A method and system for analyzing the reliability of a maglev train suspension system

Abstract

This invention relates to a reliability analysis method and system for a maglev train levitation system. First, a representative sample set of track irregularities is simulated and generated using the spectral representation-random function method as input. Second, a levitation system model is established, and the time history data of the levitation gap / car body vertical acceleration are calculated. Then, the probability density evolution equations for the levitation gap / car body vertical acceleration are established and solved. Finally, the reliability of the corresponding levitation system indicators is obtained using the equivalent extreme value method and the absorbing boundary method. Compared with existing technologies, this invention can more objectively and comprehensively evaluate the responsiveness of the levitation system under random track irregularities, and can provide a more accurate and effective evaluation of the dynamic reliability of the levitation system.

Description

Technical Field

[0001] This invention relates to the field of rail transit technology, and in particular to a reliability analysis method and system for a maglev train levitation system. Background Technology

[0002] Maglev transportation systems possess numerous advantages, including low noise, strong climbing ability, small turning radius, no pollution, low overall cost, and energy efficiency, and have gradually become a leading direction in the development of rail transit worldwide. The maglev train's suspension frame is enclosed within the track, and the lines generally employ an elevated bridge structure. During operation, the maglev vehicle and the track beam generate unique coupled vibration phenomena, forming a coupled vibration that interacts and influences the "vehicle system - suspension control system - track beam system."

[0003] The maglev vehicle suspension system is a complex time-varying stochastic system. Internal excitations include track irregularities and stochastic system parameters, while external excitations include wind and earthquakes, all of which have strong stochastic characteristics. Therefore, stochastic vibration theory is needed to analyze the characteristics and laws of the system's stochastic vibration response.

[0004] In recent years, although some scholars at home and abroad have applied some random vibration theories and analysis methods to the random vibration problems of traditional wheel-rail-vehicle coupled systems, relatively little research has been conducted on the random vibration of maglev vehicle suspension systems. Furthermore, it is difficult to achieve a good balance between computational accuracy and efficiency in solving random motion equations and analyzing their random characteristics. At the same time, research on random dynamic responses often focuses on the statistical characteristics of samples, and the study of the evolution of probability distributions and probability densities over time is still immature. The probability density evolution method has achieved relatively systematic results in the analysis of random responses and reliability calculations of linear and nonlinear multi-degree-of-freedom structural systems, and can be applied to the stochastic analysis of maglev vehicle suspension systems. Summary of the Invention

[0005] The purpose of this invention is to overcome the defects of the prior art by providing a reliability analysis method and system for maglev train suspension systems.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A reliability analysis method for a maglev train levitation system includes the following steps:

[0008] The time histories of random irregularity samples are established based on the random irregularity spectrum of the orbit to characterize the random excitation sources of the suspension system;

[0009] A mathematical model of the suspension system is established based on its physical model, and numerical simulation of the suspension system is performed.

[0010] Based on the mathematical model of the suspension system and the time history of the random irregularities in the track, a feedback control algorithm is designed to form a closed loop of the suspension system, so that the suspension gap is kept within a safe range and the vertical acceleration of the vehicle body meets the comfort requirements.

[0011] The time history of the random irregularity sample of the track is input into the closed loop of the suspension system to obtain the response sample of the suspension gap;

[0012] A generalized probability density evolution equation for the suspension gap / vehicle body vertical acceleration is constructed, and the probability density evolution characteristics of the suspension gap / vehicle body vertical acceleration are solved.

[0013] Based on the probability density evolution characteristics of the suspension gap / vehicle vertical acceleration, and combined with the safety criteria of maglev trains operating without contact, the reliability of the suspension system is obtained.

[0014] Furthermore, the random irregularity spectrum of the track is simulated using the magnetic levitation track irregularity spectrum. The simulation method used is the spectral representation-random function method, and the spectral representation simulation formula is as follows:

[0015]

[0016] In the formula, S x (w) represents the power spectral density, Δw represents the frequency dispersion measure, N represents the number of frequency cutoff terms, and w1 and w N These are the lower cutoff frequency and the upper cutoff frequency, respectively. k and Y k It is an orthogonal random variable.

[0017] Furthermore, the random irregularity spectrum of the track is simulated using the magnetic levitation track irregularity spectrum, specifically including the following steps:

[0018] The basic random variable θ is uniformly discretized on the interval (-π, π). The number of frequency cutoff terms N is set, and the discrete representative point set of the basic random variable θ is calculated. Then, each discrete representative point θ in the discrete representative point set is obtained. i The assigned probability P i ;

[0019] Based on discrete representative point θ i Calculate the orthogonal random variable {X} k ,Y k Representative values ​​of}, (1,2,3,…,N);

[0020] The spectral representation is used to obtain a representative set of samples with irregular orbits, and the probability of each representative sample is equal to the probability P of the corresponding discrete representative point. i .

[0021] Furthermore, the time history of the random irregularity sample of the track is input into the closed loop of the suspension system, and a feedback control algorithm is used to calculate the response sample of the suspension gap.

[0022] Furthermore, the expression for the generalized probability density evolution equation is:

[0023]

[0024] In the formula, Z(θ,t) represents the time history of the suspension system gap, p ZΘ (z,θ,t) represents the joint probability density function of Z(t) and θ, where θ is a basic random variable. The time derivative of the displacement time history.

[0025] Furthermore, based on representative samples of orbital irregularities in the orbital random irregularity spectrum, initial probability values ​​are assigned. The generalized probability density evolution equation is solved using a difference scheme with a flux limiter that reduces total variation, thereby obtaining the solution of the system response and the probability density function of the system response.

[0026] Furthermore, the reliability of the corresponding indicators of the suspension system is obtained by using the equivalent extreme value method and the absorption boundary method;

[0027] The equivalent extreme value method treats the entire time history as a series system, transforms the dynamic reliability problem into time-invariant reliability by constructing equivalent extreme value events, and then introduces virtual time to solve the generalized probability density evolution equation.

[0028] The absorbing boundary method introduces absorbing boundary conditions into the generalized probability density evolution equation. First-overpass failure refers to the structural failure considered to occur when the structural response first exceeds a given threshold. In the probability density evolution method, the probability density function evolves over time like a river, causing the random response to either cross the given threshold. In the definition of first-overpass reliability, once the structural response crosses the given threshold, the structure fails, and the failed structure will not return to a safe state; that is, the probability of this crossing event is 0. This process can be achieved by applying a forced absorbing boundary condition to the generalized probability density evolution equation.

[0029] A reliability analysis system for a maglev train suspension system is provided to implement the reliability analysis method for a maglev train suspension system as described above. The system includes a time history generation unit for random samples of track irregularities, a numerical simulation unit for the suspension system, a control unit for the suspension system, a probability density evolution solution unit for the suspension system, and a reliability solution unit for the suspension system.

[0030] The orbit irregularity random sample time history generation unit is used to simulate and generate orbit irregularity random sample time histories using the spectral representation-random function method;

[0031] The numerical simulation unit for the suspension system is used to establish its mathematical model based on the physical model of the suspension system and to perform numerical simulation of the suspension system.

[0032] The suspension system control unit is used to design a feedback control algorithm based on the mathematical model of the suspension system and the time history of random track irregularities, forming a closed loop of the suspension system to ensure the safety and stability of the maglev train operation.

[0033] The probability density evolution solving unit of the suspension system is used to establish the generalized probability density evolution equation of the suspension gap / vehicle body vertical acceleration, and the probability density evolution characteristics of the suspension system gap / vehicle body vertical acceleration are obtained by solving the finite difference method.

[0034] The reliability solution unit for the suspension system is used to obtain the reliability of the corresponding indicators of the suspension system using the equivalent extreme value method and the absorbing boundary method.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] 1. This invention uses the spectral representation-random function method to simulate the random irregularity spectrum of a track. It can construct a strongly constrained orthogonal random variable form, and only one basic random variable is needed to accurately simulate the random irregularity of the track. Moreover, the representative sample set generated by the simulation has a complete probability set. This feature makes it naturally consistent with the probability density evolution method, and it can be convenient to analyze the random vibration response.

[0037] 2. This invention establishes a closed-loop circuit for the suspension system based on a mathematical model of the suspension system and a feedback control algorithm. Unlike the traditional, simplified spring-damping model, the analysis object is more complete and comprehensive and can take into account the influence of different control algorithms and control parameters.

[0038] 3. This invention utilizes the probability density evolution method, which, compared to the conventional Monte Carlo method which requires calculating the responses of thousands or even tens of thousands of orbital irregularities, can significantly improve computational efficiency while ensuring the accuracy of the calculation results, thereby reducing the human, time, and economic costs required in the simulation process.

[0039] 4. This invention utilizes the equivalent extreme value method and the absorption boundary method to analyze the probability level of a suspension system in different performance states, providing a more comprehensive and systematic reliability assessment result. It has certain guiding significance for the risk assessment, design, and performance optimization of suspension systems, and has significant application value. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the process of the present invention.

[0041] Figure 2This is a schematic diagram of a representative sample set of orbit irregularities simulated by the spectral representation-random function method in an embodiment of the present invention.

[0042] Figure 3 This is a schematic diagram of a simulation model built using Simulink in an embodiment of the present invention.

[0043] Figure 4 This is a probability density evolution diagram of the gap in the suspension system after track irregularity excitation in an embodiment of the present invention.

[0044] Figure 5 This is a probability density curve of the gap in the suspension system after track irregularity excitation in an embodiment of the present invention.

[0045] Figure 6 This represents the average gap in the suspension system after the track irregularity excitation in this embodiment of the invention.

[0046] Figure 7 This represents the standard deviation of the gap in the suspension system after the track irregularity excitation in this embodiment of the invention.

[0047] Figure 8 This is a schematic diagram of the extreme probability density function curve of the gap in the suspension system in an embodiment of the present invention.

[0048] Figure 9 This is a schematic diagram of the system composition of the present invention. Detailed Implementation

[0049] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0050] Example 1:

[0051] (1) This embodiment considers the response of the high-speed maglev vehicle suspension system at a speed of 400 km / h. The widely used Shi Jin high-speed maglev track irregularity spectrum is used to simulate the track random irregularity spectrum. The simulation method used is the spectrum representation-random function method, and the specific formula is:

[0052]

[0053] In the formula, the power spectral density is S x (w), where Δw is the frequency deviation step size, N is the number of frequency cutoff terms, and w1 and w N These are the lower cutoff frequency and the upper cutoff frequency, respectively.

[0054] When simulating random irregularities in the orbit, the basic random variable θ is first uniformly discretized over the interval (-π, π). In the spectral representation simulation, this embodiment sets the number of frequency cutoff terms N = 1600, and calculates the discrete representative point set {θ1, θ2, θ3, ... θ} of the basic random variable. 144}, and obtain the assigned probability of the discrete representative point set, then assign the discrete representative point value θ i Substitute into the calculation of the orthogonal random variable {X} k ,Y k The i-th representative value of (1,2,3,…,N) is obtained; finally, the spectral representation is applied to obtain the i-th representative sample. As i is calculated sequentially from 1 to 144, a set of 144 representative samples with irregular tracks can be obtained, and the probability assigned to each representative sample is the probability P assigned to the corresponding discrete representative point. i .

[0055] The generated N=144 time history curves of orbital irregularities with probabilities are as follows: Figure 2 The method exhibits the stability characteristics of track irregularities. The average power spectrum of 144 representative sample sets is compared with the target power spectrum in the time domain. The average power spectrum of the representative sample sets and the target power spectrum have a high degree of consistency, indicating that the method used is accurate in simulating track irregularities.

[0056] (2) The dynamic equations of the suspension system are established based on the model. In this embodiment, the Matlab / Simulink toolbox is used for numerical simulation and controller design. The simulation model established in Simulink is as follows: Figure 3 As shown, the model consists of three parts: a control system, a suspension system, and a track system. The control system calculates the required control current based on the feedback air gap and acceleration values, and the electromagnetic force generated by the current adjusts the size of the suspension gap. The suspension system calculates a new system response as its output based on parameters such as the input current and track displacement, and the track system calculates the track displacement based on the load force.

[0057] (3) Input the generated series of random track irregularity sample time histories into the established suspension system closed loop, and use the classic PID control algorithm to obtain a series of suspension gap responses;

[0058] (4) Construct the generalized probability density evolution equation of the suspension gap, and substitute the series of suspension gap / vehicle body vertical acceleration responses into the equation to obtain the probability density evolution characteristics of the suspension gap.

[0059] The formula for the generalized probability density evolution equation is as follows:

[0060]

[0061] In the formula, Z(θ,t) represents the time history of the suspension system gap, p zΘ (z,θ,t) represents the joint probability density function of Z(t) and θ, where θ is the basic random variable. The time derivative of the displacement time history.

[0062] This embodiment utilizes a difference scheme with a flux limiter to reduce the total variation and solve the partial differential equation. The assigned probability of each track irregularity and the time histories of 144 suspension system gaps are incorporated into the generalized probability density evolution equation of the suspension system gaps, ultimately yielding the probability density function p of the suspension system gaps at each time step. ZΘ The numerical solution for (z,θ,t) yields the probability density function of the suspension gap / vehicle vertical acceleration at different times, such as... Figures 4 to 7 As shown.

[0063] (5) Based on the probability density evolution characteristics of the suspension system gap / vehicle body vertical acceleration, and combined with the safety assessment criteria of the suspension system, the reliability of the corresponding indicators of the suspension system is obtained by using the equivalent extreme value method and the absorption boundary method.

[0064] The probability density evolution method based on absorbing boundary conditions (PDEM-A) can obtain the reliability change of the structure over the entire duration, while the probability density evolution method based on the equivalent extreme value method (PDEM-E) can obtain the reliability change of the structure over the entire duration. Figure 8 The extreme probability density curves obtained using PDEM-E at a suspension gap threshold of 8 mm are shown. Integration yields a reliability of 0.2464, which is extremely close to the minimum reliability obtained using the absorbing boundary method, demonstrating the good validation of both methods. This indicates that while the initial reliability of the suspension system is low, it follows the track well over time, ensuring a stable suspension gap and good ride comfort. The feedback control algorithm effectively meets the requirements for stable suspension. Under track irregularities, the current flowing through the electromagnet responds quickly to changes in the suspension gap, demonstrating the good steady-state and dynamic performance of the suspension control system.

[0065] Example 2

[0066] This embodiment provides a reliability analysis system for a maglev train levitation system, used to implement the reliability analysis method for a maglev train levitation system as described in Embodiment 1. The system structure is as follows. Figure 9 As shown, it includes: a time history generation unit for random samples of track irregularities, a numerical simulation unit for the suspension system, a control unit for the suspension system, a probability density evolution solution unit for the suspension system, and a reliability solution unit for the suspension system;

[0067] Among them, the orbit irregularity random sample time history generation unit is used to simulate and generate orbit irregularity random sample time histories using the spectral representation-random function method;

[0068] The numerical simulation unit for suspension systems is used to establish the mathematical model of the suspension system based on its physical model, and to perform numerical simulation using the Matlab / Simulink toolbox.

[0069] The suspension system control unit is used to design feedback control algorithms based on the mathematical model of the suspension system and the time history of random irregularities in the track, forming a closed loop of the suspension system to ensure the safety and stability of the suspension system.

[0070] The probability density evolution solution unit for the suspension system is used to establish the generalized probability density evolution equation of the suspension gap / vehicle body vertical acceleration, and the probability density evolution characteristics of the suspension system gap / vehicle body vertical acceleration are obtained by solving the finite difference method.

[0071] The reliability solution unit for the suspension system is used to obtain the reliability of the corresponding indicators of the suspension system using the equivalent extreme value method and the absorbing boundary method.

[0072] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A reliability analysis method for a maglev train levitation system, characterized in that, Includes the following steps: The time histories of random irregularity samples are established based on the random irregularity spectrum of the orbit to characterize the random excitation sources of the suspension system; A mathematical model of the suspension system is established based on its physical model, and numerical simulation of the suspension system is performed. Based on the mathematical model of the suspension system and the time history of the random irregularities in the track, a feedback control algorithm is designed to form a closed loop of the suspension system, so that the suspension gap is kept within a safe range and the vertical acceleration of the vehicle body meets the comfort requirements. The time history of the random irregularity sample of the track is input into the closed loop of the suspension system to obtain the response sample of the suspension gap; A generalized probability density evolution equation for the suspension gap / vehicle body vertical acceleration is constructed, and the probability density evolution characteristics of the suspension gap / vehicle body vertical acceleration are solved. Based on the probability density evolution characteristics of the suspension gap / vehicle vertical acceleration, combined with the safety criteria of maglev trains under non-contact operation, the dynamic reliability of the suspension system is obtained. The reliability of the corresponding indicators of the suspension system is obtained by using the equivalent extreme value method and the absorption boundary method; The equivalent extreme value method treats the entire time history as a series system, transforms the dynamic reliability problem into time-invariant reliability by constructing equivalent extreme value events, and then introduces virtual time to solve the generalized probability density evolution equation. The absorbing boundary method introduces absorbing boundary conditions into the generalized probability density evolution equation.

2. The reliability analysis method for a maglev train levitation system according to claim 1, characterized in that, The random irregularity spectrum of the maglev track is simulated using the track irregularity spectrum. The simulation method used is the spectral representation-random function method, and the spectral representation simulation formula is as follows: In the formula, Power spectral density For the frequency to be far from the walking distance, The number of frequency truncation terms. and These are the lower cutoff frequency and the upper cutoff frequency, respectively. and It is an orthogonal random variable.

3. The reliability analysis method for a maglev train levitation system according to claim 2, characterized in that, The random irregularity spectrum of the track is simulated using the magnetic levitation track irregularity spectrum, specifically including the following steps: basic random variables In the interval Uniform discretization is performed on the surface, and the number of frequency cutoff terms is set. The basic random variable is calculated. The discrete representative point set is obtained, and each discrete representative point in the discrete representative point set is obtained. The probability of assignment ; Based on discrete representative points Calculate orthogonal random variables Representative value; The spectral representation is used to obtain a representative set of samples with irregular orbits, and the probability of each representative sample is the same as the probability of the corresponding discrete representative point. .

4. The reliability analysis method for a maglev train levitation system according to claim 1, characterized in that, The time history of the random irregularity sample of the track is input into the closed loop of the suspension system, and a feedback control algorithm is used to calculate the response sample of the suspension gap.

5. The reliability analysis method for a maglev train levitation system according to claim 1, characterized in that, The expression for the generalized probability density evolution equation is: In the formula, express and The joint probability density function, For the basic random variable, The time derivative of the displacement time history.

6. The reliability analysis method and system for a maglev train levitation system according to claim 5, characterized in that, Initial probability values ​​are assigned to representative samples of orbital irregularities in the random irregularity spectrum. The generalized probability density evolution equation is solved using a difference scheme with flux limiter to reduce total variation, thereby obtaining the solution of the system response and the probability density function of the system response.

7. A reliability analysis system for a maglev train levitation system, characterized in that, The method for implementing the reliability analysis of a maglev train suspension system as described in any one of claims 1-6 includes a track irregularity random sample time history generation unit, a suspension system numerical simulation unit, a suspension system control unit, a suspension system probability density evolution solution unit, and a suspension system reliability solution unit. The orbit irregularity random sample time history generation unit is used to simulate and generate orbit irregularity random sample time histories using the spectral representation-random function method; The numerical simulation unit for the suspension system is used to establish its mathematical model based on the physical model of the suspension system and to perform numerical simulation of the suspension system. The suspension system control unit is used to design a feedback control algorithm based on the mathematical model of the suspension system and the time history of random track irregularities, forming a closed loop of the suspension system to ensure the safety and stability of the maglev train operation. The probability density evolution solving unit of the suspension system is used to establish the generalized probability density evolution equation of the suspension gap / vehicle body vertical acceleration, and the probability density evolution characteristics of the suspension system gap / vehicle body vertical acceleration are obtained by solving the finite difference method. The reliability solution unit for the suspension system is used to obtain the reliability of the corresponding indicators of the suspension system using the equivalent extreme value method and the absorbing boundary method.

8. The reliability analysis system for a maglev train suspension system according to claim 7, characterized in that, In the time history generation unit for random samples of track irregularities, the random track irregularity spectrum is simulated using the magnetic levitation track irregularity spectrum. The simulation method used is the spectral representation-random function method, and the spectral representation simulation formula is: In the formula, Power spectral density For the frequency to be far from the walking distance, The number of frequency truncation terms. and These are the lower cutoff frequency and the upper cutoff frequency, respectively. and It is an orthogonal random variable; The random irregularity spectrum of the track is simulated using the magnetic levitation track irregularity spectrum, specifically including the following steps: basic random variables In the interval Uniform discretization is performed on the surface, and the number of frequency cutoff terms is set. The basic random variable is calculated. The discrete representative point set is obtained, and each discrete representative point in the discrete representative point set is obtained. The probability of assignment ; Based on discrete representative points Calculate orthogonal random variables Representative value; The spectral representation is used to obtain a representative set of samples with irregular orbits, and the probability of each representative sample is the same as the probability of the corresponding discrete representative point. .

9. The reliability analysis system for a maglev train levitation system according to claim 7, characterized in that, In the probability density evolution solution unit of the suspension system, the expression of the generalized probability density evolution equation is: In the formula, express and The joint probability density function, For the basic random variable, The time derivative of the displacement time history.

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