Large-diameter bearing quenching optimization method and system based on multi-model set membership estimation

Abstract

The invention relates to a large-diameter bearing quenching optimization method and system based on multi-model set membership estimation. The method comprises the following steps: determining a plurality of state parameters of a target quenching measurement system; constructing a system model based on fusion of a plurality of set membership estimation models through a Kalman filtering method according to the state parameters and a holosymmetric polytope method; determining a prediction state equation and a probability density function of each set membership estimation model; according to the dimension of an output matrix of a real-time quenching measurement system, updating a probability density function of each set membership estimation model prediction set; calculating the prediction set of the system model through the Bayesian theorem based on the probability density function of the prediction set of each set membership estimation model; and based on the prediction set and the error set of the system model, solving an optimal gain matrix of the target quenching measurement system by minimizing the radius of the set. According to the method, through multi-model set membership estimation and the Bayesian theorem, the stability and robustness of quenching optimization control of the large-diameter bearing are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of quenching technology and nonlinear control technology, and in particular relates to a large-diameter bearing quenching optimization method and system based on multi-model set membership estimation. Background Art

[0002] Large-diameter bearings play a critical role in heavy machinery and aerospace applications, and their quenching process directly impacts bearing fatigue life and performance. Traditional quenching optimization methods often rely on a single model, making it difficult to handle complex process uncertainties. Quenching optimization objectives may be to minimize residual stress or temperature gradients to reduce deformation and cracking. Set membership estimation is a control theory technique used to estimate states in the presence of system uncertainty, particularly well-suited to handling measurement noise or model parameter uncertainty.

[0003] In set membership estimation, system uncertainty is often used to represent unknown but bounded noise / disturbance 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 with unknown but bounded noise. Summary of the Invention

[0004] In order to improve the stability and robustness of large-diameter bearing quenching optimization control, a first aspect of the present invention provides a large-diameter bearing quenching optimization method based on multi-model set membership estimation, comprising: Determine multiple state parameters of the target quenching measurement system; construct an uncertain system based on discrete time and a first uncertain parameter set through state parameters and a fully symmetric polyhedral method; based on the coefficient matrix of the uncertain system, construct a system model based on the fusion of multiple set membership estimation models through the Kalman filtering method; according to the system model and the first uncertain parameter set, determine the predicted state equation, the second uncertain parameter set and the probability density function of each set membership estimation model; according to the dimension of the output matrix of the real-time quenching measurement system and the second uncertain parameter set, update the probability density function of the prediction set of each set membership estimation model; based on the probability density function of the prediction set of each set membership estimation model, calculate the prediction set of the system model through the Bayesian theorem; based on the prediction set and error set of the system model, solve the optimal gain matrix of the target quenching measurement system by minimizing the set radius.

[0005] In some embodiments of the present invention, determining the predicted state equation, the second uncertain parameter set and the probability density function of each set membership estimation model based on the system model and the first uncertain parameter set includes: determining the predicted state equation of each set membership estimation model based on the system model and the first uncertain parameter set; updating the prediction set of each set membership estimation model based on the state estimation of the system model at the previous moment; defining a residual set; and determining the probability density function of each set membership estimation model by Bayes' theorem based on the updated prediction set and residual set.

[0006] In some embodiments of the present invention, updating the probability density function of each set membership 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 variables of the probability density function of each set membership 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 membership estimation model prediction set based on the spatial dimension of the value range and the random variables.

[0007] Furthermore, the updating of the probability density function of the prediction set of each set membership estimation model based on the spatial dimension and random variables of the value range includes: if the dimension of the output matrix is ​​1, the probability density function is uniformly distributed in the prediction set within the domain interval; if the dimension of the output matrix is ​​2, the probability density function is uniformly distributed in the area domain of the prediction set; if the dimension of the output matrix is ​​greater than or equal to 3, the probability density function is uniformly distributed in the volume domain of the prediction set.

[0008] In some embodiments of the present invention, the method 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 central matrix and generating matrix of the prediction set of each set membership estimation model 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 according to the coefficient matrix of the system model, the updated central matrix and the generating matrix.

[0009] Furthermore, the method 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 the linear matrix inequality based on the coefficient matrix, the updated center matrix and the generator matrix of the system model.

[0010] The second aspect of the present invention provides a large-diameter bearing quenching optimization system based on multi-model set membership estimation, including: a first determination module for determining multiple state parameters of the target quenching measurement system; constructing an uncertain system based on discrete time and a first uncertain parameter set through state parameters and a fully symmetric polyhedral method; a second determination module for constructing a system model based on the fusion of multiple set membership estimation models through a Kalman filtering method based on the coefficient matrix of the uncertain system; determining the predicted state equation, the second uncertain parameter set and the probability density function of each set membership estimation model according to the system model and the first uncertain parameter set; an updating module for updating the probability density function of the prediction set of each set membership estimation model according to the dimension of the output matrix of the real-time quenching measurement system and the second uncertain parameter set; a calculation module for calculating the prediction set of the system model through Bayes' theorem based on the probability density function of the prediction set of each set membership 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.

[0011] The third aspect of the present invention provides an electronic device comprising: one or more processors; 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 membership estimation provided in the first aspect of the present invention.

[0012] A fourth aspect of the present invention provides a computer-readable medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the large-diameter bearing quenching optimization method based on multi-model set membership estimation provided in the first aspect of the present invention is implemented.

[0013] The beneficial effects of the present invention are: This paper proposes a multi-model set membership estimation method based on Bayesian theory for a linear uncertain system used in large-diameter bearing quenching, where the statistical characteristics of the noise are unknown. This method solves the state estimation problem for this linear uncertain system. Furthermore, based on the proposed set membership estimation probability density function, a new model probability update formula is presented. By minimizing the set P-radius, the designed observer gain matrix ensures the stability of the quenching process control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Schematic diagram of the basic process of the large-diameter bearing quenching optimization method based on multi-model set membership estimation in some embodiments of the present invention; Figure 2 Schematic diagram of a specific process of a large-diameter bearing quenching optimization method based on multi-model set membership estimation in some embodiments of the present invention; Figure 3 Schematic diagram of the structure of a large-diameter bearing quenching optimization system based on multi-model set membership estimation in some embodiments of the present invention; Figure 4 Schematic diagram of the structure of an electronic device in some embodiments of the present invention. DETAILED DESCRIPTION

[0015] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0016] refer to Figure 1 and Figure 2 In a first aspect of the present invention, a large diameter bearing quenching optimization method based on multi-model set membership estimation is provided, comprising: S100. Determine multiple state parameters of the target quenching measurement system; construct a discrete-time based uncertain system and a first set of uncertain parameters by using state parameters and a fully symmetric polyhedral method; S200. Based on the coefficient matrix of the uncertain system, construct a system model based on the fusion of multiple set membership estimation models using the Kalman filter method; based on the system model and the first uncertain parameter set, determine the predicted state equation, the second uncertain parameter set, and the probability density function of each set membership estimation model; S300. Update the probability density function of each set of member estimation models predicting the set according to the dimension of the output matrix of the real-time quenching measurement system and the second set of uncertain parameters; S400. Based on the probability density function of the prediction set of each set membership estimation model, the prediction set of the system model is calculated by Bayes' theorem; S500. Based on the prediction set and the error set of the system model, the optimal gain matrix of the target quenching measurement system is solved by minimizing the set radius.

[0017] In step S100 of some embodiments of the present invention, a plurality of state parameters of a target quenching measurement system are determined; a discrete-time-based uncertain system and a first set of uncertain parameters are constructed using the state parameters and a fully symmetric polytope method; Specifically, to establish an uncertain system model, consider the following discrete-time linear system: (1) (2) in, is the system status, is the control input, is the system output, For system interference, To measure noise.

[0018] Assumptions , , ,in, Indicates the center point is , the generated matrix is The fully symmetric polytope of , . 、 and The same definition is used for the following fully symmetric polytopes, and the same method is used to represent and calculate them. Indicates that the corresponding matrix contains parameter uncertainty, N is the number of models.

[0019] For example, With form ,in, is the natural frequency. However, the designer does not know The exact value of ; Therefore, the matrix Containing uncertainty, there are three different subsystems.

[0020] The present invention assumes that the matrix At time k, it can be expressed as follows: (3) in, , .

[0021] More specifically, the dynamics of the quenching process is described by the heat conduction equation: ; Considering boundary conditions (such as convection cooling): , For the convenience of estimation, it is discretized into a finite-dimensional linear system. Assume that the bearing is simplified to a one-dimensional rod, discretized into n points, and the state vector Using the finite difference method, the dynamics of the interior points are: ; Boundary points (such as = 1) Consider convection: ; Similar treatment Tn , its matrix form is: , in: is a tridiagonal matrix with element dependence and thermal conductivity h. Including boundary conditions T ∞ term, if T ∞ is the control input, then = T ∞.

[0022] Going further, the measurement equation is: , Where C selects the measurement point (such as surface temperature), is the measurement noise, defined as ; represents the state vector, the discretized temperature distribution, in °C; Represents the system matrix, dependent parameters , reflecting thermal diffusion and boundary conditions, represents density, represents specific heat capacity; represents the input matrix, if = T ∞, it affects the boundary temperature dynamics. C represents the measurement matrix, which is defined as a subset of the identity matrix and selects the sensor locations. represents the measurement noise, whose error Determined by the sensor accuracy; Indicates an uncertain parameter set, which may include .

[0023] Understandably, during the quenching process of large-diameter bearings, the ensemble estimation uses thermal properties, heat transfer coefficients, geometric dimensions, initial temperature distribution, quenching medium temperature, and measurements as state parameters. Uncertainty in these state parameters is addressed through a multi-model framework, ensuring robust state estimation. Based on the discretization of the heat conduction equation, this approach is suitable for optimizing residual stresses or temperature gradients, and its adaptability offers potential for industrial applications.

[0024] In step S201 of some embodiments of the present invention, a system model based on the fusion of multiple set membership estimation models is constructed by a Kalman filtering method based on the coefficient matrix of the uncertain system; Specifically, define is the parameter set (the first parameter set), assuming have N different values, namely .

[0025] Therefore, the i The model corresponds to an uncertain parameter set , .

[0026] If so, the system state estimator is expressed as: (4) in, L is the estimator gain matrix, yes N The result of state fusion is predicted by each sub-model.

[0027] In step S202 of some embodiments of the present invention, determining the predicted state equation, the second uncertain parameter set, and the probability density function of each set membership estimation model based on the system model and the first uncertain parameter set includes: S2021. Determine a prediction state equation for each set membership estimation model based on the system model and the first set of uncertain parameters; S2022. Update the prediction set of each set membership estimation model based on the state estimate of the system model at the previous moment; Specifically, the prediction state corresponding to each sub-model is obtained by the following formula: (5) in, For the i The state prediction value of the estimator, .

[0028] If in k The estimated set at time -1 satisfies , then i The estimator in k The prediction set at time satisfies ,in , (6) S2023. Define residual set; Specifically, define , we can get , in, , .

[0029] S2024. Based on the updated prediction set and residual set, determine the probability density function of each set member estimation model using Bayes' theorem.

[0030] Specifically, according to Bayes' theorem, we can get (7) in, is the probability density function, represents the probability function.

[0031] if ,So Depend on OK. So we can get , If the estimated state is accurate, then there is and .

[0032] Taking into account , we can get .because , so the variable In the collection The medium obeys uniform distribution.

[0033] In step S300 of some embodiments of the present invention, updating the probability density function of each set membership estimation model prediction set according to the dimension of the output matrix of the real-time quenching measurement system and the second set of uncertain parameters includes: S301. Determine the random variables of the probability density function of each set membership estimation model prediction set based on the second uncertain parameter set; S302. Determine 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; S303. Update the probability density function of each set membership estimation model prediction set based on the spatial dimension of the value range and the random variables.

[0034] Furthermore, the updating of the probability density function of the prediction set of each set membership estimation model based on the spatial dimension and random variables of the value range includes: if the dimension of the output matrix is ​​1, the probability density function is uniformly distributed in the prediction set within the domain interval; if the dimension of the output matrix is ​​2, the probability density function is uniformly distributed in the area domain of the prediction set; if the dimension of the output matrix is ​​greater than or equal to 3, the probability density function is uniformly distributed in the volume domain of the prediction set.

[0035] Specifically, consider the following three cases: , and , .

[0036] 1) In this case, the collection can be expressed as an interval, i.e. Therefore, the probability density function It can be designed as follows: (8) It can be seen that: , ,so Satisfy the conditions of the probability density function.

[0037] 2) In this case the probability density function Can be written as Therefore, the corresponding probability density function It can be designed as follows: (9) in, For collection It can be seen that , so Satisfy the conditions of the probability density function.

[0038] 3) , In this case the probability density function Can be written as Therefore, the corresponding probability density function It can be designed as follows: (10) in, For collection The volume of . It can be seen that , ,so Satisfy the conditions of the probability density function. In particular, if is a diagonal matrix, that is Then the set It can be expressed as ,in , , , Therefore, the corresponding probability density function can be designed as follows: (11) It can be seen from the above formula that , .

[0039] so Satisfy the conditions of the probability density function.

[0040] 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 membership estimation model; Specifically, according to Bayesian theory, we have .exist k Time, measurement output is certain and known, so , .

[0041] On this basis, the state estimation set at time k can be obtained , , (12) in, , is the identity matrix of suitable dimension, , , , .

[0042] In step S500 of some embodiments of the present invention, solving the optimal gain matrix of the target quenching measurement system by minimizing the set radius based on the prediction set and the error set of the system model includes: S501. Based on the prediction set and error set of the system model, update the center matrix and generator matrix of each set membership estimation model prediction set; Specifically, a gain matrix is ​​calculated based on the estimated error set.

[0043] Defining the estimation error , then: (13) in, , .

[0044] if , and , then , (14) (15) in, , , , .

[0045] S502. According to the coefficient matrix of the system model, the updated center matrix and the generator matrix, the optimal gain matrix of the target quenching measurement system is solved by minimizing the set radius.

[0046] Specifically, the method of 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 the generator matrix includes: solving the optimal gain matrix of the target quenching measurement system by minimizing the set radius and linear matrix inequality based on the coefficient matrix of the system model, the updated center matrix and the generator matrix.

[0047] because and is unknown, so the above formula can be converted into the following formula: (16) (17) in, , .

[0048] By solving the following matrix inequality, we can get the matrix X and a positive definite symmetric matrix P , then the observer gain matrix L Can be achieved through Obtain.

[0049] (18) in, , .

[0050] Example 2 refer to Figure 3 In a second aspect of the present invention, a large diameter bearing quenching optimization system 1 based on multi-model set membership estimation is provided, comprising: The first determination module 11 is used to determine multiple state parameters of the target quenching measurement system; construct an uncertain system based on discrete time and a first uncertain parameter set through the state parameters and the fully symmetric polytope method; A second determination module 12 is configured to construct a system model based on the fusion of multiple set membership estimation models using a Kalman filter method based on the coefficient matrix of the uncertain system; and determine a predicted state equation, a second uncertain parameter set, and a probability density function of each set membership estimation model based on the system model and the first uncertain parameter set; An updating module 13 is configured to update the probability density function of each set membership estimation model prediction set according to the dimension of the output matrix of the real-time quenching measurement system and the second uncertain parameter set; A calculation module 14 is configured to calculate a prediction set of the system model using Bayes' theorem based on the probability density function of the prediction set of each set membership estimation model; The solving module 15 is configured to solve the optimal gain matrix of the target quenching measurement system by minimizing the set radius based on the prediction set and the error set of the system model.

[0051] Furthermore, the second determination module 12 includes: a first determination unit, used to determine the prediction state equation of each set membership estimation model based on the system model and the first uncertain parameter set; an updating unit, used to update the prediction set of each set membership estimation model based on the state estimation of the system model at the previous moment; a second determination unit, used to define a residual set, and based on the updated prediction set and residual set, determine the probability density function of each set membership estimation model through Bayes' theorem.

[0052] Example 3 refer to Figure 4 According to the third aspect of the present invention, an electronic device is provided, comprising: one or more processors; 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 membership estimation in the first aspect of the present invention.

[0053] The electronic device 500 may include a processing device (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 a read-only memory (ROM) 502 or a program loaded from a storage device 508 into a random access memory (RAM) 503. Various programs and data required for the operation of the electronic device 500 are also stored in the RAM 503. The processing device 501, the ROM 502, and the RAM 503 are connected to each other via a bus 504. An input / output (I / O) interface 505 is also connected to the bus 504.

[0054] Typically, the following devices may be connected to the I / O interface 505: an input device 506 including, for example, a touch screen, a touchpad, a keyboard, a mouse, a camera, a microphone, an accelerometer, a gyroscope, etc.; an output device 507 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; a storage device 508 including, for example, a hard disk, etc.; and a communication device 509. The communication device 509 may allow the electronic device 500 to communicate with other devices wirelessly or by wire to exchange data. Figure 4 The electronic device 500 is shown with various devices, but 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 instead. Figure 4Each block shown in the figure may represent one device, or may represent multiple devices as needed.

[0055] In particular, according to an embodiment of the present disclosure, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication device 509, or installed from the storage device 508, or installed from the ROM 502. When the computer program is executed by the processing device 501, the above-mentioned functions defined in the method of the embodiment of the present disclosure are executed. It should be noted that the computer-readable medium described in the embodiment of the present disclosure can be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to, an electrical connection having one or more conductors, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In embodiments of the present disclosure, a computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In embodiments of the present disclosure, a computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. Such a propagated data signal may take a variety of forms, including, but not limited to, an electromagnetic signal, an optical signal, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium that can transmit, propagate, or transfer a program for use by or in conjunction with an instruction execution system, apparatus, or device. Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wire, optical cable, RF (radio frequency), etc., or any suitable combination thereof.

[0056] The computer-readable medium may be included in the electronic device, or may exist independently without being incorporated into the electronic device. The computer-readable medium carries one or more computer programs, which, when executed by the electronic device, cause the electronic device to: Computer program code for performing the operations of embodiments of the present disclosure may be written in one or more programming languages, or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, C++, Python, and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a stand-alone 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 a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., through the Internet using an Internet service provider).

[0057] The flowcharts and block diagrams in the accompanying drawings illustrate the possible implementation architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each box in the flowchart or block diagram can represent a module, program segment, or a part of code, and the module, program segment, or a part of code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order than that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should be noted that each box in the block diagram and / or flowchart, and the combination of the boxes in the block diagram and / or flowchart, can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0058] 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 in the scope of protection of the present invention.

Claims

1. A large diameter bearing quenching optimization method based on multi-model set membership estimation is characterized by: include: determining a plurality of state parameters of a target quenching measurement system; By using the state parameter and fully symmetric polytope method, the discrete-time uncertain system and the first uncertain parameter set 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 a Kalman filtering method; based on the system model and the first uncertain parameter set, a prediction state equation, a second uncertain parameter set, and a probability density function of each set membership estimation model are determined; 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 uncertain parameter set; Based on the probability density function of the prediction set of each set membership estimation model, the prediction set of the system model is calculated by Bayes' theorem; Based on the prediction set and the 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 large diameter bearing quenching optimization method based on multi-model set membership estimation according to claim 1 is characterized in that: Determining the predicted state equation, the second uncertain parameter set, and the probability density function of each set-member estimation model according to the system model and the first uncertain parameter set includes: Determining a prediction state equation of each set member estimation model based on the system model and the first uncertain parameter set; Based on the state estimation of the system model at the previous moment, update the prediction set of each set estimation model; Define the residual set; based on the updated prediction set and residual set, determine the probability density function of each set member estimation model using Bayes' theorem.

3. The large diameter bearing quenching optimization method based on multi-model set membership estimation according to claim 1 is characterized in that: The updating of the probability density function of each set membership estimation model prediction set according to the dimension of the output matrix of the real-time quenching measurement system and the second uncertain parameter set comprises: Determining a random variable of a probability density function of a prediction set of each set member estimation model based on a second set of uncertain parameters; According to 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 variable, the probability density function of each set membership estimation model prediction set is updated.

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

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

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

7. A large diameter bearing quenching optimization system based on multi-model set membership estimation is characterized by: include: A first determination module is used to determine multiple state parameters of the target quenching measurement system; By using the state parameter and fully symmetric polytope method, the discrete-time uncertain system and the first uncertain parameter set are constructed. a second determination module configured to construct, based on the coefficient matrix of the uncertain system, a system model based on the fusion of multiple set membership estimation models using a Kalman filter method; and determine, based on the system model and the first uncertain parameter set, a predicted state equation, a second uncertain parameter set, and a probability density function of each set membership estimation model; An updating module, configured to update a probability density function of a prediction set of each set membership estimation model according to the dimension of an output matrix of the real-time quenching measurement system and a second set of uncertain parameters; A calculation module, for estimating the probability density function of the prediction set of the model based on each set member, and calculating the prediction set of the system model by Bayes' theorem; A 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 the error set of the system model.

8. The large diameter bearing quenching optimization system based on multi-model set membership estimation according to claim 7 is characterized in that: The second determining module includes: a first determining unit, configured to determine a prediction state equation of each set 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 set estimation model based on the state estimation of the system model at the previous moment; The second determination unit is used to define a residual set, and determine the probability density function of each set member estimation model through Bayes' theorem based on the updated prediction set and the residual set.

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

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