A systematic optimization method for quenching large-diameter bearings based on multi-model set member estimation.

Abstract

This invention relates to a method and system for optimizing the quenching of large-diameter bearings based on multi-model set membership estimation. The method includes: determining multiple state parameters of the target quenching measurement system; constructing a system model based on the fusion of multiple set membership estimation models using the state parameters and a fully symmetric multi-cell method, employing a Kalman filter; determining the predicted state equation and probability density function of each set membership estimation model; updating the probability density function of the predicted set of each set membership estimation model according to the dimension of the output matrix of the real-time quenching measurement system; calculating the predicted set of the system model using Bayes' theorem based on the probability density function of the predicted set of each set membership estimation model; and solving for the optimal gain matrix of the target quenching measurement system by minimizing the set radius based on the predicted set and error set of the system model. This invention improves the stability and robustness of the optimized control for quenching large-diameter bearings through multi-model set membership estimation and Bayes' theorem.

Description

Technical Field

[0001] This invention belongs to the fields of quenching technology and nonlinear control technology, specifically relating to a quenching optimization method and system for large-diameter bearings based on multi-model set member estimation. Background Technology

[0002] Large-diameter bearings play a crucial role in heavy machinery and aerospace applications, and their quenching process directly affects their fatigue life and performance. Traditional quenching optimization methods often rely on a single model, making it difficult to handle complex process uncertainties. The goal of quenching optimization may be to minimize residual stress or temperature gradients to reduce deformation and cracking. Collective estimation, a control theory technique, is used to estimate the state of a system when uncertainties exist, and is particularly suitable for handling measurement noise or uncertainties in model parameters.

[0003] In multi-model estimation, system uncertainty is typically used to represent unknown but bounded noise / disturbances and initial conditions. Unlike standard linear time-varying models, uncertain linear time-varying systems are considered a class of uncertain systems because their parameters cannot be measured during execution. Therefore, it is essential to study the multi-model estimation problem for uncertain linear systems containing unknown but bounded noise. Summary of the Invention

[0004] To improve the stability and robustness of quenching optimization control for large-diameter bearings, a first aspect of this invention provides a quenching optimization method for large-diameter bearings based on multi-model set member estimation, comprising:

[0005] Multiple state parameters of the target quenching measurement system are determined. Using the state parameters and a fully symmetric multi-cell method, a discrete-time uncertain system and a first set of uncertain parameters are constructed. Based on the coefficient matrix of the uncertain system, a system model based on the fusion of multiple set-membership estimation models is constructed using the Kalman filter method. According to the system model and the first set of uncertain parameters, the predicted state equation, a second set of uncertain parameters, and a probability density function for each set-membership estimation model are determined. Based on the dimension of the output matrix of the real-time quenching measurement system and the second set of uncertain parameters, the probability density function of the predicted set of each set-membership estimation model is updated. Based on the probability density function of the predicted set of each set-membership estimation model, the prediction set of the system model is calculated using Bayes' theorem. Based on the prediction set and error set of the system model, the optimal gain matrix of the target quenching measurement system is solved by minimizing the set radius.

[0006] In some embodiments of the present invention, determining the prediction state equation, the second uncertainty parameter set, and the probability density function of each member estimation model based on the system model and the first uncertainty parameter set includes: determining the prediction state equation of each member estimation model based on the system model and the first uncertainty parameter set; updating the prediction set of each member estimation model based on the state estimate of the system model at the previous time step; defining the residual set; and determining the probability density function of each member estimation model using Bayes' theorem based on the updated prediction set and the residual set.

[0007] In some embodiments of the present invention, updating the probability density function of each set member estimation model prediction set based on the dimension of the output matrix of the real-time quenching measurement system and the second uncertain parameter set includes: determining the random variable of the probability density function of each set member estimation model prediction set based on the second uncertain parameter set; determining the spatial dimension of the value range of the probability density function based on the dimension of the output matrix of the real-time quenching measurement system; and updating the probability density function of each set member estimation model prediction set based on the spatial dimension of the value range and the random variable.

[0008] Furthermore, the step of updating the probability density function of the prediction set of each set member estimation model based on the spatial dimension of the value range and random variables includes: if the dimension of the output matrix is ​​1, then the probability density function is a uniform distribution of the prediction set within the domain interval; if the dimension of the output matrix is ​​2, then the probability density function is a uniform distribution within the area domain of the prediction set; if the dimension of the output matrix is ​​greater than or equal to 3, then the probability density function is a uniform distribution within the volume domain of the prediction set.

[0009] In some embodiments of the present invention, the step of solving the optimal gain matrix of the target quenching measurement system by minimizing the set radius based on the prediction set and error set of the system model includes: updating the center matrix and generator matrix of each set member estimation model prediction set based on the prediction set and error set of the system model; and solving the optimal gain matrix of the target quenching measurement system by minimizing the set radius based on the coefficient matrix of the system model, the updated center matrix and generator matrix.

[0010] Furthermore, the step of solving the optimal gain matrix of the target quenching measurement system by minimizing the set radius based on the coefficient matrix, the updated center matrix, and the generator matrix of the system model includes: solving the optimal gain matrix of the target quenching measurement system by minimizing the set radius and linear matrix inequalities based on the coefficient matrix, the updated center matrix, and the generator matrix of the system model.

[0011] A second aspect of the present invention provides a large-diameter bearing quenching optimization system based on multi-model set member estimation, comprising: a first determining module for determining multiple state parameters of a target quenching measurement system; constructing a discrete-time uncertain system and a first set of uncertain parameters using the state parameters and a fully symmetric multi-cell method; a second determining module for constructing a system model based on the coefficient matrix of the uncertain system using a Kalman filter method; determining the prediction state equation, a second set of uncertain parameters, and a probability density function for each set member estimation model according to the system model and the first set of uncertain parameters; an updating module for updating the probability density function of the prediction set of each set member estimation model according to the dimension of the output matrix of the real-time quenching measurement system and the second set of uncertain parameters; a calculation module for calculating the prediction set of the system model using Bayes' theorem based on the probability density function of the prediction set of each set member estimation model; and a solving module for solving the optimal gain matrix of the target quenching measurement system by minimizing the set radius based on the prediction set and error set of the system model.

[0012] A third aspect of the present invention provides an electronic device comprising: one or more processors; and a storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the large-diameter bearing quenching optimization method based on multi-model set member estimation provided in the first aspect of the present invention.

[0013] In a fourth aspect, the present invention provides a computer-readable medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the large-diameter bearing quenching optimization method based on multi-model set member estimation provided in the first aspect of the present invention.

[0014] The beneficial effects of this invention are:

[0015] This invention addresses the linear uncertain system of quenching large-diameter bearings with unknown noise statistical characteristics. Based on Bayesian theory, it proposes a multi-model set membership estimation method to solve the state estimation problem of linear uncertain systems. Furthermore, based on the proposed set membership estimation probability density function, this invention also provides a new model probability update formula; by minimizing the set P-radius, the designed observer gain matrix can guarantee the stability of the quenching process system control. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the basic process of the large-diameter bearing quenching optimization method based on multi-model set member estimation in some embodiments of the present invention;

[0017] Figure 2This is a schematic diagram illustrating the specific process of the large-diameter bearing quenching optimization method based on multi-model set member estimation in some embodiments of the present invention.

[0018] Figure 3 This is a schematic diagram of the structure of a large-diameter bearing quenching optimization system based on multi-model set member estimation in some embodiments of the present invention;

[0019] Figure 4 This is a schematic diagram of the structure of an electronic device in some embodiments of the present invention. Detailed Implementation

[0020] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0021] refer to Figure 1 and Figure 2 In a first aspect of the present invention, a method for optimizing the quenching of large-diameter bearings based on multi-model set member estimation is provided, comprising:

[0022] S100. Determine multiple state parameters of the target quenching measurement system; construct an uncertain system and a first set of uncertain parameters based on discrete time using the state parameters and the fully symmetric multicell method;

[0023] S200. Based on the coefficient matrix of the uncertain system, a system model based on the fusion of multiple set-membership estimation models is constructed using the Kalman filtering method; according to the system model and the first set of uncertain parameters, the prediction state equation, the second set of uncertain parameters, and the probability density function of each set-membership estimation model are determined.

[0024] S300. Based on the dimension of the output matrix of the real-time quenching measurement system and the second set of uncertain parameters, update the probability density function of the prediction set of each set member estimation model;

[0025] S400. Based on the probability density function of the prediction set of each set member estimation model, calculate the prediction set of the system model using Bayes' theorem;

[0026] S500. Based on the prediction set and error set of the system model, the optimal gain matrix of the target quenching measurement system is solved by minimizing the set radius.

[0027] In step S100 of some embodiments of the present invention, multiple state parameters of the target quenching measurement system are determined; and an uncertain system based on discrete time and a first set of uncertain parameters are constructed using the state parameters and the fully symmetric multicellular method.

[0028] Specifically, we establish an uncertain system model, considering the following discrete-time linear system:

[0029] (1)

[0030] (2)

[0031] in, For system status, To control the input, For system output, For system interference, For measuring noise.

[0032] Assumption , , ,in, Indicates the center point as The generating matrix is The fully symmetrical multicellular form, i.e. , . , and With the same definition, subsequent fully symmetric polytopes are also represented and calculated using the same method. (Subscript) This indicates that the corresponding matrix contains parameter uncertainties. N The number of models.

[0033] For example, Having form ,in, It is a natural frequency. However, the designer did not know this. The exact value is only known. Therefore, the matrix It contains uncertainty and has three distinct subsystems.

[0034] Assumption Matrix of this Invention At time k, it can be expressed in the following form:

[0035] (3)

[0036] in, , .

[0037] More specifically, the dynamics of the quenching process are described by the heat conduction equation:

[0038] ;

[0039] Consider boundary conditions (such as convection cooling):

[0040] ,

[0041] To facilitate estimation, it is discretized into a finite-dimensional linear system. Assume the bearing is simplified to a one-dimensional rod, discretized into n points, with a state vector... Using the finite difference method, the dynamics of the interior points are:

[0042] ;

[0043] Boundary points (such as) = 1) Consider convection:

[0044] ;

[0045] similar processing Tn Its matrix form is:

[0046] ,

[0047] in: It is a tridiagonal matrix, element-dependent. And the thermal conductivity h. Including boundary conditions T ∞ terms, if T If ∞ is the control input, then = T ∞.

[0048] Furthermore, the measurement equation is:

[0049] ,

[0050] C is where the measurement point is selected (e.g., surface temperature). It is measurement noise, defined as ; This represents the state vector, and the discretized temperature distribution, in °C. Represents the system matrix, dependent on parameters Reflecting thermal diffusion and boundary conditions, Indicates density, Indicates specific heat capacity; Represents the input matrix, if = T ∞ will affect the boundary temperature dynamics. C represents the measurement matrix, defined as a subset of the identity matrix, and is used to select the sensor location. This represents the measurement noise, and its error. Determined by sensor accuracy; This represents an uncertain set of parameters, which may include... .

[0051] It is understandable that during the quenching process of large-diameter bearings, the ensemble estimation considers thermal properties, thermal conductivity, geometric dimensions, initial temperature distribution, quenching medium temperature, and measurements as state parameters. The uncertainties of these state parameters are handled through a multi-model framework to ensure the robustness of the state estimation. Based on the discretization of the heat conduction equation, it is suitable for optimizing residual stress or temperature gradients, and its adaptability offers potential for industrial applications.

[0052] In step S201 of some embodiments of the present invention, a system model based on the fusion of multiple set member estimation models is constructed by Kalman filtering based on the coefficient matrix of the uncertain system.

[0053] Specifically, define Let the parameter set (first parameter set) be assumed. have N Two different values, namely .

[0054] Therefore, the first i Each model corresponds to an uncertain set of parameters. , .

[0055] If so, the system state estimator is expressed as:

[0056] (4)

[0057] in, L The estimator gain matrix, yes N Each sub-model predicts the result of state fusion.

[0058] In step S202 of some embodiments of the present invention, determining the prediction state equation, the second set of uncertain parameters, and the probability density function of each set member estimation model based on the system model and the first set of uncertain parameters includes:

[0059] S2021. Determine the prediction state equation for each member estimation model based on the system model and the first set of uncertain parameters; S2022. Update the prediction set for each member estimation model based on the state estimate of the system model at the previous time step;

[0060] Specifically, the predicted state corresponding to each sub-model is calculated by the following formula:

[0061] (5)

[0062] in, For the first i The state prediction value of the estimator .

[0063] If ink The estimated set at time -1 satisfies , then the first i An estimator in k The prediction set at time satisfies ,in

[0064] , (6)

[0065] S2023. Define the residual set;

[0066] Specifically, define You can get

[0067] ,

[0068] in, , .

[0069] S2024. Based on the updated prediction set and residual set, determine the probability density function of the estimation model for each set member using Bayes' theorem.

[0070] Specifically, according to Bayes' theorem, we can obtain

[0071] (7)

[0072] in, Let be the probability density function. This represents a probability function.

[0073] if ,So Depend on Confirmed. Therefore, we can obtain... , If the state is estimated It is accurate, then there is and .

[0074] Considering You can get .because Therefore, variables In the set The middle follows a uniform distribution.

[0075] In step S300 of some embodiments of the present invention, updating the probability density function of the prediction set of each set member estimation model based on the dimension of the output matrix of the real-time quenching measurement system and the second set of uncertain parameters includes:

[0076] S301. Based on the second set of uncertain parameters, determine the random variable of the probability density function of the prediction set of each set member estimation model; S302. Based on the dimension of the output matrix of the real-time quenching measurement system, determine the spatial dimension of the value range of the probability density function; S303. Based on the spatial dimension of the value range and the random variable, update the probability density function of the prediction set of each set member estimation model.

[0077] Furthermore, the step of updating the probability density function of the prediction set of each set member estimation model based on the spatial dimension of the value range and random variables includes: if the dimension of the output matrix is ​​1, then the probability density function is a uniform distribution of the prediction set within the domain interval; if the dimension of the output matrix is ​​2, then the probability density function is a uniform distribution within the area domain of the prediction set; if the dimension of the output matrix is ​​greater than or equal to 3, then the probability density function is a uniform distribution within the volume domain of the prediction set.

[0078] Specifically, consider the following three cases: , and , .

[0079] 1)

[0080] In this case, the set It can be represented as an interval, that is Therefore, the probability density function It can be designed in the following form:

[0081] (8)

[0082] It can be seen that: ,

[0083] ,so The conditions for satisfying the probability density function are met.

[0084] 2)

[0085] In this case, the probability density function It can be written as Therefore, the corresponding probability density function It can be designed in the following form:

[0086] (9)

[0087] in, For set The area. It can be seen that, ,

[0088]

[0089] so The conditions for satisfying the probability density function are met.

[0090] 3) ,

[0091] In this case, the probability density function It can be written as Therefore, the corresponding probability density function It can be designed in the following form:

[0092] (10)

[0093] in, For set The volume. It can be seen that... ,

[0094]

[0095]

[0096] ,so The conditions for satisfying the probability density function are met. Specifically, if... It is a diagonal matrix, that is So, the set It can be represented as ,in , , , Therefore, the corresponding probability density function can be designed as follows:

[0097] (11)

[0098] It can be seen from the above formula ,

[0099]

[0100]

[0101] .

[0102] so The conditions for satisfying the probability density function are met.

[0103] In step S400 of some embodiments of the present invention, the prediction set of the system model is calculated by Bayes' theorem based on the probability density function of the prediction set of each set member estimation model.

[0104] Specifically, according to Bayesian theory, there is .exist k Time, measurement output It is definite and known, therefore , .

[0105] Based on this, the state estimation set at time k can be obtained. ,

[0106] , (12)

[0107] in, , For an identity matrix of appropriate dimension,

[0108] , ,

[0109] , .

[0110] In step S500 of some embodiments of the present invention, the step of solving the optimal gain matrix of the target quenching measurement system by minimizing the set radius based on the prediction set and error set of the system model includes:

[0111] S501. Based on the prediction set and error set of the system model, update the center matrix and generator matrix of the prediction set of each set member estimation model;

[0112] Specifically, the gain matrix is ​​calculated based on the estimated error set.

[0113] Define estimation error Then we have:

[0114] (13)

[0115] in, , .

[0116] if , and Then there is ,

[0117] (14)

[0118] (15)

[0119] in, , , , .

[0120] S502. Based on the coefficient matrix, updated center matrix, and generator matrix of the system model, solve for the optimal gain matrix of the target quenching measurement system by minimizing the set radius.

[0121] Specifically, the step of solving for the optimal gain matrix of the target quenching measurement system by minimizing the set radius based on the coefficient matrix, the updated center matrix, and the generator matrix of the system model includes: solving for the optimal gain matrix of the target quenching measurement system by minimizing the set radius and linear matrix inequalities based on the coefficient matrix, the updated center matrix, and the generator matrix of the system model.

[0122] because and Since it is unknown, the above formula can be transformed into the following formula to obtain it.

[0123] (16)

[0124] (17)

[0125] in, , .

[0126] The matrix can be obtained by solving the following matrix inequality. X and positive definite symmetric matrix P Then the observer gain matrix L It can be done To obtain.

[0127] (18)

[0128] in, , .

[0129] Example 2

[0130] refer to Figure 3 A second aspect of the present invention provides a large-diameter bearing quenching optimization system 1 based on multi-model set member estimation, comprising:

[0131] The first determining module 11 is used to determine multiple state parameters of the target quenching measurement system; and to construct an uncertain system based on discrete time and a first set of uncertain parameters by using the state parameters and the fully symmetric polytope method.

[0132] The second determining module 12 is used to construct a system model based on the coefficient matrix of the uncertain system by using the Kalman filtering method, which is based on the fusion of multiple set member estimation models; and to determine the prediction state equation, the second set of uncertain parameters, and the probability density function of each set member estimation model according to the system model and the first set of uncertain parameters.

[0133] Update module 13 is used to update the probability density function of each set member estimation model prediction set based on the dimension of the output matrix of the real-time quenching measurement system and the second set of uncertain parameters.

[0134] Calculation module 14 is used to calculate the prediction set of the system model based on the probability density function of the prediction set of the estimation model for each set member using Bayes' theorem.

[0135] The solver module 15 is used to solve the optimal gain matrix of the target quenching measurement system by minimizing the set radius based on the prediction set and error set of the system model.

[0136] Furthermore, the second determining module 12 includes: a first determining unit, used to determine the prediction state equation of each member estimation model based on the system model and the first uncertain parameter set; an updating unit, used to update the prediction set of each member estimation model based on the state estimate of the system model at the previous time step; and a second determining unit, used to define the residual set, and to determine the probability density function of each member estimation model by Bayes' theorem based on the updated prediction set and the residual set.

[0137] Example 3

[0138] refer to Figure 4 In a third aspect, the present invention provides an electronic device comprising: one or more processors; and a storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the large-diameter bearing quenching optimization method based on multi-model set member estimation of the first aspect of the present invention.

[0139] Electronic device 500 may include a processing unit (e.g., a central processing unit, a graphics processing unit, etc.) 501, which can perform various appropriate actions and processes according to a program stored in read-only memory (ROM) 502 or a program loaded from storage device 508 into random access memory (RAM) 503. The RAM 503 also stores various programs and data required for the operation of electronic device 500. The processing unit 501, ROM 502, and RAM 503 are interconnected via bus 504. An input / output (I / O) interface 505 is also connected to bus 504.

[0140] Typically, the following devices can be connected to I / O interface 505: input devices 506 including, for example, touchscreens, touchpads, keyboards, mice, cameras, microphones, accelerometers, gyroscopes, etc.; output devices 507 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 508 including, for example, hard disks; and communication devices 509. Communication device 509 allows electronic device 500 to communicate wirelessly or wiredly with other devices to exchange data. Although Figure 4 An electronic device 500 with various devices is shown; however, it should be understood that it is not required to implement or possess all of the devices shown. More or fewer devices may be implemented or possessed alternatively. Figure 4 Each box shown can represent a device or multiple devices as needed.

[0141] Specifically, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device 509, or installed from a storage device 508, or installed from a ROM 502. When the computer program is executed by a processing device 501, it performs the functions defined in the methods of embodiments of this disclosure. It should be noted that the computer-readable medium described in embodiments of this disclosure can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In embodiments of this disclosure, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In embodiments of this disclosure, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. Program code contained on a computer-readable medium may be transmitted using any suitable medium, including but not limited to: wires, optical fibers, RF (radio frequency), etc., or any suitable combination thereof.

[0142] The aforementioned computer-readable medium may be included in the aforementioned electronic device; or it may exist independently and not assembled into the electronic device. The aforementioned computer-readable medium carries one or more computer programs, which, when executed by the electronic device, cause the electronic device to:

[0143] Computer program code for performing the operations of embodiments of this disclosure can be written in one or more programming languages ​​or a combination thereof. Programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, C++, and Python—and conventional procedural programming languages—such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0144] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0145] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the quenching of large-diameter bearings based on multi-model set member estimation, characterized in that, include: Determine multiple state parameters of the target quenching measurement system; By using state parameters and the fully symmetric polytope method, an uncertain system based on discrete time and a set of first uncertain parameters are constructed. Based on the coefficient matrix of the uncertain system, a system model based on the fusion of multiple set membership estimation models is constructed using the Kalman filtering method; according to the system model and the first set of uncertain parameters, the prediction state equation, the second set of uncertain parameters, and the probability density function of each set membership estimation model are determined. Based on the dimension of the output matrix of the real-time quenching measurement system and the second set of uncertain parameters, update the probability density function of the prediction set of each set member estimation model; Based on the probability density function of the prediction set of each set member estimation model, the prediction set of the system model is calculated using Bayes' theorem; Based on the prediction set and error set of the system model, the optimal gain matrix of the target quenching measurement system is solved by minimizing the set radius.

2. The quenching optimization method for large-diameter bearings based on multi-model set member estimation according to claim 1, characterized in that, The step of determining the prediction state equation, the second set of uncertain parameters, and the probability density function of each set member estimation model based on the system model and the first set of uncertain parameters includes: Based on the system model and the first set of uncertain parameters, determine the predicted state equation of each set member estimation model; Based on the state estimate of the system model at the previous time step, update the prediction set of the estimation model for each set member; Define the residual set; based on the updated prediction set and residual set, determine the probability density function of the estimation model for each set member using Bayes' theorem.

3. The large-diameter bearing quenching optimization method based on multi-model set member estimation according to claim 1, characterized in that, The step of updating the probability density function of the prediction set of each set member estimation model based on the dimension of the output matrix of the real-time quenching measurement system and the second set of uncertain parameters includes: Based on the second set of uncertain parameters, determine the random variables of the probability density function of the predicted set for each set member estimation model; Based on the dimension of the output matrix of the real-time quenching measurement system, the spatial dimension of the value range of the probability density function is determined; based on the spatial dimension of the value range and the random variables, the probability density function of the prediction set of each set member estimation model is updated.

4. The quenching optimization method for large-diameter bearings based on multi-model set member estimation according to claim 3, characterized in that, The method for updating the probability density function of the predicted set for each set member estimation model, based on the spatial dimension of the value range and random variables, includes: If the dimension of the output matrix is ​​1, then the probability density function is a uniform distribution of the prediction set within the domain. If the dimension of the output matrix is ​​2, then the probability density function is a uniform distribution within the area of ​​the prediction set; If the dimension of the output matrix is ​​greater than or equal to 3, then the probability density function is a uniform distribution within the volume domain of the prediction set.

5. The quenching optimization method for large-diameter bearings based on multi-model set member estimation according to claim 1, characterized in that, The optimal gain matrix of the target quenching measurement system, obtained by minimizing the set radius of the prediction set and error set based on the system model, includes: Based on the prediction set and error set of the system model, update the center matrix and generator matrix of the prediction set of each set member estimation model; Based on the coefficient matrix, updated center matrix, and generator matrix of the system model, the optimal gain matrix of the target quenching measurement system is solved by minimizing the set radius.

6. The quenching optimization method for large-diameter bearings based on multi-model set member estimation according to claim 5, characterized in that, The process of solving for the optimal gain matrix of the target quenching measurement system by minimizing the set radius, based on the coefficient matrix, updated center matrix, and generator matrix of the system model, includes: Based on the coefficient matrix, updated center matrix, and generator matrix of the system model, the optimal gain matrix of the target quenching measurement system is solved by minimizing the set radius and linear matrix inequalities.

7. A large-diameter bearing quenching optimization system based on multi-model set member estimation, characterized in that, include: The first determining module is used to determine multiple state parameters of the target quenching measurement system; By using state parameters and the fully symmetric polytope method, an uncertain system based on discrete time and a set of first uncertain parameters are constructed. The second determining module is used to construct a system model based on the coefficient matrix of the uncertain system by using the Kalman filtering method, which is based on the fusion of multiple set membership estimation models; and to determine the prediction state equation, the second set of uncertain parameters, and the probability density function of each set membership estimation model according to the system model and the first set of uncertain parameters. The update module is used to update the probability density function of the prediction set of each set member estimation model based on the dimension of the output matrix of the real-time quenching measurement system and the second set of uncertain parameters. The computation module is used to calculate the prediction set of the system model based on the probability density function of the prediction set of each set member estimation model using Bayes' theorem. The solution module is used to solve the optimal gain matrix of the target quenching measurement system by minimizing the set radius based on the prediction set and error set of the system model.

8. The large-diameter bearing quenching optimization system based on multi-model set member estimation according to claim 7, characterized in that, The second determining module includes: The first determining unit is used to determine the predictive state equation of each set member estimation model based on the system model and the first uncertain parameter set. The update unit is used to update the prediction set of each member estimation model based on the state estimate of the system model at the previous time step. The second determining unit is used to define the residual set, and based on the updated prediction set and residual set, to determine the probability density function of the estimation model for each set member using Bayes' theorem.

9. An electronic device, comprising: One or more processors; A storage device for storing one or more programs, which, when executed by one or more processors, cause the one or more processors to implement the large-diameter bearing quenching optimization method based on multi-model set member estimation as described in any one of claims 1 to 6.

10. A computer-readable medium having a computer program stored thereon, wherein, When the computer program is executed by the processor, it implements the large-diameter bearing quenching optimization method based on multi-model set member estimation as described in any one of claims 1 to 6.

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