Probability density evolution analysis method, medium and equipment for maglev train suspension system

Abstract

The invention discloses a probability density evolution analysis method, medium and equipment for a maglev train suspension system, and belongs to the technical field of suspension control. The method comprises the following steps: acquiring a probability density true value of a target quantity of the suspension system; performing supervised training on a target quantity probability density output value of the physical information neural network based on the probability density truth value to obtain a trained basic physical information neural network model; forming a correction matrix by using a set of target quantity output values, correcting a target quantity probability density value output by the trained basic physical information neural network model until an expected error is met, and obtaining a target quantity probability density physical information neural network based on residual enhancement; and predicting probability density evolution of a future time target quantity by using the target quantity probability density physical information neural network based on residual enhancement. The method effectively improves the calculation efficiency on the premise of ensuring the target quantity probability density calculation precision, and can be used for target quantity probability density evolution prediction.

Description

Technical Field

[0001] The present invention relates to the field of suspension control, and more specifically, to a probability density evolution analysis method, medium and equipment for a maglev train suspension system based on a residual enhanced physical information neural network. Background Art

[0002] Maglev trains are becoming a new land transportation mode that has attracted much attention due to their advantages such as low noise, low emissions, low maintenance costs and no risk of derailment. As the speed of maglev trains increases to 600 km / h and above, the demand for improvements in vehicle structure and optimization of suspension system control has become stronger.

[0003] The suspension system of a maglev train is a complex random system. The existence of random track irregularities, structural parameters of the bridge system, and multiple random external load sources makes the random dynamic characteristics of the system more difficult to estimate. In addition, different suspension system input parameters have different effects on the uncertainty of the system output. Previous studies have shown that the randomness of parameters such as vehicle structure and track irregularities has a significant impact on the response of the suspension system. Using only deterministic analysis methods may lead to an incomplete understanding of the system's dynamic behavior. In order to more comprehensively reveal the random response characteristics of the suspension system and clarify the main influencing factors of the random response of the suspension system, it is necessary to study the random system from a new perspective of the propagation of randomness in the suspension system, so as to better grasp the random vibration response mechanism of the high-speed maglev train suspension system, further optimize the relevant design variables, and accelerate the engineering promotion and application of high-speed maglev trains.

[0004] The probability density evolution theory is a random dynamic analysis method developed in recent years. It can be used to solve complex nonlinear random systems and has been widely used in the field of maglev train-bridge coupled vibration analysis. Using the probability density evolution method, high-precision system response statistics can be obtained, including mean, standard deviation and evolution probability density curve, which can provide a strong reference for system reliability analysis and optimization control. When using the probability density evolution method to perform random dynamic analysis on the suspension system of a maglev train, it is necessary to solve the probability density evolution equation. Although the finite difference method can be used to numerically solve the probability density evolution equation, facing a complex suspension system, there is still an undesirable balance between accuracy and efficiency when determining the number of representative point sets. The physical information neural network, which has been widely developed in recent years, has been successfully applied to the solution of nonlinear partial differential equations. Using the physical information neural network to solve the probability density evolution equation can achieve an effective fusion of the probability density evolution mechanism and data. At present, there have been studies using the physical information neural network to solve the probability density evolution equation. Compared with the finite difference method, the physical information neural network can better balance the calculation accuracy and efficiency when solving the probability density evolution equation. Although physical information neural networks have achieved remarkable success in solving probability density evolution equations, they have not yet been applied to solving the maglev train suspension system. Physical information neural networks still face challenges in solving complex problems and need to be further refined and improved in a targeted manner according to the application system. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a probability density evolution analysis method, medium and equipment for a maglev train suspension system to solve the technical problems of imbalance between calculation accuracy and efficiency and poor applicability in such a complex random nonlinear system as a maglev train suspension system.

[0006] According to a first aspect of the present invention, a method for analyzing the probability density evolution of a maglev train suspension system is provided. The method comprises the following steps: Obtain the true value of the probability density of the target quantity of the suspension system; Based on the true value of the probability density, supervised training is performed on the target quantity probability density output value of the physical information neural network to obtain a trained basic physical information neural network model, wherein the input of the physical information neural network includes the suspension system target quantity and time, and the output includes the probability density of the target quantity and the derivative of the target quantity with respect to time; A correction matrix is ​​formed by using a set set of target quantity output values, and the probability density value of the target quantity output by the trained basic physical information neural network model is corrected until the expected error is met, thereby obtaining a target quantity probability density physical information neural network based on residual enhancement; The residual-enhanced target quantity probability density physical information neural network is used to predict the probability density evolution of the target quantity in the future.

[0007] According to a second aspect of the present invention, there is provided a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-mentioned method for analyzing the probability density evolution of a maglev train suspension system.

[0008] According to a third aspect of the present invention, there is provided a computer device comprising a memory and a processor, wherein the memory stores a computer program that can be run on the processor, and when the processor executes the computer program, the steps of the above-mentioned method for analyzing the probability density evolution of a maglev train suspension system are implemented.

[0009] Compared with the prior art, the advantages of the present invention are that, by utilizing a physical information neural network based on residual enhancement, the inherent limitations of the basic physical information neural network when applied to a complex random nonlinear system such as a maglev train suspension system are solved, and the accuracy of the physical information neural network for probability density evolution analysis of a maglev train suspension system is significantly improved; compared with traditional numerical algorithms, the physical information neural network based on residual enhancement solves the probability density evolution equation of the target quantity of the suspension system, and the calculation efficiency is greatly improved, achieving a balance between calculation accuracy and efficiency; the physical information neural network based on residual enhancement can predict the probability density evolution of the target quantity in the future; the provided method for solving the probability density of the target quantity of the maglev train suspension system is generally applicable to high, medium and low speed maglev trains.

[0010] Further features and advantages of the present invention will become apparent from the following detailed description of exemplary embodiments of the present invention with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.

[0012] Figure 1 is a flow chart of a probability density evolution analysis method for a maglev train suspension system according to an embodiment of the present invention; Figure 2 is a process schematic diagram of a method for calculating a probability density of a target quantity according to an embodiment of the present invention; Figure 3 is a schematic diagram of the structure of a basic physical neural network according to an embodiment of the present invention; Figure 4 is a schematic structural diagram of a high-speed maglev train according to an embodiment of the present invention; Figure 5is a schematic structural diagram of a single-point suspension system according to an embodiment of the present invention; In the attached figure, 1 is carriage; 2 is secondary suspension; 3 is bogie; 4 is guide electromagnet; 5 is suspension electromagnet; 6 is track; 7 is secondary suspension stiffness; 8 is secondary suspension damping; 9 is single point suspension system load. DETAILED DESCRIPTION

[0013] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that the relative arrangement of components and steps, numerical expressions and numerical values ​​set forth in these embodiments do not limit the scope of the present invention unless otherwise specifically stated.

[0014] The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses.

[0015] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered as part of the specification.

[0016] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limiting. Therefore, other examples of the exemplary embodiments may have different values.

[0017] It should be noted that like reference numerals and letters refer to similar items in the following figures, and therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0018] In general, the physical information neural network provided by the present invention includes two parts: a basic physical information neural network and a target quantity forward correction method, or a residual enhanced physical information neural network. The target quantity includes but is not limited to the vertical acceleration of the suspension system body, the suspension gap, the train running stability index, the control performance index, etc. After using a small amount of target quantity probability density true value for supervised training to obtain the target quantity probability density basic physical information network model, the target quantity forward correction method is further used to obtain the corrected target quantity probability density physical information network model.

[0019] Specifically, combined Figure 1 and Figure 2 As shown, the provided maglev train suspension system probability density evolution analysis method comprises the following steps: Step S1, obtaining the true value of the probability density of the target quantity of the maglev train system.

[0020] The true value of the probability density of the target quantity can be obtained through actual operation data, test data or traditional numerical algorithms (such as finite difference method). The obtained true value of the probability density of the target quantity can be used for subsequent training, correction or verification of the physical information neural network. For example, part of the true value can be used for supervised training of the probability density output of the basic physical information neural network and correction of the training results of the basic physical information neural network, and the other part of the true value can be used to verify the effectiveness of the proposed probability density evolution analysis method of the magnetic levitation system based on the residual enhanced physical information neural network.

[0021] In one embodiment, the target quantity includes but is not limited to the vertical acceleration of the suspension system body, the suspension gap, the train running stability index, the control performance index, etc.

[0022] Step S2, performing supervised training on the physical information neural network based on the true value of the target quantity probability density to obtain a trained basic physical information neural network model.

[0023] For example, the probability density output value of the target quantity in the basic physical information neural network is supervised by using the true value of part of the probability density to obtain the basic physical information neural network model of the probability density of the target quantity of the suspension system.

[0024] like Figure 3 As shown in the figure, the basic physical information neural network includes an input layer, multiple hidden layers and an output layer. The input layer has two input quantities, namely, the target quantity of the suspension system and time . The hidden layer is marked Represents the activation process. The output of the output layer includes the probability density of the target quantity and the time derivative of the target quantity The probability density of the target quantity in the output layer can be supervised by using a small number of true values ​​of the target quantity probability density. Indicates time The differential of Indicates the target amount The differential of . Loss Indicates loss.

[0025] In one embodiment, the overall loss function used to train the basic physical information neural network includes the error term between the probability density value of the target quantity obtained through training and the true value, the error term of the residual of the probability density evolution equation, the non-negative error term of the probability density value, etc., which are marked as M u , M f and M r The overall loss function can be the weighted sum of the three types of error terms, with the weight coefficient , and It can be determined according to actual needs or simulation.

[0026] Step S3, using any group of target quantity output values ​​to form a correction matrix, correcting the probability density value output by the trained basic physical information neural network model based on the relative bi-norm error, and obtaining a target quantity probability density physical information neural network based on residual enhancement.

[0027] In step S3, a set of target output values ​​is used to form a correction matrix, and the probability density value output by the basic physical information neural network model is corrected based on the relative two-norm error. In this article, this correction method is called the target forward correction method.

[0028] The target quantity forward correction method uses the target quantity matrix corresponding to any set of random parameter samples (such as vehicle structure parameters, track beam structure parameters, etc.) to form a correction matrix to correct the probability density calculation results of the basic physical neural network, thereby making the probability density calculation results more accurate.

[0029] Specifically, the target quantity forward correction method is: each element in the probability density matrix calculated by the basic physical neural network is translated by the corresponding unit according to the value of the same position in the correction matrix, so as to obtain the corrected probability density matrix.

[0030] In one embodiment, the correction matrix is ​​obtained by multiplying the target quantity matrix by the correction coefficient, wherein the correction coefficient is the coefficient obtained when the relative two-norm error reaches the expected value. The relative two-norm error is obtained by the true value of the target quantity probability density used in supervised training and the probability density value obtained by the corresponding basic physical information neural network training. In this article, the physical information neural network after correction training is also referred to as the target quantity probability density physical information neural network based on residual enhancement.

[0031] Step S4, using the target quantity probability density physical information neural network based on residual enhancement, predicting the probability density evolution of the target quantity in the future.

[0032] The modified and trained physical information neural network model can be used to predict the probability density of the target quantity at future moments. In the model application process, only the required solution moment is brought into the model to obtain the probability density distribution curve at that moment.

[0033] Furthermore, in order to verify the effectiveness of the present invention, an experimental verification was conducted. The hardware and software equipment used in the experiment include a sensor device for collecting target quantities of a real maglev train suspension system, a physical information neural network model training program, a suspension system dynamics model solving program, a target quantity forward correction method program, and a real maglev train suspension system signal acquisition device. In the experiment, the target quantity is the vertical acceleration of the high-speed maglev train body, and the finite difference method, i.e., the traditional numerical solution algorithm, is used to obtain the true value of the probability density of the vertical acceleration of the body.

[0034] Specifically, the structure of the high-speed maglev train is as follows: Figure 4 As shown in the figure, since the target quantity is the vertical dynamic response of the suspension system, that is, the vertical acceleration of the vehicle body, the suspension system can be simplified into a single-point suspension system including a secondary suspension system.

[0035] The structure of single point suspension system is as follows: Figure 5 As shown. According to the structure of the single-point suspension system, the dynamic equation of the single-point suspension system can be further established. By bringing different random parameter samples into the dynamic equation, different vehicle body vertical acceleration response outputs can be obtained. The finite difference method is used to solve the probability density evolution equation of the vehicle body vertical acceleration response to obtain the true value of the probability density of the vehicle body vertical acceleration response. The partial probability density true value obtained by the finite difference method is used for supervised training of the basic physical neural network. The correction matrix is ​​formed by using the numerical matrix of the vehicle body vertical acceleration response under any set of random parameter samples to correct the probability density results obtained by the basic physical neural network training. When the relative two-norm error between the true value of the probability density used for supervised training and the corresponding probability density value obtained by the basic physical neural network training is less than the expected value, the correction coefficient of the correction matrix, the probability density value corrected by the correction matrix, and the physical information neural network model of the vehicle body vertical acceleration response probability density based on residual enhancement are output. Furthermore, the future time can be substituted into the model to predict the evolution of the probability density of the vehicle body vertical acceleration response at the future time.

[0036] In summary, the present invention effectively improves the calculation efficiency while ensuring the calculation accuracy of the target quantity probability density, and can be applied to the prediction of the evolution of the target quantity probability density, laying a solid foundation for the development of the intelligent control framework and performance-driven structural optimization in the maglev transportation system. The present invention may be a system, a method and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for causing a processor to implement various aspects of the present invention.

[0037] Computer readable storage medium can be a tangible device that can hold and store instructions used by an instruction execution device. Computer readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination thereof. More specific examples (non-exhaustive list) of computer readable storage medium include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, for example, a punch card or a convex structure in a groove on which instructions are stored, and any suitable combination thereof. The computer readable storage medium used here is not interpreted as a transient signal itself, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagated by a waveguide or other transmission medium (for example, a light pulse by an optical fiber cable), or an electrical signal transmitted by a wire.

[0038] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in the computer-readable storage medium in each computing / processing device.

[0039] The computer program instructions for performing the operation of the present invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages, such as Smalltalk, C++, Python, etc., and conventional procedural programming languages, such as "C" language or similar programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer, partially on a remote computer, or entirely on a remote computer or server. In the case of 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., using an Internet service provider to connect through the Internet). In some embodiments, by using the state information of the computer-readable program instructions to personalize an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), the electronic circuit may execute the computer-readable program instructions, thereby implementing various aspects of the present invention.

[0040] Various aspects of the present invention are described herein with reference to the flowcharts and / or block diagrams of the methods, devices (systems) and computer program products according to embodiments of the present invention. It should be understood that each box of the flowchart and / or block diagram and the combination of the boxes in the flowchart and / or block diagram can be implemented by computer-readable program instructions.

[0041] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, thereby producing a machine, so that when these instructions are executed by the processor of the computer or other programmable data processing device, a device that implements the functions / actions specified in one or more boxes in the flowchart and / or block diagram is generated. These computer-readable program instructions can also be stored in a computer-readable storage medium, and these instructions cause the computer, programmable data processing device, and / or other equipment to work in a specific manner, so that the computer-readable medium storing the instructions includes a manufactured product, which includes instructions for implementing various aspects of the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0042] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device so that a series of operating steps are performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to implement the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0043] The flow charts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the systems, methods and computer program products according to multiple embodiments of the present invention. In this regard, each box in the flow chart or block diagram can represent a part of a module, a program segment or an instruction, and a part of the module, a program segment or an instruction contains one or more executable instructions for realizing the specified logical function. In some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be implemented by a dedicated hardware-based system that performs the specified function or action, or can be implemented by a combination of dedicated hardware and computer instructions. It is well known to those skilled in the art that it is equivalent to implement it by hardware, implement it by software, and implement it by combining software and hardware.

[0044] Embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles of the embodiments, practical applications, or technical improvements in the marketplace, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein. The scope of the present invention is defined by the appended claims.

Claims

1. A probability density evolution analysis method for a maglev train suspension system, comprising the following steps: Obtain the true value of the probability density of the target quantity of the suspension system; Based on the true value of the probability density, supervised training is performed on the target quantity probability density output value of the physical information neural network to obtain a trained basic physical information neural network model, wherein the input of the physical information neural network includes the suspension system target quantity and time, and the output includes the probability density of the target quantity and the derivative of the target quantity with respect to time; A correction matrix is ​​formed by using a set set of target quantity output values, and the probability density value of the target quantity output by the trained basic physical information neural network model is corrected until the expected error is met, thereby obtaining a target quantity probability density physical information neural network based on residual enhancement; The residual-enhanced target quantity probability density physical information neural network is used to predict the probability density evolution of the target quantity in the future.

2. The method according to claim 1, characterized in that The target output value includes one or more of the vertical acceleration of the suspension system vehicle body, the suspension gap, the train running stability index, and the control performance index.

3. The method according to claim 1, characterized in that The overall loss function for training the physical information neural network is a weighted sum of the error term between the target quantity probability density value and the true value, the error term of the residual of the probability density evolution equation, and the non-negative error term of the probability density value.

4. The method according to claim 1, characterized in that: The correction matrix is ​​obtained by multiplying a target quantity matrix corresponding to a set of random parameter samples by a correction coefficient.

5. The method according to claim 4, characterized in that The random parameters include vehicle structural parameters or track beam structural parameters.

6. The method according to claim 1, characterized in that Correcting the probability density values ​​output by the trained basic physical information neural network model includes: translating each element in the probability density value matrix of the target quantity output by the basic physical information neural network model by the corresponding unit according to the value at the same position in the correction matrix, thereby obtaining a corrected probability density matrix.

7. The method according to claim 1, characterized in that The error is a relative two-norm error, which is obtained based on the true value of the probability density of the target quantity used in supervised training and the probability density value obtained by training the corresponding physical information neural network.

8. A computer-readable storage medium having a computer program stored thereon, wherein: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

9. A computer device comprising a memory and a processor, wherein a computer program capable of running on the processor is stored in the memory, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 7 are implemented.

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