CN115600495A

CN115600495A - Hybrid prediction method and system for performance degradation of solid oxide fuel cell

Info

Publication number: CN115600495A
Application number: CN202211253043.1A
Authority: CN
Inventors: 李曦; 盛闯; 俎焱敏; 傅俊; 曾令鸿; 邓忠华
Original assignee: Huazhong University of Science and Technology
Current assignee: Huazhong University of Science and Technology
Priority date: 2022-10-13
Filing date: 2022-10-13
Publication date: 2023-01-13

Abstract

The invention discloses a hybrid prediction method and a hybrid prediction system for performance degradation of a solid oxide fuel cell. The method comprises the following steps: capturing the degradation trend of the voltage of the fuel cell in a preset prediction time period by adopting a first prediction method based on a grey prediction model to obtain a first prediction result of a target moment; acquiring local nonlinear characteristics in the degradation process of the fuel cell voltage by using a second prediction method of the data-driven adaptive neural fuzzy system to obtain a second prediction result of a target moment; and performing data fusion on the first prediction result and the second prediction result at the target moment by a sliding window and data fusion method to obtain a mixed prediction result of the target voltage corresponding to the target moment. The method solves the problems that the existing fuel cell performance prediction method has limitation and poor prediction accuracy, realizes the capture of the long-term fuel cell voltage degradation trend, simultaneously keeps the details of the short-term nonlinear degradation characteristic, and has the beneficial effect of higher prediction accuracy.

Description

Hybrid prediction method and system for performance degradation of solid oxide fuel cell

Technical Field

The invention belongs to the field of fuel cells, and particularly relates to a hybrid prediction method and a hybrid prediction system for performance degradation of a solid oxide fuel cell.

Background

The Solid Oxide Fuel Cell (SOFC) can realize the direct conversion from chemical energy to electric energy under medium-high temperature conditions, does not need precious metal electrode materials such as Pt and the like, has the advantages of low cost, high efficiency, no pollution, wide fuel sources and the like, becomes one of the most promising green energy sources in the 21 st century, and the performance degradation and the durability of the SOFC become bottlenecks which hinder large-scale commercialization of the SOFC. The method can accurately predict the performance degradation trend of the SOFC, diagnose faults in time, maintain and adjust equipment in advance, and is beneficial to prolonging the service life of the SOFC.

Conventional prediction methods are generally classified into model-based and data-driven. The method based on the model has simple design thought and low experimental cost, but an accurate mechanism model is difficult to establish. The data driving-based method has a huge data requirement and certain limitations.

Disclosure of Invention

Aiming at the defects of the related art, the invention aims to provide a hybrid prediction method and a hybrid prediction system for performance degradation of a solid oxide fuel cell, and aims to solve the problems that when the performance of the fuel cell is predicted, a model is difficult to accurately establish based on a model prediction method, the data requirement of a data-driven method is huge, certain limitation is caused, and the prediction precision is poor.

To achieve the above object, the present invention provides a hybrid prediction method for performance degradation of a solid oxide fuel cell, comprising:

capturing the degradation trend of the voltage of the fuel cell in a preset prediction time period by adopting a first prediction method based on a grey prediction model to obtain a first prediction result of a target moment;

acquiring local nonlinear characteristics in the degradation process of the fuel cell voltage by using a second prediction method of a data-driven adaptive neural fuzzy system to obtain a second prediction result of the target moment;

and performing data fusion on the first prediction result and the second prediction result of the target moment by a sliding window and data fusion method to obtain a mixed prediction result of the target voltage corresponding to the target moment.

Optionally, the gray prediction model adopts a GM (1, 1) first order univariate gray prediction model.

Optionally, the building of the first-order univariate gray prediction model includes:

defining a raw fuel cell voltage sequence u ⁽⁰⁾ Comprises the following steps:

u ⁽⁰⁾ ＝{u ⁽⁰⁾ (1),u ⁽⁰⁾ (2),u ⁽⁰⁾ (3),...,u ⁽⁰⁾ (n)}

where n is the sample size of the voltage sequence, u ⁽⁰⁾ (k) Kth data of a fuel cell voltage series;

generating a new sequence u by first-order accumulation of the initial voltage sequence ⁽¹⁾ Comprises the following steps:

u ⁽¹⁾ ＝{u ⁽¹⁾ (1),u ⁽¹⁾ (2),u ⁽¹⁾ (3),...,u ⁽¹⁾ (n)}

wherein u is ⁽¹⁾ (k) Is a series u ⁽⁰⁾ Corresponding to the accumulation of the front k items of data, the specific calculation formula is as follows:

thereafter defining a neighboring average sequence Z ⁽¹⁾ ：

Z ⁽¹⁾ ＝{Z ⁽¹⁾ (1),Z ⁽¹⁾ (2),Z ⁽¹⁾ (3),...,Z ⁽¹⁾ (n)}

Wherein Z is ⁽¹⁾ (k) Is an average sequence Z ⁽¹⁾ The k-th data of (2) is specifically calculated as follows:

Z ⁽¹⁾ (1)＝u ⁽¹⁾ (1)

Z ⁽¹⁾ (k)＝0.5·[u ⁽¹⁾ (k)+u ⁽¹⁾ (k-1)],k＝2,3,...,n

GM (1, 1) first order Gray differential equation:

u ⁽⁰⁾ (k)+a·Z ⁽¹⁾ (k)＝b

its whitening function can be expressed as follows:

according to the least square method, the estimated values of two parameters a and b can be obtained

Will be provided with

Substituting the whitening function, the solution of the gray differential equation can be found as:

u ⁽¹⁾ (0)＝u ⁽⁰⁾ (1)

the predicted value can be obtained by reducing the sequence into the original sequence

Comprises the following steps:

wherein the content of the first and second substances,

in order to accumulate the predicted values of the sequence,

is a predicted value of the original sequence.

Optionally, the establishing of the first-order univariate gray prediction model further includes:

carrying out error correction on the first-order univariate grey prediction model;

introducing error correction factors psi, u ⁽¹⁾ (t)＝0.5·[u ⁽¹⁾ (k)+u ⁽¹⁾ (k-1)-ψ]；

The new gray differential equation can be written as:

wherein the estimated value of the intermediate parameter m, n

Comprises the following steps:

the solution of the gray differential equation can thus be found as:

wherein

Estimation of two new parameters mu, upsilon

Also can pass through the minimumTwo multiplications result in:

wherein

The final first prediction result can be obtained by the error correction model

Wherein, when k =2,3, \8230, n can obtain a fitting value of the initial voltage attenuation sequence, and when k > n can obtain a first prediction result of the voltage attenuation sequence.

Optionally, the fuzzy rule selection policy of the adaptive neuro-fuzzy system is ANFIS-SC, and the parameters are respectively set as follows: maximum iteration number, target training error, initial training step size, step size reduction rate and step size increase rate.

Optionally, the performing data fusion on the first prediction result and the second prediction result at the target time by using a sliding window and data fusion method to obtain a mixed prediction result of the target voltage corresponding to the target time includes:

constructing an input matrix and the mixed prediction result matrix through a sliding window;

in order to predict target voltages at N target moments in the future, the input matrix is to input the existing m voltage data, and the input matrix is:

wherein each column of the m × K matrix represents a sequence of input samples; n is the window sliding size, K represents the actual prediction step, K =0 is the initial sequence, K =1 represents the 1 st prediction step, and K is the total sliding step number;

the hybrid prediction result matrix is:

the N multiplied by K matrix represents a predicted target, each element represents a target voltage needing to be predicted, and the value of each element represents a mixed prediction result of the target voltage corresponding to each target moment; the m inputs in each column of the m x K matrix correspond to the N target voltages that need to be predicted for that number of steps in each column of the N x K matrix.

Optionally, the performing data fusion on the first predicted result and the second predicted result at the target time by using a sliding window and data fusion method to obtain a mixed predicted result of the target voltage corresponding to the target time, further includes:

evaluating the fitting ability of the first prediction method and the second prediction method in each step of iterative prediction process, specifically:

comparing the fuel cell voltage measured value used for evaluation in the step (k-1) with the first prediction result and the second prediction result obtained in the step (k-1) by the first prediction method and the second prediction method respectively to obtain a first residual error and a second residual error;

calculating a weight factor of a first prediction result of the target voltage corresponding to the kth step according to the first residual error;

calculating a weight factor of a second prediction result of the target voltage corresponding to the kth step according to the second residual error;

due to the addition of a new measured value, the weight factor of each iteration step in the process of hybrid prediction is dynamically adjusted;

wherein the weight factor w _p,k The sum of the accuracy of the first prediction result or the second prediction result and the absolute value of the residual error in the actual prediction processInversely proportional;

the weight factor calculation formula is as follows:

wherein p =1 represents a first prediction result based on a gray prediction model, and p =2 represents a second prediction result based on an adaptive neuro-fuzzy system; k represents the actual prediction step; u. of _p,k-1 Representing the voltage value actually measured in the k-1 step during the evaluation,

representing the voltage value predicted by the model in the step k-1 in the evaluation process;

blending the predicted results

Expressed according to a weighted average:

wherein the content of the first and second substances,

representing prediction data of a grey prediction model or an adaptive neuro-fuzzy system in the future prediction process, w _norm,p,k A weight factor representing the normalization, calculated by:

in a second aspect, the present invention provides a hybrid prediction system for performance degradation of a solid oxide fuel cell, comprising:

the first prediction module is used for capturing the degradation trend of the voltage of the fuel cell in a preset prediction time period by adopting a first prediction method based on a grey prediction model to obtain a first prediction result of a target moment;

the second prediction module is used for acquiring local nonlinear characteristics in the degradation process of the fuel cell voltage by using a second prediction method of a data-driven adaptive neural fuzzy system to obtain a second prediction result of the target moment;

and the hybrid prediction module is used for performing data fusion on the first prediction result and the second prediction result of the target moment through a sliding window and data fusion method to obtain a hybrid prediction result of the target voltage corresponding to the target moment.

In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:

(1) The method has the advantages of two methods, and can capture the voltage degradation trend of the long-term fuel cell and simultaneously maintain the details of the short-term nonlinear degradation characteristic;

(2) Compared with the conventional single model prediction result, the hybrid prediction method provided by the invention has higher prediction precision and better robustness.

Drawings

Fig. 1 is a schematic flow chart of a hybrid prediction method for performance degradation of a solid oxide fuel cell according to an embodiment of the present invention;

FIG. 2 is a diagram illustrating error correction factors according to an embodiment of the present invention;

FIG. 3 is a schematic diagram of a sliding window provided in accordance with an embodiment of the present invention;

fig. 4 is a schematic diagram of a hybrid prediction method for performance degradation of a solid oxide fuel cell according to an embodiment of the present invention;

fig. 5 is a schematic structural diagram of a hybrid prediction system for performance degradation of a solid oxide fuel cell according to the second embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is 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 of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

Example one

As shown in fig. 1, a hybrid prediction method for performance degradation of a solid oxide fuel cell includes:

s1, capturing the degradation trend of the voltage of the fuel cell in a preset prediction time period by adopting a first prediction method based on a grey prediction model, and obtaining a first prediction result of a target moment.

And S2, acquiring local nonlinear characteristics in the degradation process of the fuel cell voltage by using a second prediction method of the data-driven adaptive neural fuzzy system to obtain a second prediction result of the target moment.

And S3, performing data fusion on the first prediction result and the second prediction result at the target moment through a sliding window and data fusion method to obtain a mixed prediction result of the target voltage corresponding to the target moment.

The embodiment of the invention provides a hybrid prediction method based on an empirical model and data driving fusion for performance attenuation prediction of a solid oxide fuel cell, the prediction method based on a gray prediction model can capture the voltage degradation trend in a longer prediction time, the prediction method based on a data-driven adaptive neural fuzzy system (ANFIS) can better describe local nonlinear characteristics in the degradation process, a new data set is obtained according to the two methods, and different prediction results are fused by adopting a sliding window technology based on the new data set and a data fusion method, so that the prediction precision is improved, and real-time monitoring can be realized. The galvanic pile voltage is the most direct and effective index for representing the degradation of the SOFC system under the condition of stable load, so the galvanic pile voltage attenuation data obtained from experiments are selected to verify the hybrid model prediction method provided by the invention. And predicting a target voltage value corresponding to a certain target moment in the future through the hybrid model, thereby monitoring the performance of the battery.

The first prediction method is a gray prediction model in S1, and the gray prediction model adopts a GM (1, 1) first-order univariate gray prediction model. The establishment of the first-order univariate grey prediction model comprises the following steps:

u ⁽⁰⁾ ≥0,k＝1,2,3,…,n

where n is the sample size of the voltage sequence, u ⁽⁰⁾ (k) Kth data for a fuel cell voltage sequence;

u ⁽¹⁾ ＝{u ⁽¹⁾ (1),u ⁽¹⁾ (2),u ⁽¹⁾ (3),…,u ⁽¹⁾ (n)}

wherein u is ⁽¹⁾ (k) Is a number sequence u ⁽⁰⁾ Corresponding to the accumulation of the previous k items of data, the specific calculation formula is as follows:

then define the adjacent average sequence Z ⁽¹⁾ ：

Z ⁽¹⁾ ＝{Z ⁽¹⁾ (1),Z ⁽¹⁾ (2),Z ⁽¹⁾ (3),…,Z ⁽¹⁾ (n)}

Wherein, Z ⁽¹⁾ (k) Is an average sequence Z ⁽¹⁾ The k-th data of (2) is specifically calculated as follows:

Z ⁽¹⁾ (1)＝u ⁽¹⁾ (1)

Z ⁽¹⁾ (k)＝0.5·[u ⁽¹⁾ (k)+u ⁽¹⁾ (k-1)],k＝2,3,…,n

GM (1, 1) first order Gray differential equation:

u ⁽⁰⁾ (k)+a·Z ⁽¹⁾ (k)＝b

wherein a and b are undetermined parameters, and the estimated values of the two parameters a and b can be obtained according to the least square method

Wherein Y and B are both intermediate variables, B ^T A transposed matrix representing a matrix B, B ^-1 The inverse matrix representing B, B and Y can be obtained by:

the corresponding whitening function of the GM (1, 1) model:

wherein the content of the first and second substances,

for implementing a first order gray differential equation and an approximate representation of the model's corresponding whitening function.

Will be provided with

u ⁽¹⁾ (0)＝u ⁽⁰⁾ (1)

Comprises the following steps:

wherein the content of the first and second substances,

is an accumulated sequence u ⁽¹⁾ (k) The predicted value of (a) is obtained,

is an original sequence u ⁽⁰⁾ (k) The predicted value of (2).

As shown in FIG. 2, point M is the midpoint of the straight line segment PQ, u ⁽¹⁾ (ξ ') is the function value for the intersection M' of the extension line of point M and the curve PQ, u is the function value ⁽¹⁾ And ξ is the function value for tangent point N of curve PQ. In the conventional GM (1, 1) model described above, u is due to reality ⁽¹⁾ (t)≤0.5·[u ⁽¹⁾ (k)+u ⁽¹⁾ (k-1)]Therefore, an error correction model is provided, and the error of the original model is eliminated on the basis of keeping the simplicity and the rapidity of the model.

Further, the establishment of the first-order univariate gray prediction model further comprises:

correcting errors of the first-order univariate grey prediction model;

introducing error correction factors psi, u ⁽¹⁾ (t)＝0.5·[u ⁽¹⁾ (k)+u ⁽¹⁾ (k-1)-ψ](ii) a Wherein ψ is u ⁽¹⁾ (xi') and u ⁽¹⁾ (xi) difference.

The new gray differential equation can be written as:

wherein the estimated value of the intermediate parameter m, n

Comprises the following steps:

based on the solution of the gray differential equation, one can obtain a solution of the gray differential equation as:

wherein the content of the first and second substances,

two new parameters mu, u

It can also be obtained by the least squares method:

wherein

The final first prediction result of the gray prediction model can be obtained through the error correction model

The second prediction method is ANFIS adopted in S2, which has a strong nonlinear mapping capability that is well suited for achieving short-term prediction of the future aging trend (FDT) of the solid oxide fuel cell. The ANFIS model structure is formed by combining the adaptive network and the fuzzy inference system, inherits the interpretability characteristic of the fuzzy inference system and the learning capability of the adaptive network in function, and can change system parameters according to prior knowledge so that the output of the system is closer to the real output.

ANFIS typically consists of five layers, where x ₁ And x ₂ The input variables are represented by a representation of,

representing the output of the ith node in the kth layer.

The first layer is called the fuzzy layer, the nodes are all self-adaptive nodes, the input variable is fuzzified, and the output corresponds to the membership degree of different fuzzy sets, as shown in the following formula:

wherein, the first and the second end of the pipe are connected with each other,

and

respectively, the membership degrees of the fuzzy sets Ai and Bi, and μ (x) represents a membership function, which is generally chosen as shown in the following formula:

where ai, bi and ci represent the parameters of the membership functions.

The nodes of the second layer are all fixed nodes, and the excitation intensity omega of each rule is calculated _i As follows:

the nodes of the third layer are all fixed nodes, and the node of the previous layer is connected with the node of the third layerThe normalization of the excitation intensity of each rule obtained in (1) is obtained

The trigger weight of the rule in the whole rule base is characterized as follows:

the nodes of the fourth layer are all self-adaptive nodes, input variables are linearly combined and multiplied by the normalized excitation intensity of the previous layer, and the output is as follows:

wherein p is _i ，q _i And r _i Representing a conclusion parameter.

The fifth level nodes are all fixed nodes, defuzzification is performed to obtain exact output, and the final system output result is the weighted average of the results of each rule, as follows:

and constructing ANFIS according to the five-layer nodes.

Further, ANFIS typically has three different fuzzy rule selection strategies, namely mesh partitioning (GP), subtractive Clustering (SC), and fuzzy c-means clustering (FCM). Preferably, the fuzzy rule selection strategy is Subtractive Clustering (SC).

And S3, obtaining a hybrid prediction method by adopting a sliding window method and a data fusion method. The main purpose of using the sliding window technique is to input a new data set in the prediction process to dynamically update the training model, and provide a dynamic weight factor to further improve the prediction accuracy. This method has a small computational burden and uses only measured voltage data within a short period of time before the target voltage at the predicted time as input. Secondly, the method ensures a close relationship between the input data and the predicted voltage data by updating the input data. As shown in fig. 3, the length of the sliding window includes three parts, a training part, an evaluation part, and a prediction part. In each prediction step, the data in the training portion is used to train a previously developed model, and then the data in the evaluation portion is used to evaluate the fitting ability of the updated model, the data in the prediction portion being future data points that need to be predicted from the model.

Take the first model-based GM method as an example. Assuming that the number of data in the training section, the evaluation section, and the prediction section are defined as p, q, N, respectively, the size of the movement between each prediction step is also set to N. At the kth prediction step, p measured training data (from 1 to p) located at the beginning of the sliding window are applied to train the kth model, then the measured data from p +1 to p + q are used to evaluate the model prediction accuracy, and the prediction data are given from p + q +1 to p + q + N. When the prediction iterates from the kth step to the k +1 th step, the aging data previously measured within the solid box a is applied to train the k +1 model, the measurement data within the dashed box b is used to evaluate the accuracy of the k +1 model, and prediction data from p + q + N +1 to p + q +2N are given. The sliding window technique has a similar iterative process in the ANFIS method.

Optionally, performing data fusion on the first prediction result and the second prediction result at the target time by using a sliding window technique and a data fusion method to obtain a mixed prediction result of the target voltage corresponding to the target time, where the method includes:

in order to predict target voltages at N target times in the future, an input matrix is to input existing m voltage data, where the input matrix is:

wherein each column of the m × K matrix represents a sequence of input samples; n is the window sliding size, K represents the actual prediction step, K =0 is the initial sequence, K =1 represents the 1 st step prediction, and K is the total sliding step number.

The hybrid prediction result matrix is:

Optionally, the data fusion is performed on the first prediction result and the second prediction result at the target time by using a sliding window and data fusion method, so as to obtain a mixed prediction result of the target voltage corresponding to the target time, and the method further includes:

and evaluating the fitting capacity of the first prediction method and the second prediction method in each step of iterative prediction process, namely evaluating the fitting capacity of two single prediction methods, namely GM and ANFIS. The method comprises the following specific steps:

and A1, comparing the fuel cell voltage measured value used for evaluation in the step (k-1) with a first prediction result and a second prediction result obtained in the step (k-1) by a first prediction method and a second prediction method respectively to obtain a first residual error and a second residual error.

And A2, calculating a weight factor of a first prediction result of the target voltage corresponding to the k step according to the first residual error.

And A3, calculating a weight factor of a second prediction result of the target voltage corresponding to the k step according to the second residual error.

Weight factor w _p,k And the accuracy degree of the first prediction result or the second prediction result in the actual prediction process is expressed in inverse proportion to the sum of the absolute values of the residual errors. The calculation formula is as follows:

wherein p =1 represents a first prediction result based on a gray prediction model, and p =2 represents a second prediction result based on an adaptive neuro-fuzzy system; k represents the actual predicted step; u. u _p,k-1 Representing the voltage value actually measured in step k-1 of the evaluation process,

representing the voltage value predicted by the model in the step k-1 in the evaluation process.

In the process of mixed prediction, due to the addition of new measured values, the weight factor of each iteration is dynamically adjusted, and the result of mixed prediction is obtained

Expressed according to a weighted average:

wherein the content of the first and second substances,

the overall structure of the proposed hybrid prediction algorithm is shown in fig. 4. In fig. 4, N is the window sliding size, N is the number of actual prediction data, K is the actual prediction step, and K is the total sliding step number.

The accuracy of the prediction model can be assessed by three common criteria, mean Absolute Percent Error (MAPE), root Mean Square Error (RMSE), and coefficient of determination (R) ² ). The smaller the MAPE and RMSE values, the smaller the error and the more accurate the prediction, conversely R ² The larger the value of (A) is, the more accurate the prediction result is. If a predictive model is completely accurate, then the values of MAPE and RMSE are equal to 0 ² Is equal to 1. The expressions of these three predicted performance evaluation indexes are as follows:

wherein u (t) represents the actual measured voltage value,

the voltage values predicted by the model are represented,

represents the average value of the actual voltage data, and M represents the total length of the predicted voltage data.

The prediction method of the GM model can accurately follow the degradation trend of the battery voltage, and in order to determine the influence of different window sliding sizes on the prediction result, under the condition of setting different sliding window sizes, the prediction result of the GM model is evaluated according to the obtained measured experimental data, so that the appropriate sliding window size is determined. The sliding window sizes are set to be 3, 5, 10 and 15 time units respectively, and the prediction result is best when the window sliding size is 5 time units according to the evaluation index analysis of the table 1. The window sliding is thus set to a size of 5, i.e. each step predicts a voltage of 5 time units in the future.

TABLE 1 GM evaluation index results at different window sliding sizes

And performing degradation prediction on the selected voltage decay time sequence by using the established ANFIS model and combining three different fuzzy rule selection strategies. Parameters are respectively set according to empirical analysis and actual conditions: the maximum iteration number is 100, the target training error is 0.0001, the initial training step size is 0.01, the step size reduction rate is 0.9, and the step size increase rate is 1.1. Meanwhile, in order to ensure the implementation of the hybrid prediction method, the ANFIS model moving window size N is also set to 5 time units.

As shown in Table 2, according to the prediction precision and the running time of different methods, it can be seen that the prediction performance of ANFIS-GP is poor, and ANFIS-FCM and ANFIS-SC have higher precision and shorter running time, compared with ANFIS-SC, ANFIS-SC has the best prediction performance. Therefore, in the present embodiment, the fuzzy rule selection strategy of the adaptive neuro-fuzzy system is ANFIS-SC.

And 2, ANFIS evaluation index results under different fuzzy rule selection strategies.

The degradation prediction of the fuel cell voltage not only needs to ensure the accuracy, but also needs to be capable of tracking the degradation trend in the prediction process, so the embodiment proposes to combine the model-based GM method and the data-driven ANFIS method for prediction. According to the evaluation indexes in the table 3, the root mean square error of the hybrid prediction method is 0.1024, which is respectively reduced by 20.62% compared with the single model ANFIS-SC prediction result and 8.57% compared with the single model GM prediction result; the average absolute percentage error of the mixed prediction method is 0.1992, which is 46.69 percent less than the result of single model ANFIS-SC prediction and 9.71 percent less than the result of single model GM prediction; the decision coefficient of the hybrid prediction method is 0.9952, which is 0.09% higher than the result of single model ANFIS-SC prediction and 0.28% higher than the result of single model GM prediction. Comprehensively, the hybrid prediction method not only can integrate the advantages of the two methods, but also improves the prediction precision, and proves the effectiveness and the accuracy of the method provided by the invention.

Table 3 evaluation index results of the three prediction methods.

According to the technical scheme, a first prediction result of the target time obtained based on a gray prediction model and a second prediction result of the target time obtained based on a self-adaptive neural fuzzy system are fused through a sliding window and a data fusion method to obtain a mixed prediction calculation mode of the target voltage, the prediction method based on the gray prediction model can capture the voltage degradation trend within a longer prediction time, the prediction method based on the data-driven self-adaptive neural fuzzy system (ANFIS) can better describe local nonlinear characteristics in the degradation process, and the mixed prediction method after fusion based on the empirical model and the prediction results driven by the data solves the problems that the existing performance prediction method of the fuel cell has certain limitation and poor prediction precision, achieves the advantages of two methods, can capture the voltage degradation trend of the long-term fuel cell, and meanwhile keeps the details of short-term nonlinear degradation characteristics, and has the advantages of higher prediction precision and better robustness.

Example two

As shown in fig. 5, a hybrid prediction system for performance degradation of a solid oxide fuel cell includes:

the first prediction module 210 is configured to capture a degradation trend of the fuel cell voltage within a preset prediction time period by using a first prediction method based on a gray prediction model, so as to obtain a first prediction result at a target time.

And the second prediction module 220 is configured to obtain a local nonlinear characteristic in the degradation process of the fuel cell voltage by using a second prediction method based on a data-driven adaptive neuro-fuzzy system, so as to obtain a second prediction result of the target time.

And the hybrid prediction module 230 is configured to perform data fusion on the first prediction result and the second prediction result at the target time through a sliding window and data fusion method, so as to obtain a hybrid prediction result of the target voltage corresponding to the target time.

The hybrid prediction system for the performance degradation of the solid oxide fuel cell provided by the embodiment of the invention can execute the hybrid prediction method for the performance degradation of the solid oxide fuel cell provided by any embodiment of the invention, and has corresponding functional modules and beneficial effects of the execution method.

It will be understood by those skilled in the art that the foregoing is only an exemplary embodiment of the present invention, and is not intended to limit the invention to the particular forms disclosed, since various modifications, substitutions and improvements within the spirit and scope of the invention are possible and within the scope of the appended claims.

Claims

1. A hybrid prediction method for performance degradation of a solid oxide fuel cell, comprising:

acquiring a local nonlinear characteristic in the degradation process of the fuel cell voltage by using a second prediction method of a data-driven adaptive neural fuzzy system to obtain a second prediction result of the target moment;

2. The method of claim 1, wherein the gray prediction model employs a GM (1, 1) first order univariate gray prediction model.

3. The method of claim 2, wherein the building of the first order univariate gray prediction model comprises:

defining raw fuelSeries u of cell voltages ⁽⁰⁾ Comprises the following steps:

u ⁽⁰⁾ ＝{u ⁽⁰⁾ (1),u ⁽⁰⁾ (2),u ⁽⁰⁾ (3),…,u ⁽⁰⁾ (n)}

u ⁽¹⁾ ＝{u ⁽¹⁾ (1),u ⁽¹⁾ (2),u ⁽¹⁾ (3),…,u ⁽¹⁾ (n)}

thereafter defining a neighboring average sequence Z ⁽¹⁾ ：

Z ⁽¹⁾ ＝{Z ⁽¹⁾ (1),Z ⁽¹⁾ (2),Z ⁽¹⁾ (3),…,Z ⁽¹⁾ (n)}

Z ⁽¹⁾ (1)＝u ⁽¹⁾ (1)

Z ⁽¹⁾ (k)＝0.5·[u ⁽¹⁾ (k)+u ⁽¹⁾ (k-1)],k＝2,3,…,n

GM (1, 1) first order Gray differential equation:

u ⁽⁰⁾ (k)+a·Z ⁽¹⁾ (k)＝b

its whitening function can be expressed as follows:

Will be provided with

u ⁽¹⁾ (0)＝u ⁽⁰⁾ (1)

Comprises the following steps:

in order to accumulate the predicted values of the sequence,

is a predicted value of the original sequence.

4. The method of claim 3, wherein the building of the first order univariate gray prediction model further comprises:

carrying out error correction on the first-order univariate gray prediction model;

The new gray differential equation can be written as:

wherein the estimated value of the intermediate parameter m, n

Comprises the following steps:

the solution to the gray differential equation can thus be found as:

wherein

Two new parameters mu, u

It can also be obtained by the least squares method:

wherein

The final first prediction result can be obtained through the error correction model

Wherein, when k =2,3, \8230;, n, a fitting value of an initial voltage decay sequence can be obtained, and when k > n, a first prediction result of the voltage decay sequence can be obtained.

5. The method of claim 1, wherein the fuzzy rule selection strategy of the adaptive neuro-fuzzy system is ANFIS-SC, setting parameters: maximum iteration number, target training error, initial training step size, step size reduction rate and step size increase rate.

6. The method according to claim 1, wherein the data fusion of the first predicted result and the second predicted result at the target time by a sliding window and data fusion method to obtain a mixed predicted result of the target voltage corresponding to the target time comprises:

wherein each column of the mxk matrix represents a sequence of input samples; n is the window sliding size, K represents the actual prediction step, K =0 is the initial sequence, K =1 represents the 1 st prediction step, and K is the total sliding step number;

the hybrid prediction result matrix is:

the N multiplied by K matrix represents a predicted target, each element represents a target voltage needing to be predicted, and the value of each element represents a mixed prediction result of the target voltage corresponding to each target moment; the m inputs for each column of the m × K matrix correspond to the N target voltages to be predicted for that number of steps per column of the N × K matrix.

7. The method of claim 6, wherein the data fusing the first predicted result and the second predicted result at the target time by a sliding window and data fusion method to obtain a mixed predicted result of the target voltage corresponding to the target time, further comprises:

comparing the fuel cell voltage measured value used for evaluation in the step (k-1) with the first prediction result and the second prediction result obtained by the first prediction method and the second prediction method in the step (k-1) respectively to obtain a first residual error and a second residual error;

wherein the weight factor w _p,k The accuracy degree of the first prediction result or the second prediction result in the actual prediction process is represented and is inversely proportional to the sum of the absolute values of the residual errors;

the weight factor calculation formula is as follows:

wherein p =1 represents a first prediction result based on a gray prediction model, and p =2 represents a second prediction result based on an adaptive neuro-fuzzy system; k represents the actual prediction step; u. u _p,k-1 Representing the voltage value actually measured in the k-1 step during the evaluation,

representing the voltage value predicted by the model in the step (k-1) in the evaluation process;

blending predicted results

Expressed according to a weighted average:

8. a hybrid prediction system for performance degradation of a solid oxide fuel cell, comprising: