Method for selecting key performance parameters of fuel cell system and method for determining values of key performance parameters

Abstract

This invention belongs to the field of fuel cell systems, specifically relating to a method for selecting and determining the values ​​of key performance parameters for fuel cell systems. The method includes determining multiple parameters reflecting fuel cell performance, calculating the mutual information value between each parameter and voltage, selecting the top N parameters based on the mutual information value as key performance parameters, and collecting parameter data for each input parameter of the prediction model based on a multi-input multi-output (MIMO) model to obtain parameter data for each output parameter. The parameter data of each input parameter and each output parameter constitute the values ​​of the key performance parameters of the fuel cell system. The prediction model is constructed by collecting N parameter data of the fuel cell system at multiple time points to construct training samples. Each sample uses a portion of the parameters that are relatively easy to measure as input and the remaining parameters as output, training the prediction model. This invention reduces the dimensionality of parameters characterizing system performance changes in nonlinear systems and effectively optimizes sensor layout design.

Description

Technical Field

[0001] This invention belongs to the field of fuel cell systems, and more specifically, relates to a method for selecting key performance parameters of fuel cell systems and a method for determining their values. Background Technology

[0002] A fuel cell (FC) system is an electrochemical energy conversion device. It can convert the chemical energy of fuel into electrical energy with high efficiency. Therefore, it shows great market potential in transportation fields such as vehicles, trams, ships, and aircraft. However, due to various complex reasons, the health of FC systems inevitably degrades. In this situation, ensuring the safe, efficient, and reliable operation of FC systems has become an urgent problem to be solved. Performance prediction technology can judge and predict potential future performance changes based on known operating conditions and data. This helps determine the timing of degradation, thereby allowing for the scheduling of reasonable maintenance and the design of corresponding management strategies. Therefore, performance prediction technology is one of the effective methods to improve the safety and reliability of FC systems.

[0003] Current FC performance prediction research primarily reflects system performance changes by predicting the FC's output voltage. While voltage contains rich information about system performance, predicting and analyzing only voltage is insufficient to fully understand the FC system's operating state. The variables reflecting FC system performance changes may differ across application scenarios. Therefore, to gain a more comprehensive understanding of FC performance evolution, it is necessary to extract and predict parameters of variables sensitive to FC system performance changes.

[0004] Furthermore, with the rapid development of sensor technology, condition monitoring technology has become one of the effective means to assist in predicting the performance of fuel cell (FC) systems. To obtain the most comprehensive system information, a large number of different types of sensors are typically deployed in the FC system. However, the data collected by the sensors contains a significant amount of redundant information. Some collected parameters not only fail to reflect changes in system performance but may also mislead researchers' analysis of FC performance. In addition, deploying too many sensors can also affect system performance. For example, embedding thermocouples in the fuel cell stack can easily lead to cell breakage. Therefore, parameter extraction methods can not only help find the optimal prediction target but also improve FC system performance and reduce system costs by optimizing sensor layout.

[0005] Current parameter extraction methods are all developed based on the Euclidean distance between data points, requiring a known data distribution and only applicable to linear parameters. Since FC systems are complex nonlinear systems, the above methods are not well-suited for them.

[0006] Therefore, finding a reliable and easy-to-implement method for extracting and predicting key performance parameters of FC systems has become a technical problem that the industry urgently needs to solve. Summary of the Invention

[0007] To address the shortcomings and improvement needs of existing technologies, this invention provides a method for selecting and determining the values ​​of key performance parameters for a fuel cell system. The aim is to reduce the dimensionality of parameters characterizing changes in battery system performance in nonlinear systems, thereby effectively optimizing sensor layout design.

[0008] To achieve the above objectives, according to one aspect of the present invention, a method for selecting key performance parameters of a fuel cell system is provided, comprising:

[0009] Determine multiple parameters that reflect the performance of the fuel cell, calculate the mutual information value between each parameter and the voltage, which is the target parameter; based on the magnitude of the mutual information value, select the top N parameters as key performance parameters to complete the selection of key performance parameters for the fuel cell system.

[0010] Furthermore, it also includes: training and testing the classifier using the selected optimal parameters to verify the accuracy of the optimal parameters.

[0011] The present invention also provides a method for determining the values ​​of key performance parameters of a fuel cell system, comprising: based on a trained multi-input multi-output prediction model, collecting parameter data of each input parameter of the prediction model of the fuel cell system, and inputting the data into the prediction model to obtain parameter data of each output parameter, wherein the parameter data of each input parameter and the parameter data of each output parameter constitute the values ​​of key performance parameters of the fuel cell system.

[0012] The prediction model is constructed in the following manner:

[0013] Data on N parameters of the fuel cell system are collected at multiple time points, with each time point corresponding to a set of optimal parameter data as a training sample. Based on multiple samples, each sample uses some parameters that are relatively easy to measure as input and the remaining parameters as output to train a machine learning model, thereby obtaining a multi-input multi-output prediction model. The N parameters are the key performance parameters selected using the key performance parameter selection method for the fuel cell system described above.

[0014] Furthermore, based on the particle swarm optimization algorithm, a backpropagation neural network is trained to obtain the multi-input multi-output prediction model.

[0015] Furthermore, the fuel cell system is a solid oxide fuel cell, and the N parameters include: methane flow rate, current, deionized water pressure, power, fuel-air heat exchanger center temperature, air-exhaust heat exchanger center temperature, combustion chamber center temperature, bypass air flow rate, cathode air flow rate, anode inlet temperature, cathode output pressure, and reformer center temperature.

[0016] The present invention also provides a device for determining key performance parameters of a fuel cell system, comprising: a memory, a processor, and a transceiver;

[0017] The memory is used to store computer instructions;

[0018] The processor is used to execute the computer instructions stored in the memory to perform a method for selecting key performance parameters of a fuel cell system as described above and / or a method for determining the values ​​of key performance parameters of a fuel cell system as described above.

[0019] The present invention also provides a computer-readable storage medium comprising a stored computer program, wherein, when the computer program is executed by a processor, it controls the device where the storage medium is located to execute a method for selecting key performance parameters of a fuel cell system as described above and / or a method for determining the values ​​of key performance parameters of a fuel cell system as described above.

[0020] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:

[0021] (1) The parameter selection algorithm extracts variables sensitive to changes in SOFC system performance. It can select the most noteworthy parameters, helping researchers to more effectively predict and analyze SOFC system performance. Simultaneously, it eliminates redundant parameter information, reducing the computational burden of SOFC system performance prediction. Furthermore, it helps optimize sensor layout, reducing the impact of sensor installation on SOFC system performance. This invention's MI-based parameter selection algorithm solves the problem that traditional algorithms often have poor interpretability of the extracted results regarding their physical meaning, making them unsuitable for subsequent sensor layout optimization and key performance prediction. Moreover, this invention can quantify the correlation between parameters without requiring the assumption that the data distribution is known. Additionally, it can capture the nonlinear characteristics between variables, making it suitable for nonlinear systems.

[0022] (2) The prediction model proposed in this invention can predict multiple variables simultaneously. Furthermore, it can use easily measurable data such as flow rate, pressure, and current to predict variables that are difficult to measure directly, such as temperature. It not only helps to achieve more comprehensive analysis and optimization of SOFC system performance, but can also be designed as a temperature observer for soft temperature measurement.

[0023] (3) The traditional BP neural network was optimized using the particle swarm optimization algorithm. This improved the prediction accuracy and speed of the prediction model. It solved the problems of slow learning convergence speed, inability to guarantee convergence to the global minimum, and difficulty in determining the network structure of the traditional BP neural network. Attached Figure Description

[0024] Figure 1 A schematic diagram illustrating a method for selecting key performance parameters of a fuel cell system provided in an embodiment of the present invention;

[0025] Figure 2 A flowchart illustrating the implementation of the parameter selection algorithm based on mutual information provided in this embodiment of the invention;

[0026] Figure 3 A flowchart illustrating the implementation of parameter selection and parameter value prediction in an embodiment of the present invention;

[0027] Figure 4 A flowchart illustrating the implementation of a particle swarm optimization BP neural network according to an embodiment of the present invention;

[0028] Figure 5 A flowchart illustrating the training process of a BP neural network provided in an embodiment of the present invention;

[0029] Figure 6 The flowchart for the particle swarm optimization algorithm provided in this embodiment of the invention is as follows:

[0030] Figure 7 A graph showing the changes in the values ​​of various variables collected over time in the SOFC system provided in this embodiment of the invention;

[0031] Figure 8 A bar chart showing the mutual information between various parameters and voltage provided in the embodiments of the present invention;

[0032] Figure 9 This is a classifier accuracy map obtained by training based on the extracted parameters, provided in an embodiment of the present invention.

[0033] Figure 10 This is a classifier accuracy map obtained from full parameter training, provided in an embodiment of the present invention.

[0034] Figure 11 A comparison chart of prediction results of the PSOBP, BP, and ARMA algorithms provided in the embodiments of the present invention;

[0035] Figure 12 The prediction error diagrams of the PSOBP, BP, and ARMA algorithms provided in the embodiments of the present invention. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical parameters involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0037] Example 1

[0038] A method for selecting key performance parameters of a fuel cell system, such as Figure 1 As shown, it includes:

[0039] Determine multiple parameters that reflect the performance of the fuel cell, calculate the mutual information value between each parameter and the voltage, which is the target parameter; based on the magnitude of the mutual information value, select the top N parameters as key performance parameters to complete the selection of key performance parameters for the fuel cell system.

[0040] Preferably, the method further includes: training and testing the classifier using the selected optimal parameters to verify the accuracy of the optimal parameters.

[0041] The mutual information-based parameter selection algorithm selects the subset of parameters most sensitive to changes in the performance of a SOFC system by calculating the mutual information between parameters. This method provides optimal prediction targets for subsequent performance prediction algorithms. It also accelerates the training speed of the prediction model and improves learning efficiency by removing redundant parameters, while ensuring high accuracy of the prediction results. Compared with other parameter extraction methods, this method has the advantages of quantifying the information correlation between parameters, not requiring assumptions about known data distribution, and effectively estimating the nonlinear relationships between parameters.

[0042] In probability theory and information theory, the mutual information of two random variables is a measure of the interdependence between them. Suppose we have random variables X = {x1, x2, ..., x...} n} and Y = {y1, y2, ..., y n If P(x) i ) and P(y j P(x) and Y are the marginal probabilities of random variables X and Y, respectively. i ,y j Let be the joint probability distribution function of X and Y. Then the mutual information I(X;Y) between X and Y is defined as:

[0043]

[0044] If random variables X and Y are independent, then there is no correlation between them, and in this case, p(x,y) = p(x)p(y), and the mutual information I(X;Y) = 0. The more correlation there is between random variables X and Y, or the stronger the dependence between them, the greater their mutual information value will be.

[0045] The steps of the parameter selection algorithm based on mutual information are as follows:

[0046] (1) Divide the dataset;

[0047] (2) Calculate the mutual information value between each candidate parameter and the target parameter voltage;

[0048] (3) Select the first N parameters as the optimal parameters based on the magnitude of the mutual information value;

[0049] (4) Train the SVM classifier model using the selected N parameters;

[0050] (5) Verify the accuracy of parameter extraction based on the classification accuracy of the SVM classifier on the test set.

[0051] In the process of implementing the parameter selection algorithm based on MI, it is necessary to focus on the target parameters, termination conditions, and result verification.

[0052] The output voltage of an SOFC system contains a wealth of information about its performance variations. Due to the strong thermoelectric coupling characteristic of SOFC systems, the system's thermal, electrical, and degradation characteristics can all be partially reflected in the voltage. Therefore, this invention selects the voltage signal as the target parameter and extracts effective parameters by calculating the mutual information values ​​between various variables and the voltage.

[0053] Parameter selection controls the algorithm's termination based on whether a termination condition is met. A common termination condition is that the evaluation function reaches its optimal value. The evaluation function is used to assess the importance of candidate parameters; in the MI-based parameter selection algorithm, the evaluation function is the mutual information value, as shown below:

[0054] J MI (X i )=I(X i ;Y)(2)

[0055] Based on engineering experience, this embodiment selects variables with mutual information values ​​greater than 0.8 as the variables most sensitive to changes in system performance.

[0056] Parameter selection algorithms reduce the dimensionality of a parameter set without altering its original structure or reducing the amount of information it contains. Therefore, the results need to be validated after parameter selection. This embodiment uses the selected subset of parameters to train and validate an SVM classifier model. The accuracy of the SVM classifier indirectly proves the accuracy of the parameter selection results. This is because a classifier can only achieve good classification results if its input and output have a sufficiently high correlation. The implementation process of the MI-based parameter selection algorithm is as follows: Figure 2 As shown.

[0057] The MI algorithm extracts key parameters from variables obtained from sensors by measuring the information entropy between parameters. This method not only provides effective prediction targets for prediction algorithms but also helps optimize sensor layout and reduce the impact of sensor installation on SOFC system performance.

[0058] Example 2

[0059] A method for determining the values ​​of key performance parameters of a fuel cell system, such as Figure 3 As shown, it includes: based on a trained multi-input multi-output prediction model, collecting parameter data of each input parameter of the prediction model of the fuel cell system, and inputting it into the prediction model to obtain parameter data of each output parameter. The parameter data of each input parameter and the parameter data of each output parameter constitute the key performance parameter values ​​of the fuel cell system.

[0060] The prediction model is constructed in the following manner:

[0061] Data on N parameters of the fuel cell system are collected at multiple time points, with each time point corresponding to a set of optimal parameter data as a training sample. Based on multiple samples, each sample uses some parameters that are relatively easy to measure as input and the remaining parameters as output to train a machine learning model, thereby obtaining a multi-input multi-output prediction model. The N parameters are the key performance parameters selected using the key performance parameter selection method for a fuel cell system as described in Example 1.

[0062] Predictive models can simultaneously predict multiple key parameters, helping to provide a more comprehensive understanding of system performance changes. Researchers can then implement appropriate control strategies based on the prediction results to maintain optimal system performance and prevent damage from malfunctions.

[0063] The method in this embodiment can use easily measurable variables to predict variables that are difficult to measure directly, thereby enabling functions such as temperature observation.

[0064] The relevant technical solutions are the same as those in Embodiment 1 and Embodiment 2, and will not be repeated here.

[0065] As a preferred implementation, a BP neural network can be trained based on the particle swarm optimization algorithm to obtain the multi-input multi-output prediction model.

[0066] Backpropagation (BP) neural networks are a classic neural network model widely used in various prediction applications. However, the prediction results of BP neural networks are highly sensitive to the initial values ​​of their parameters; different initial values ​​can lead to different prediction results. Inappropriate initial weights and biases may cause the BP neural network to get stuck in local optima, resulting in poor prediction accuracy. Furthermore, if the BP neural network is trained starting with random initial parameters, it requires significant computational resources, resulting in long training times and high computational costs. Therefore, to optimize traditional BP neural networks, this embodiment preferably uses the Particle Swarm Optimization (PSO) algorithm to optimize the weights and biases of the BP neural network, thereby shortening the training time and improving prediction accuracy.

[0067] The essence of the PSO_BP algorithm is to determine the initial weights and biases of the BP neural network using the particle swarm optimization algorithm. First, the fitness function (objective function) in the PSO algorithm is set to the prediction error of the BP neural network. Then, the PSO algorithm uses the fitness function to find the optimal particle position and velocity, thereby initializing the optimal BP weights and biases. A more detailed implementation process is as follows... Figure 4 As shown.

[0068] The parameters that need to be optimized in a BP neural network actually include four parts: weights from the input layer to the hidden layer, biases of hidden layer neurons, weights from the hidden layer to the output layer, and output layer biases. For the PSO algorithm, the particle velocity and position need to be continuously updated to select the weights and biases that optimize the objective function. Since this embodiment uses the prediction result of the BP neural network as the objective function of the PSO algorithm, the smaller the objective function, the more accurate the prediction. If the objective function is 0, it indicates that the prediction is completely accurate.

[0069] The detailed steps for PSO optimization of the BP neural network are as follows:

[0070] (1) Data preparation: Prepare training dataset and test dataset.

[0071] (2) Parameter initialization. Initialize the weights and biases of the BP neural network. Initialize the PSO algorithm, using particles in the algorithm to represent the weights and biases of the BP neural network.

[0072] (3) Calculate the objective function (fitness function). The mean square error of the prediction results of the BP neural network is selected as the objective function of the PSO algorithm.

[0073] (4) Iteratively update the optimal solution of the PSO algorithm. Use the optimal value update formula of the particle swarm optimization algorithm to optimize the weights and bias parameters of the BP neural network.

[0074] (5) Update the parameters of the BP neural network. Assign the optimized weights and bias parameters to the BP neural network.

[0075] (6) Train the BP neural network. Use the training dataset to train the neural network, and adjust the network's weights and biases to make the network's output as close as possible to the actual results.

[0076] (7) Verify algorithm performance. Use the trained neural network to predict unknown data, and perform error analysis and accuracy comparison with the unoptimized BP neural network.

[0077] The training process of a BP neural network mainly consists of two stages. The first stage is the forward propagation of the signal, where information travels from the input layer through the hidden layers and finally reaches the output layer. The second stage is the backward propagation of the error, where the error travels from the output layer to the hidden layers and finally to the input layer. Then, based on the error value, the weights and biases from the hidden layers to the output layer, and from the input layer to the hidden layers, are adjusted sequentially, as follows: Figure 5 As shown.

[0078] Forward propagation: BP neural networks propagate information by iteratively applying the following formula. First, based on the output a of the (l-1)th layer neuron... (l-1) Calculate the net input value z of the neurons in layer l. (l) Then, z (l0 After passing through an activation function, the output value a of the l-th layer neuron is obtained. (l) As shown in the formula below, a feedforward neural network can obtain the final output 'a' of the network through the layer-by-layer information transmission. (L) .

[0079] z (l) =W (l) a (l-1) +b (l) (3)

[0080] a (l) =f l (z (l) (4)

[0081] L is the number of layers in the neural network. f l (· represents the activation function of neurons in layer l. W) (l) It is the weight matrix from layer (l-1) to layer l. (l) It is the offset from layer (l-1) to layer l. (l) This is the net input to the neurons in layer l. (l)This represents the output of the neurons in layer l.

[0082] Backpropagation (BP) is a learning mechanism that continuously optimizes the model's parameters to approach their optimal state. The error term of a neuron in layer l is the sum of the weights of the error terms of all neurons in layer l+1 connected to that neuron, multiplied by the gradient of the neuron's activation function. After calculating the error term of each layer, the gradient of the parameters for each layer can be obtained. Assuming a sample (x, y) is input into a BP neural network model, the network output is... The formula for calculating the error term of the l-th layer is as follows.

[0083]

[0084] in, This represents the loss function. ⊙ is the dot product operator for vectors, indicating element-wise multiplication.

[0085] To perform parameter learning, it is necessary to calculate the derivative of the loss function with respect to each parameter.

[0086] Regarding the weight W of the l-th layer (l) The gradient is:

[0087]

[0088] Regarding the weight b of the l-th layer (l) The gradient is:

[0089]

[0090] Finally, the weights and biases of the BP neural network are updated based on the derivative of the loss function with respect to each parameter.

[0091] W (l) ←W (l) -α(δ (l) (a (l-1) ) T +λW (l) (8)

[0092] b (l) ←b (l) -αδ (l) (9)

[0093] Where α is the learning rate and λ is the regularization coefficient.

[0094] Stop updating when the error rate of the neural network model on the validation set no longer decreases.

[0095] Therefore, the training process using a BP neural network can be summarized in the following three steps:

[0096] (1) Forward propagation: Calculate the net input z of each layer. (l) and activation value a (l) , until the last floor;

[0097] (2) Backpropagation: Calculate the error term δ for each layer. (l) ;

[0098] (3) Parameter update: Calculate the partial derivatives of the parameters of each layer and update the weights and biases of the BP neural network.

[0099] Introduction to Particle Swarm Optimization Algorithm:

[0100] Particle Swarm Optimization (PSO) is a swarm intelligence-based optimization algorithm originating from studies of bird flock foraging behavior. This algorithm leverages information sharing among individuals to drive an evolutionary process from disorder to order within the flock, ultimately finding the optimal solution. Similar to genetic algorithms, PSO starts with random solutions, iteratively searches for the optimal solution, and evaluates the solution's quality using fitness (the objective function). However, PSO has simpler rules than genetic algorithms, lacking the "crossover" and "mutation" operations of genetic algorithms. It finds the global optimum by following the currently found best solution. This algorithm has gained attention due to its ease of implementation, high accuracy, and fast convergence, demonstrating its superiority in solving practical problems.

[0101] The PSO algorithm first initializes a swarm of random particles, each with two attributes: position and velocity. Then, it iteratively finds the optimal position and velocity for each particle based on the objective function. In each iteration, the particle updates its position and velocity by tracking two "extreme values" (pbest and gbest). pbest is the optimal solution found by the particle itself, representing an individual extreme value. gbest is the optimal solution found by the entire swarm so far, representing a global extreme value. After finding these two extreme values, the particle updates its velocity and position using these values, as shown in the formula below. The iteration stops when the particle satisfies the objective function.

[0102] x i =x i +v i (10)

[0103] v i =ω×v i +c1×rand()×(pbset i -x i )+c2×rand()×(gbest i -x i ) (11)

[0105]

[0106] x i This represents the position of particle i. i This represents the rate at which particle i's position is updated. (pbest) i It is the individual extreme value found by particle i, gbest i This represents the population extrema. c1 and c2 are learning factors. A larger c1 indicates a greater contribution of locally found individual extrema to the speed update. A larger c2 indicates a greater contribution of the globally found population extrema to the speed update. Here, based on engineering experience, both c1 and c2 are set to 1.49445. ω is the inertia weight. max For the maximum inertia weight, ω min The minimum inertia weight is given by `run`, where `run` is the current iteration number. max Let ω be the total number of iterations of the algorithm. A larger ω results in better global convergence of the iterative formula, while a smaller ω results in stronger local convergence. Therefore, as the number of iterations increases, the inertia weight ω should be continuously reduced, so that the particle swarm optimization algorithm has strong global convergence in the early stages and strong local convergence in the later stages. Here, based on engineering experience, ω is... max Set it to 0.9, and set ω min Set it to 0.4.

[0107] The implementation process of the particle swarm optimization algorithm is as follows:

[0108] (1) Initialize a group of particles (group size N), including random positions and velocities;

[0109] (2) Calculate the objective function based on the position and velocity of each particle;

[0110] (3) For each particle, compare its objective function with the objective function of the best position pbest it has passed through. If it is better, then take it as the current best position pbest.

[0111] (4) For each particle, compare its objective function with the objective function of the best position gbest it has passed through. If it is better, then take it as the current best position gbest.

[0112] (5) Adjust the speed and position of the particles according to formulas (10)-(12);

[0113] (6) If the termination condition is not met, proceed to step (2).

[0114] The implementation flowchart of the PSO algorithm is as follows: Figure 6As shown, the PSO algorithm has advantages such as global search capability and high efficiency in optimization problems. Therefore, it can use the prediction error of the BP neural network as the objective function to optimize the initial weights and biases of the BP neural network. The PSO algorithm can improve the accuracy, prediction ability, robustness, and stability of the BP neural network, thereby solving problems such as slow learning convergence speed, inability to guarantee convergence to the global minimum, and difficulty in determining the network structure.

[0115] To better illustrate the effectiveness of this embodiment, an SOFC battery system is used as an example to select and determine the values ​​of key performance parameters using the method of this embodiment.

[0116] This example aims to extract the parameters most sensitive to changes in the performance of an SOFC system and design an algorithm capable of predicting these variables. First, parameters are extracted by calculating the mutual information between each candidate variable and the voltage. Then, the extracted parameter set is divided into easily measurable and difficult-to-measurable parameters. These two types of parameters are used as input and output, respectively, to train the PSO_BP prediction model. Finally, the prediction accuracy of the PSO_BP algorithm is validated using parameters such as absolute error, root mean square error, and squared absolute percentage error, and the prediction results are compared with those of traditional BP neural networks and ARIMA prediction models. The implementation flow of this example is as follows: Figure 3 As shown.

[0117] Data from a 1kW SOFC power generation system fueled by natural gas was used to validate the parameter extraction and performance prediction algorithms. During the experiment, multiple sensors, including voltmeters, ammeters, temperature sensors, pressure sensors, and gas flow meters, were deployed within the system to provide the most detailed understanding of the performance evolution of each component. The information collected by the sensors was recorded by a PLC (Programmable Logic Controller). The PLC recorded a total of 41 variables, including gas pressure, fuel / air flow rate, reformer temperature, heat exchanger temperature, combustion chamber temperature, stack temperature, current, voltage, and power, as shown in Table 1.

[0118] Table 1 System Acquisition Parameters

[0119]

[0120] The 41 variables collected in the SOFC system change over time as follows: Figure 7 As shown.

[0121] The parameter selection algorithm based on mutual information calculates the mutual information values ​​between the system voltage and the remaining 40 variables, and the results are as follows: Figure 8 As shown.

[0122] Variables with mutual information values ​​greater than 0.8 were selected as those most sensitive to changes in system performance. A total of 12 variables were extracted, namely methane flow rate, current, deionized water pressure, power, fuel-air heat exchanger center temperature, air-exhaust gas heat exchanger center temperature, combustion chamber center temperature, bypass air flow rate, cathode air flow rate, anode inlet temperature, cathode output pressure, and reformer mid-section temperature, as shown in Table 2.

[0123] Table 2 Parameter Extraction Results

[0124]

[0125] To verify the accuracy of parameter extraction, an SVM classifier model was trained using the extracted 12 variables to predict voltage values. 75% of the data was randomly selected as the training set, and the remaining 25% as the test set. Simultaneously, 40 variables without parameter extraction were input into the SVM model for comparison. The initial parameters of the SVM classifier were: Decision function shape = OVR, Penalty factor = 1, Kernel = RBF. The prediction results of the test set on the SVM classifier model are as follows: Figure 9 and Figure 10 As shown, the results indicate that the SVM classifier trained using the 12 extracted parameters has good prediction results, with a root mean square error (RMSE) of 0.021985 and a squared absolute percentage error (SSE) of 0.077% (the definitions of RMSE and SSE are introduced in the next chapter). However, when all 40 parameters are used as input to the SVM, the RMSE is 0.030884 and the SSE is 0.11%. The classifier trained with all parameters did not achieve better results. This is because redundant parameters and erroneous information in the dataset reduce the classifier's performance. The SVM model trained using the parameters extracted by the MI method has a very small prediction error, indicating that the 12 extracted variables are highly correlated with voltage. The system performance change information contained in voltage can be reflected using these 12 variables. Therefore, the 12 extracted variables are all highly sensitive to changes in system performance. These variables can be used to predict and analyze system performance.

[0126] The extracted 12 variables were further validated mechanistically: Since the SOFC system used in this study is a current-controlled system, the current represents the system load. The methane flow rate represents the amount of fuel introduced into the system. Deionized water is used to react with methane gas to generate hydrogen. Since there is no flow meter for measuring deionized water in the system, the deionized water pressure reflects the amount of deionized water. It affects the amount of hydrogen participating in the discharge reaction in the stack. The cathode air flow rate and cathode output pressure represent the amount of air entering and leaving the stack, respectively. They together reflect the amount of air consumed in the stack. Bypass air is used to regulate system temperature; therefore, the bypass air flow rate is an important variable affecting system temperature. These six variables are all important operational variables in the system, directly affecting the performance of the SOFC system. Therefore, it is reasonable to consider them as the variables most sensitive to changes in system performance. Furthermore, these six variables, as flow rate, pressure, and current variables, are all easily measurable. At the same time, the sensors used to measure these six variables are low-cost and have little impact on system performance.

[0127] The power variable, determined by the system's input current and output voltage, directly reflects the system's electrical characteristics. The stack anode inlet temperature, fuel-air heat exchanger center temperature, and air-exhaust heat exchanger center temperature collectively determine the internal temperature of the stack, directly affecting the intensity of electrochemical reactions within the stack. The reformer center temperature reflects the intensity of the reforming reaction, determining the hydrogen content entering the stack. Unreacted fuel in the stack undergoes complete combustion in the combustion chamber, and the resulting heat is supplied to the heat exchangers to preheat the fuel and hydrogen. Therefore, the combustion chamber center temperature affects the overall system temperature. These six variables are all important performance variables representing the system's performance. They reflect the performance evolution of different components of the system, making them reasonable as the most sensitive variables to changes in system performance. Furthermore, focused observation of these variables allows for more accurate assessment of whether system degradation has occurred.

[0128] Of the 12 extracted variables, power, fuel-air heat exchanger center temperature, air-exhaust heat exchanger center temperature, combustion chamber temperature, fuel cell stack anode inlet temperature, and reformer mid-section temperature are identified as key performance variables, revealing patterns in SOFC system performance changes. Predicting these variables helps in implementing appropriate control strategies in advance to maintain the safe and efficient operation of the SOFC system. Conventional methods for obtaining temperature data require deploying numerous temperature sensors within the SOFC system. However, deploying temperature sensors is difficult and expensive. This is because the temperatures in SOFC systems are extremely high, and installing high-temperature sensors not only incurs significant costs but may also affect system performance. For example, embedding thermocouples in the fuel cell stack can easily lead to cell breakage. Therefore, in commercial SOFC systems, the number of sensors should be minimized. In this study, the PSO_BP algorithm will be used to predict performance variables (such as temperature) that are difficult to measure directly, using easily measurable variables (such as flow rate and pressure).

[0129] First, the PSO_BP prediction model is trained using readily available operational variables such as current, pressure, and flow rate as inputs, and less readily available or important performance variables as outputs. The input and output variables used in training the prediction model are shown in Table 3. Then, temperature and power data are predicted using current, pressure, and flow rate data that were not used for training. The accuracy of the PSO_BP prediction model is judged based on the prediction results. Finally, the prediction results are compared with those of traditional BP neural networks and ARIMA prediction algorithms.

[0130] Table 3 Input and output variables used for training the prediction model

[0131]

[0132] The prediction results of the PSO_BP, BP, and ARIMA prediction models are as follows: Figure 11 As shown. A comparison of the absolute errors in the predictions. Figure 12 As shown.

[0133] The predictive performance of a model can be measured by three commonly used statistical metrics, including absolute error, root mean square error, and squared absolute percentage error.

[0134] Absolute error: The absolute value of the difference between the actual measured value and the predicted value, describing the degree of deviation from the prediction.

[0135]

[0136] Among them, y i It is the actual value. This is a predicted value.

[0137] Root Mean Square Error (RMSE): It combines the absolute error of the predicted variable values ​​at each time step, reflecting the overall accuracy of the prediction. The smaller the RMSE, the better the model's predictive performance.

[0138]

[0139] Where N is the total number of time steps in the prediction phase.

[0140] Squared absolute percentage error (MAPE): MAPE considers not only the error between the predicted and the true values, but also the ratio between the error and the true value. The smaller the MAPE, the better the model's predictive performance.

[0141]

[0142] The prediction performance of PSO_BP, BP, and ARIMA for variables such as power, fuel-air heat exchanger center temperature, air-exhaust heat exchanger center temperature, combustion chamber center temperature, stack anode inlet temperature, and reformer mid-section temperature is shown in Table 4. Training the ARIMA prediction model took 26.567 seconds. Training the unoptimized BP neural network prediction model took 2.43 seconds. The PSO-optimized BP neural network model only took 1.98 seconds to train.

[0143] Table 4 Prediction Errors of PSOBP, BP, and ARIMA Algorithms

[0144]

[0145]

[0146] The prediction results show that the PSO_BP prediction model has the best prediction performance. It has the smallest prediction error for all six variables, with the percentage error not exceeding 0.5%. Compared with unoptimized BP neural networks and ARIMA prediction models, it achieves more accurate predictions and faster training speed. PSO_BP solves the problems of slow learning convergence and low prediction accuracy of traditional BP algorithms. While the ARIMA model performs well on data with high linearity, it performs poorly on variables with high nonlinearity. Therefore, PSO_BP can accurately predict multiple system indicators simultaneously.

[0147] In other words, this example proposes a method for extracting and predicting key performance parameters of a solid oxide fuel cell (SOFC) system based on mutual information and a backpropagation (BP) neural network. This example helps researchers gain a more accurate and comprehensive understanding of the performance evolution of SOFC systems. The parameter extraction algorithm can eliminate redundant and irrelevant parameters, providing effective prediction targets for subsequent performance prediction algorithms, thereby improving their performance. It can also help optimize the sensor layout in the SOFC system, reducing the impact of sensor installation on SOFC system performance and minimizing sensor costs. The performance prediction algorithm can help researchers take appropriate control strategies in advance to avoid catastrophic accidents and improve system reliability. Furthermore, it can be designed as a temperature observer for SOFC systems, predicting temperature data that is difficult to measure directly using easily measurable variables. Therefore, this example, as a reliability research scheme for SOFC systems, can help researchers optimize system performance.

[0148] Example 3

[0149] A device for determining key performance parameters of a fuel cell system includes: a memory, a processor, and a transceiver;

[0150] The memory is used to store computer instructions;

[0151] The processor is used to execute the computer instructions stored in the memory to perform a method for selecting key performance parameters of a fuel cell system as described above and / or a method for determining key performance parameters of a fuel cell system as described above.

[0152] The relevant technical solutions are the same as those in Embodiment 1 and Embodiment 2, and will not be repeated here.

[0153] Example 4

[0154] A computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed by a processor, it controls the device where the storage medium is located to perform a method for selecting key performance parameters of a fuel cell system as described above and / or a method for determining key performance parameters of a fuel cell system as described above.

[0155] The relevant technical solutions are the same as those in Embodiment 1 and Embodiment 2, and will not be repeated here.

[0156] In summary, this invention proposes a method for extracting and predicting key performance parameters of a fuel cell system based on mutual information and neural networks. A parameter selection algorithm based on mutual information is used to extract key parameters from variables obtained from sensors. Then, a parameter prediction method based on neural networks is used to simultaneously predict multiple extracted key parameters.

[0157] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for determining a value of a key performance parameter of a fuel cell system, characterized by, include: Based on the trained multi-input multi-output prediction model, the parameter data of each input parameter of the prediction model of the fuel cell system is collected and input into the prediction model to obtain the parameter data of each output parameter. The parameter data of each input parameter and the parameter data of each output parameter constitute the values ​​of the key performance parameters of the fuel cell system. The prediction model is constructed in the following manner: Data on N parameters of the fuel cell system at multiple time points are collected, with each time point corresponding to a set of optimal parameter data, serving as a training sample. Based on multiple samples, each sample uses some relatively easy-to-measure parameters as input and the remaining parameters as output. A backpropagation neural network is trained using a particle swarm optimization algorithm to obtain a multi-input multi-output prediction model. The N parameters are determined as follows: multiple parameters reflecting fuel cell performance are determined, and the mutual information value between each parameter and the voltage, which is the target parameter, is calculated. Based on the magnitude of the mutual information value, the top N parameters are selected as key performance parameters. The method for training the BP neural network is as follows: (1) Data preparation: Prepare training and test datasets; (2) Parameter initialization: Initialize the weights and biases of the BP neural network; initialize the PSO algorithm, using particles in the algorithm to represent the weights and biases of the BP neural network; (3) Calculate the objective function, i.e. the fitness function: select the mean square error of the prediction results of the BP neural network as the objective function of the PSO algorithm; (4) Iteratively update the optimal solution of the PSO algorithm: Use the optimal value update formula of the particle swarm optimization algorithm to optimize the weights and bias parameters of the BP neural network; (5) Update the parameters of the BP neural network: Assign the optimized weights and bias parameters to the BP neural network; (6) Training the BP neural network: Use the training dataset to train the neural network, adjust the weights and biases of the network, so that the output of the network is as close as possible to the actual result; (7) Verify algorithm performance: Use the trained neural network to predict unknown data, and perform error analysis and accuracy comparison with the unoptimized BP neural network.

2. The method of claim 1, wherein, In determining the N parameters, the method further includes: training and testing the classifier using the selected optimal parameters to verify the accuracy of the optimal parameters.

3. The method of claim 1, wherein, The fuel cell system is a solid oxide fuel cell, and the N parameters include: methane flow rate, current, deionized water pressure, power, fuel-air heat exchanger center temperature, air-exhaust heat exchanger center temperature, combustion chamber center temperature, bypass air flow rate, cathode air flow rate, anode inlet temperature, cathode output pressure, and reformer center temperature.

4. A device for determining key performance parameters of a fuel cell system, characterized in that, include: Memory, processor, and transceiver; The memory is used to store computer instructions; The processor is used to execute computer instructions stored in the memory to perform a method for determining the values ​​of key performance parameters of a fuel cell system as described in any one of claims 1 to 3.

5. A computer readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed by a processor, it controls the device where the storage medium is located to perform a method for determining the values ​​of key performance parameters of a fuel cell system as described in any one of claims 1 to 3.

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