cell output variable. FM and FF are the ability of the fuel cell to predict the optimal position.
Mating patterns are as follows:
X i,m ＝X i,m +c 3 ×M m ×rand×(Q×X i,f -X i,m ) (20)
X i,f ＝X i,f +c 3 ×M f ×rand×(Q×X i,m -X i,f ) (21)
M m and M f The optimizing capability of the performance degradation trend of the fuel cell.
After mating is completed, the female population will spawn and choose whether to hatch to replace the worst male and female individuals in the current population as follows:
X worst,m ＝X min +rand×(X max -X min ) (22)
X worst,f ＝X min +rand×(X max -X min ) (23)
X worst,m and X worst,f Representing worst male and female individuals, X max ，X min Is the upper and lower boundary of the fuel cell performance degradation input variable.
Step 4: and (3) establishing an improved snake algorithm optimized random vector function connection network (CSO-RVFL), dividing the data of the optimal input variable set obtained in the step (2) into a training set and a testing set, and inputting the training set and the testing set into a (CSO-RVFL) model to obtain a degradation trend DT2 of stack output voltage and fuel cell service time, wherein the degradation trend DT2 is shown in FIG. 5.
The weight and deviation between the input layer and the hidden layer of the RVFL network are fixed in the learning process, and adjustment in the training stage is not needed, so that the RVFL model has higher convergence speed and analysis precision. RVFL is a single-layer feedforward neural network, the output weight can be obtained through ridge regression calculation, the learning rate of RVFL is optimized by an improved SO algorithm, the hidden layer number and the threshold value are optimized, and a CSO-RVFL prediction model is built, wherein the method comprises the following specific steps:
(1) initializing parameters of RVFL, randomly setting learning rate of RVFL, hidden layer number and threshold value.
(2) The improved CSO-RVFL model is used for training and predicting the input variable set data representing the degradation of the fuel cell, and optimizing the super parameters of the model.
(3) The current food quantity Q and temperature T in the algorithm are initialized and the population is divided into a female population and a male population.
(4) And calculating the fitness value of the super parameter in the RVFL model, updating the optimal super parameter value, and decoding the optimal position of the snake to obtain the optimal super parameter after the maximum iteration number is reached.
(5) The input variable data set is divided into a training set and a testing set, and the RVFL model is trained to obtain a fuel cell performance degradation trend result DT2.
The CSO-RVFL model has better robustness on performance degradation index data of the fuel cell, can avoid the phenomenon of overfitting, and expands the capacity of global search.
And establishing a semi-empirical model of the voltage attenuation of the PEMFC according to the polarization curve and the polarization equation of the fuel cell. The polarization curve of a fuel cell is a plot of cell potential versus current density and is a standard for fuel cell output performance, since cell operation depends on the driving of a voltage differential, and the losses therein are known as polarization, typically consisting of active polarization and ohmic and concentration polarization. Thus, the stack output voltage of the fuel cell can be expressed by:
V cell ＝E o -△V act -△V ohm -△V conc (24)
E o is open circuit voltage, deltaV act And DeltaV conc Active polarization and concentration polarization of battery anode and cathode sounding respectively, deltaV ohm Is ohmic polarized.
The degradation information of the hydrogen fuel cell can be determined according to the polarization curve of the fuel cell, the degradation information of the hydrogen fuel cell can be represented by the polarization curve, the time-varying parameters can be determined through fitting and deducing the equation of the polarization curve, and a semi-empirical model of the voltage attenuation of the cell can be established.
With analysis of the fuel cell and polarization curve, the polarization equation semi-empirical equation is as follows:
V st and i is voltage and current, respectively, N is the number of cells in the stack, T is temperature, and a and b are Tafel constant and concentration constant. The parameter to be identified is the open circuit voltage E 0 Total resistance of battery R, exchange current density i 0 And limiting current density i L 。
Total resistance and exchange current density i according to polarization equation and polarization curve 0 As a time-varying parameter, a semi-empirical model of PEMFC voltage decay can be established. R and i in steady state operation 0 The time variation almost follows a linear equation, which needs to be coupled with each other first, and R and i in a semi-empirical model are changed by adopting a single variable parameter connection 0 The formula is as follows:
α (t) =β.t, β being the degradation rate; r (0) and i 0 (0) Initial values of total resistance and switching current density, respectively. As the PEMFC degrades, the total resistance R increases and the exchange current density i 0 And (3) reducing. The semi-empirical degradation models for hydrogen fuel cells, coupled with equations (25) and (26), are as follows:
i (t) is the exchange current density of the hydrogen fuel cell at the present moment, and alpha (t) is the total resistance R and the current density i of the fuel cell in the steady state 0 Is a relationship of (3).
Step 6: as shown in fig. 6, a semi-empirical model (physical model) is nested by particle filtering, firstly, the parameter ranges of a state equation and an observation equation in the physical model are obtained by training and iterating experimental voltage data, then, parameter optimization is carried out by a particle swarm optimization algorithm, and finally, the degradation trend DT3 of the fuel cell voltage and the service time of the fuel cell is obtained by using the parameter back-push voltage in the physical model.
The PF model is composed ofTime-dependent unobservable state sequence x k And a set of observation sequences z k The specific formula is as follows:
the equation of state: x is x k ＝f(x k-1 ,Θ k-1 ,n k ) (28)
Observation equation: z k ＝h(x k ,v k ) (29)
Where k is a discrete time series; x is x k Is a system state sequence; f is a state transfer function; Θ is a model parameter vector; n is n k Is state noise; z k For observing sequences; h is an observation function of the state; v k To observe noise.
The standard particle filtering algorithm is applied to the prediction of the time sequence, and the unknown parameters in the state equation are updated by learning the existing data.
According to the semi-empirical model of PEMFC voltage attenuation, determining a state equation and an observation equation of the PF model
The model is as follows:
z k i is the observed voltage of the fuel cell k Alpha is the observed current of the fuel cell k For resistors R and i 0 Is the sampling period of data, R 0 N is the number of cells in the stack, T is the temperature, and a and b are the Tafel constant and the concentration constant. The parameter to be identified is the open circuit voltage E 0 Total resistance R of battery 0 Initial time current density i 0,k And limiting current density i L 。
The PSO optimization algorithm is combined with a semi-empirical model of a PF model nested hydrogen fuel cell, and the service life prediction of the fuel cell is as follows:
(1) the voltage data of the fuel cell is transmitted to a semi-empirical model of the PF nested hydrogen fuel cell for cyclic iteration, and the maximum iteration number is reached to output the parameter open-circuit voltage E of the PEMFC model 0 Total resistance R of battery 0 Initial time current density i 0,k And limiting current density i L 。
(2) The value of the output PEMFC model parameter is obtained by iterative optimization of particle swarm 0 Total resistance R of battery 0 Initial time current density i 0,k And limiting current density i L Optimum value.
(3) And putting the obtained parameter optimal value into a state space model transfer particle of a semi-empirical model system of the PF nested hydrogen fuel cell to carry out loop iteration.
(4) And outputting a fuel cell performance degradation trend result DT3 predicted by the physical model after the maximum iteration number is reached.
Step 7: as shown in fig. 7, the fuel cell degradation trend results obtained in steps 3, 4, 6 were combined with prediction of remaining service life by Blending ensemble learning (F RUL ) The formula predicts the residual life of the proton exchange membrane battery.
The health indexes commonly used for representing the health condition of the PEMFC at present include stack output voltage, stack output power, stack output current, stack internal impedance and the like, wherein the stack output voltage is easy to measure and can most intuitively represent the output performance of the PEMFC, so that the stack output voltage is used as the health index of the PEMFC. A suitable failure threshold is defined based on the initial stack voltage data of the PEMFC, and the stack voltage after the initial stack voltage drop {3.5%,4%,5.5% } is generally defined as the PEMFC failure threshold.
Calculating observed remaining useful life (M) at different failure thresholds RUL ) And predicted remaining useful life (F RUL ) The calculation formula is as follows:
M RUL ＝T mFT -T fred
F RUL ＝T fFT -T fred (32)
t in the above fred To predict the time of onset, T mFT For the time when the observed stack voltage first reaches the failure threshold, T fFT Is the time at which the predicted stack voltage first reaches the failure threshold.
Predictive evaluation index: to evaluate the model's effect on the PEMFC stack output voltage degradation trend prediction, a Root Mean Square Error (RMSE), a Mean Absolute Percentage Error (MAPE) and a R square (R 2 ) And (5) an index. Wherein smaller RMSE and MAPE indicate that the predicted value is closer to the observed value; r is R 2 The closer to 1, the better the fitting effect of the model. The calculation formulas of the three indexes are as follows:
the predicted fuel cell degradation trend results are divided into a training set (train-set), a validation set (validation-set) and a test set (test-set). The DT1, DT2 and DT3 datasets were randomly extracted from them 60% as training set, 20% as validation set and 20% as test set
A plurality of models of the first layer are created, the plurality of models are trained by using the train-set, and then the well-trained models are used for predicting the valid-set and the test-set, so that the valid-prediction and the test-prediction 1 are obtained. A class K model is created using the training set, which is a first layer model. After training the model, inputting the verification set into the model for prediction to obtain K different outputs, and recording as A 1 ,…,A k Then inputting the testing machine into the K-class model to output K groups, and marking as B 1 ,…,B k Wherein A is i Is consistent with the verification set, wherein B i Number of samples of (a)Consistent with the verification set.
A second layer model is created, and the second layer model is trained using the validation-prediction as a training set. Obtaining results A of the validation set using samples of the K groups 1 ,…,A k Training a second-tier classifier as a feature of the second-tier classifier
And predicting a second-layer test set test_prediction 1 by using a second-layer trained model, wherein the result is the result of the whole test set. Obtaining the result B of the test set from the samples of the K groups 1 ,…,B k And inputting the second layer of classifier to obtain the fuel cell degradation trend prediction result of the test set.
Finally, the predicted remaining service life under different failure thresholds is combined (F RUL ) Obtaining a proton exchange membrane fuel cell life prediction result RUL.
The blending integrated learning carries out regression fitting on the results of the mechanism model prediction of the data driving and fuel cells, and the accuracy of the result predicted by the hybrid method is obviously higher than that of a single predicted result. The rapid and accurate prediction of the degradation trend result of the fuel cell is realized.
Claims (6)
1. A method for predicting the life of a proton exchange membrane fuel cell, comprising the steps of:
(1) Acquiring monitoring data of a proton exchange membrane fuel cell in advance; and preprocessing the data;
(2) Processing the data acquired in the step (1) based on a principal component analysis method of mutual information, filtering noise peaks through a Gaussian kernel function method, acquiring an input variable set, and dividing the input variable set into a training set and a testing set;
(3) Establishing an improved snake algorithm optimized convolutional neural network model CSO-CNN, inputting the training set obtained in the step (2) into the CSO-CNN model for training, and obtaining a degradation trend DT1 of stack output voltage and fuel cell service time through a test set;
(4) Establishing an improved snake algorithm optimized random vector function connection network model CSO-RVFL, inputting the training set obtained in the step (2) into the CSO-RVFL model for training, and obtaining a degradation trend DT2 of stack output voltage and fuel cell service time through a test set;
(5) Establishing a semi-empirical model of PEMFC voltage attenuation according to a polarization curve and a polarization equation of the fuel cell;
(6) Firstly, training and iterating experimental voltage data to obtain a parameter range of a state equation and an observation equation in a physical model by utilizing a particle filter nesting semi-empirical model, then carrying out parameter optimization by utilizing a particle swarm optimization algorithm, and finally obtaining a degradation trend DT3 of fuel cell voltage and fuel cell service time by utilizing a parameter back-push voltage in the physical model;
(7) And (3) combining the fuel cell degradation trend results obtained in the steps (3), (4) and (6) through Blending integrated learning, and predicting the residual life of the proton exchange membrane cell.
2. The method of claim 1, wherein the pem fuel cell life prediction data of step (1) includes aging time, cell and stack voltage, current density, hydrogen inlet and outlet temperatures, air inlet and outlet temperatures, cooling water inlet and outlet temperatures, hydrogen inlet and outlet pressures, air inlet and outlet pressures, hydrogen inlet and outlet flow rates, air inlet and outlet flow rates, cooling water flow rates.
3. A method for predicting the life of a proton exchange membrane fuel cell according to claim 1, wherein said step (2) is implemented as follows:
(21) The raw data matrix is as follows:
wherein X is a sample data set of the fuel cell, and i is the number of original data; j is the number of monitoring parameters of the fuel cell;
(22) Mutual information measures the degree of mutual dependence between two variables, and represents the content of mutual possession information between the two variables, and given two random variables X and Y, if their respective edge probability distributions and joint probability distributions are p (X), p (Y) and p (X, Y), respectively, the mutual information I (X; Y) between them is defined as:
(23) The replacement of covariance matrix with mutual information in principal component analysis is as follows:
A T ∑I X,Y A＝Λ (3)
wherein: Σi X,Y Is the mutual information matrix of the data set, A is the characteristic vector beta n Matrix of composition, Λ is eigenvalue v n A diagonal matrix formed;
(24) The principal component matrix z based on mutual information is:
z＝A T x (4)
principal component vectorAnd are orthogonal to each other, beta n Is the principal component vector z n Is a conversion coefficient of (a);
(25) Determining the dimension j of the principal component, and defining the principal component contribution rate sigma of MIPCA n The ratio of the single principal component to the total principal component information amount is:
wherein v n Is a mutual information matrix Sigma I X,Y The nth eigenvalue represents the principal component vector z n Is an information amount of (a); definition of principal component cumulative contribution Rate δ of MIPCA n The sum of the contribution rates of the first n principal components is:
selecting parameters represented by the first W main components with the sum of the contribution rates being more than 90% as an input variable set;
(26) The data is filtered and smoothed, and a Gaussian kernel function formula is adopted as follows:
the filtered data were:
where si=k [ (tj-ti)/h ], h is the bandwidth, controlling the warp range of the function.
4. A method for predicting the life of a proton exchange membrane fuel cell according to claim 1, wherein said step (3) is implemented as follows:
the improved snake optimization algorithm CSO is characterized in that Chebyshev mapping initialization is introduced in the process of initializing the snake population, so that the snake population can be searched more widely, and the searching efficiency of the algorithm is improved:
X i ＝cos(karccosx n ),x n ∈[-1,1](10)
wherein X is i Is the position of the ith individual in the whole population, namely the position of the fuel cell input variable, k is the dimension of the fuel cell input variable, x n Is [ -1,1]Random numbers of (a);
simulating different behavior modes of the snakes under different temperatures and different food conditions, and optimizing the input variables of the fuel cell; the fuel cell input variables are sent to CSO and then exist in the form of groups, which are the optimized real content, and the group scale and the iteration number are selected by experience;
the snake population was divided into two groups, female and male, each group accounting for 50%:
N m ≈N/2(11)
N f ＝N-N m (12)
n is the population size of the snake and is set according to the data size and experience of the fuel cell sample, N m And N f The number of males and the number of females, respectively;
the individual finding the best position in the male, female and whole population is to update the input variable position of the fuel cell, X best,m ，X best,f ，X food The method comprises the steps of carrying out a first treatment on the surface of the Calculating the fitness f of the fuel cell input variables best,m ，f best,f ，f food The method comprises the steps of carrying out a first treatment on the surface of the Define the current temperature Temp and the food quantity Q:
c 1 set to a constant of 0.5, t 0 The current iteration number is T, and the maximum iteration number is T;
according to the mating model of the snakes, mating behaviors of the snakes can be generated under the conditions of low temperature and sufficient food; otherwise the snake would look for food or eat stored food;
the search process is divided into two phases, exploration and development: the exploration mode occurs in the case of insufficient food, i.e. Q <0.25, where each individual of the snake population explores around looking for food and updates their position; the following is shown:
X i,m ＝X rand,m ±c 2 ×A m ×(Limits×rand+X min ) (15)
X i,f ＝X rand,f ±c 2 ×A f ×(Limits×rand+X min ) (16)
wherein X is i,m And X i,f The position of the ith individual, i.e. the position of the fuel cell input variable, X rand,m And X rand,f Representing random male and female positions, c 2 Is constant 0.05, limits is the difference between the upper and lower boundaries of the hyper-parameters of the model, rand is a random number of (0, 1), X min Is the lower boundary of the fuel cell input variable, A m And A f The ability to find the optimal location of the fuel cell input variables;
if food is abundant, Q >0.25, will be in development mode; at higher temperatures, temperature >0.6, the snake will only look for food and the location update formula is as follows:
X i ＝X food ±c 3 ×Temp×rand×(X food -X i ) (17)
X food representing the best individual position in the whole population, namely the optimal value of fuel cell degradation trend prediction; c 3 Is a constant; temp is the current temperature;
while in case of lower temperature of <0.6, combat mode or mating process will occur; the combat pattern is as follows:
X i,m ＝X i,m +c 3 ×FM×rand×(Q×X best,f -X i,m ) (18)
X i,f ＝X i,f +c 3 ×FF×rand×(Q×X best,m -X i,f ) (19)
rand is a random number of (0, 1), X best,m And X best,f The best individual position in males and females represents the optimal value of the fuel cell output variable; FM and FF are the ability of the fuel cell to predict the optimal position;
mating patterns are as follows:
X i,m ＝X i,m +c 3 ×M m ×rand×(Q×X i,f -X i,m ) (20)
X i,f ＝X i,f +c 3 ×M f ×rand×(Q×X i,m -X i,f ) (21)
c 3 is set to be constant of 2, M m And M f Optimizing capacity of fuel cell performance degradation trend;
after mating is completed, the female population will spawn and choose whether to hatch to replace the worst male and female individuals in the current population as follows:
X worst,m ＝X min +rand×(X max -X min ) (22)
X worst,f ＝X min +rand×(X max -X min ) (23)
X worst,m and X worst,f Representing worst male and female individuals, X max ，X min Upper and lower boundaries of the fuel cell performance degradation input variables;
optimizing the super parameters of the CNN by adopting a CSO algorithm, and establishing a CSO-CNN prediction model: initializing parameters of a CNN model, and randomly setting weights, thresholds and learning rates of CNNs; performing super-parameter optimization on the model by using a training set through a CSO-CNN prediction model; initializing a snake population, initializing the current food quantity Q and the temperature T, and dividing the population into a female population and a male population; calculating fitness values of male and female, and updating the optimal position and fitness value of the snake, namely the optimal value of the parameter; after the maximum iteration times are reached, decoding the optimal position of the snake to obtain the optimal super-parameters; and inputting the test set into an optimized CSO-CNN prediction model to obtain the degradation trend DT1 of the stack output voltage and time of the fuel cell.
5. A method for predicting the life of a proton exchange membrane fuel cell according to claim 1, wherein said step (5) is implemented as follows:
the cell voltage of the fuel cell is:
V cell ＝E o -△V act -△V ohm -△V conc (24)
E o is open circuit voltage, deltaV act And DeltaV conc Activated polarization and concentration polarization respectively occurring at the anode and cathode of the cell, deltaV ohm Is ohm polarized;
with analysis of the fuel cell and polarization curve, the polarization equation semi-empirical equation is as follows:
wherein V is st And i is voltage and current, N is the number of cells in the stack, T is temperature, and a and b are Tafel constant and concentration constant; the parameter to be identified is the open circuit voltage E 0 Total resistance of battery R, exchange current density i 0 And limiting current density i L ；
Total resistance and exchange current density i according to polarization equation and polarization curve 0 As a time-varying parameter, establishing a semi-empirical model of PEMFC voltage attenuation; r and i in steady state operation 0 The time variation follows a linear equation, which is firstly coupled with each other, and a single variable parameter is adopted to connect R and i in a semi-empirical model 0 The formula is as follows:
α (t) =β·t, β being the degradation rate; r (0) and i 0 (0) Initial values of total resistance and exchange current density, respectively; as the PEMFC degrades, the total resistance R increases and the exchange current density i 0 A reduction; the semi-empirical degradation model of a hydrogen fuel cell is as follows:
where i (t) is the exchange current density of the hydrogen fuel cell at the present moment, and α (t) is the total resistance R and current density i of the fuel cell in the steady state 0 Is a relationship of (3).
6. A method for predicting the life of a proton exchange membrane fuel cell according to claim 1, wherein said step (6) is implemented as follows:
according to the semi-empirical model of PEMFC voltage attenuation, determining the state equation and the observation equation of the PF model, and comparing the state equation and the observation equationEquation redefinition x k ＝[α k ,β k ] T ，z k ＝V st And k is the state space model of the PEMFC is:
wherein z is k I is the observed voltage of the fuel cell k Alpha is the observed current of the fuel cell k For the total resistance R and i 0 Is the sampling period of data, R 0 N is the number of cells in the stack, T is the temperature, and a and b are Tafel constant and concentration constant; nk is state noise, and the parameter to be identified is open circuit voltage E 0 Initial value R of total resistance of battery 0 Initial time current density i 0,k And limiting current density i L ；
PSO optimization algorithm is combined with a semi-empirical model of PF model nested hydrogen fuel cell, and the service life prediction step of the fuel cell is as follows: the voltage data of the fuel cell is transmitted to a semi-empirical model of the PF nested hydrogen fuel cell for cyclic iteration, and the maximum iteration number is reached to output the parameter open-circuit voltage E of the PEMFC model 0 Initial value R of total resistance of battery 0 Initial time current density i 0,k And limiting current density i L The method comprises the steps of carrying out a first treatment on the surface of the The value of the output PEMFC model parameter is obtained by iterative optimization of particle swarm 0 Initial value R of total resistance of battery 0 Initial time current density i 0,k And limiting current density i L An optimal value; putting the obtained parameter optimal value into a state space model transfer particle of a semi-empirical model system of the PF nested hydrogen fuel cell for cyclic iteration; and outputting a degradation trend DT3 of the mechanism model PEMFC stack voltage and time after the maximum iteration number is reached.
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