A fuel cell performance prediction method based on a hybrid probabilistic data-driven model

Abstract

A fuel cell performance prediction method based on a hybrid probability data-driven model, comprising the following steps: preprocessing a sample data set by using principal component analysis, and splitting the processed data set into a training set and a test set; establishing a large model neural network, taking the data in the training set as the input of the large model neural network, training the parameters of the large model neural network using an optimization algorithm, and obtaining an optimized large model neural network; calculating the mean and variance of the prediction results of the optimized large model neural network at each time, obtaining a hybrid probability data-driven model, optimizing the weight coefficients of the hybrid probability data-driven model, and obtaining an optimized hybrid probability data-driven model; taking the data in the test set as the input of the optimized hybrid probability data-driven model, and obtaining a fuel cell performance prediction result.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of proton exchange membrane fuel cell power generation, and particularly relates to a fuel cell performance prediction method based on a hybrid probabilistic data-driven model. BACKGROUND

[0002] A fuel cell is a new type of electrochemical energy storage battery, which effectively utilizes hydrogen energy, and converts chemical energy into electrical energy through an electrochemical reaction in an efficient and environmentally friendly manner. Among various types of fuel cells, a proton exchange membrane fuel cell has the characteristics of low noise, zero pollution, no corrosion, long service life, and also has the advantages of large output current, low working temperature, high energy efficiency, fast startup, compact structure, etc., and is widely used in portable power sources, motor vehicle power sources and small and medium-sized power generation systems. At the same time, a power station established on the basis of a proton exchange membrane fuel cell can be connected with a power grid dispatching system during a power consumption peak period to balance the power grid load.

[0003] However, proton exchange membrane fuel cells have problems such as short service life and poor reliability, which limit their large-scale industrial development. The power station based on proton exchange membrane fuel cells will encounter problems of fuel cell life and reliability, and the performance of the fuel cell should be predicted in real time and the faults related to the operating performance should be corrected in time to avoid serious damage to the power generation system. For a proton exchange membrane fuel cell system, real-time performance prediction can determine the operating state of the fuel cell and predict its remaining useful life, providing a reference for precise control decisions. Based on the performance prediction results, the operating conditions can be adjusted to enable the fuel cell to operate efficiently and safely. In the past few decades, performance prediction of proton exchange membrane fuel cells has received increasing attention from academia and industry. Performance prediction of proton exchange membrane fuel cells mainly includes remaining useful life prediction and stack voltage decay prediction. In recent years, with the development of machine learning, more and more data-driven methods have been applied to the field of fuel cell performance prediction. In related technologies, for example, the performance prediction method suitable for proton exchange membrane fuel cells under dynamic load is disclosed in CN202210878290.4, which mainly includes: inputting the voltage of each test step in a cycle of the fuel cell into the autoencoder network, and the target output of the autoencoder network is also the voltage; the intermediate layer output of the autoencoder network is used as the health index of the fuel cell; the cycle number and the health index of the fuel cell obtained in the first stage are used as the input of the long short-term memory network to predict the future change of the health state of the fuel cell; the predicted health state of the fuel cell is input into the decoder of the autoencoder network to obtain the predicted voltage. CN201911276297.3 proposes a fuel cell system output performance prediction method and device based on a neural network, selects feature parameters that affect the output performance of the fuel cell, tests by changing the values corresponding to the feature parameters, obtains the power / current output of the fuel cell system, selects the maximum power / current output from the output results, and obtains training samples; the values corresponding to the feature parameters are used as the input of the neural network, and the maximum power output is used as the output of the neural network to construct an output performance prediction model, and the training samples are used to train the output performance prediction model; the feature parameter values of the fuel cell system currently obtained are substituted into the trained output performance prediction model to obtain the prediction of the current maximum power output, solving the problem of low system operation efficiency and poor output performance caused by the inability to judge the maximum allowable output power of the fuel cell system in real time.

[0004] The fuel cell performance prediction method in the related art is realized by a deterministic neural network, point estimation of performance prediction is provided, and the quantification of uncertainty is not considered. These deep learning-based methods may be difficult to give the confidence of the method itself to the prediction results, and even the prediction results may be unreliable. In addition, control decisions based on single-point prediction are prone to errors, which may lead to potential safety problems. SUMMARY

[0005] The present application provides a fuel cell performance prediction method based on a hybrid probabilistic data-driven model, which incorporates uncertainty representation into the most advanced data-driven model to realize uncertainty quantification in fuel cell performance prediction, solving the problem of low fault tolerance, accuracy and reliability of control decisions in existing performance prediction.

[0006] To solve the above technical problems, the present application provides a fuel cell performance prediction method based on a hybrid probabilistic data-driven model, comprising the following steps:

[0007] Step S1: Preprocessing the sample data set by principal component analysis, and splitting the processed data set into a training set and a test set;

[0008] Step S2: Establishing a large model neural network, taking the data in the training set as the input of the large model neural network, training the parameters of the large model neural network using an optimization algorithm, and obtaining an optimized large model neural network;

[0009] Step S3: Calculating the mean and variance of the prediction results of the optimized large model neural network at each time, obtaining a hybrid probabilistic data-driven model, optimizing the weight coefficients of the hybrid probabilistic data-driven model, and obtaining an optimized hybrid probabilistic data-driven model;

[0010] Step S4: Taking the data in the test set as the input of the optimized hybrid probabilistic data-driven model to obtain the fuel cell performance prediction result.

[0011] Preferably, step S1 comprises the following steps:

[0012] Step S11: Obtaining index data of the original sample according to fuel cell operation data, and representing the index data as a matrix:

[0013]

[0014] In the formula, x1, x2, …, x p are index data when the fuel cell is running, x p = [x 1p , x 2p , … x np ] T;

[0015] Step S12: Standardize the matrix:

[0016]

[0017]

[0018] Step S13: Calculate the correlation coefficient matrix of the original samples:

[0019]

[0020]

[0021] Step S14: Calculate the eigenvalues ​​and corresponding eigenvectors of the correlation coefficient matrix, and calculate the contribution rate of each eigenvalue:

[0022]

[0023] In the formula, λ i Let i be an eigenvalue, i∈(1,2…p);

[0024] Step S15: Using principal component analysis, the contribution rates are sorted in descending order, and the feature vectors corresponding to the top k contribution rates are taken as the processed dataset. The dataset is then split into a training set and a test set.

[0025] Preferably, step S2 includes the following steps:

[0026] Step S21: Establish a large-scale neural network, which includes a recurrent neural network (RNN), a long short-term memory recurrent neural network (LSTM), and a gated recurrent unit neural network (GRU).

[0027] Step S22: Optimize the parameters of the large model neural network using the adaptive time estimation method ADAM to obtain the optimized large model neural network.

[0028] Preferably, the recurrent neural network (RNN) in step S21 includes an input layer, a hidden layer, and an output layer, and the output y of the RNN is... t For y t =w hy h t w hy The hidden layer h is the weight parameter matrix from the hidden layer to the output layer. t The activation value is updated by the following formula:

[0029] h t =f w (w hh h t-1 +wsh x t +b);

[0030] where h t is a new state quantity, h t-1 is an old state quantity, f w is a weight parameterized nonlinear function, w hh is a weight parameter matrix of a hidden layer to a hidden layer, w sh is a weight parameter matrix of an input layer to a hidden layer, x t is an input feature at a current moment, and b is a bias parameter.

[0031] Each unit of the long short-term memory recurrent neural network LSTM includes a forgetting gate, an input gate, and an output gate, the forgetting gate forgets irrelevant parts of a previous state, selectively updates a cell state value, and the output gate outputs some parts of the cell state for a next cell; a calculation formula of each gate variable in the long short-term memory recurrent neural network LSTM is as follows:

[0032] i t =σ(W xi x t +W hi h t-1 +b i );

[0033] f t =σ(W xf x t +W hf h t-1 +b f );

[0034] o t =σ(W xo x t +W ho h t-1 +b o );

[0035] In the above formulas, i t , f t , and o t are outputs of an input gate, a forgetting gate, and an output gate respectively; W xi , W xf , and W xo are weight parameter matrices connected with an input x i ; W hi , W hf , and W ho are weight parameter matrices connected with a hidden layer input h t ; b i , b f , and b o are bias parameters.for the corresponding bias parameter, and σ is an activation function;

[0036] The internal state c of the LSTM cell t The calculation formula is:

[0037]

[0038]

[0039] The hidden layer input h t The calculation formula is:

[0040] h t = o t ⊙ tanh (c t ) ;

[0041] In the above formulae, tanh is an activation function, and is the multiplication of vector elements;

[0042] The gated recurrent unit neural network GRU includes an update gate and a reset gate, and the output calculation formula of the update gate is:

[0043] z t = σ (W xz x t + W hz h t-1 + b z ) ;

[0044] The calculation formula of the reset gate is:

[0045] r t = σ (W xr x t + W hr h t-1 + b r ) ;

[0046] The calculation formula of the hidden layer state quantity h t

[0047]

[0048] The calculation formula of the candidate state

[0049]

[0050] In the above formulae, W xz , W xr , and W xh are weight parameter matrices connected with the input x i ; W hz , W hr , and W hh ​​where h is the input of the hidden layer t a weight parameter matrix connected to the input of the hidden layer, b z , b r and b h are corresponding bias parameters, and σ is an activation function.

[0051] Preferably, step S22 comprises the following steps:

[0052] Step S221: calculating the gradient of the loss function f(θ) with respect to θ:

[0053]

[0054] where f(θ) represents the loss function in the neural network training process, θ is an internal parameter of the neural network, g t is the gradient of the loss function f(θ) with respect to θ at time t-1;

[0055] Step S222: calculating the first moment and the second moment of the gradient, the expression of the first moment being:

[0056] m t = β1·m t-1 +(1-β2)·g t ;

[0057] where β1 and β2 are the first and second exponential decay rates, respectively;

[0058] The expression of the second moment is:

[0059]

[0060] Step S223: correcting the first moment m t and the second moment v t , the correction calculation formula of the first moment being:

[0061]

[0062] The correction calculation formula of the second moment is:

[0063]

[0064] In the above formulas, and are the corresponding first and second exponential decay rates at time t, respectively;

[0065] Step S224: updating the parameter θ t of the large model neural network:

[0066]

[0067] α is a learning rate, and ε is a constant 10 -8 .

[0068] Preferably, step S3 comprises the following steps:

[0069] Step S31: Calculate the mean and variance of the prediction results of the optimized large model neural network at each time point by using weighted average, and establish a hybrid probability data-driven model;

[0070] Step S32: Optimize the weight coefficients of the mean and variance respectively by using a particle swarm algorithm to obtain an optimized hybrid probability data-driven model.

[0071] Preferably, the calculation formula of the mean in step S31 is:

[0072]

[0073] In the formula, are the prediction results of the RNN, LSTM, and GRU models at the i-th time point; α1, α2, and α3 are the weight coefficients corresponding to the RNN, LSTM, and GRU models, respectively, and satisfy α1+α2+α3=1; μ i is the mean corresponding to the prediction result at the i-th time point;

[0074] The calculation formula of the variance is:

[0075]

[0076] In the formula, are the prediction results of the RNN, LSTM, and GRU models at the i-th time point; β1, β2, and β3 are the weight coefficients corresponding to the RNN, LSTM, and GRU models, respectively, and satisfy β1+β2+β3=1; σ i and are the variances corresponding to the prediction result at the i-th time point.

[0077] Preferably, the particle swarm algorithm in step S32 comprises the following steps:

[0078] Step S321: Initialize the particle population under the constraint condition of β1+β2+β3=1, and assign each particle a random speed and position;

[0079] Step S322: Calculate the fitness value of each particle. When there exists a particle whose fitness value is better than the historical particle fitness value, update the individual historical best value p best and the population historical best position g best ;

[0080] Step S323: Update the speed and position of the particle:

[0081]

[0082] wherein k represents the iteration number thereof; x i represents the position vector of particle i; v i represents the velocity vector of particle i; the parameter ω represents the inertia weight; p i represents the historical optimal position vector of particle i; g i represents the historical optimal position vector of all particles in the particle swarm; C1 represents the self-learning factor; C2 represents the group learning factor; r1 and r2 are pseudo-random numbers uniformly distributed in the interval; p g represents the historical optimal position vector of particle, represents the current position vector of particle;

[0083] Step S324: repeating steps S321 to S323 until the absolute value of the instantaneous prediction result error obtained by iteration is smaller than a set value, and outputting the weight α and β corresponding to the mean and variance.

[0084] Preferably, step S4 comprises the following steps:

[0085] Step S41: taking the data of the test set as input, calculating the weight coefficients corresponding to the mean and variance of the prediction result in each time according to the optimization of the mixed probability data-driven model;

[0086] Step S42: calculating the corresponding confidence interval according to the mean and variance of the prediction result, and calculating the confidence interval length according to the confidence interval;

[0087] Step S43: drawing the corresponding probability density distribution diagram according to the mean and variance of the prediction result, and providing a basis for actual control decision.

[0088] The beneficial effects of the present application at least include:

[0089] 1. A variety of neural network models are combined, and the uncertainty quantification is introduced into the performance prediction of the proton exchange membrane fuel cell, a performance prediction model of the proton exchange membrane fuel cell based on the mixed probability data-driven model is established, the single-point estimation of the prediction result is converted into the interval estimation considering the uncertainty, and the accuracy of the performance prediction and the reliability of the control decision are improved.

[0090] 2. The principal component analysis method is used for pre-processing the data set, the main data features are selected as the input of the mixed probability data-driven model, the complexity of the data set is reduced, and the model solving speed is faster. BRIEF DESCRIPTION OF DRAWINGS

[0091] Figure 1 The method flowchart of the embodiment of the present application;

[0092] Figure 2A flow chart of the ADAM optimization algorithm of the embodiment of the present application;

[0093] Figure 3 The performance prediction result of the fuel cell in the embodiment of the present application. DETAILED DESCRIPTION

[0094] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0095] As shown in Figure 1 , the embodiment of the present application provides a fuel cell performance prediction method based on a hybrid probability data-driven model, comprising the following steps:

[0096] Step S1: The principal component analysis method is used to pretreat the sample data set, and the pretreated data set is split into a training set and a test set.

[0097] Specifically, the following steps are included:

[0098] Step S11: The index data of the original sample is obtained according to the fuel cell operation data, and the index data is expressed as a matrix:

[0099]

[0100] In the formula, x1, x2, …, x p are the index data when the fuel cell is running, x p = [x 1p , x 2p , … x np ] T .

[0101] Step S12: The matrix is standardized:

[0102]

[0103]

[0104] Step S13: The correlation coefficient matrix of the original sample is calculated:

[0105]

[0106]

[0107] The closer |r ij | is to 1, the variable x ix j The more similar, the closer to 0, the weaker the similarity.

[0108] Step S14: Calculate the eigenvalues of the correlation coefficient matrix and the corresponding eigenvectors, and calculate the contribution rate of each eigenvalue:

[0109]

[0110] Wherein, the eigenvalues are λ1, λ2... λ p ; eigenvectors are a1, a2... a p .

[0111] Step S15: Using principal component analysis, arrange the contribution rate in descending order, and take the eigenvectors corresponding to the first k contribution rates as the processed data set, and split the data set into training set and test set.

[0112] Specifically, the principal component analysis is used to extract data features from the original data set, and the features with a cumulative contribution rate of 90% are selected as the input of the subsequent hybrid probability data-driven model, and the data set after data feature extraction is divided into training set and test set according to 6:4, and the principal components selected in the embodiment of the application are shown in Table 1.

[0113] Table 1 Principal components selected in the embodiment of the application

[0114]

[0115]

[0116] Step S2: Establish a large model neural network, use the data in the training set as the input of the large model neural network, use the optimization algorithm to train the parameters of the large model neural network, and obtain the optimized large model neural network.

[0117] Specifically, step S2 includes the following steps:

[0118] Step S21: Establish a large model neural network, the large model neural network includes a recurrent neural network RNN, a long short-term memory recurrent neural network LSTM and a gated recurrent unit neural network GRU.

[0119] The recurrent neural network RNN is a new type of neural network with short-term memory capability, which has been widely applied to the fields of speech recognition, language model and natural language processing, etc., including input layer, hidden layer and output layer. The output y t of the recurrent neural network RNN is y t = w hy h t , w hy is the weight parameter matrix from the hidden layer to the output layer, and the hidden layer h tThe activation value is updated by the following formula:

[0120] h t =f w (w hh h t-1 +w sh x t +b);

[0121] In the formula, h t is a new state quantity, h t-1 is an old state quantity, f w is a weight parameterized nonlinear function, w hh is a weight parameter matrix of a hidden layer to a hidden layer, and w sh is a weight parameter matrix of an input layer to a hidden layer, and b is a bias parameter.

[0122] The RNN structure established in the embodiment of the application is as follows: the numbers of input, hidden and output layers are 1, 2 and 1 respectively; the input layer has a total of 60 neurons, each neuron has 100 weight parameters and 100 bias parameters; the first hidden layer has a total of 100 neurons, each neuron has 80 weight parameters and 80 bias parameters; the second hidden layer has a total of 80 neurons, each neuron has 10 weight parameters and 10 bias parameters; and the output layer with 1 weight parameter and 1 bias parameter has 10 neurons.

[0123] Each unit of the long short-term memory recurrent neural network LSTM includes a forgetting gate, an input gate and an output gate, the forgetting gate forgets irrelevant parts of a previous state, selectively updates a cell state value, and the output gate outputs some parts of the cell state to a next cell; and the calculation formula of each gate variable in the long short-term memory recurrent neural network LSTM is as follows:

[0124] i t =σ(W xi x t +W hi h t-1 +b i );

[0125] f t =σ(W xf x t +W hf h t-1 +b f );

[0126] o t =σ(W xo x t +W ho h t-1 +b o );

[0127] i t , f t and o t are the outputs of the input gate, the forget gate and the output gate respectively; W xi , W xf and W xo are the weight parameter matrices connected with the input x i ; W hi , W hf and W ho are the weight parameter matrices connected with the hidden layer input h t ; b i , b f and b o are the corresponding bias parameters, and σ is an activation function;

[0128] The internal state c t of the LSTM cell controls the transmission of the loop information and sends it to the output of the hidden layer h t , and the calculation formula of the internal state c t is as follows:

[0129]

[0130]

[0131] The calculation formula of the hidden layer output h t is as follows:

[0132] h t = o t ⊙tanh(c t ).

[0133] In the above formulae, tanh is an activation function, and ⊙ is the multiplication of vector elements.

[0134] The LSTM structure established in the embodiment of the application is as follows: the number of the input layer, the hidden layer and the output layer is 1, 2 and 1 respectively; the input layer has a total of 60 neurons, each neuron has 100 weight parameters and 100 bias parameters; the first hidden layer has a total of 100 neurons, each neuron has 80 weight parameters and 80 bias parameters; the second hidden layer has a total of 80 neurons, each neuron has 10 weight parameters and 10 bias parameters; the output layer with 1 weight parameter and 1 bias parameter has 10 neurons.

[0135] Gated recurrent unit neural network (GRU) is a kind of recurrent neural network, and like LSTM, it is also proposed to solve the problems of long-term memory and gradient in back propagation. Compared with LSTM, GRU combines the input gate and the forgetting gate into an update gate, and the structure is more concise. GRU includes an update gate and a reset gate, and the output calculation formula of the update gate is:

[0136] z t =σ(W xz x t +W hz h t-1 +b z );

[0137] The calculation formula of the reset gate is:

[0138] r t =σ(W xr x t +W hr h t-1 +b r );

[0139] The calculation formula of the hidden layer state quantity h t is:

[0140]

[0141] The calculation formula of the candidate state is:

[0142]

[0143] In the above formulas, W xz , W xr and W xh are weight parameter matrices connected with the input x i ; W hz , W hr and W hh are weight parameter matrices connected with the hidden layer input h t ; b z , b r and b h are corresponding bias parameters.

[0144] The GRU structure established in the embodiment of the application is as follows: the number of input layers, hidden layers and output layers is 1, 2 and 1 respectively; the input layer has a total of 60 neurons, each neuron has 100 weight parameters and 100 bias parameters; the first hidden layer has a total of 100 neurons, each neuron has 80 weight parameters and 80 bias parameters; the second hidden layer has a total of 80 neurons, each neuron has 10 weight parameters and 10 bias parameters; the output layer with 1 weight parameter and 1 bias parameter has 10 neurons.

[0145] Step S22: the parameters of the large model neural network are optimized by using the adaptive time estimation method ADAM optimization algorithm as shown in the formula (1) to obtain the optimized large model neural network. Figure 2

[0146] Specifically, step S22 includes the following steps:

[0147] Step S221: the gradient of the objective function f(θ) with respect to θ is calculated:

[0148]

[0149] Step S222: the first moment of the gradient, i.e., the average of the past gradient and the current gradient, and the second moment of the gradient, i.e., the average of the square of the past gradient and the square of the current gradient, are calculated, and the expression of the first moment is:

[0150] m t = β1·m t-1 +(1-β2)·g t ;

[0151] In the formula, β1 and β2 are the first and second exponential decay rates respectively, β1 = 0.9 and β2 = 0.999; and m0 = 0 and v0 = 0.

[0152] The expression of the second moment is:

[0153]

[0154] Step S223: the first moment m t and the second moment v t are corrected, because the initial values of the first moment and the second moment are 0, so it will be biased to zero, so after this processing, the influence of this bias will be reduced, and the correction calculation formula of the first moment is:

[0155]

[0156] The correction calculation formula of the second moment is:

[0157]

[0158] In the above formulas,​ and are the first and second exponential decay rates corresponding to time t, respectively;

[0159] Step S224: updating the parameters θ of the large model neural network t At this time, the learning rate of the updated parameters θ t , and m is regarded as the gradient of the updated parameters θ t :

[0160]

[0161] In the formula, a = 0.1 is the learning rate, and ε = 10 -8 is a constant

[0162] Step S3: calculating the mean and variance of the prediction results of the optimized large model neural network at each time, obtaining a hybrid probability data-driven model, optimizing the weight coefficients of the hybrid probability data-driven model, and obtaining an optimized hybrid probability data-driven model.

[0163] Specifically, step S3 includes the following steps:

[0164] Step S31: calculating the mean and variance of the prediction results of the optimized large model neural network at each time by using weighted average, and establishing a hybrid probability data-driven model.

[0165] The mean of the prediction results at each time is calculated by using weighted average, and the formula is as follows:

[0166]

[0167] wherein, are the prediction results of the RNN, LSTM, and GRU models at the i-th time, a1, a2, and a3 are the weight coefficients corresponding to the RNN, LSTM, and GRU models, respectively, and satisfy a1+a2+a3=1, μ i and are the mean values corresponding to the prediction results at the i-th time.

[0168] The variance of the prediction results at each time is calculated by using weighted average, and the formula is as follows:

[0169]

[0170] wherein, are the prediction results of the RNN, LSTM, and GRU models at the i-th time, b1, b2, and b3 are the weight coefficients corresponding to the RNN, LSTM, and GRU models, respectively, and satisfy b1+b2+b3=1, σ i and are the variance values corresponding to the prediction results at the i-th time.

[0171] Step S32: the weight coefficients of the mean and the variance are optimized respectively by using the particle swarm algorithm to obtain an optimized hybrid probability data-driven model.

[0172] Specifically, the particle swarm algorithm in step S32 includes the following steps:

[0173] Step S321: under the constraint condition that β1+β2+β3=1, a population containing N particles is initialized, the dimension D of the particles, the total number of iterations iter of the algorithm, the range of the position and the speed, the inertia weight ω, the self-learning factor C1 and the group learning factor C2 are determined, and each particle is assigned a random speed and position;

[0174] Step S322: the fitness value of each particle is calculated, and when there is a particle whose fitness value is better than the historical particle, the individual historical optimal value p best and the population historical optimal position g best are updated;

[0175] Step S323: the speed and the position of the particle are updated:

[0176]

[0177] In the formula, k represents the iteration number; x i represents the position vector of the particle i; v i represents the speed vector of the particle i; the parameter ω represents the inertia weight; p i represents the historical optimal position vector of the particle i; g i represents the historical optimal position vector of all particles in the particle swarm; C1 represents the self-learning factor; C2 represents the group learning factor; r1 and r2 are pseudo-random numbers uniformly distributed in the interval; p g represents the historical optimal position vector of the particle, represents the current position vector of the particle;

[0178] Step S324: steps S321 to S323 are repeated until the absolute value of the instantaneous prediction result error obtained by iteration is smaller than a set value, and the weights α and β corresponding to the mean and the variance are output.

[0179] Step S4: the data in the test set is taken as the input of the optimized hybrid probability data-driven model to obtain a fuel cell performance prediction result.

[0180] Specifically, step S4 includes the following steps:

[0181] Step S41: the data of the test set is taken as the input, and the mean and the variance of the prediction result at each time are calculated according to the weight coefficients corresponding to the mean and the variance in the optimized hybrid probability data-driven model;

[0182] Step S42: calculating the confidence interval corresponding to the mean and variance of the prediction result, and calculating the confidence interval length according to the confidence interval;

[0183] Step S43: drawing the corresponding probability density distribution graph according to the mean and variance of the prediction result, and providing the basis for actual control decision.

[0184] The embodiment of the present application is based on the data of fuel cells in IEEE PHM 2014 data challenge, and the prediction result of the mixed data-driven model is as shown in the following table 1, wherein the interval estimation result of FC1 data set is as shown in table 2, and the interval estimation result of FC2 data set is as shown in table 3. Figure 3

[0185] Table 2: Interval estimation result of FC1 data set

[0186]

[0187]

[0188] Table 3: Interval estimation result of FC2 data set

[0189]

[0190] The above embodiments can be combined with each other, and for the sake of brevity, not all possible combinations of the above embodiments are described, only the preferred embodiments of the present application are expressed, which are more specific and detailed, but it should not be understood as limiting the scope of the present application. As long as the combination of these technical features does not exist, it should be considered as the scope of the present application.

[0191] It should be noted that for those skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are within the scope of the present application. Therefore, the scope of protection of the present application should be subject to the appended claims.​

Claims

1. A method for fuel cell performance prediction based on a hybrid probabilistic data-driven model, characterized in that: The method comprises the following steps: Step S1: preprocessing the sample data set by using principal component analysis method, and splitting the processed data set into a training set and a test set; Step S2: establishing a large model neural network, inputting the data in the training set into the large model neural network, training the parameters of the large model neural network by using an optimization algorithm, and obtaining an optimized large model neural network; Step S3: calculating the mean and variance of the prediction results of the optimized large model neural network at each time point by using weighted average to obtain a hybrid probability data-driven model, and optimizing the weight coefficients of the mean and variance by using a particle swarm algorithm to obtain an optimized hybrid probability data-driven model; The calculation formula of the mean is: ； In the formula, , , The RNN, LSTM, and GRU models were respectively selected at the 1st... The prediction result at any given time; , , These are the weight coefficients for the RNN, LSTM, and GRU models, respectively, and they satisfy... ; For the first The mean of the prediction results at time 1; The calculation formula of the variance is: ； In the formula, , , The RNN, LSTM, and GRU models were respectively selected at the 1st... The prediction result at any given time; , , These are the weight coefficients for the RNN, LSTM, and GRU models, respectively, and they satisfy... ; The sum of the first The variance corresponding to the prediction result at time; Step S4: inputting the data in the test set into the optimized hybrid probability data-driven model to obtain a fuel cell performance prediction result.

2. The method of claim 1, wherein the method is based on a hybrid probabilistic data-driven model. Step S1 comprises the following steps: Step S11: obtaining index data of original samples according to fuel cell operation data, and representing the index data as a matrix: ； wherein are index data for the operation of the fuel cell, respectively, ; Step S12: standardizing the matrix: ； Step S13: calculating a correlation coefficient matrix of the original samples: ； Step S14: calculating eigenvalues and corresponding eigenvectors of the correlation coefficient matrix, and calculating contribution rates of the eigenvalues: ； In the formula, are eigenvalues, i∈(1,2…p); Step S15: using principal component analysis method, arranging the contribution rates in descending order, taking the eigenvectors corresponding to the first k contribution rates as a processed data set, and splitting the data set into a training set and a test set.

3. The method of claim 1, wherein the method comprises: Step S2 comprises the following steps: Step S21: establishing a large model neural network, wherein the large model neural network comprises a recurrent neural network RNN, a long short-term memory recurrent neural network LSTM, and a gated recurrent unit neural network GRU; Step S22: optimizing the parameters of the large model neural network by using an adaptive time estimation method ADAM to obtain an optimized large model neural network.

4. The method of claim 3, wherein the method further comprises: The recurrent neural network RNN of step S21 comprises an input layer, a hidden layer and an output layer, the output of the recurrent neural network RNN is , is a weight parameter matrix from the hidden layer to the output layer, the hidden layer is updated by the following equation: ； wherein is a new state quantity, is an old state quantity, is a weight parameterized nonlinear function, is a weight parameter matrix from the input layer to the hidden layer, is a weight parameter matrix from the input layer to the hidden layer, is a bias parameter; Each unit of the long short-term memory recurrent neural network LSTM comprises a forgetting gate, an input gate, and an output gate, the forgetting gate forgets irrelevant parts of the previous state, selectively updates the cell state value, and the output gate outputs certain parts of the cell state for the next cell; the calculation formula of each gate variable in the long short-term memory recurrent neural network LSTM is: ； ； ； In the above formulas, , and are the outputs of the input gate, the forget gate and the output gate, respectively; , and are the weight parameter matrices connected with the input ; , and are the weight parameter matrices connected with the hidden layer input ; , and are the corresponding bias parameters, is the activation function. Internal state of an LSTM cell The calculation formula is: ； ； The hidden layer input The calculation formula is: ； In the above formulas, is an activation function, is a multiplication of vector elements; The gated recurrent unit neural network GRU comprises an update gate and a reset gate, the output calculation formula of the update gate is: ； The calculation formula of the reset gate is: ； Hidden layer state quantity The calculation formula is: ； candidate state The calculation formula is: ； wherein, , and are weight parameter matrices connected to the input , , and are weight parameter matrices connected to the hidden layer input , , and are the corresponding bias parameters.

5. The method of claim 3, wherein the method further comprises: Step S22 comprises the following steps: Step S221: calculating the objective function the gradient of the gradient of ； Step S222: calculating the first moment and the second moment of the gradient, the expression of the first moment is: ； The expression of the second moment is: ； Step S223: Correcting the first moment and the second moment The correction formula of the first moment is as follows: ； The correction calculation formula of the second moment is: ； In the above formulas, and respectively are the first and second exponential decay rates corresponding to the time instant Step S224: updating the parameters of the large model neural network : ； for the learning rate, for the constant 10 -8 .

6. The method of claim 1, wherein: The particle swarm algorithm in step S32 comprises the following steps: Step S321: Within the constraint condition of initialize the particle population, and give each particle a random velocity and position; Step S322: calculate the fitness value of each particle, and update the individual historical optimal value of the particle when the fitness value of the particle is better than the fitness value of the historical particle with the population historical optimal position ; Step S323: updating the velocity and position of the particle: ； wherein denotes the iteration number thereof; denotes the position vector of the particle ; denotes the velocity vector of the particle ; denotes the inertia weight; denotes the historical best position vector of the particle ; denotes the historical best position vector of all particles within the swarm; denotes the historical best position vector of all particles within the swarm; denotes the self-learning factor; denotes the swarm-learning factor; and are pseudo-random numbers uniformly distributed within the interval (0,1), denotes the historical best position vector of the particle, denotes the current position vector of the particle; Step S324: repeating steps S321 to S323 until the absolute value of the instantaneous prediction error obtained by iteration is smaller than a set value, outputting the weight corresponding to the mean and variance and .

7. The method of claim 1, wherein: Step S4 comprises the following steps: Step S41: inputting the data of the test set, calculating the mean and variance of the prediction result at each time point according to the weight coefficients corresponding to the mean and variance in the optimized hybrid probability data-driven model; Step S42: calculating the corresponding confidence interval according to the mean and variance of the prediction result, and calculating the confidence interval length according to the confidence interval; Step S43: drawing the corresponding probability density distribution diagram according to the mean and variance of the prediction result, and providing the basis for actual control decision.

8. An electronic device comprising: Memory, processor and computer program, characterized in that: the computer program is stored in the memory and is configured to be executed by the processor to realize the fuel cell performance prediction method based on the hybrid probability data-driven model in any one of claims 1 to 7.

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