CN111310305A - Method for acquiring oscillation variable of solid oxide fuel cell system - Google Patents

Method for acquiring oscillation variable of solid oxide fuel cell system Download PDF

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CN111310305A
CN111310305A CN202010058149.0A CN202010058149A CN111310305A CN 111310305 A CN111310305 A CN 111310305A CN 202010058149 A CN202010058149 A CN 202010058149A CN 111310305 A CN111310305 A CN 111310305A
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李曦
仲小博
王贝贝
蒋建华
刘艳琳
郑依
李冬
赵东琦
陈孟婷
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Huazhong University of Science and Technology
Ezhou Institute of Industrial Technology Huazhong University of Science and Technology
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Abstract

The invention discloses a method and a device for acquiring oscillation variables of a solid oxide fuel cell system, wherein the method comprises the following steps: determining input variables, output variables and state variables describing the SOFC system; acquiring a plurality of partial differential equations contained in the SOFC system; establishing a state space model of the SOFC system according to the input variable, the output variable, the state variable and the plurality of partial differential equations; obtaining a subset of significant oscillations according to a state space model and experimental data of n process variables of the SOFC system with oscillations of different degrees; wherein n is a positive integer; obtaining a frequency domain grand causal relationship of the process variables in the subset of significant oscillations according to the subset of significant oscillations; constructing a qualitative model corresponding to the SOFC system according to the working principle and the working process of the SOFC system; and obtaining an oscillation root variable of the SOFC system according to the frequency domain Glanberg causal relationship and a qualitative model. The method can quickly and accurately determine the SOFC system oscillation source.

Description

Method for acquiring oscillation variable of solid oxide fuel cell system
Technical Field
The invention relates to the technical field of high-temperature fuel cells, in particular to a method for acquiring oscillation variables of a solid oxide fuel cell system.
Background
Solid Oxide Fuel Cells (SOFC), one of the most promising clean energy sources, have attracted much attention at home and abroad due to their outstanding characteristics of environmental protection, quietness, no noise, high power generation efficiency, and the like. SOFC systems consist of multiple subsystems, each containing multiple variables. When an oscillation is generated somewhere, the effect of the oscillation propagates to other locations in the system. Small scale oscillations are acceptable for some variables. However, oscillations of certain variables in SOFC systems are intolerable and, once they occur, can severely impact the useful life of the system and the performance of the system. For example, when the discharge voltage of the SOFC system oscillates, the output electrical characteristics of the SOFC system will be severely affected, the load will not work properly, and the battery life will be greatly shortened. When the temperature of the key position of the SOFC system oscillates, the material is heated unevenly, and in severe cases, the key part can crack or even fail. Fuel and air are the basis for electrochemical reactions that become unstable when the air supply system oscillates, which affects the oscillations of other process variables (e.g., voltage and temperature) and ultimately the performance of the system.
Due to more oscillation factors of the SOFC system, only the root cause of the SOFC system oscillation can be determined, and the targeted analysis and improvement can be performed, so that a method capable of determining the root cause of the SOFC system oscillation is urgently needed at present.
Disclosure of Invention
In view of the above problems, the present invention provides a method and an apparatus for acquiring oscillation variables of a solid oxide fuel cell system, which can quickly and accurately determine the oscillation source of the SOFC system.
In a first aspect, the present application provides the following technical solutions through an embodiment of the present application:
a solid oxide fuel cell system oscillation variable acquisition method comprises the following steps:
determining input variables, output variables and state variables describing the SOFC system;
establishing a state space model of the SOFC system according to the input variable, the output variable and the state variable;
obtaining a subset of significant oscillations according to the state space model and experimental data of n process variables of the SOFC system with oscillations of different degrees; wherein n is a positive integer;
obtaining a frequency domain grand cause-effect relationship of the process variable in the subset of significant oscillations from the subset of significant oscillations;
constructing a qualitative model corresponding to the SOFC system according to the working principle and the working process of the SOFC system; wherein the qualitative model is a adjacency matrix and a reachability matrix describing relationships between different process variables;
and obtaining an oscillation root variable of the SOFC system according to the frequency domain Glanberg causal relationship and the qualitative model.
Preferably, the obtaining a subset of significant oscillations from the state space model and experimental data of n process variables of the SOFC system with different degrees of oscillation comprises:
obtaining a state variable subset based on the state space model according to the state space model;
obtaining a characteristic variable subset based on experimental data according to the n experimental data of the SOFC system;
carrying out consistency comparison on the state variable subsets and the characteristic variable subsets to obtain k state variables; wherein k is a positive integer less than or equal to n;
according to the k state variables, eliminating the process variables of which the oscillation significance indexes are smaller than a preset set value from the n process variables to obtain a subset of significant oscillation; wherein the oscillatability index is indicative of a severity of a corresponding process variable oscillation.
Preferably, the obtaining, according to the state space model, a state variable subset based on the state space model includes:
performing elementary row transformation and column transformation on a system matrix of the state space model to obtain a characteristic value of the system matrix;
obtaining a state transition matrix according to the characteristic value; the state transition matrix is used for describing the state transition condition of the system;
solving a state equation of the state space model to obtain a state vector;
and sorting the characteristic values corresponding to the state vectors, eliminating state variables smaller than a preset threshold value, and obtaining the state variable subset based on the state space model.
Preferably, the obtaining a subset of characteristic variables based on experimental data from the n experimental data of the SOFC system includes:
constructing an original data matrix according to the n experimental data of the SOFC system; each set of experimental data comprises m time series data samples, wherein m is a positive integer;
calculating a covariance matrix of the original data matrix based on a principal component analysis method;
calculating an eigenvalue and an eigenvector of the covariance matrix through singular value decomposition;
and sorting the characteristic values from large to small, and selecting the largest k characteristic values to form a characteristic variable subset based on experimental data.
Preferably, the removing, according to the k state variables, the process variables of which the oscillation significance index is smaller than a preset set value from the n process variables to obtain a subset of significant oscillation includes:
respectively taking the eigenvectors corresponding to the k state variables as column vectors to form an eigenvector matrix;
calculating the oscillation significance index of each process variable data according to the eigenvector matrix;
and according to the oscillation significance index, removing the process variables of which the oscillation significance index is smaller than a preset set value from the n process variables to obtain a subset of significant oscillation.
Preferably, the obtaining a frequency domain grand cause and effect relationship of the process variable in the subset of significant oscillations from the subset of significant oscillations comprises:
establishing an autoregressive model between data corresponding to two process variables in the subset of significant oscillations;
performing a Fourier transform on the autoregressive model to obtain a frequency domain Glanberg causal relationship for the process variable in the subset of significant oscillations.
Preferably, the constructing a qualitative model corresponding to the SOFC system according to the working principle and the working process of the SOFC system includes:
determining the relevance among the n process variables according to the working principle and the working process of the SOFC system; wherein the correlation of the two process variables indicates that there is a direct effect of one process variable on the other process variable
Constructing a directed graph of the SOFC system according to the relevance among the n process variables; wherein each of the process variables is a node of the directed graph;
and calculating and obtaining the adjacency matrix and the reachability matrix according to the directed graph.
Preferably, before obtaining the frequency domain grand cause and effect relationship of the process variable in the subset of significant oscillations from the subset of significant oscillations, the method further comprises:
and carrying out stabilization processing on the process data with the unit root after dimension reduction by adopting a difference method.
In a second aspect, based on the same inventive concept, the present application provides the following technical solutions through an embodiment of the present application:
an oscillation variable acquiring apparatus of a solid oxide fuel cell system, comprising:
the description variable determining module is used for determining input variables, output variables and state variables describing the SOFC system;
the spatial model building module is used for building a state spatial model of the SOFC system according to the input variable, the output variable and the state variable;
the subset acquisition module of the significant oscillation is used for acquiring a subset of the significant oscillation according to the state space model and n experimental data of process variables of the SOFC system with different degrees of oscillation; wherein n is a positive integer;
a granger causal relationship acquisition module to obtain a frequency domain granger causal relationship of the process variable in the subset of significant oscillations according to the subset of significant oscillations;
the qualitative model building module is used for building a qualitative model corresponding to the SOFC system according to the working principle and the working process of the SOFC system; wherein the qualitative model is a adjacency matrix and a reachability matrix describing relationships between different process variables;
and the oscillation root source determining module is used for obtaining the oscillation root source variable of the SOFC system according to the frequency domain Glanberg causal relationship and the qualitative model.
In a third aspect, based on the same inventive concept, the present application provides the following technical solutions through an embodiment of the present application:
a computer-readable storage medium, having stored thereon a computer program which, when being executed by a processor, carries out the steps of the method of any of the first aspects.
In one embodiment of the present invention, a method is provided,
determining input variables, output variables and state variables describing the SOFC system; acquiring a plurality of partial differential equations contained in the SOFC system; establishing a state space model of the SOFC system according to the input variable, the output variable, the state variable and the plurality of partial differential equations; obtaining a subset of significant oscillations according to the state space model and experimental data of n process variables of the SOFC system with oscillations of different degrees; wherein n is a positive integer; therefore, the acquisition of the SOFC system process variable data is based on the whole stage of experimental operation, so that the method has practical significance and obtains more real and reliable results; and the subset of the significant oscillation is selected based on the state space model and the experimental data, so that redundant variables can be screened out, the calculation load is obviously reduced, and the efficiency of the method is improved. Obtaining a frequency domain grand cause-effect relationship of the process variable in the subset of significant oscillations from the subset of significant oscillations; constructing a qualitative model corresponding to the SOFC system according to the working principle and the working process of the SOFC system; wherein the qualitative model is a adjacency matrix and a reachability matrix describing relationships between different process variables; and obtaining an oscillation root variable of the SOFC system according to the frequency domain Glanberg causal relationship and the qualitative model. In the process of determining the oscillation root variable, the experimental historical data is combined with the system process knowledge and the topological model, so that a complete program for analyzing and diagnosing the oscillation root of the system is provided, and an accurate result can be obtained. The method can quickly and accurately determine the SOFC system oscillation source.
The foregoing description is only an overview of the technical solutions of the present invention, and the embodiments of the present invention are described below in order to make the technical means of the present invention more clearly understood and to make the above and other objects, features, and advantages of the present invention more clearly understandable.
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Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings. In the drawings:
fig. 1 is a flowchart illustrating a method for acquiring oscillation variables of a solid oxide fuel cell system according to a first embodiment of the present invention;
fig. 2 shows a schematic diagram of the effect of a subset of significant oscillations obtained by feature selection of experimental data corresponding to process variables of the SOFC system in a first embodiment of the present invention;
FIG. 3 shows a schematic diagram of the effect of frequency domain Glanberg causal results production in a first embodiment of the invention;
fig. 4 shows a directed diagram of a SOFC system in a first embodiment of the invention;
fig. 5 shows a schematic effect diagram of an adjacency matrix corresponding to a directed graph of the SOFC system in the first embodiment of the present invention;
fig. 6 is a schematic diagram showing the effect of the reachability matrix corresponding to the directed graph of the SOFC system in the first embodiment of the present invention.
Fig. 7 shows a functional block diagram of an oscillation variable acquiring apparatus of a solid oxide fuel cell system according to a second embodiment of the present invention.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
First embodiment
Referring to fig. 1, a method for acquiring oscillation variables of a solid oxide fuel cell system according to a first embodiment of the present invention is shown, where the method includes:
step S10: determining input variables, output variables and state variables describing the SOFC system; acquiring a plurality of partial differential equations contained in the SOFC system;
step S20: establishing a state space model of the SOFC system according to the input variable, the output variable, the state variable and the plurality of partial differential equations;
step S30: obtaining a subset of significant oscillations according to the state space model and experimental data of n process variables of the SOFC system with oscillations of different degrees; wherein n is a positive integer;
step S40: obtaining a frequency domain grand cause-effect relationship of the process variable in the subset of significant oscillations from the subset of significant oscillations;
step S50: constructing a qualitative model corresponding to the SOFC system according to the working principle and the working process of the SOFC system; wherein the qualitative model is a adjacency matrix and a reachability matrix describing relationships between different process variables;
step S60: and obtaining an oscillation root variable of the SOFC system according to the frequency domain Glanberg causal relationship and the qualitative model.
In steps S10-S20, according to a Solid Oxide Fuel Cell (SOFC) system model (hereinafter referred to as SOFC system) and its operating principle, input variables, output variables, and state variables describing the system are selected, and a plurality of partial differential equations in the system model are converted into a state space model describing the system dynamic characteristics. In the context of the state space model,
Figure BDA0002373484340000071
in the equation, x (t) is a state vector, u (t) is an input vector, y (t) is an output vector, a is a system matrix, B is an input matrix, C is an output matrix, and D is a direct transfer matrix. For a non-linear system, the non-linear function may be linearized at a system equilibrium point.
It should be noted that a plurality of partial differential equations in the SOFC system are determined by a system model used in practice, and are well known to those skilled in the art and will not be described in detail.
Step S30: obtaining a subset of significant oscillations according to the state space model and experimental data of n process variables of the SOFC system with oscillations of different degrees; wherein n is a positive integer.
In step S30, the state space model corresponding to the SOFC system and the data corresponding to the n process variables having different degrees of oscillation in the system power generation experiment are combined and analyzed, and the two are mutually adjuvanted to select the characteristic variables, so as to obtain a subset of significant oscillations.
Specifically, step S30 includes:
step S31: obtaining a state variable subset based on the state space model according to the state space model;
step S32: obtaining a characteristic variable subset based on experimental data according to the n experimental data of the SOFC system;
step S33: carrying out consistency comparison on the state variable subsets and the characteristic variable subsets to obtain k state variables; wherein k is a positive integer less than or equal to n;
step S34: according to the k state variables, eliminating the process variables of which the oscillation significance indexes are smaller than a preset set value from the n process variables to obtain a subset of significant oscillation; wherein the oscillatability index is indicative of a severity of a corresponding process variable oscillation.
The step S31 specifically includes the following sub-steps:
1. performing elementary row transformation and column transformation on a system matrix of the state space model to obtain a characteristic value of the system matrix;
2. obtaining a state transition matrix according to the characteristic value; the state transition matrix is used for describing the state transition condition of the system;
3. solving a state equation of the state space model to obtain a state vector;
4. and sorting the characteristic values corresponding to the state vectors, eliminating state variables smaller than a preset threshold value, and obtaining the state variable subset based on the state space model.
For example, performing elementary row transformation and column transformation on the system matrix a to obtain the rank of the system matrix a, and obtaining the eigenvalue of the system matrix a, that is, the eigenvalue of the SOFC system; according to the characteristic value of the system, a state transition matrix e capable of describing the state transition condition of the system is obtainedAt(ii) a Solving the equation of state of the SOFC system, i.e.
Figure BDA0002373484340000081
Wherein t is0Is an initial time, x0Is the initial state of the system; and sorting the characteristic values corresponding to the state vectors x (t), and eliminating the state variables smaller than a set threshold value to obtain a state variable subset based on the state space model.
In step S32, the method specifically includes the following sub-steps:
1. constructing an original data matrix according to the n experimental data of the SOFC system; each set of experimental data comprises m time series data samples, wherein m is a positive integer;
2. calculating a covariance matrix of the original data matrix based on a principal component analysis method;
3. calculating an eigenvalue and an eigenvector of the covariance matrix through singular value decomposition;
4. and sorting the characteristic values from large to small, and selecting the largest k characteristic values to form a characteristic variable subset based on experimental data.
For example, based on n sets of experimental process data, each set of process data including m time series data samples, an original data matrix X is constructed, where X ∈ Rm×n(ii) a When a principal component analysis method is used based on experimental data, singular value decomposition is carried out on a covariance matrix of an original data matrix X, and an eigenvalue lambda of the covariance matrix1、λ2...λnAnd performing descending arrangement, and selecting the characteristic variable subset of which the largest k principal component components are based on experimental data.
In step S33, the state-space-model-based state variable subset and the experimental-data-based feature variable subset are analyzed and compared to ensure consistency.
In step S34, the method specifically includes the following sub-steps:
1. and respectively taking the eigenvectors corresponding to the k state variables as column vectors to form an eigenvector matrix.
2. Calculating the oscillation significance index of each process variable data according to the eigenvector matrix; the embodiment for acquiring the oscillation significance index specifically comprises the following steps: constructing a principal component variance vector VAR2PC and a coefficient matrix LAMBDA according to the variances and coefficients of k principal components, and calculating an oscillation significance index OSI-VAR 2PC2*LAMBDA。
3. And according to the oscillation significance index, removing the process variables of which the oscillation significance index is smaller than a preset set value from the n process variables to obtain a subset of significant oscillation.
Specifically, referring to fig. 2, 7 process variables are finally screened out of 34 process variables, resulting in a subset of significant oscillations. The process variables included in the subset of significant oscillations are methane flow feedback value, bypass air pressure, reformer temperature TC0, combustor temperature TC17, combustor temperature TC18, and voltage.
Step S40: from the subset of significant oscillations, a frequency domain glottal causal relationship is obtained for the process variable in the subset of significant oscillations.
In step S40, the method specifically includes:
step S41: establishing an autoregressive model between data corresponding to two process variables in the subset of significant oscillations;
step S42: performing a Fourier transform on the autoregressive model to obtain a frequency domain Glanberg causal relationship for the process variable in the subset of significant oscillations.
For example, for the 7 process variables screened in S30, the time series x of any two of the variables is takeni(t) and xj(t) they areAre each xi(t-k),xj(t-k), k 1.. and l, establishing an autoregressive model, wherein the formula is as follows:
Figure BDA0002373484340000101
Figure BDA0002373484340000102
wherein, aii,k,aij,k,aji,k,ajj,kIs the coefficient of the model, ei(t) and ej(t) is the model prediction error and l is the model lag order.
Performing Fourier transform on the autoregressive model to obtain:
Figure BDA0002373484340000103
where H (f) is a transfer function matrix, let x bei(t) has a power spectrum of Sii(f) The residual covariance matrix is sigma, where,
Figure BDA0002373484340000104
from x at frequency fj(t) to xi(t) a frequency domain grand jean relationship, specifically:
Figure BDA0002373484340000105
further, the effect of frequency domain grand cause and effect can be seen in fig. 3.
Further, the time series for analyzing the granger' S causal must satisfy the generalized stationarity requirement, and therefore before the causality analyzing the feature-selected process variable data based on the significant oscillation subset, the method further comprises, before step S40:
and carrying out stabilization processing on the process data with the unit root after dimension reduction by using a difference method.
Step S50: constructing a qualitative model corresponding to the SOFC system according to the working principle and the working process of the SOFC system; wherein the qualitative model is a adjacency matrix and a reachability matrix describing the relationship between different process variables.
In step S50, the qualitative model specifically includes an adjacency matrix and a reachability matrix.
Specifically, the execution of step S50 includes:
step S51: determining the relevance among the n process variables according to the working principle and the working process of the SOFC system; wherein the correlation of the two process variables indicates that there is a direct effect of one process variable on the other process variable
Step S52: constructing a directed graph of the SOFC system according to the relevance among the n process variables; wherein each of the process variables is a node of the directed graph;
step S53: and calculating and obtaining the adjacency matrix and the reachability matrix according to the directed graph.
In steps S51-S53, for example, referring to fig. 4, the SOFC system operation schematic diagram is obtained according to the system operation principle and flow, 34 process variables in the figure are labeled, and these variables are used as nodes. If one variable has a direct effect on another variable, a directed edge is drawn between the two variables. And obtaining the directed graph of the system after finishing the drawing of all the nodes and the directed edges. Wherein, TC0-TC27 represent temperature information collected by thermocouples at corresponding positions.
And obtaining a corresponding adjacency matrix according to the SOFC system directed graph. The adjacency matrix is a square matrix whose rows and columns represent the process variables in the directed graph. Typically, the rows represent source variables, the columns represent affected process variables, and the binary numbers in the matrix represent directed edges. If there is a directed edge from node i to node j in the directed graph, the value of the element (i, j) of the adjacency matrix is set to 1, which indicates that node i has a direct causal relationship to node j, otherwise 0 indicates no direct causal relationship. Finally, the effect plot of the SOFC system directed graph against the corresponding adjacency matrix is presented in fig. 5, where the variable labeled green is the process variable in the significant oscillation subset.
Specifically, there are 34 nodes in the SOFC system directed graph, and assuming that the obtained adjacency matrix is X, the corresponding reachability matrix formula is as follows:
R＝A#＝(X+X2+X3+…+XN)#
wherein A is#Representing the Boolean equivalent of the matrix A, A#Can be expressed as:
Figure BDA0002373484340000121
the reachability matrix indicates any length of path from node i to node j in the directed graph. If the value of the element (i, j) of the reachability matrix is set to 1, it means that the influence caused by the node i can reach the node j.
Effect map of reachability matrix for SOFC system directed graph see fig. 6, where the variable labeled green is the process variable in the subset of significant oscillations.
Step S60: and obtaining an oscillation root variable of the SOFC system according to the frequency domain Glanberg causal relationship and the qualitative model.
In step S60, the magnitude of the Glanberg causal relationship from each variable to the others in the oscillation frequency range 0-0.05Hz is shown, for example, in FIG. 3. In this fig. 3, the (i, j) -th sub-graph shows the degree of influence of the oscillation variable j on the variable i in the frequency range. As can be seen in fig. 3, the voltage of the SOFC system is affected by a number of variables, such as the methane flow feedback value, the bypass air pressure, the bypass air flow feedback value, and TC 0. Causal feedback also exists between other variables, indicating that the SOFC system is a multivariable coupled system. From the point of view of the variable methane flow feedback value, it can be seen from the second column that it has a strong causal relationship with some other variables (including voltage, TC0, TC17, and TC18) in the oscillation frequency range. Furthermore, as can be seen in the second row of fig. 3, the methane flow feedback value is not affected by the other 6 variables in the oscillation frequency range, or the causal relationship is negligible. Therefore, it can be assumed that the methane flow feedback value has a strong causal relationship with other oscillating process variables of the SOFC system, and the methane flow feedback value is the root cause of the SOFC system oscillation. The results obtained here are also consistent with the results of fig. 2 in which the methane flow feedback value is the largest percentage of the oscillation significance indicator.
Due to the complexity of the whole SOFC system and the difficulty in determining causal relationships, the oscillation sources analyzed by data alone are not necessarily accurate, and therefore a qualitative model that can provide process knowledge is needed for the secondary analysis.
In particular, see fig. 6. The value of the element at the (i, j) position in fig. 6 is set to 1, which means that the influence caused by the node i can reach the node j. In fig. 6 it can be seen that if the oscillations are initiated from some process variable in the SOFC system, the most likely bypass air pressure or methane flow feedback values. Since these two process variables can affect the variable scores of the SOFC system more than the other four variables labeled green. And combining the results of the granger causal analysis to obtain a methane flow feedback value which is the root of SOFC system oscillation.
The method for analyzing and diagnosing the oscillation source of the solid oxide fuel cell system provided by the embodiment at least has the following technical effects or advantages:
it should be added that there are many process variables in the SOFC system, and analyzing the irrelevant process variables increases the computational burden and time. Therefore, before formal analysis and diagnosis are carried out on the SOFC system oscillation root, variables which are irrelevant to oscillation or process variables with smaller oscillation can be eliminated. In addition, the selection of the subsequent characteristic variables can adopt a mechanism model and a data-driven method, wherein the mechanism model is established on the basis of deep understanding of process characteristics, material and energy balance characteristics and the like. The parameters have very definite physical meanings and strong description capacity on system process knowledge, and a mechanism model is usually represented by a plurality of partial differential equations. In order to contain all information of the SOFC system as much as possible and reveal all motion characteristics of the system, intermediate variables in the system need to be described, and therefore, an SOFC system mechanism model is converted into a state space model describing the dynamic characteristics of the system. In addition, aiming at the problem of SOFC system oscillation root positioning, the mechanism model analysis can provide good guiding significance for the data driving method. However, for the complicated working principle and flow of the SOFC system, the equation of the mechanism model is large in scale, partial mechanism information is usually not enough to establish a complete mechanism model, or some coefficients in the expression are difficult to determine, the simulation effect of the model is affected, so that data is required to continuously modify the mechanism model. The data driving method is based on a process data driving modeling technology, does not need to clear a model structure, can consider a more comprehensive operation scene, fuses data of multiple systems, excavates deep and nonlinear correlation relationships, and improves the accuracy of results. However, the data driving effect excessively depends on the quality of modeling data, and the extrapolation capability is poor, so that the data driving method makes use of the description capability of a mechanism model to the working process of the SOFC system to make up for the defects of the data driving method, further improves the analysis and prediction capability of the data, and continues to exert the online application capability of the data driving method. Therefore, in the process of analyzing and diagnosing the oscillation root cause of the actual SOFC system, a mechanism model and data drive are required to be mutually supplemented and iterated, and process knowledge is combined with a data method, so that the accuracy of the positioning of the oscillation root cause is improved.
Determining input variables, output variables and state variables describing the SOFC system; establishing a state space model of the SOFC system according to the input variable, the output variable and the state variable; obtaining a subset of significant oscillations according to the state space model and experimental data of n process variables of the SOFC system with oscillations of different degrees; wherein n is a positive integer; therefore, the acquisition of the SOFC system process variable data is based on the whole stage of experimental operation, so that the method has practical significance and obtains more real and reliable results; and the subset of the significant oscillation is selected based on the state space model and the experimental data, so that redundant variables can be screened out, the calculation load is obviously reduced, and the efficiency of the method is improved. Obtaining a frequency domain grand cause-effect relationship of the process variable in the subset of significant oscillations from the subset of significant oscillations; constructing a qualitative model corresponding to the SOFC system according to the working principle and the working process of the SOFC system; wherein the qualitative model is a adjacency matrix and a reachability matrix describing relationships between different process variables; and obtaining an oscillation root variable of the SOFC system according to the frequency domain Glanberg causal relationship and the qualitative model. In the process of determining the oscillation root variable, the experimental historical data is combined with the system process knowledge and the topological model, so that a complete program for analyzing and diagnosing the oscillation root of the system is provided, and an accurate result can be obtained. The method can quickly and accurately determine the SOFC system oscillation source.
Second embodiment
Based on the same inventive concept, the second embodiment of the present invention provides an oscillation variable acquiring apparatus 300 of a solid oxide fuel cell system. Fig. 7 shows a functional block diagram of an oscillation variable acquiring apparatus 300 of a solid oxide fuel cell system according to a second embodiment of the present invention.
The apparatus 300, comprising:
a description variable determining module 301, configured to determine input variables, output variables, and state variables describing the SOFC system; and for obtaining a plurality of partial differential equations contained in the SOFC system;
a spatial model building module 302, configured to build a state space model of the SOFC system according to the input variable, the output variable, the state variable, and the partial differential equations;
a significant oscillation subset obtaining module 303, configured to obtain a significant oscillation subset according to the state space model and experimental data of n process variables of the SOFC system, where there are oscillations of different degrees; wherein n is a positive integer;
a granger causal relationship acquisition module 304 for obtaining a frequency domain granger causal relationship of the process variable in the subset of significant oscillations from the subset of significant oscillations;
a qualitative model constructing module 305, configured to construct a qualitative model corresponding to the SOFC system according to the working principle and the working flow of the SOFC system; wherein the qualitative model is a adjacency matrix and a reachability matrix describing relationships between different process variables;
and an oscillation root determining module 306, configured to obtain an oscillation root variable of the SOFC system according to the frequency domain glange causal relationship and the qualitative model.
It should be noted that the implementation and technical effects of the oscillation variable obtaining apparatus 300 of the solid oxide fuel cell system according to the embodiment of the present invention are the same as those of the foregoing method embodiment, and for the sake of brief description, reference may be made to the corresponding contents in the foregoing method embodiment where no mention is made in the apparatus embodiment.
The device-integrated functional modules provided by the present invention may be stored in a computer-readable storage medium if they are implemented in the form of software functional modules and sold or used as separate products. Based on such understanding, all or part of the flow of the method of implementing the above embodiments may also be implemented by a computer program, which may be stored in a computer readable storage medium and used by a processor to implement the steps of the above embodiments of the method. Wherein the computer program comprises computer program code, which may be in the form of source code, object code, an executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, usb disk, removable hard disk, magnetic disk, optical disk, computer Memory, Read-Only Memory (ROM), Random Access Memory (RAM), electrical carrier wave signals, telecommunications signals, software distribution medium, and the like. It should be noted that the computer readable medium may contain content that is subject to appropriate increase or decrease as required by legislation and patent practice in jurisdictions, for example, in some jurisdictions, computer readable media does not include electrical carrier signals and telecommunications signals as is required by legislation and patent practice.
The algorithms and displays presented herein are not inherently related to any particular computer, virtual machine, or other apparatus. Various general purpose systems may also be used with the teachings herein. The required structure for constructing such a system will be apparent from the description above. Moreover, the present invention is not directed to any particular programming language. It is appreciated that a variety of programming languages may be used to implement the teachings of the present invention as described herein, and any descriptions of specific languages are provided above to disclose the best mode of the invention.
In the description provided herein, numerous specific details are set forth. It is understood, however, that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.
Similarly, it should be appreciated that in the foregoing description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. However, the disclosed method should not be interpreted as reflecting an intention that: that the invention as claimed requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this invention.
Those skilled in the art will appreciate that the modules in the device in an embodiment may be adaptively changed and disposed in one or more devices different from the embodiment. The modules or units or components of the embodiments may be combined into one module or unit or component, and furthermore they may be divided into a plurality of sub-modules or sub-units or sub-components. All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and all of the processes or elements of any method or apparatus so disclosed, may be combined in any combination, except combinations where at least some of such features and/or processes or elements are mutually exclusive. Each feature disclosed in this specification (including any accompanying claims, abstract and drawings) may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise.
Furthermore, those skilled in the art will appreciate that while some embodiments herein include some features included in other embodiments, rather than other features, combinations of features of different embodiments are meant to be within the scope of the invention and form different embodiments. For example, in the following claims, any of the claimed embodiments may be used in any combination.
The various component embodiments of the invention may be implemented in hardware, or in software modules running on one or more processors, or in a combination thereof. Those skilled in the art will appreciate that a microprocessor or Digital Signal Processor (DSP) may be used in practice to implement some or all of the functionality of some or all of the components in an apparatus according to an embodiment of the invention. The present invention may also be embodied as apparatus or device programs (e.g., computer programs and computer program products) for performing a portion or all of the methods described herein. Such programs implementing the present invention may be stored on computer-readable media or may be in the form of one or more signals. Such a signal may be downloaded from an internet website or provided on a carrier signal or in any other form.
It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be able to design alternative embodiments without departing from the scope of the appended claims. In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim. The word "comprising" does not exclude the presence of elements or steps not listed in a claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In the unit claims enumerating several means, several of these means may be embodied by one and the same item of hardware. The usage of the words first, second and third, etcetera do not indicate any ordering. These words may be interpreted as names.

Claims (10)

1. A solid oxide fuel cell system oscillation variable acquisition method is characterized by comprising the following steps:
determining input variables, output variables and state variables describing the SOFC system; acquiring a plurality of partial differential equations contained in the SOFC system;
establishing a state space model of the SOFC system according to the input variable, the output variable, the state variable and the plurality of partial differential equations;
obtaining a subset of significant oscillations according to the state space model and experimental data of n process variables of the SOFC system with oscillations of different degrees; wherein n is a positive integer;
obtaining a frequency domain grand cause-effect relationship of the process variable in the subset of significant oscillations from the subset of significant oscillations;
constructing a qualitative model corresponding to the SOFC system according to the working principle and the working process of the SOFC system; wherein the qualitative model is a adjacency matrix and a reachability matrix describing relationships between different process variables;
and obtaining an oscillation root variable of the SOFC system according to the frequency domain Glanberg causal relationship and the qualitative model.
2. The method of claim 1 where obtaining a subset of significant oscillations from the state space model and experimental data of n process variables of the SOFC system with different degrees of oscillation comprises:
obtaining a state variable subset based on the state space model according to the state space model;
obtaining a characteristic variable subset based on experimental data according to the n experimental data of the SOFC system;
carrying out consistency comparison on the state variable subsets and the characteristic variable subsets to obtain k state variables; wherein k is a positive integer less than or equal to n;
according to the k state variables, eliminating the process variables of which the oscillation significance indexes are smaller than a preset set value from the n process variables to obtain a subset of significant oscillation; wherein the oscillatability index is indicative of a severity of a corresponding process variable oscillation.
3. The method of claim 2, wherein obtaining, from the state space model, a subset of state variables based on the state space model comprises:
performing elementary row transformation and column transformation on a system matrix of the state space model to obtain a characteristic value of the system matrix;
obtaining a state transition matrix according to the characteristic value; the state transition matrix is used for describing the state transition condition of the system;
solving a state equation of the state space model to obtain a state vector;
and sorting the characteristic values corresponding to the state vectors, eliminating state variables smaller than a preset threshold value, and obtaining the state variable subset based on the state space model.
4. The method of claim 2, where the obtaining a subset of characteristic variables based on experimental data from the n experimental data of the SOFC system comprises:
constructing an original data matrix according to the n experimental data of the SOFC system; each set of experimental data comprises m time series data samples, wherein m is a positive integer;
calculating a covariance matrix of the original data matrix based on a principal component analysis method;
calculating an eigenvalue and an eigenvector of the covariance matrix through singular value decomposition;
and sorting the characteristic values from large to small, and selecting the largest k characteristic values to form a characteristic variable subset based on experimental data.
5. The method according to claim 2, wherein the removing the process variables of which the oscillation significance index is smaller than a preset set value from the n process variables according to the k state variables to obtain the subset of significant oscillations comprises:
respectively taking the eigenvectors corresponding to the k state variables as column vectors to form an eigenvector matrix;
calculating the oscillation significance index of each process variable data according to the eigenvector matrix;
and according to the oscillation significance index, removing the process variables of which the oscillation significance index is smaller than a preset set value from the n process variables to obtain a subset of significant oscillation.
6. The method of claim 1, wherein obtaining the frequency domain grand cause and effect relationship of the process variable in the subset of significant oscillations from the subset of significant oscillations comprises:
establishing an autoregressive model between data corresponding to two process variables in the subset of significant oscillations;
performing a Fourier transform on the autoregressive model to obtain a frequency domain Glanberg causal relationship for the process variable in the subset of significant oscillations.
7. The method of claim 1, wherein constructing a corresponding qualitative model of the SOFC system based on the principles and flow of operation of the SOFC system comprises:
determining the relevance among the n process variables according to the working principle and the working process of the SOFC system; wherein the correlation of the two process variables indicates that there is a direct effect of one process variable on the other process variable
Constructing a directed graph of the SOFC system according to the relevance among the n process variables; wherein each of the process variables is a node of the directed graph;
and calculating and obtaining the adjacency matrix and the reachability matrix according to the directed graph.
8. The method of claim 1, wherein prior to obtaining the frequency domain grand cause and effect relationship for the process variable in the subset of significant oscillations from the subset of significant oscillations, further comprising:
and carrying out stabilization processing on the process data with the unit root after dimension reduction by adopting a difference method.
9. An oscillation variable acquiring apparatus of a solid oxide fuel cell system, comprising:
the description variable determining module is used for determining input variables, output variables and state variables describing the SOFC system; and for obtaining a plurality of partial differential equations contained in the SOFC system;
the spatial model building module is used for building a state spatial model of the SOFC system according to the input variable, the output variable, the state variable and the partial differential equations;
the subset acquisition module of the significant oscillation is used for acquiring a subset of the significant oscillation according to the state space model and n experimental data of process variables of the SOFC system with different degrees of oscillation; wherein n is a positive integer;
a granger causal relationship acquisition module to obtain a frequency domain granger causal relationship of the process variable in the subset of significant oscillations according to the subset of significant oscillations;
the qualitative model building module is used for building a qualitative model corresponding to the SOFC system according to the working principle and the working process of the SOFC system; wherein the qualitative model is a adjacency matrix and a reachability matrix describing relationships between different process variables;
and the oscillation root source determining module is used for obtaining the oscillation root source variable of the SOFC system according to the frequency domain Glanberg causal relationship and the qualitative model.
10. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 8.
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