Two-stage Filtered Maximum Likelihood Stochastic Gradient Identification Method for MIMO Systems

Abstract

The present application discloses a two-stage filtering maximum likelihood stochastic gradient identification method for MIMO systems, the method comprising: constructing intermediate variables for the MIMO system output error autoregressive sliding average model to determine the model intermediate variable expression; constructing a single output for the MIMO system output error autoregressive sliding average model according to the model intermediate variable expression to obtain a multi-input single-output subsystem model group; obtaining a filtering identification model through MIMO system identification model construction; constructing a criterion function for the filtering identification model to determine the identification model criterion function; obtaining the identification model initial configuration parameters through the identification model initial configuration; determining an information vector group, and determining parameter estimation data through parameter estimation comparison and judgment based on the information vector group. The present application solves the technical problems of insufficient parameter estimation accuracy, high model complexity and overfitting risk for multi-input multi-output systems through the above method.

Description

Technical Field

[0001] The present application relates to the field of adaptive control identification, and in particular to a two-stage filtering maximum likelihood stochastic gradient identification method for MIMO systems. Background Art

[0002] System identification is widely used in many scientific and engineering fields, such as aerospace, chemical engineering, adaptive control and fault diagnosis, which all require identification technology to determine the mathematical model based on the observed data. Mathematical model is the basis of controller design and system analysis. For multiple-input multiple-output (MIMO) systems, due to the complexity of their model structure, their parameter identification method and identification accuracy depend on the specific model structure and parameter quantity.

[0003] In the prior art, for random systems under colored noise interference, data filtering technology is used to filter the input and output data, and the original system with sliding average noise is converted into a system under white noise interference, which can be identified and processed by the maximum likelihood stochastic gradient (AM-ML-SG) algorithm based on an auxiliary model. However, in practical applications, the identification of multiple-input multiple-output (MIMO) systems through the above-mentioned maximum likelihood stochastic gradient algorithm has technical problems such as insufficient parameter estimation accuracy, high model complexity and the risk of overfitting. Summary of the invention

[0004] The embodiment of the present application provides a two-stage filtered maximum likelihood stochastic gradient identification method for a MIMO system, which solves the technical problems in the prior art of insufficient parameter estimation accuracy, high model complexity and the risk of overfitting for a multi-input multi-output system.

[0005] The embodiment of the present application provides a two-stage filtered maximum likelihood stochastic gradient identification method for a MIMO system, the method comprising: based on a preset MIMO system, determining an autoregressive sliding average model of an output error of the MIMO system, and constructing intermediate variables for the autoregressive sliding average model of the output error of the MIMO system to determine an expression of the intermediate variables of the model; according to the expression of the intermediate variables of the model, constructing a single output for the autoregressive sliding average model of the output error of the MIMO system to obtain a multi-input single-output subsystem model group; based on the multi-input single-output subsystem model group, obtaining a filtering identification model through MIMO system identification model construction; constructing a criterion function for the filtering identification model to determine an identification model criterion function; according to the identification model criterion function, obtaining identification model initial configuration parameters through identification model initial configuration; determining an information vector group based on the identification model initial configuration parameters and preset system input and output data; and determining parameter estimation data through parameter estimation comparison and judgment according to the information vector group.

[0006] In one implementation of the present application, intermediate variables are constructed for the MIMO system output error autoregressive sliding average model to determine the model intermediate variable expression, specifically including: based on the MIMO system output error autoregressive sliding average model, the model first intermediate variable expression is determined through state coefficient intermediate variable construction; according to the preset random white noise that obeys the Gaussian distribution, the model second intermediate variable expression is determined through colored noise configuration; based on the model first intermediate variable expression and the model second intermediate variable expression, the model intermediate variable expression is determined.

[0007] In one implementation of the present application, a single-output construction is performed on the MIMO system output error autoregressive sliding average model according to the model intermediate variable expression to obtain a multi-input single-output subsystem model group, specifically including: converting the MIMO system output error autoregressive sliding average model into a model block diagram to obtain a MIMO system output error autoregressive sliding average model block diagram; based on the MIMO system output error autoregressive sliding average model block diagram, the multi-input single-output subsystem model group is determined by distinguishing and constructing the model output; wherein the multi-input single-output subsystem model group is represented by the following formula: ;in, The system output for the MIMO system, is the output sequence number, System input for MIMO system, To input the serial number, , , , is the unit shift operator polynomial.

[0008] In one implementation of the present application, based on a multi-input single-output subsystem model group, a filter identification model is obtained through MIMO system identification model construction, which specifically includes: constructing a general identification model for the multi-input single-output subsystem model group to obtain a general identification model; based on the multi-input single-output subsystem model group, through filter identification model construction, determining the filter identification model.

[0009] In one implementation of the present application, according to the identification model criterion function, by identifying the initial configuration of the model, the initial configuration parameters of the identification model are obtained, which specifically includes: The initial value of is set to 1, and the preset parameter vector is initially configured to obtain the first configuration parameter; the fitting intermediate variable is initially configured to determine the second configuration parameter; according to the first configuration parameter and the second configuration parameter, the identification model initial configuration parameter is obtained.

[0010] In one implementation of the present application, an information vector group is determined based on the initial configuration parameters of the identification model and the preset system input and output data, specifically including: determining the information vector group construction data based on the initial configuration parameters of the identification model and the system input and output data; determining the first information vector, the second information vector, the third information vector, and the fourth information vector through the first vector model, the second vector model, the third vector model, and the fourth vector model respectively according to the information vector construction data; determining the fifth information vector through the identification moment configuration according to the preset estimated value; determining the information vector group based on the first information vector, the second information vector, the third information vector, the fourth information vector, and the fifth information vector.

[0011] In one implementation of the present application, parameter estimation data is determined based on an information vector group through parameter estimation judgment, specifically including: based on the information vector group, filtering information parameters are determined through filtering parameter analysis; wherein, the filtering information parameters include: filtering input, filtering output, and filtering information vector; maximum likelihood analysis is performed on the filtering information parameters to obtain maximum likelihood filtering information data; wherein, the maximum likelihood filtering information data includes: maximum likelihood filtering vector and filtering variables; according to the maximum likelihood filtering information data, the analysis parameters to be updated are determined through the analysis of the variables at the previous moment of the model; a first parameter estimation analysis is performed on the analysis parameters to be updated to determine the first parameter estimation data; a second parameter estimation analysis is performed on the first parameter estimation data to determine the second parameter estimation data; when the moment variable is equal to a preset threshold, the first parameter estimation data and the second parameter estimation data are set as the parameter estimation data; when the variable at the current moment is less than the preset threshold, the variable at the current moment is increased by the preset moment value, and the maximum likelihood filtering information data after the preset moment value is increased is re-analyzed as the variable at the previous moment of the model to determine the parameter estimation data.

[0012] In one implementation of the present application, based on the information vector group, the filter information parameter is determined by filter parameter analysis, specifically including: based on the information vector group, the filter output is determined by filter output analysis; wherein the filter output analysis is represented by the following formula: ;in, For the filter output, For parameter estimation, is the order; the filter input is determined by filter input analysis; wherein the filter input analysis is expressed by the following formula: ;in, is the filter input; according to the information vector group, the filter information vector is determined by filter vector analysis; wherein the filter vector analysis is represented by the following formula: ;in, is the filtering information vector, is the information vector.

[0013] In one implementation of the present application, maximum likelihood analysis is performed on the filter information parameters to obtain maximum likelihood filter information data, specifically including: based on the filter information parameters, determining the maximum likelihood filter vector through maximum likelihood filter vector analysis; performing filter variable analysis on the maximum likelihood filter vector to determine the filter variable.

[0014] In one implementation of the present application, parameter estimation analysis is performed on the analysis parameters to be updated to determine first parameter estimation data, specifically including: based on the analysis parameters to be updated, determining the updated parameter estimation data through first parameter estimation update analysis; performing variable moment analysis on the updated parameter estimation data to obtain intermediate parameters to be updated; wherein the intermediate parameters to be updated include: maximum likelihood intermediate variables, noise parameters; based on the intermediate parameters to be updated, determining the first parameter estimation data through second parameter estimation update analysis.

[0015] The embodiment of the present application provides a two-stage filtered maximum likelihood stochastic gradient identification method for a MIMO system. Through the comprehensive processing of the filtered maximum likelihood method and the stochastic gradient method, the technical problems in the prior art of insufficient parameter estimation accuracy, high model complexity and the risk of overfitting for a multi-input multi-output system are solved, and accurate parameter estimation of the multi-input multi-output system is achieved, the interference of the system caused by noise is reduced, the risk of overfitting of parameter estimation is reduced and the generalization ability of the model is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0017] Figure 1 A flow chart of a two-stage filtering maximum likelihood stochastic gradient identification method for a MIMO system provided in an embodiment of the present application;

[0018] Figure 2 A block diagram of an error autoregressive sliding average model for a MIMO system provided in an embodiment of the present application.

[0019] Figure 3 A schematic diagram of a maximum likelihood stochastic gradient algorithm provided in an embodiment of the present application.

[0020] Figure 4 A noise variation curve diagram of an experimental system provided in an embodiment of the present application.

[0021] Figure 5 A comparison diagram of estimation errors of a maximum likelihood stochastic gradient algorithm based on an auxiliary model provided in an embodiment of the present application.

[0022] Figure 6 A floating point comparison chart of a maximum likelihood stochastic gradient algorithm based on an auxiliary model provided in an embodiment of the present application. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical solution and advantages of the present application clearer, the technical solution of the present application will be clearly and completely described below in combination with the specific embodiments of the present application and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present application.

[0024] The embodiment of the present application provides a two-stage filtered maximum likelihood stochastic gradient identification method for a MIMO system. Through the comprehensive processing of the filtered maximum likelihood method and the stochastic gradient method, the technical problems in the prior art of insufficient parameter estimation accuracy, high model complexity and the risk of overfitting for a multi-input multi-output system are solved, and accurate parameter estimation of the multi-input multi-output system is achieved, the interference of the system caused by noise is reduced, the risk of overfitting of parameter estimation is reduced and the generalization ability of the model is improved.

[0025] The technical solution proposed in the embodiments of the present application is described in detail below with reference to the accompanying drawings.

[0026] Figure 1 A flow chart of a two-stage filtering maximum likelihood stochastic gradient identification method for a MIMO system provided in an embodiment of the present application. Figure 1 As shown, the embodiment of the present application provides a two-stage filtering maximum likelihood stochastic gradient identification method for a MIMO system, which specifically includes the following steps:

[0027] Step 101: Based on a preset MIMO system, determine an autoregressive sliding average model of the MIMO system output error, and construct intermediate variables for the autoregressive sliding average model of the MIMO system output error to determine an expression of the intermediate variables of the model.

[0028] Specifically, it includes: based on the MIMO system output error autoregressive sliding average model, the model's first intermediate variable expression is determined through state coefficient intermediate variable construction; according to the preset random white noise that obeys the Gaussian distribution, the model's second intermediate variable expression is determined through colored noise configuration; based on the model's first intermediate variable expression and the model's second intermediate variable expression, the model's intermediate variable expression is determined.

[0029] The present application determines the autoregressive sliding average model of the MIMO system output error based on a preset MIMO system, and constructs intermediate variables for the autoregressive sliding average model of the MIMO system output error to determine the intermediate variable expression of the model, thereby realizing the construction of the basic model and key parameters of the multi-input multi-output system, and providing the data and environment basis for the two-stage filtered maximum likelihood stochastic gradient identification.

[0030] In the examples of the present application, a detailed explanation is given by the following Example 1.

[0031] Example 1: Multiple-Input Multiple-Output (MIMO) refers to a system with multiple inputs or outputs, also known as a multivariable system. It is widely used in industrial control (chemical industry, etc. that requires automatic control) and wireless communication.

[0032] According to the system that needs to be parameter identified, the MIMO system output error autoregressive sliding average model is constructed. The mathematical representation of the model is expressed by the following formula:

[0033] (1)

[0034] in, , , …, is the input of the system; , , …, is the output of the system, , , , is the unit shift operator polynomial.

[0035] After determining the autoregressive moving average model of the MIMO system output error, it is necessary to determine the intermediate variable (one of the key parameters) for the construction of the identification model. The expression is expressed by the following formula:

[0036] (2)

[0037] (3)

[0038] in, , ;

[0039] is colored noise;

[0040] is a random white noise that follows a Gaussian distribution with a mean of 0 and a variance of ;

[0041] , is the order of the model matrix.

[0042] It should be noted that, assuming , , .when Time (the timing or moment of the system), , ; , , .

[0043] Step 102: According to the model intermediate variable expression, a single-output autoregressive sliding average model of the MIMO system output error is constructed to obtain a multi-input single-output subsystem model group.

[0044] Specifically, it includes: transforming the MIMO system output error autoregressive sliding average model into a model block diagram to obtain the MIMO system output error autoregressive sliding average model block diagram; based on the MIMO system output error autoregressive sliding average model block diagram, determining the multi-input single-output subsystem model group by distinguishing and constructing the model output; wherein the multi-input single-output subsystem model group is represented by the following formula: ;in, The system output for the MIMO system, is the output sequence number, System input for MIMO system, To input the serial number, , , , is the unit shift operator polynomial.

[0045] According to the expression of the intermediate variables of the model, the present application constructs a single-output autoregressive sliding average model of the MIMO system output error to obtain a multi-input single-output subsystem model group, thereby realizing the multi-input single-output conversion of the multi-input multi-output system and reducing the analysis and calculation amount and system complexity of the multi-input multi-output system.

[0046] Figure 2 A block diagram of an error autoregressive sliding average model of a MIMO system provided in an embodiment of the present application is explained in detail through the following Example 2 in an embodiment of the present application.

[0047] Example 2: Due to the inherent properties of the output data of the MIMO system, directly identifying and modeling the MIMO system will result in excessive computational complexity. In practical applications, this will lead to low efficiency in data analysis in production and data analysis, which in turn will affect production and other issues.

[0048] In order to solve the above problems, the present application transforms the output error autoregressive moving average model of the MIMO system into a single output form to obtain a multi-input single-output subsystem model, which is expressed by the following formula:

[0049] (4)

[0050] in, The system output for the MIMO system, is the output sequence number, System input for MIMO system, To input the serial number, , , , is the unit shift operator polynomial.

[0051] By reducing the dimension of the multi-input multi-output system, we can obtain a multi-input single-output subsystem model group, where each single output corresponds to a , and contains the information of the above intermediate parameters. Since the number of subsystems depends on the output of the multi-input multi-output system, all subsystems are used as the data basis for construction when constructing the identification model.

[0052] Step 103: Based on the multi-input single-output subsystem model group, a filter identification model is obtained by constructing a MIMO system identification model.

[0053] Specifically, it includes: constructing a general identification model for the multi-input single-output subsystem model group to obtain a general identification model; and determining a filtering identification model through filtering identification model construction based on the multi-input single-output subsystem model group.

[0054] The present application is based on a multi-input single-output subsystem model group and obtains a filter identification model through MIMO system identification model construction, thereby realizing the construction of a general identification model and a filter identification model for the MIMO system error autoregressive sliding average model.

[0055] In the examples of the present application, a detailed explanation is given by the following Example 4.

[0056] Example 4: The identification model for the MIMO system is the parameter identification model of the error autoregressive moving average model.

[0057] First, a general identification model is constructed for the multi-input single-output subsystem model group to obtain a general identification model, which is expressed by the following formula:

[0058] (5)

[0059] Based on the multi-input single-output subsystem model group, the filter identification model is constructed to determine the filter identification model, and its expression is expressed by the following formula:

[0060] (6)

[0061] Among them, the above two formulas ;

[0062] is the output under the filter identification model;

[0063] , , is the information vector;

[0064] , , is the parameter to be identified (estimated), ;

[0065] is the transpose of the information vector.

[0066] Step 104: construct a criterion function for the filter identification model and determine the identification model criterion function.

[0067] The present application constructs a criterion function for the filter identification model and determines the criterion function of the identification model, thereby realizing the construction of key parameters of the MIMO system identification model and further optimizing the identification model.

[0068] In one implementation of the present application, a detailed explanation is given through the following Example 5.

[0069] Example 5: There are two identification model criterion functions, which are expressed by the following formulas:

[0070] (7)

[0071] (8)

[0072] Step 105: Obtain the identification model initial configuration parameters by identifying the model initial configuration according to the identification model criterion function.

[0073] Specifically include: The initial value of is set to 1, and the preset parameter vector is initially configured to obtain the first configuration parameter; the fitting intermediate variable is initially configured to determine the second configuration parameter; according to the first configuration parameter and the second configuration parameter, the identification model initial configuration parameter is obtained.

[0074] The present application obtains the initial configuration parameters of the identification model by initial configuration of the identification model based on the identification model criterion function, thereby improving the operation efficiency and identification accuracy of the identification model of the multi-input and multi-output system.

[0075] In the examples of the present application, this is explained in detail through the following Example 6.

[0076] Example 6: First, let The initial value of is set to 1, and on this basis, the above parameters are configured. The specific initial values ​​are: , , ;

[0077] , , ;

[0078] , .

[0079] in, ;

[0080] is the initial parameter, and its value is generally around 10^6;

[0081] , is the intermediate variable, , are the filter output and filter input.

[0082] Step 106: Determine the information vector group based on the initial configuration parameters of the identification model and the preset system input and output data.

[0083] Specifically, it includes: determining the information vector group construction data based on the initial configuration parameters of the identification model and the system input and output data; determining the first information vector, the second information vector, the third information vector, and the fourth information vector through the first vector model, the second vector model, the third vector model, and the fourth vector model respectively according to the information vector construction data; determining the fifth information vector through the identification moment configuration according to the preset estimated value; determining the information vector group based on the first information vector, the second information vector, the third information vector, the fourth information vector, and the fifth information vector.

[0084] This application determines the information vector group based on the initial configuration parameters of the identification model and the preset system input and output data, and realizes the information vector construction for multi-input and multi-output identification.

[0085] In the examples of the present application, this is explained in detail through the following Example 7.

[0086] Example 7: First, collect the relevant input and output data of the multi-input multi-output system, and build the first vector model based on the above data, which is expressed by the following formula:

[0087] (9)

[0088] The second vector model is expressed by the following formula:

[0089] (10)

[0090] The third vector model is expressed by the following formula:

[0091] (11)

[0092] The fourth vector model is expressed by the following formula:

[0093] (12)

[0094] The fifth information vector is expressed by the following formula:

[0095] (13)

[0096] Step 107: Determine parameter estimation data through parameter estimation comparison and judgment based on the information vector group.

[0097] Specifically, it includes: determining the filter information parameters through filter parameter analysis based on the information vector group; wherein the filter information parameters include: filter input, filter output, and filter information vector; performing maximum likelihood analysis on the filter information parameters to obtain maximum likelihood filter information data; wherein the maximum likelihood filter information data includes: maximum likelihood filter vector and filter variable; determining the analysis parameters to be updated through the model's previous moment variable analysis based on the maximum likelihood filter information data; performing a first parameter estimation analysis on the analysis parameters to be updated to determine the first parameter estimation data; performing a second parameter estimation analysis on the first parameter estimation data to determine the second parameter estimation data; when the moment variable is equal to a preset threshold, setting the first parameter estimation data and the second parameter estimation data as parameter estimation data; when the current moment variable is less than the preset threshold, increasing the current moment variable by the preset moment value, and re-performing the model's previous moment variable analysis on the maximum likelihood filter information data after the preset moment value is increased to determine the parameter estimation data.

[0098] Based on the information vector group, the filter information parameters are determined through filter parameter analysis, specifically including: based on the information vector group, the filter output is determined through filter output analysis; wherein the filter output analysis is represented by the following formula: ;in, For the filter output, For parameter estimation, is the order; the filter input is determined by filter input analysis; wherein the filter input analysis is expressed by the following formula: ;in, is the filter input; according to the information vector group, the filter information vector is determined by filter vector analysis; wherein the filter vector analysis is represented by the following formula: ;in, is the filtering information vector, is the information vector.

[0099] The maximum likelihood analysis is performed on the filter information parameters to obtain the maximum likelihood filter information data, specifically including: based on the filter information parameters, determining the maximum likelihood filter vector through maximum likelihood filter vector analysis; performing filter variable analysis on the maximum likelihood filter vector to determine the filter variable.

[0100] Performing parameter estimation analysis on the analysis parameters to be updated to determine first parameter estimation data, specifically including: determining updated parameter estimation data through first parameter estimation update analysis based on the analysis parameters to be updated; performing variable moment analysis on the updated parameter estimation data to obtain intermediate parameters to be updated; wherein the intermediate parameters to be updated include: maximum likelihood intermediate variables, noise parameters; determining first parameter estimation data through second parameter estimation update analysis based on the intermediate parameters to be updated.

[0101] This application determines parameter estimation data based on the information vector group through parameter estimation comparison and judgment, reduces the noise interference of the multi-input and multi-output system, reduces the model complexity through filtering, reduces the risk of algorithm overfitting, and improves the generalization ability of the model.

[0102] Figure 3 A schematic diagram of a maximum likelihood stochastic gradient algorithm is provided for an embodiment of the present application. In the embodiment of the present application, it is explained in detail through the following Example 8.

[0103] Example 8: After determining the information vector, it is necessary to analyze it based on the gradient of the maximum likelihood itself and the stochastic gradient algorithm respectively.

[0104] First, the maximum likelihood filter vector and filter variable are solved and expressed by the following formula:

[0105] (14)

[0106] (15)

[0107] in, is the maximum likelihood filter vector, is the filter vector, is the filter output.

[0108] Then, according to the maximum likelihood filter vector and the filter variable, the maximum likelihood filter information vector is determined and expressed by the following formula:

[0109] (16)

[0110] in, is the maximum likelihood filtering information vector.

[0111] Since the maximum likelihood algorithm includes gradient analysis, the subsequent gradient algorithm needs to determine the inverse of the step size (i.e., the gradient) for the multi-input multi-output system, which is expressed by the following formula:

[0112] (17)

[0113] (18)

[0114] (19)

[0115] (20)

[0116] (twenty one)

[0117] (twenty two)

[0118] in, is the step size of the maximum likelihood gradient part, , ;

[0119] is the parameter vector;

[0120] is the step size of the gradient algorithm part, , ;

[0121] is the parameter vector, Indicates the last moment of the system.

[0122] if ,make Jump to the node of input and output data and re-perform maximum likelihood stochastic gradient identification; otherwise, terminate the algorithm and obtain parameter estimates and .

[0123] In this application, the definition , , , , , , for Point (or time) , , , , , , The estimated value of . , , , , , , for Point (or time) , , , , The estimated value of .

[0124] Figure 4 An experimental system noise variation curve diagram provided for an embodiment of the present application is explained in detail through the following Example 9.

[0125] Example 9: The noise variance used in the experiment includes: , , .

[0126] The specific configuration of the parameters to be identified is: , , , , , , , , , , , .

[0127] Coordinate horizontal axis is the time (the unit is different in different systems, it can be in steps or seconds), the vertical axis To estimate the error, it can be seen that as the time progress of the MIMO system changes, the influence of noise gradually decreases and the error becomes smaller.

[0128] Figure 5 A comparison diagram of the estimation error of the maximum likelihood stochastic gradient algorithm based on the auxiliary model provided in an embodiment of the present application is explained in detail through the following Example 10.

[0129] Example 10: The auxiliary model-based maximum likelihood stochastic gradient (AM-ML-SG) algorithm is used in multi-input multi-output system identification as an experimental comparison item for the filtering-based two-stage maximum likelihood stochastic gradient (TS-F-ML-SG) identification adopted in this application.

[0130] Among them, the horizontal axis of the coordinate is the moment of the MIMO system (or time sequence, representing the time change, the unit is different in different systems, it can be a step size or a second), the vertical axis This is the estimation error.

[0131] It can be seen that only when the time is about 200, the estimation error of the maximum likelihood stochastic gradient identification based on the auxiliary model is smaller than that of this scheme, but at this time the estimation errors of both are relatively large.

[0132] At time 500, the error estimates of the two are similar, but as time goes on, the estimation error of the two-stage maximum likelihood stochastic gradient identification based on filtering is smaller than that of the maximum likelihood stochastic gradient identification based on the auxiliary model, and the difference between the two is obvious.

[0133] It can be proved that the two-stage maximum likelihood stochastic gradient identification based on filtering can have higher performance and efficiency in error identification and noise filtering of multi-input multi-output systems.

[0134] Figure 6 A floating point comparison chart of a maximum likelihood stochastic gradient algorithm based on an auxiliary model provided in an embodiment of the present application is explained in detail through the following Example 11.

[0135] Example 11: The auxiliary model-based maximum likelihood stochastic gradient (AM-ML-SG) algorithm is used in multi-input multi-output system identification as an experimental comparison item for the filtering-based two-stage maximum likelihood stochastic gradient (TS-F-ML-SG) identification adopted in this application.

[0136] Among them, the vertical axis of the coordinate is a floating point number with an order of magnitude of 10^6. The floating point number represents the size of the parameter identification calculation amount of this multi-input and multi-output system; the left sides of the horizontal axis are r and m, r is the input number, and m is the output number. The above coordinate axis parameters have no units (the unit is 1).

[0137] It can be seen that under the same circumstances, the floating-point number of the two-stage maximum likelihood stochastic gradient based on filtering is smaller than that of the maximum likelihood stochastic gradient based on the auxiliary model. In practical applications, the computational complexity of the identification model will also be lower, which can improve efficiency while preventing overfitting.

[0138] Each embodiment in this application is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the IoT device and medium embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiments.

[0139] The system and medium provided in the embodiments of the present application correspond one-to-one to the method. Therefore, the system and medium also have similar beneficial technical effects to the corresponding methods. Since the beneficial technical effects of the methods have been described in detail above, the beneficial technical effects of the system and medium will not be repeated here.

[0140] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0141] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0142] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1A function specified in one or more boxes.

[0143] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0144] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0145] Memory may include non-permanent storage in a computer-readable medium, in the form of random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of a computer-readable medium.

[0146] Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0147] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0148] The above are only embodiments of the present application and are not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included within the scope of the claims of the present application.

Claims

1. A two-stage filtered maximum likelihood stochastic gradient identification method for MIMO systems, characterized in that: The method comprises: Based on a preset MIMO system, determine an autoregressive sliding average model of the MIMO system output error, and construct intermediate variables for the autoregressive sliding average model of the MIMO system output error to determine an expression of the intermediate variables of the model; According to the intermediate variable expression of the model, a single-output construction is performed on the MIMO system output error autoregressive sliding average model to obtain a multi-input single-output subsystem model group; Based on the multi-input single-output subsystem model group, a filter identification model is obtained by constructing a MIMO system identification model; Constructing a criterion function for the filtering identification model and determining the criterion function of the identification model; According to the identification model criterion function, by identifying the initial configuration of the model, an identification model initial configuration parameter is obtained; Determining an information vector group based on the initial configuration parameters of the identification model and preset system input and output data; According to the information vector group, parameter estimation data is determined through parameter estimation comparison and judgment.

2. A two-stage filtered maximum likelihood stochastic gradient identification method for MIMO systems according to claim 1, characterized in that: The intermediate variables of the MIMO system output error autoregressive sliding average model are constructed to determine the model intermediate variable expressions, specifically including: Based on the MIMO system output error autoregressive sliding average model, the first intermediate variable expression of the model is determined by constructing the state coefficient intermediate variable; According to the preset random white noise that obeys Gaussian distribution, the expression of the second intermediate variable of the model is determined through the configuration of colored noise; The model intermediate variable expression is determined based on the model first intermediate variable expression and the model second intermediate variable expression.

3. The two-stage filtered maximum likelihood stochastic gradient identification method for MIMO systems according to claim 1, characterized in that: According to the model intermediate variable expression, the MIMO system output error autoregressive sliding average model is constructed with a single output to obtain a multi-input single-output subsystem model group, which specifically includes: The MIMO system output error autoregressive sliding average model is converted into a model block diagram to obtain a MIMO system output error autoregressive sliding average model block diagram; Based on the error autoregressive sliding average model block diagram of the MIMO system, the multi-input single-output subsystem model group is determined by distinguishing and constructing the model output; wherein the multi-input single-output subsystem model group is represented by the following formula: in, The system output for the MIMO system, is the output sequence number, System input for MIMO system, To input the serial number, , , , is the unit shift operator polynomial.

4. The two-stage filtered maximum likelihood stochastic gradient identification method for MIMO systems according to claim 1, characterized in that: Based on the multi-input single-output subsystem model group, a filter identification model is obtained through MIMO system identification model construction, which specifically includes: Constructing a general identification model for the multi-input single-output subsystem model group to obtain a general identification model; Based on the multi-input single-output subsystem model group, the filter identification model is determined through filter identification model construction.

5. The two-stage filtered maximum likelihood stochastic gradient identification method for MIMO systems according to claim 1, characterized in that: According to the identification model criterion function, the identification model initial configuration parameters are obtained by identifying the model initial configuration, which specifically include: Will The initial value of is set to 1, and the preset parameter vector is initially configured to obtain a first configuration parameter; Performing initial parameter configuration on the fitting intermediate variables to determine the second configuration parameters; The identification model initial configuration parameters are obtained according to the first configuration parameters and the second configuration parameters.

6. The two-stage filtered maximum likelihood stochastic gradient identification method for MIMO systems according to claim 1, characterized in that: Based on the initial configuration parameters of the identification model and the preset system input and output data, an information vector group is determined, specifically including: Determining information vector group construction data based on the identification model initial configuration parameters and the system input and output data; Constructing data according to the information vector, determining a first information vector, a second information vector, a third information vector, and a fourth information vector through a first vector model, a second vector model, a third vector model, and a fourth vector model respectively; Determining a fifth information vector by identifying the time configuration according to the preset estimated value; The information vector group is determined based on the first information vector, the second information vector, the third information vector, the fourth information vector, and the fifth information vector.

7. A two-stage filtered maximum likelihood stochastic gradient identification method for MIMO systems according to claim 1, characterized in that: According to the information vector group, parameter estimation data is determined through parameter estimation, specifically including: Based on the information vector group, filter information parameters are determined through filter parameter analysis; wherein the filter information parameters include: filter input, filter output, and filter information vector; Performing maximum likelihood analysis on the filtering information parameters to obtain maximum likelihood filtering information data; wherein the maximum likelihood filtering information data includes: a maximum likelihood filtering vector and a filtering variable; According to the maximum likelihood filtering information data, the analysis parameters to be updated are determined by analyzing the variables of the model at the previous moment; Performing a first parameter estimation analysis on the analysis parameter to be updated to determine first parameter estimation data; performing a second parameter estimation analysis on the first parameter estimation data to determine second parameter estimation data; When the moment variable is equal to a preset threshold, setting the first parameter estimation data and the second parameter estimation data to the parameter estimation data; When the variable at the current moment is less than the preset threshold, the variable at the current moment is increased by the preset moment value, and the maximum likelihood filtering information data after the increase of the preset moment value is re-analyzed as the variable at the previous moment of the model to determine the parameter estimation data.

8. The two-stage filtered maximum likelihood stochastic gradient identification method for MIMO systems according to claim 7, characterized in that: Based on the information vector group, filtering information parameters are determined through filtering parameter analysis, specifically including: Based on the information vector group, the filter output is determined by filter output analysis; wherein the filter output analysis is represented by the following formula: in, is the filtering output, For parameter estimation, is the order; The filter input is determined by filter input analysis; wherein the filter input analysis is represented by the following formula: in, is the filtering input; According to the information vector group, the filtering information vector is determined by filtering vector analysis; wherein the filtering vector analysis is represented by the following formula: in, is the filtering information vector, is the information vector.

9. The two-stage filtered maximum likelihood stochastic gradient identification method for MIMO systems according to claim 7, characterized in that: Performing maximum likelihood analysis on the filtering information parameters to obtain maximum likelihood filtering information data specifically includes: Based on the filter information parameters, determining the maximum likelihood filter vector by maximum likelihood filter vector analysis; Perform filter variable analysis on the maximum likelihood filter vector to determine the filter variable.

10. The two-stage filtered maximum likelihood stochastic gradient identification method for MIMO systems according to claim 7, characterized in that: Performing parameter estimation analysis on the analysis parameters to be updated to determine first parameter estimation data specifically includes: Based on the analysis parameters to be updated, determining update parameter estimation data through a first parameter estimation update analysis; Performing variable time analysis on the update parameter estimation data to obtain the intermediate parameters to be updated; wherein the intermediate parameters to be updated include: maximum likelihood intermediate variables and noise parameters; According to the intermediate parameter to be updated, the first parameter estimation data is determined through second parameter estimation update analysis.

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