Health assessment and prediction method for solid oxide fuel cell system and system thereof

Abstract

The application discloses a kind of health evaluation and prediction method and system of solid oxide fuel cell system, with health index SOH as the evaluation index of system attenuation state to assess the health state of fuel cell system in dynamic condition: wherein, P out It is the output power of the stack after attenuation, P0 is the ideal output power of the stack without attenuation, the value of SOH is between 0-1, the greater the value of health index SOH, the smaller the attenuation degree of the reaction system, the smaller the value of health index SOH, the greater the attenuation degree of the reaction system. The ratio of ideal non-degradation output power and actual output power is used to form the health index SOH of the system, which can effectively avoid the above problems, quickly and accurately evaluate and predict the attenuation state of solid oxide fuel cell system.

Description

Technical Field

[0001] This invention belongs to the field of solid oxide fuel cell technology, and more specifically, relates to a method and system for health assessment and prediction of a solid oxide fuel cell system. Background Technology

[0002] Solid oxide fuel cells (SOFCs), as a highly efficient and low-emission energy conversion technology, possess advantages such as an all-solid-state structure, good fuel adaptability, power generation efficiency up to 60%, and combined heat and power energy recovery efficiency up to 90%, making them one of the most promising energy conversion technologies today. In recent decades, SOFC research has progressed from mature battery materials and manufacturing processes to the currently widely focused application-oriented system integration and control. However, the short lifespan remains a bottleneck for the large-scale commercial application of SOFCs, because its numerous degradation mechanisms can affect the operation of SOFC systems. Furthermore, further degradation can easily lead to various failures, which will significantly impact the operating life of SOFC systems, making it difficult to achieve the expected 40,000-hour target.

[0003] The degradation of SOFC systems stems primarily from three factors: First, the inherent natural degradation of the stack's materials, caused by electrochemical reactions involving various chemical kinetic mechanisms. For example, nickel migration in the anode leads to decreased conductivity, and carbon deposition, among others, are major contributors to performance decline. Second, suboptimal operating conditions result in physical deformations, including varying coefficients of thermal expansion of different materials, internal temperature gradients, and mechanical stresses. Degradation caused by physical and microstructural changes directly impacts the stack's electrical characteristics, such as increasing ohmic resistance and activation losses, which are represented by state variables like stack temperature and temperature gradient. Third, the accumulated degradation over long-term operation inevitably alters the system's state and input-output relationships. If the control system fails to recognize these accumulated degradations, mismatched control parameters further deteriorate the system's operating condition, accelerating natural degradation. The combined effect of these three factors accelerates the degradation rate of SOFC systems and significantly shortens their lifespan.

[0004] Typically, the output voltage of a SOFC is considered a health indicator. However, the operating conditions of a SOFC have a significant impact on the voltage because, under dynamic operating conditions, it is difficult to distinguish whether the voltage drop is caused by performance degradation or changes in operating conditions. Some common health indicators used to assess the degree of degradation also have other problems. For example, the area ratio resistance (ASR) is often difficult to observe, while ordinary resistance spectrum analysis (EIS) contains too much redundant information and requires complex spectrum analysis and filtering.

[0005] Therefore, the study of the attenuation mechanism and its characterization in SOFC systems is crucial for the subsequent control of SOFC systems to achieve high performance and long lifespan. Summary of the Invention

[0006] In view of the above-mentioned defects or improvement needs of the prior art, the present invention provides a health assessment method and system for a solid oxide fuel cell system, the purpose of which is to quickly and accurately assess and predict the degradation state of the solid oxide fuel cell system.

[0007] To achieve the above objectives, according to one aspect of the present invention, a method for health assessment and prediction of a solid oxide fuel cell system is provided, using health indicators... As an evaluation index of system degradation state, it is used to assess the health status of the fuel cell system in real time under dynamic operating conditions:

[0008] in, This represents the attenuated output power of the fuel cell stack. For ideal, undiminished fuel cell stack output power, The value ranges from 0 to 1; health indicators The higher the value, the smaller the degree of decay of the reaction system, and the better the health indicator. The smaller the value, the greater the degree of decay of the reaction system.

[0009] In one embodiment, the method further includes: training a non-degradation model of the solid oxide fuel cell system based on historical data using a neural network to obtain an ideal, non-degradation stack output power; rapidly determining the ideal, non-degradation stack output power of the solid oxide fuel cell system under arbitrary input parameters using the trained non-degradation model; and converting the degraded stack output power... Compared to the ideal, undiminished output power of the fuel cell stack Substitution The calculation formula enables real-time assessment of the health status of solid oxide fuel cell systems.

[0010] In one embodiment, based on real-time sampled values ​​of key state variables of the actual system, and real-time evaluation obtained... Based on the value of the Gaussian process regression prediction model, a Gaussian process regression prediction model is established to predict the future decay of the system. Then, based on this model, the future decay of the system is predicted. The value of the critical state quantity is the average temperature of the fuel cell stack. Temperature gradient of fuel cell stack and fuel utilization rate .

[0011] In one embodiment, the average temperature of the fuel cell stack is measured in critical states. Temperature gradient of fuel cell stack and fuel utilization rate For input ,by For output and based on When establishing a Gaussian process regression prediction model, the collected data are used as the basis for the prediction. As training samples, predict the latest input vector. Corresponding output The prediction formula is expressed as:

[0012]

[0013]

[0014] in, Indicates the first i The three-dimensional input vector in each training sample The input vector is Collected at that time value, This represents the latest input vector. Indicates that the input vector is Predicting future moments value, Let be the latent function of the input vector. N It represents the number of training data samples.

[0015] In one embodiment, using a given input... and output training set In the new input The predicted distribution of the calculated output is specifically represented as follows:

[0016]

[0017]

[0018]

[0019] in, This represents the input element of the training set. This represents the output element of the training set. Represents the kernel function. , Represents the mean function and is set to 0. and The joint normal distribution of the two is as follows:

[0020]

[0021]

[0022] Given of The conditional probability distribution follows a Gaussian distribution, and its prediction form is as follows:

[0023]

[0024]

[0025] The best estimate of is the mean of the distribution, that is: =

[0026] in This represents a Bayesian probability model.

[0027] In one embodiment, a kernel function combining a squared exponential kernel function and a Matrn-like kernel function is used to evaluate the system. To make predictions, among which, Squared exponential kernel function SE for:

[0028] The Matrn kernel function is:

[0029] in, This represents the two input feature vectors. This is the bandwidth hyperparameter of the squared exponential kernel function. This is the bandwidth hyperparameter for the Matrn class kernel function. For characteristic length, For smooth hyperparameters, It is a modified Bessel function.

[0030] In one embodiment, the accuracy of the prediction is evaluated using two evaluation metrics: root mean square error and mean absolute percentage error.

[0031] In one embodiment, when When the value is 0.8, the corresponding time is the end of the lifespan. t eolAccording to the current time t 0 and end of life t eol Jointly determine the remaining lifespan of the system RUL : .

[0032] According to another aspect of the present invention, a health assessment and prediction system for a solid oxide fuel cell system is provided, comprising: health indicators Computing unit

[0033] in, This represents the attenuated output power of the fuel cell stack. For ideal, undiminished fuel cell stack output power, The value ranges from 0 to 1; health indicators The higher the value, the smaller the degree of decay of the reaction system, and the better the health indicator. The smaller the value, the greater the degree of decay of the reaction system.

[0034] In one embodiment, it further includes: The Gaussian process regression prediction unit is used to establish a Gaussian process regression prediction model that can predict the future degradation of the system based on the real-time sampled values ​​of the key state variables of the actual system, and to predict the future degradation of the system based on the Gaussian process regression prediction model. The value, the key state quantity is the average temperature of the fuel cell stack. Temperature gradient of fuel cell stack and fuel utilization rate .

[0035] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: This invention defines an index for measuring the health status of a solid oxide fuel cell system. Since the health status of a system cannot be assessed by output voltage under dynamic operating conditions, and indicators such as equivalent resistance parameters are too complex and difficult to observe, the ratio of ideal undiminished output power to actual output power is used as the system's health indicator. This can effectively avoid the above problems and quickly and accurately assess and predict the degradation status of solid oxide fuel cell systems. Attached Figure Description

[0036] Figure 1 This is a diagram showing the core steps of a health assessment and prediction method for a solid oxide fuel cell system in one embodiment; Figure 2 This is obtained through Gaussian process regression in one embodiment. A comparison chart of predicted and experimental values. Detailed Implementation

[0037] 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 features 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.

[0038] like Figure 1 As shown, the health assessment and prediction method for solid oxide fuel cell systems of the present invention mainly includes: Obtain the degraded output power of the fuel cell stack and ideal, undiminished fuel cell stack output power ; Health indicators As an evaluation index of system degradation state, it is used to assess the health status of the fuel cell system in real time under dynamic operating conditions.

[0039] The value ranges from 0 to 1; health indicators The higher the value, the smaller the degree of decay of the reaction system, and the better the health indicator. The smaller the value, the greater the degree of decay of the reaction system.

[0040] When performing real-time health assessments of a solid oxide fuel cell system, the stack output power after current system degradation is obtained. By substituting these values ​​into the above formula, the real-time health status of the solid oxide fuel cell system can be obtained.

[0041] In one embodiment, the power output at the initial startup of the system can be used as the ideal, non-degrading stack output power. At this point, the system attenuation can be ignored. In one embodiment, historical data can be used to train a non-attenuating SOFC model through a neural network, and the ideal non-attenuating stack output power of the system under arbitrary input parameters can be quickly determined using the trained non-attenuating SOFC model.

[0042] Specifically, the system's fuel flow rate, air flow rate, and current are the three inputs most closely related to the system's output power. Therefore, the undiminished output power of the system is predicted using these three easily measurable inputs. Based on the constructed neural network model, data is traversed across all operating conditions. The system's fuel flow rate, air flow rate, and current are used as input layer neurons, and the initial stack voltage from historical data of the solid oxide fuel cell system is used as the output for training the BP neural network model. The process of training the neural network model includes: The number of nodes in the input layer, hidden layer, and output layer of the network is determined based on the system's input-output sequence. The connection weights between these three layers are initialized, as are the thresholds for the hidden and output layers. The learning rate and neuron activation functions are then given. Calculate the outputs of the hidden and output layers, and adjust the network parameters using the error between the model output and the output in the existing data; The network connection weights and node thresholds are updated based on the network prediction error.

[0043] Since the training samples used in the training are essentially attenuated data from the initial operation of the system, the trained neural network model can reflect the relationship between the system input and the attenuated power, thus obtaining the SOFC attenuated model. Based on this SOFC attenuated model, the attenuated output power under any input can be quickly determined. .

[0044] In one embodiment, when predicting the health of a solid oxide fuel cell system, the prediction can be based on real-time sampled values ​​of key state variables of the actual system. and the real-time assessment obtained value A Gaussian process regression prediction model capable of predicting the future decay of a system is established. Based on the Gaussian process regression prediction model, the future decay of the system is predicted. The value of the critical state quantity is the average temperature of the fuel cell stack. Temperature gradient of fuel cell stack and fuel utilization rate .

[0045] Specifically, the average temperature of the fuel cell stack at critical states is measured. Temperature gradient of fuel cell stack and fuel utilization rate For input ,by For output and based on When establishing a Gaussian process regression prediction model, the collected data are used as the basis for the prediction. As training samples, predict the latest input vector. Corresponding output The prediction formula is expressed as:

[0046]

[0047]

[0048] in, Indicates the first i The three-dimensional input vector in each training sample Indicates that the input vector is Collected at that time value, This represents the latest input vector. Indicates that the input vector is Predicting future moments value, Let be the latent function of the input vector. N It represents the number of training data samples.

[0049] Furthermore, utilizing the given input... and output training set In the new input The predicted distribution of the calculated output is specifically represented as follows:

[0050]

[0051]

[0052]

[0053] in, This represents the input element of the training set. This represents the output element of the training set. Represents the kernel function. , Represents the mean function and is set to 0. and The joint normal distribution of the two is as follows:

[0054]

[0055]

[0056] Given of The conditional probability distribution follows a Gaussian distribution, and its prediction form is as follows:

[0057]

[0058]

[0059] The best estimate of is the mean of the distribution, that is: =

[0060] in This represents a Bayesian probability model.

[0061] Among them, a kernel function combining the squared exponential kernel function and the Matrn-type kernel function can be used to analyze the system. To make predictions, among which, Squared exponential kernel function SE for:

[0062] The Matrn kernel function is:

[0063] in, This represents the two input feature vectors. This is the bandwidth hyperparameter of the squared exponential kernel function. This is the bandwidth hyperparameter for the Matrn class kernel function. For characteristic length, For smooth hyperparameters, It is a modified Bessel function. When When the values ​​are 1 / 2, 3 / 2, and 5 / 2, they are called the Ma1, Ma3, and Ma5 kernel functions, respectively.

[0064] Simultaneously, two evaluation indicators, Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE), are introduced to assess the accuracy of the prediction, and are expressed by the following formulas: RMSE=

[0065] MAPE=

[0066] in, Represents the quantity of predicted data. This represents the true value of the test data. This represents the algorithm's predicted value.

[0067] In one embodiment, the above Gaussian process regression prediction model can be validated using a decay model, which can be expressed as: fuel 0.59) (

[0068]

[0069]

[0070] in, The resistance attenuation rate, For the temperature gradient of the fuel cell stack, The average temperature of the fuel cell stack. For the fuel cell stack current, This is the equivalent resistance of the fuel cell stack. , , These are the ohmic loss, activation loss, and concentration loss of the fuel cell stack, respectively. This is the open-circuit voltage of the fuel cell stack. This represents the output voltage after the stack has decayed. Ohmic loss, activation loss, concentration loss, and open-circuit circuitry can all be determined using the mechanistic formulas of a solid oxide fuel cell system. Running this decay model allows us to obtain state and output data after a certain operating time.

[0071] It should be noted that the three key state variables identified above were determined using principal component analysis for this degradation model, and were not arbitrarily chosen. Considering the complexity of battery systems, which involve numerous state variables, the computational load would be extremely high if all state variables were considered when establishing a Gaussian process regression prediction model. Therefore, in this embodiment, the degradation model is analyzed, and principal component analysis is used to determine several key state variables that best reflect the battery system's degradation rate for use in establishing the Gaussian process regression prediction model. This reduces the computational load while maintaining prediction accuracy.

[0072] When using the above decay model for prediction verification, key state variables during model runtime can be collected first. and the corresponding value Then, the Gaussian process regression prediction model introduced above is established, based on the current state variables. Predicting future time t value Simultaneously, run the above decay model up to time t, and directly obtain the value at time t. The value is compared with the predicted value to verify whether the predicted value matches the experimental value. For example... Figure 2 As shown in the figure, a, b, and c represent the attenuation curves under different system inputs, where, The predicted values ​​are in good agreement with the experimental values ​​obtained directly from running the decay model, and the predicted values ​​remain accurate even when the system input is changed.

[0073] In one embodiment, with =0.8 is used as the system lifetime termination limit, when the system When the value reaches 0.8, it indicates the end of the system's lifespan; therefore, it can be predicted that... Lifetime end time: 0.8 t eol According to the current time t 0 and end of life t eol Jointly determine the remaining lifespan of the system RUL : .

[0074] Accordingly, the present invention also relates to a health assessment and prediction system for a solid oxide fuel cell system, which includes health indicators. Computing unit

[0075] in, This represents the attenuated output power of the fuel cell stack. For ideal, undiminished fuel cell stack output power, The value ranges from 0 to 1; health indicators The higher the value, the smaller the degree of decay of the reaction system, and the better the health indicator. The smaller the value, the greater the degree of decay of the reaction system.

[0076] In one embodiment, the system further includes a Gaussian process regression prediction unit, used to establish a Gaussian process regression prediction model capable of predicting the future degradation of the system based on real-time sampled values ​​of key state variables of the actual system, and to predict the future degradation of the system based on the Gaussian process regression prediction model. The value, the key state quantity is the average temperature of the fuel cell stack. Temperature gradient of fuel cell stack and fuel utilization rate .

[0077] In one embodiment, the system further includes a trained neural network model to quickly determine the ideal, undiminished stack output power of the solid oxide fuel cell system under arbitrary input parameters, and to determine the degraded stack output power. Compared to the ideal, undiminished output power of the fuel cell stack Substitution The calculation formula enables real-time assessment of the health status of solid oxide fuel cell systems.

[0078] 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 health assessment and prediction of a solid oxide fuel cell system, characterized in that, The power output of the solid oxide fuel cell system during its initial operation is obtained as the ideal, non-degrading stack output power. Alternatively, based on historical data, a non-degradation model of the solid oxide fuel cell system can be trained using a neural network to achieve the ideal non-degradation stack output power. This trained non-degradation model can then be used to quickly determine the ideal non-degradation stack output power of the solid oxide fuel cell system under arbitrary input parameters. Health indicators As an evaluation index of system degradation state, it is used to assess the health status of the fuel cell system in real time under dynamic operating conditions: ； in, This represents the attenuated output power of the fuel cell stack. For ideal, undiminished fuel cell stack output power, The value ranges from 0 to 1; health indicators The higher the value, the smaller the degree of decay of the reaction system, and the better the health indicator. The smaller the value, the greater the degree of decay of the reaction system; Based on the real-time sampled values ​​of the key state variables of the actual system, and the results obtained from real-time evaluation... Based on the value of the Gaussian process regression prediction model, a Gaussian process regression prediction model capable of predicting the future decay of the system is established. Then, based on the Gaussian process regression prediction model, the future decay of the system is predicted. The value of the critical state quantity is the average temperature of the fuel cell stack. Temperature gradient of fuel cell stack and fuel utilization rate ; Among them, the average temperature of the fuel cell stack under critical conditions is measured. Temperature gradient of fuel cell stack and fuel utilization rate For input ,by For output and based on When establishing a Gaussian process regression prediction model, the collected data are used as the basis for the prediction. As training samples, predict the latest input vector. Corresponding output The prediction formula is expressed as: ； ； ； in, Indicates the first i The three-dimensional input vector in each training sample The input vector is Collected at that time value, Represents the latest input vector. The input vector is Predicting future moments value, Let be the latent function of the input vector. N It represents the number of training data samples.

2. The health assessment and prediction method for a solid oxide fuel cell system as described in claim 1, characterized in that, Using the given included input and output training set In the new input The predicted distribution of the calculated output is specifically represented as follows: ； ； ； ； in, This represents the input element of the training set. This represents the output element of the training set. Represents the kernel function. , Represents the mean function and is set to 0. and The joint normal distribution of the two is as follows: ； ； ； Given of The conditional probability distribution follows a Gaussian distribution, and its prediction form is as follows: ； ； ； The best estimate of is the mean of the distribution, that is: ； in This represents a Bayesian probability model.

3. The health assessment and prediction method for a solid oxide fuel cell system as described in claim 2, characterized in that, A kernel function combining the squared exponential kernel function and the Matrn-like kernel function is used to evaluate the system. To make predictions, among which, Squared exponential kernel function SE for: ； The Matrn kernel function is: ； in, This represents the two input feature vectors. This is the bandwidth hyperparameter of the squared exponential kernel function. This is the bandwidth hyperparameter for the Matrn class kernel function. For characteristic length, For smooth hyperparameters, It is a modified Bessel function.

4. The health assessment and prediction method for a solid oxide fuel cell system as described in claim 3, characterized in that, The accuracy of the prediction is evaluated using two metrics: root mean square error and mean absolute percentage error.

5. The health assessment and prediction method for a solid oxide fuel cell system as described in claim 1, characterized in that, when When the value is 0.8, the corresponding time is the end of the lifespan. t eol According to the current time t 0 and end of life t eol Jointly determine the remaining lifespan of the system RUL : 。 6. A health assessment and prediction system for a solid oxide fuel cell system, characterized in that, include: Health indicators The calculation unit is used to perform the following calculations: ;in, This represents the attenuated output power of the fuel cell stack. For ideal, undiminished fuel cell stack output power, The value ranges from 0 to 1; health indicators The higher the value, the smaller the degree of decay of the reaction system, and the better the health indicator. The smaller the value, the greater the degradation of the reaction system; among them, the output power of an ideal, non-degrading fuel cell stack... The output power of the solid oxide fuel cell system during initial operation, or, based on historical data, a non-degradation model of the solid oxide fuel cell system trained by a neural network to obtain the ideal non-degradation stack output power, and the ideal non-degradation stack output power of the solid oxide fuel cell system determined by the trained non-degradation model of the solid oxide fuel cell system. The Gaussian process regression prediction unit is used to establish a Gaussian process regression prediction model that can predict the future degradation of the system based on the real-time sampled values ​​of the key state variables of the actual system, and to predict the future degradation of the system based on the Gaussian process regression prediction model. The value, the key state quantity is the average temperature of the fuel cell stack. Temperature gradient of fuel cell stack and fuel utilization rate Among them, the average temperature of the fuel cell stack under critical conditions is measured. Temperature gradient of fuel cell stack and fuel utilization rate For input ,by For output and based on When establishing a Gaussian process regression prediction model, the collected data are used as the basis for the prediction. As training samples, predict the latest input vector. Corresponding output The prediction formula is expressed as: ； ； ； in, Indicates the first i The three-dimensional input vector in each training sample Indicates that the input vector is Collected at that time value, This represents the latest input vector. Indicates that the input vector is Predicting future moments value, Let be the latent function of the input vector. N It represents the number of training data samples.

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