Axle system spectrum response analysis method and device, electronic equipment and medium

Abstract

The invention provides an axle system spectral response analysis method and device, electronic equipment and a medium, and belongs to the field of bridge engineering, and the method comprises the steps: carrying out the probability density analysis of random samples according to preset mechanical parameters and preset random variables of a to-be-analyzed axle system, and generating a parameter sample point set; determining bridge mechanical characteristics and a time-invariant characteristic matrix according to preset mechanical parameters, and setting an initial state of an axle system; constructing a time-varying characteristic matrix according to the initial state of the axle system, and generating external excitation according to the parameter sample point set; constructing a time-varying load vector according to the external excitation, and determining a time-history response signal according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector; and carrying out harmonic wavelet analysis on the time history response signal to obtain a spectral response analysis result. According to the method, through harmonic wavelet analysis and probability density analysis random sample generation, high precision is guaranteed, repeated calculation of a large number of samples is avoided, and the axle system spectral response analysis efficiency is effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge engineering, and in particular to a vehicle-bridge system spectrum response analysis method, device, electronic equipment and medium. Background Art

[0002] The spectral response analysis of bridges under vehicle loads is a dynamic analysis of the vehicle-bridge system, which is of great significance for vehicle operation safety assessment, bridge design, dynamic performance assessment, and reinforcement and reconstruction. Due to material variation, environmental influences, and manufacturing errors, the mechanical parameters of the vehicle-bridge system often have strong randomness. The wind load, seismic load, and track irregularity excitation to the vehicle-bridge system also have significant randomness, so the dynamic analysis of the vehicle-bridge system is essentially a complex random process analysis.

[0003] The existing common analysis methods include frequency domain method and Monte Carlo method. However, the frequency domain method cannot reasonably analyze the time-frequency characteristics of the vehicle-bridge system, resulting in large calculation errors. Compared with the frequency domain analysis method, the Monte Carlo method has improved the calculation error, but the Monte Carlo method requires a large number of random sampling and repeated time domain probability analysis of samples, which has low calculation efficiency and is not conducive to engineering applications.

[0004] Therefore, the existing technology has technical problems such as requiring a large amount of random sampling, repeated time-domain probability analysis of samples, and low computational efficiency, which need to be improved. Summary of the invention

[0005] In view of this, it is necessary to provide a vehicle-bridge system spectral response analysis method, device, electronic device and medium to solve the technical problems existing in the prior art that a large amount of random sampling is required, repeated time-domain probability analysis of samples is performed, and the calculation efficiency is low.

[0006] In order to solve the above problems, on the one hand, the present invention provides a vehicle-bridge system spectrum response analysis method, comprising: Probability density analysis random samples are generated according to preset mechanical parameters and preset random variables of the vehicle bridge system to be analyzed to obtain a parameter sample point set; Determine the mechanical characteristics and time-invariant characteristic matrix of the bridge according to the preset mechanical parameters, and set the initial state of the vehicle-bridge system; Construct a time-varying characteristic matrix based on the initial state of the vehicle-bridge system, and generate external excitation based on the parameter sample point set; A time-varying load vector is constructed according to the external excitation, and a time-history response signal is determined according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector; The spectral response analysis results are obtained by performing harmonic wavelet analysis on the time history response signal.

[0007] In a possible implementation, the preset random variables include external excitation random variables and structural system random variables.

[0008] In a possible implementation, a parameter sample point set is obtained by performing a probability density analysis random sample generation based on preset mechanical parameters and preset random variables of the vehicle-bridge system to be analyzed, including: According to the preset random variables of the bridge system to be analyzed, the generalized F-point selection method is used to construct the initial sample point set, and the probability subspace and corresponding probability weight of each sample are determined; The initial sample point set is converted into a parameter sample point set according to a preset probability distribution function and probability weight of a preset random variable.

[0009] In a possible implementation, determining the mechanical properties of the bridge according to the preset mechanical parameters includes: Finite element analysis is performed according to preset mechanical parameters to obtain a bridge mechanical model and determine the bridge mechanical characteristics of the bridge mechanical model.

[0010] In a possible implementation, a time-varying characteristic matrix is ​​constructed according to the initial state of the vehicle-bridge system, including: Determine the vehicle position according to the initial state of the vehicle-bridge system, and determine the corresponding bridge vibration mode value according to the vehicle position; A time-varying characteristic matrix is ​​constructed based on the bridge vibration mode values.

[0011] In a possible implementation, determining a time history response signal according to a time-invariant characteristic matrix, a time-varying characteristic matrix, and a time-varying load vector includes: The motion equation of the vehicle-bridge system is constructed based on the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector; The motion equation of the vehicle-bridge system is solved based on the numerical analysis method to obtain the time-history response signal.

[0012] In a possible implementation, performing harmonic wavelet analysis on the time history response signal to obtain a spectral response analysis result includes: Based on the periodic generalized harmonic wavelet, the time-history response signal is transformed into wavelet coefficients; The power spectrum of the response signal is calculated according to the wavelet coefficients to obtain the spectral response analysis results.

[0013] On the other hand, the present invention also provides a vehicle-bridge system spectrum response analysis device, comprising: A parameter sample construction unit, used to generate a parameter sample point set by performing probability density analysis on random samples according to preset mechanical parameters and preset random variables of the vehicle bridge system to be analyzed; An initial state construction unit is used to determine the mechanical properties and time-invariant characteristic matrix of the bridge according to preset mechanical parameters, and to set the initial state of the vehicle-bridge system; An external excitation generation unit, used to construct a time-varying characteristic matrix according to the initial state of the vehicle-bridge system and to generate external excitation according to a parameter sample point set; A time history signal solving unit is used to construct a time-varying load vector according to an external excitation, and determine a time history response signal according to a time-invariant characteristic matrix, a time-varying characteristic matrix and a time-varying load vector; The harmonic wavelet analysis unit is used to perform harmonic wavelet analysis on the time history response signal to obtain the spectrum response analysis result.

[0014] On the other hand, the present invention also provides an electronic device, including a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the above-mentioned vehicle-bridge system spectrum response analysis method is implemented.

[0015] On the other hand, the present invention further provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the above-mentioned vehicle-bridge system spectrum response analysis method is implemented.

[0016] The beneficial effects of the present invention are as follows: in the vehicle-bridge system spectral response analysis method provided by the present invention, firstly, a probability density analysis random sample is generated according to the preset mechanical parameters and preset random variables of the vehicle-bridge system to be analyzed to obtain a parameter sample point set; then, the mechanical characteristics of the bridge and the time-invariant characteristic matrix are determined according to the preset mechanical parameters, and the initial state of the vehicle-bridge system is set; a time-varying characteristic matrix is ​​constructed according to the initial state of the vehicle-bridge system, and an external excitation is generated according to the parameter sample point set; a time-varying load vector is constructed according to the external excitation, and a time-history response signal is determined according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector; finally, a harmonic wavelet analysis is performed on the time-history response signal to obtain a spectral response analysis result. The present invention constructs samples by using a probability density analysis random sample generation method based on harmonic wavelet analysis, which can ensure that repeated calculations of a large number of samples are avoided on the basis of high-precision probability evolution, and effectively improve the computational efficiency of the vehicle-bridge system spectral response analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0018] Figure 1 A schematic flow chart of an embodiment of a vehicle-bridge system spectrum response analysis method provided by the present invention; Figure 2 A schematic diagram of a flow chart of random sample generation for probability density analysis according to an embodiment of the present invention; Figure 3 A schematic diagram of a process of constructing a time-varying characteristic matrix according to an embodiment of the present invention; Figure 4 A schematic diagram of a process for determining a time course response signal according to an embodiment of the present invention; Figure 5 Schematic diagram of the process of harmonic wavelet analysis according to an embodiment of the present invention; Figure 6 This is a comparison diagram of the acceleration spectrum response of the left mid-span under the track irregularity excitation of an embodiment of the present invention; Figure 7 A comparison diagram of the time scale and frequency scale of the acceleration spectrum response of an embodiment of the present invention; Figure 8 A schematic structural diagram of an embodiment of a vehicle-bridge system spectrum response analysis device provided by the present invention; Fig. 9 A schematic structural diagram of an embodiment of an electronic device provided by the present invention. DETAILED DESCRIPTION

[0019] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0020] In the description of the embodiments of the present invention, unless otherwise specified, "multiple" means two or more than two. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, "A and / or B" may mean: A exists alone, A and B exist at the same time, and B exists alone.

[0021] The descriptions of "first" and "second" in the embodiments of the present invention are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the technical features defined as "first" and "second" may explicitly or implicitly include at least one of the features.

[0022] Reference to "embodiments" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present invention. The appearance of the phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0023] The present invention provides a vehicle-bridge system spectrum response analysis method, device, electronic equipment and medium, which are respectively described below.

[0024] Figure 1 A schematic flow chart of an embodiment of the vehicle-bridge system spectrum response analysis method provided by the present invention is shown in FIG. Figure 1 As shown in FIG. 1 , the vehicle-bridge system spectrum response analysis method includes: S101, performing probability density analysis on random samples according to preset mechanical parameters and preset random variables of the axle system to be analyzed to obtain a parameter sample point set; S102, determining the mechanical characteristics and time-invariant characteristic matrix of the bridge according to preset mechanical parameters, and setting the initial state of the vehicle-bridge system; S103, constructing a time-varying characteristic matrix according to the initial state of the vehicle-bridge system, and generating external excitation according to the parameter sample point set; S104, constructing a time-varying load vector according to the external excitation, and determining a time-history response signal according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector; S105, performing harmonic wavelet analysis on the time history response signal to obtain a spectral response analysis result.

[0025] Compared with the prior art, the vehicle-bridge system spectral response analysis method provided by the present invention first generates random samples by probability density analysis according to preset mechanical parameters and preset random variables of the vehicle-bridge system to be analyzed to obtain a parameter sample point set; then determines the mechanical characteristics of the bridge and the time-invariant characteristic matrix according to the preset mechanical parameters, and sets the initial state of the vehicle-bridge system; constructs a time-varying characteristic matrix according to the initial state of the vehicle-bridge system, and generates external excitation according to the parameter sample point set; constructs a time-varying load vector according to the external excitation, and determines the time-history response signal according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector; finally, performs harmonic wavelet analysis on the time-history response signal to obtain the spectral response analysis result. The present invention constructs samples by using the probability density analysis random sample generation method based on the harmonic wavelet analysis, which can avoid repeated calculations of a large number of samples on the basis of high-precision probability evolution, and effectively improves the computational efficiency of the vehicle-bridge system spectral response analysis.

[0026] In some embodiments of the present invention, the preset random variables include external excitation random variables and structural system random variables.

[0027] In some embodiments of the present invention, Figure 2 FIG. 1 is a flow chart of random sample generation for probability density analysis according to an embodiment of the present invention. Figure 2 As shown, a parameter sample point set is obtained by performing probability density analysis on random samples according to preset mechanical parameters and preset random variables of the vehicle-bridge system to be analyzed, including: S201, constructing an initial sample point set by using a generalized F-point selection method according to preset random variables of the vehicle-bridge system to be analyzed, and determining a probability subspace and a corresponding probability weight of each sample; S202: Convert the initial sample point set into a parameter sample point set according to a preset probability distribution function and probability weight of a preset random variable.

[0028] Specifically, before performing the spectral response analysis of the vehicle-bridge system, the embodiment first sets various parameters in the vehicle-bridge system, including mechanical parameters and random variables of the vehicle-bridge system. The random variables include external excitation random variables Structural system random variables related to structural system parameters The sample size of the random variable is denoted by .

[0029] Then the example uses the generalized F-point selection method to generate indivual The initial sample point set of the dimension element ,as follows:

[0030] in, , is the random variable of the bridge system Representative points, is the random variable of the bridge system The representative point coordinates, the embodiment uses the generalized F-point selection method to continuously iterate and modify the point set so that the selected point set is The samples are evenly distributed in the dimensional space, and a small number of points are used to traverse the entire sample space, which reduces the number of calculations and improves the calculation efficiency.

[0031] In the generalized F-point selection method, point The probability subspace occupied by It is expressed as:

[0032] in, for dimensional unit space, , for dimensional probability space, where the reference points are randomly selected.

[0033] Subspace The probability weight assigned It is expressed as:

[0034] in, is the probability density distribution function of the random variables of the vehicle-bridge system.

[0035] Then, according to the actual probability distribution function of the random variable of the bridge system, the initial sample point set Converted into an actual parameter sample point set , the formula is as follows:

[0036] in, Indicates the axle system Sample points, Indicates The sample point coordinates, The calculation process is as follows: For example, the axle system The random variable follows the interval The uniform distribution is:

[0037] Axle system The random variable has a mean , the variance is Normal distribution, then:

[0038] Axle system The random variable has a mean , the variance is The log-normal distribution of is:

[0039]

[0040] The embodiment effectively optimizes the sample selection through the above method, and assigns a corresponding probability to each input sample, so as to use a small number of representative sample points to traverse the entire sample space, thereby significantly improving the calculation efficiency of the spectral response of the vehicle-bridge system while ensuring the calculation accuracy.

[0041] In some embodiments of the present invention, determining the mechanical properties of a bridge according to preset mechanical parameters includes: Finite element analysis is performed according to preset mechanical parameters to obtain a bridge mechanical model and determine the bridge mechanical characteristics of the bridge mechanical model.

[0042] Specifically, the mechanical characteristics and time-invariant characteristic matrix of the bridge are determined, and the initial state of the vehicle-bridge system is set. According to the preset mechanical parameters of the bridge, the embodiment uses finite element analysis software to establish a mechanical model of the bridge and calculate the mechanical characteristics of the bridge, such as the natural frequency and vibration mode. and the natural frequency Generally, the order is 5 to 10. And the initial state vector displacement of the bridge system is set ,speed and acceleration , the formula is:

[0043] in, , and are the generalized displacement, velocity and acceleration of the bridge-related degrees of freedom, respectively, and are rank vector, is the bridge vibration mode order. , and are the displacement, velocity and acceleration of the vehicle’s relevant degrees of freedom, and are rank vector, is the number of vehicle-related degrees of freedom.

[0044] Then, according to the mechanical parameters of the vehicle-bridge system, the embodiment constructs a time-invariant characteristic matrix of the vehicle-bridge system. , and , both Order square array.

[0045] In some embodiments of the present invention, Figure 3 FIG. 1 is a flow chart of constructing a time-varying characteristic matrix according to an embodiment of the present invention. Figure 3 As shown in the figure, a time-varying characteristic matrix is ​​constructed according to the initial state of the vehicle-bridge system, including: S301, determining a vehicle position according to an initial state of a vehicle-bridge system, and determining a corresponding bridge vibration mode value according to the vehicle position; S302, constructing a time-varying characteristic matrix according to the bridge vibration mode values.

[0046] Specifically, in the process of constructing the time-varying characteristic matrix, the embodiment first determines the location of the vehicle according to the vehicle speed and running time. :

[0047] in, is the initial position of the vehicle, is the initial speed of the vehicle, is the vehicle's acceleration, The time the vehicle is running.

[0048] Then, the bridge vibration value at the position of the wheel in contact with the bridge is determined according to the position of the vehicle. , is the total number of wheels. Determine the time-varying characteristic matrix of the vehicle-bridge system according to the bridge vibration mode value , and .

[0049] Then, the embodiment generates actual external excitations, such as track unevenness loads, wind loads, and earthquake loads, according to external excitation random variables related to the vehicle-bridge system external excitations.

[0050] In some embodiments of the present invention, Figure 4 FIG. 1 is a flow chart of determining a time course response signal according to an embodiment of the present invention. Figure 4 As shown, the time history response signal is determined according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector, including: S401, constructing a vehicle-bridge system motion equation according to a time-invariant characteristic matrix, a time-varying characteristic matrix, and a time-varying load vector; S402, solving the vehicle-bridge system motion equation based on a numerical analysis method to obtain a time-history response signal.

[0051] Specifically, in the process of generating the time-history response signal, the embodiment first constructs an external time-varying load vector according to the sample value of the external excitation. , the formula is:

[0052] in, is the external time-varying load vector associated with the bridge, rank vector, is the vehicle-related external time-varying load vector, Rank vector.

[0053] And the motion equation of the vehicle-bridge system is constructed based on the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector:

[0054] Then, the embodiment takes into account that the motion equation of the vehicle-bridge system constructed is a second-order differential equation, and the coefficient matrix is ​​time-varying, so it is impossible to obtain an accurate analytical solution to the equation. Therefore, the embodiment adopts a numerical analysis method of dynamic response to solve the equation. The main calculation principle of the numerical analysis method is to discretize time, calculate the displacement, velocity and acceleration transformation within a small time interval, and use the state of the previous moment to calculate the state (displacement, velocity and acceleration) of the next moment, so as to calculate the state of each moment.

[0055] In some embodiments of the present invention, Figure 5 FIG. 1 is a flow chart of harmonic wavelet analysis according to an embodiment of the present invention. Figure 5 As shown, the harmonic wavelet analysis of the time history response signal is performed to obtain the spectral response analysis results, including: S501, performing wavelet transform on the time-history response signal based on periodic generalized harmonic wavelet to obtain wavelet coefficients; S502: Calculate the power spectrum of the response signal according to the wavelet coefficients to obtain a spectrum response analysis result.

[0056] Specifically, the harmonic wavelet function is usually a group of wavelet function families, which are respectively obtained by scaling and translating the wavelet basis functions. The embodiment uses a periodic generalized harmonic wavelet to perform wavelet transform calculation, and the expression is as follows:

[0057] in, and are the expressions of wavelet function in time domain and frequency domain respectively, and are the scale factor and translation factor of the wavelet function, is the signal length, is the sampling frequency of the signal, and are the upper and lower limits of the wavelet function frequency domain window, is the scale factor of the wavelet window, , is the Dirac function.

[0058] Then the embodiment performs wavelet transform on the time history response signal of the vehicle-bridge system:

[0059] in, is the time response signal of the vehicle-bridge system; is the complex conjugate function of the time domain expression of the wavelet function; In response to the signal The scale factor is The translation factor is According to the relevant theory of harmonic wavelet transform, the power spectrum of the response signal is calculated as follows:

[0060] in, The response signal is at a frequency , time is The power spectrum value at is the mean function. Since the vehicle-bridge system follows the law of probability conservation, that is, the system input probability and system output probability are the same. Therefore, the spectral response of the vehicle-bridge system can be expressed as:

[0061] in, It is The response sample signal has a scale factor of , the translation factor is The wavelet coefficients at is the sample probability of the system input.

[0062] Embodiment According to the above process, the sample selection of the system is optimized through generalized F-point selection, and a corresponding probability is assigned to each input sample. The overall motion equation of the vehicle-bridge system is solved using the numerical analysis method of dynamic response to obtain the time-history response of the vehicle-bridge system. The wavelet coefficient of each sample is calculated with the help of wavelet transform, and the probability of each wavelet coefficient is obtained based on the probability conservation theory. Finally, the spectral response of the vehicle-bridge system is calculated through the relevant theoretical calculation of the harmonic wavelet function.

[0063] In order to verify the effectiveness of the present invention, the present invention verifies the technical effects through the following embodiments: First, the embodiment considers that a 5-carriage train passes through a two-span equal-section continuous beam bridge (20m+20m) at a constant speed of v=360.0km / h under the excitation of track irregularity, and the vehicle spacing is 5.0m. The relevant mechanical parameters of the vehicle-bridge system are shown in Table 1 below: Table 1: Relevant mechanical parameters of the vehicle-bridge system

[0064] Then set the number of random parameter samples N = 1800 and the number of external excitation random variables , the random variables all obey the interval of uniform distribution.

[0065] Generate 1800 2D point sets using the generalized F-point selection method indivual The initial sample point set of the dimension element :

[0066]

[0067] Then calculate the probability subspace divided by each point , the probability subspace is divided into .

[0068] Then the random variable Converted into an actual parameter sample point set :

[0069] According to the relevant mechanical parameters of the vehicle-bridge system, the finite element analysis mechanical model of the bridge was established using the finite element analysis software MIDAS. The vibration mode and the corresponding natural frequency of the bridge were calculated, and the vibration mode was converted into a vibration mode with a vibration mode mass of 1. The number of vibration modes calculated subsequently was taken as 5th order.

[0070] Then consider that the vehicle goes up the bridge from rest, so the initial state vector of the vehicle-bridge system is expressed as follows:

[0071] Among them, the number of degrees of freedom related to the bridge is , vehicle-related degrees of freedom ,therefore , and Both are 35×1 dimensional vectors.

[0072] According to the mechanical parameters of the vehicle-bridge system, the time-invariant characteristic matrix of the vehicle-bridge system is constructed. , and .

[0073] In the embodiment, track irregularity is used as the external excitation of the system, and the track irregularity power spectrum adopts the German track irregularity power spectrum , the track irregularity sample is calculated as follows:

[0074] in, No. Track irregularity samples, is the frequency point number; is the frequency spacing, . and are the cosine factor and the sine factor respectively, and their expressions are as follows:

[0075] Then calculate the position of the vehicle at different times, determine the vibration mode value of the vehicle position according to the vehicle position, and construct the time-varying characteristic matrix of the vehicle-bridge system , and .

[0076] According to the vibration mode value at each wheel position, determine the external load sample vector:

[0077]

[0078]

[0079] in, and are the vehicle load vector and bridge load vector of the vehicle-bridge system respectively; , and The vehicle The track irregularity value, the first-order derivative value and the second-order derivative value of the track irregularity at the location of each wheel; For the The vibration mode value of the bridge at the location of the wheel, and They are half the frame length and half the body length respectively. , , .

[0080] Then establish the equation of motion of the vehicle-bridge system:

[0081] in, For the The external load vector sample of the bridge system. By solving it, we can get the first Time course response samples .

[0082] Final response sample to the time course Perform harmonic wavelet transform to get the wavelet coefficients Then according to the wavelet coefficients The power spectrum of the response signal is calculated to obtain the spectrum response analysis results.

[0083] The results of this embodiment are compared with the calculation results of the traditional frequency domain analysis method and the Monte Carlo method. Figure 6 and Figure 7 The comparison results, Figure 6 This is a comparison diagram of the acceleration spectrum response of the left span mid-span under the track irregularity excitation of an embodiment of the present invention. Figure 7 : is a comparison diagram of the time scale and frequency scale of the acceleration spectrum response of an embodiment of the present invention. Figure 6 From left to right, the acceleration spectrum responses of the left span of the bridge obtained by the method proposed by the present invention, the Monte Carlo method and the traditional frequency domain analysis method are shown in Figure 1. Figure 7The upper curve is the acceleration spectrum response curve at a time of 1.25s, the lower curve is the acceleration spectrum response curve at a frequency of 78rad / s, the dotted line is the calculation result of the method proposed in the present invention, the dotted line is the calculation result of the Monte Carlo method, and the double horizontal line is the calculation result of the traditional frequency domain method. In the time domain and frequency domain, the spectrum response of the vehicle-bridge system calculated by the method proposed in the present invention is highly consistent with the power spectrum calculated by the Monte Carlo method. The number of samples required by the method proposed in the present invention is only 1800, and the calculation time is 15.09s, while the Monte Carlo method requires The calculation time is 1953.08s. However, the error between the calculation results of the traditional frequency domain analysis method and the Monte Carlo method is large, and the error at the peak of the acceleration spectrum response is 19.6%. Therefore, the method proposed in this paper can reduce the number of calculations and greatly shorten the calculation time without reducing the accuracy of the calculation results, providing a reliable and fast calculation method for the spectral response analysis of the bridge system.

[0084] In summary, in the vehicle-bridge system spectral response analysis method provided by the present invention, firstly, a probability density analysis random sample is generated according to the preset mechanical parameters and preset random variables of the vehicle-bridge system to be analyzed to obtain a parameter sample point set; then, the mechanical characteristics of the bridge and the time-invariant characteristic matrix are determined according to the preset mechanical parameters, and the initial state of the vehicle-bridge system is set; a time-varying characteristic matrix is ​​constructed according to the initial state of the vehicle-bridge system, and an external excitation is generated according to the parameter sample point set; a time-varying load vector is constructed according to the external excitation, and a time-history response signal is determined according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector; finally, a harmonic wavelet analysis is performed on the time-history response signal to obtain a spectral response analysis result. The present invention constructs samples by using a probability density analysis random sample generation method based on harmonic wavelet analysis, which can avoid repeated calculations of a large number of samples on the basis of high-precision probability evolution, and effectively improve the computational efficiency of the vehicle-bridge system spectral response analysis.

[0085] In order to better implement the vehicle-bridge system spectrum response analysis method in the embodiment of the present invention, based on the vehicle-bridge system spectrum response analysis method, correspondingly, Figure 8 As shown, the present invention also provides a vehicle-bridge system spectrum response analysis device, and the vehicle-bridge system spectrum response analysis device 800 includes: A parameter sample construction unit 801 is used to generate a parameter sample point set by performing a probability density analysis on a random sample according to preset mechanical parameters and preset random variables of the vehicle bridge system to be analyzed; An initial state construction unit 802 is used to determine the mechanical properties and time-invariant properties of the bridge according to preset mechanical parameters, and to set the initial state of the vehicle-bridge system; The external excitation generation unit 803 is used to construct a time-varying characteristic matrix according to the initial state of the vehicle-bridge system and generate external excitation according to the parameter sample point set; A time history signal solving unit 804 is used to construct a time-varying load vector according to the external excitation, and determine a time history response signal according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector; The harmonic wavelet analysis unit 805 is used to perform harmonic wavelet analysis on the time history response signal to obtain a spectral response analysis result.

[0086] The vehicle-bridge system spectral response analysis device 800 provided in the above embodiment can implement the technical solution described in the above embodiment of the vehicle-bridge system spectral response analysis method. The specific implementation principles of the above modules or units can refer to the corresponding contents in the above embodiment of the vehicle-bridge system spectral response analysis method, which will not be repeated here.

[0087] like Fig. 9 As shown, the present invention also provides an electronic device 900. The electronic device 900 includes a processor 901, a memory 902 and a display 903. Fig. 9 Only some components of the electronic device 900 are shown, but it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0088] In some embodiments, the processor 901 may be a central processing unit (CPU), a microprocessor or other data processing chip, which is used to run program codes or process data stored in the memory 902, such as the vehicle-bridge system spectrum response analysis method of the present invention.

[0089] In some embodiments, the processor 901 may be a single server or a server group. The server group may be centralized or distributed. In some embodiments, the processor 901 may be local or remote. In some embodiments, the processor 901 may be implemented in a cloud platform. In one embodiment, the cloud platform may include a private cloud, a public cloud, a hybrid cloud, a community cloud, a distributed cloud, an internal cloud, a multi-cloud, etc., or any combination thereof.

[0090] In some embodiments, the memory 902 may be an internal storage unit of the electronic device 900, such as a hard disk or memory of the electronic device 900. In other embodiments, the memory 902 may also be an external storage device of the electronic device 900, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc., equipped on the electronic device 900.

[0091] Furthermore, the memory 902 may include both an internal storage unit of the electronic device 900 and an external storage device. The memory 902 is used to store application software installed in the electronic device 900 and various data.

[0092] In some embodiments, the display 903 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch device, etc. The display 903 is used to display information of the electronic device 900 and to display a visual user interface. The components 901-903 of the electronic device 900 communicate with each other through a system bus.

[0093] In one embodiment, when the processor 901 executes the vehicle-bridge system spectrum response analysis program in the memory 902, the following steps may be implemented: Probability density analysis random samples are generated according to preset mechanical parameters and preset random variables of the vehicle bridge system to be analyzed to obtain a parameter sample point set; Determine the mechanical characteristics and time-invariant characteristic matrix of the bridge according to the preset mechanical parameters, and set the initial state of the vehicle-bridge system; Construct a time-varying characteristic matrix based on the initial state of the vehicle-bridge system, and generate external excitation based on the parameter sample point set; A time-varying load vector is constructed according to external excitation, and a time-history response signal is determined according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector; The spectral response analysis results are obtained by performing harmonic wavelet analysis on the time history response signal.

[0094] It should be understood that: when the processor 901 executes the vehicle-bridge system spectrum response analysis program in the memory 902 , in addition to the above functions, other functions may also be implemented, for details, see the description of the corresponding method embodiments above.

[0095] Accordingly, an embodiment of the present application also provides a computer-readable storage medium, which is used to store computer-readable programs or instructions. When the program or instructions are executed by a processor, the steps or functions in the vehicle-bridge system spectrum response analysis method provided in the above-mentioned method embodiments can be implemented.

[0096] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware (such as a processor, a controller, etc.) through a computer program, and the computer program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0097] The above is a detailed introduction to the vehicle-bridge system spectrum response analysis method, device, electronic device and storage medium provided by the present invention. Specific examples are used herein to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims

1. A vehicle-bridge system spectrum response analysis method, characterized in that: include: Probability density analysis random samples are generated according to preset mechanical parameters and preset random variables of the vehicle bridge system to be analyzed to obtain a parameter sample point set; Determining the mechanical characteristics and time-invariant characteristic matrix of the bridge according to the preset mechanical parameters, and setting the initial state of the vehicle-bridge system; Constructing a time-varying characteristic matrix according to the initial state of the vehicle-bridge system, and generating an external excitation according to the parameter sample point set; Constructing a time-varying load vector according to the external excitation, and determining a time-history response signal according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector; Performing harmonic wavelet analysis on the time history response signal obtains a spectral response analysis result.

2. The vehicle-bridge system spectrum response analysis method according to claim 1, characterized in that: The preset random variables include external excitation random variables and structural system random variables.

3. The vehicle-bridge system spectrum response analysis method according to claim 1, characterized in that: The method of performing probability density analysis on random samples according to preset mechanical parameters and preset random variables of the axle system to be analyzed to obtain a parameter sample point set includes: According to the preset random variables of the bridge system to be analyzed, the generalized F-point selection method is used to construct the initial sample point set, and the probability subspace and corresponding probability weight of each sample are determined; The initial sample point set is converted into a parameter sample point set according to a preset probability distribution function of the preset random variable and the probability weight.

4. The vehicle-bridge system spectrum response analysis method according to claim 1, characterized in that: Determining the mechanical properties of the bridge according to the preset mechanical parameters includes: Finite element analysis is performed according to the preset mechanical parameters to obtain a bridge mechanical model and determine the bridge mechanical characteristics of the bridge mechanical model.

5. The vehicle-bridge system spectrum response analysis method according to claim 1, characterized in that: The step of constructing a time-varying characteristic matrix according to the initial state of the vehicle-bridge system includes: Determine the position of the vehicle according to the initial state of the vehicle-bridge system, and determine the corresponding bridge vibration mode value according to the vehicle position; A time-varying characteristic matrix is ​​constructed according to the bridge vibration shape values.

6. The vehicle-bridge system spectrum response analysis method according to claim 1, characterized in that: The determining of the time history response signal according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector comprises: Constructing a vehicle-bridge system motion equation according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector; The motion equation of the vehicle-bridge system is solved based on a numerical analysis method to obtain a time-history response signal.

7. The vehicle-bridge system spectrum response analysis method according to claim 1, characterized in that: The performing harmonic wavelet analysis on the time history response signal to obtain a spectral response analysis result includes: Performing wavelet transformation on the time-history response signal based on periodic generalized harmonic wavelet to obtain wavelet coefficients; The power spectrum of the response signal is calculated according to the wavelet coefficients to obtain a spectrum response analysis result.

8. A vehicle-bridge system spectrum response analysis device, characterized in that: include: A parameter sample construction unit, used to generate a parameter sample point set by performing probability density analysis on random samples according to preset mechanical parameters and preset random variables of the vehicle bridge system to be analyzed; An initial state construction unit, used to determine the mechanical properties and time-invariant property matrix of the bridge according to the preset mechanical parameters, and to set the initial state of the vehicle-bridge system; An external excitation generating unit, used to construct a time-varying characteristic matrix according to the initial state of the vehicle-bridge system, and to generate external excitation according to the parameter sample point set; A time history signal solving unit, used for constructing a time-varying load vector according to the external excitation, and determining a time history response signal according to the time-invariant characteristic matrix, the time-varying characteristic matrix and the time-varying load vector; The harmonic wavelet analysis unit is used to perform harmonic wavelet analysis on the time history response signal to obtain a spectral response analysis result.

9. An electronic device comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the vehicle-bridge system spectrum response analysis method according to any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the vehicle-bridge system spectrum response analysis method according to any one of claims 1 to 7 is implemented.

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