Pantograph base vibration signal construction method based on measured power spectral density

Abstract

The application discloses a pantograph base vibration signal construction method based on a measured power spectral density, and relates to the technical field of vehicle dynamics simulation.The method calculates a target power spectral density based on a measured response signal of a target measuring point; a target spectrum envelope is constructed based on the target power spectral density, a frequency band compensation function is introduced, and an equivalent boundary input spectrum is obtained through iterative correction in combination with a simulation response spectrum calculated based on a transfer relationship established based on a vehicle dynamics transfer model; a single-channel reference time history is generated based on the equivalent boundary input spectrum, and the single-channel reference time history is mapped into a multi-dimensional boundary excitation by using a spatial phase relationship of a vehicle rigid body motion mode.The application can truly restore the vehicle vibration transfer characteristics and multi-dimensional attitude changes, and improve the accuracy of the simulation boundary conditions.

Description

Technical Field

[0001] This application relates to the field of vehicle dynamics simulation technology, specifically to a method for constructing a pantograph base vibration signal based on measured power spectral density. Background Technology

[0002] Electrified highways achieve dynamic power supply to vehicles during operation by deploying an overhead contact line and drawing current from the onboard pantograph. Compared to railway vehicles, highway vehicles are more significantly affected by road irregularities, tire-suspension systems, cab mounting, and changes in vehicle posture. The pantograph base experiences complex boundary movements such as vertical vibration, pitch, and lateral tilt. These vibrations directly alter the relative displacement and contact force between the pantograph's contact wire and the contact plate, thus affecting current collection stability, the risk of disconnection, and the service life of the pantograph-catenary components.

[0003] Current pantograph-catenary simulations often use single-frequency sine waves, standard random road surface spectra, or empirical amplitudes as inputs to the pantograph base. These methods struggle to reflect the true spectral characteristics of measured pantograph base vibrations. Especially in electrified highway scenarios, vehicle vibration transmission paths are complex, and the power spectral density of the pantograph base often exhibits significant multi-peak characteristics, low-frequency amplification, and mid-to-high-frequency attenuation. Directly using a single sine function or an uncalibrated random signal as the boundary excitation will lead to discrepancies between the simulated pantograph-catenary contact force results and actual measured conditions. Summary of the Invention

[0004] This application provides a method for constructing pantograph base vibration signals based on measured power spectral density, which can more realistically describe the frequency domain effect of vehicle vibration on the pantograph base.

[0005] This application provides a method for constructing the vibration signal of a pantograph base based on measured power spectral density, including:

[0006] Calculate the target power spectral density based on the measured response signal of the target measurement point;

[0007] A target spectral envelope is constructed based on the target power spectral density. An equivalent boundary input spectrum is determined based on the target spectral envelope and the frequency band compensation function. The frequency band compensation function is iteratively corrected based on the simulation response spectrum calculated by the transfer relationship established by the vehicle dynamics transfer model.

[0008] A single-channel reference time history is generated based on the equivalent boundary input spectrum, and the single-channel reference time history is mapped to a multi-dimensional boundary excitation by utilizing the spatial phase relationship of the vehicle rigid body motion modes.

[0009] Based on the multidimensional boundary excitation and the transmission relationship, the vibration signal of the pantograph base is calculated.

[0010] Optionally, the bandwidth compensation function includes a local compensation term and a broadband trend compensation term;

[0011] The local compensation term is used to correct the amplitude deviation between the simulated response spectrum calculated based on the transfer relationship and the target power spectral density in the local frequency band;

[0012] The broadband trend compensation term is used to correct the overall spectral amplitude deviation between the simulated response spectrum and the target power spectral density within a preset broadband band.

[0013] Optionally, the formula for calculating the frequency band compensation function is:

[0014] ;

[0015] in, The frequency band compensation function is... For the current frequency, Let J be the compensation amplitude for the j-th local frequency band. Let j be the compensation center frequency of the j-th frequency band. The compensation bandwidth for the j-th frequency band is... For the aforementioned local compensation term, To compensate for the amplitude of broadband trend, For the maximum frequency, For exponential parameters, This is the broadband trend compensation term.

[0016] Optionally, the iterative correction process includes:

[0017] Perform a superposition step, which includes superimposing the target spectral envelope with the frequency band compensation function to obtain the equivalent boundary input spectrum;

[0018] The input step includes calculating the simulation response spectrum based on the equivalent boundary input spectrum and the transfer relationship;

[0019] The adjustment steps include: if the simulated response spectrum is higher than the target power spectral density in the target frequency band, then reducing the compensation amplitude or the broadband trend compensation amplitude corresponding to the target frequency band; if the simulated response spectrum is lower than the target power spectral density in the target frequency band, then increasing the compensation amplitude or the broadband trend compensation amplitude corresponding to the target frequency band.

[0020] Repeat the superposition step, the input step, and the adjustment step until the deviation between the simulated response spectrum and the target power spectral density meets the preset convergence condition.

[0021] Optionally, the multidimensional boundary excitation includes vertical excitation, roll excitation, and pitch excitation, and the mapping of the single-channel reference time history to multidimensional boundary excitation using the spatial phase relationship of the vehicle rigid body motion modes includes:

[0022] The single-channel reference time history is mapped to multiple support corner points of the vehicle in an in-phase input manner to generate the vertical excitation;

[0023] The single-channel reference time history is mapped to the multiple support corner points in a left-right inverted input manner to generate the tilt excitation;

[0024] The single-channel reference time history is mapped to the multiple support corner points in a forward-backward inverted input manner to generate the pitch excitation.

[0025] Optionally, generating a single-channel reference time history based on the equivalent boundary input spectrum includes:

[0026] The equivalent boundary input spectrum is discretized into multiple discrete frequency components;

[0027] Based on the power spectral density value and frequency resolution of each of the plurality of discrete frequency components, the corresponding displacement amplitude is calculated.

[0028] Based on the displacement amplitude, the discrete frequency components, and the random phase, the single-channel reference time history is generated by superposition.

[0029] The formula for calculating the single-channel reference time history is as follows:

[0030] ;

[0031] in, The single-channel reference time history, This represents the total number of the discrete frequency components involved in the synthesis. The displacement amplitude corresponds to the kth discrete frequency component. For the k-th discrete frequency component, The random phase.

[0032] Optionally, constructing the target spectral envelope based on the target power spectral density includes:

[0033] Key frequency points are extracted from the curve of the target power spectral density, and the key frequency points include at least one of local peak points, local valley points, frequency band boundary points, and points where the spectral slope changes.

[0034] Based on the key frequency points and their corresponding power spectral density values, a continuous target spectral envelope is constructed using a piecewise interpolation method.

[0035] Optionally, the vehicle dynamics transfer model is a multi-degree-of-freedom coupled dynamics model, and the calculation of the simulation response spectrum based on the equivalent boundary input spectrum and the transfer relationship includes:

[0036] Based on the aforementioned transfer relationship, the multidimensional boundary excitation is applied to multiple support corner points to calculate the vertical displacement of the vehicle's center of mass and the rotation angle around the preset coordinate axis.

[0037] Based on the vertical displacement of the vehicle's center of gravity, the rotation angle, and the position parameters of the vehicle's center of gravity to the target measuring point, the vertical displacement and attitude angle of the target measuring point are calculated;

[0038] The simulation response spectrum is determined based on the vertical displacement and attitude angle of the target measuring point.

[0039] Optionally, the target power spectral density is calculated using the following methods:

[0040] The measured response signal is segmented to obtain multiple signal segments;

[0041] After applying a window function to each signal segment, perform a Fast Fourier Transform.

[0042] The target power spectral density is obtained by averaging the transformation results of each signal segment.

[0043] Optionally, the equivalent boundary input spectrum is generated in the following ways:

[0044] The target spectrum envelope is superimposed on the frequency band compensation function in the logarithmic domain;

[0045] The superposition result is transformed from the logarithmic domain to the linear domain to obtain the equivalent boundary input spectrum.

[0046] As described above, the method for constructing pantograph base vibration signals based on measured power spectral density provided in this application has the following beneficial effects:

[0047] The method for constructing pantograph base vibration signals based on measured power spectral density provided in this application effectively counteracts the amplitude distortion of vibration signals caused by the vehicle system's transmission characteristics by introducing a frequency band compensation function and combining iterative correction with a vehicle dynamics transfer model. Compared to directly using standard spectra or empirical formulas, the equivalent boundary input spectrum derived by this method, after model transfer, maintains consistency with the measured target power spectral density in terms of peak position, frequency band energy distribution, and overall trend, thus improving the frequency domain realism of simulation boundary conditions. Furthermore, by utilizing the spatial phase relationship of the vehicle's rigid body motion modes, the single-channel reference time history is mapped to multi-dimensional boundary excitations in vertical, roll, and pitch directions. This not only recreates the complex attitude coupling vibrations of the vehicle during actual operation but also ensures the consistency of the frequency domain statistical characteristics of the excitations in each dimension. Attached Figure Description

[0048] The accompanying drawings, which are provided to further illustrate the embodiments of this application and form part of this application, are not intended to limit the embodiments of this application.

[0049] Figure 1 This is a schematic flowchart of the method for constructing the pantograph base vibration signal based on the measured power spectral density according to an embodiment of this application;

[0050] Figure 2 This is a schematic diagram illustrating the target power spectral density of a pantograph base, as shown in an exemplary embodiment of this application;

[0051] Figure 3 This is a schematic diagram of the simulation response spectrum of a pantograph base, illustrating an exemplary embodiment of this application;

[0052] Figure 4 This is a schematic diagram of a four-degree-of-freedom coupled dynamic model of the seat-cab, as illustrated in an exemplary embodiment of this application.

[0053] Figure 5 This is a schematic diagram illustrating the change of contact force under vertical excitation, as shown in an exemplary embodiment of this application;

[0054] Figure 6 This is a schematic diagram illustrating the change of contact force under tilting excitation, as shown in an exemplary embodiment of this application.

[0055] Figure 7 This is a schematic diagram illustrating the change of contact force under pitch excitation, as shown in an exemplary embodiment of this application. Detailed Implementation

[0056] To better understand the above-mentioned objectives, features, and advantages of this application, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, where there is no conflict, the embodiments and features described in the embodiments of this application can be combined with each other.

[0057] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Therefore, the scope of protection of this application is not limited to the specific embodiments disclosed below.

[0058] Please see Figure 1 This is a flowchart illustrating a method for constructing a pantograph base vibration signal based on measured power spectral density, as shown in an exemplary embodiment of this application. (See reference...) Figure 1 It can be seen that the method for constructing the pantograph base vibration signal based on the measured power spectral density may include steps S110 to S140.

[0059] Step S110: Calculate the target power spectral density based on the measured response signal of the target measurement point.

[0060] In one embodiment of this application, the target measuring point refers to a key location on the vehicle where vibration environment reproduction or coupling analysis is required. In this embodiment, the target measuring point can be the pantograph base, or it can be the cab floor or seat rail, etc. The measured response signal can be time-domain vibration data acquired by a displacement sensor. By performing spectral analysis on this time-domain signal, it can be converted into power spectral density (PSD) in the frequency domain. The target power spectral density can characterize the distribution characteristics of vibration energy with frequency at the target measuring point under actual operating conditions.

[0061] Step S120: Construct the target spectral envelope based on the target power spectral density; determine the equivalent boundary input spectrum based on the target spectral envelope and the frequency band compensation function; and iteratively correct the simulation response spectrum calculated based on the transfer relationship established by the vehicle dynamics transfer model using the frequency band compensation function.

[0062] In one embodiment of this application, since the vehicle system itself is a complex dynamic transmission system, there are inherent frequency response characteristics between the boundary input point and the target measurement point. Directly using the target spectrum as input often leads to the output response being amplified or attenuated in certain frequency bands, thus deviating from the measured results. Therefore, the discrete target power spectral density curve can be smoothed to construct the target spectral envelope, removing random noise interference and retaining the main spectral shape. The band compensation function can be used to counteract the amplitude distortion caused by the system's transmission characteristics. A dynamic transmission model including elements such as the vehicle suspension and body structure can be established. The equivalent boundary input spectrum obtained by superimposing the target spectral envelope and the band compensation function is used as a temporary input for forward simulation calculation to obtain the simulated response spectrum. By comparing the deviation between the simulated response spectrum and the target power spectral density, the parameters of the band compensation function are dynamically adjusted: if the simulated value of a certain frequency band is too high, the compensation amount is reduced; if it is too low, the compensation amount is increased. The true boundary input energy distribution required to offset the system's transmission distortion is searched, and finally, the accurate equivalent boundary input spectrum is obtained through convergence. The iterative correction process does not rely on specific human experience and can be based on automated optimization of the mathematical model.

[0063] It should be noted that the transfer relationship can characterize the mathematical mapping relationship between the boundary input (displacement excitation of the four support corner points) and the response of the target measuring point (pantograph base) in the vehicle dynamics transfer model.

[0064] Step S130: Generate a single-channel reference time history based on the equivalent boundary input spectrum, and map the single-channel reference time history into a multi-dimensional boundary excitation by utilizing the spatial phase relationship of the vehicle rigid body motion modes.

[0065] In one embodiment of this application, after obtaining the equivalent boundary input spectrum in the frequency domain, it is necessary to convert the equivalent boundary input spectrum in the frequency domain into a time domain signal for time-domain dynamics simulation. A single-channel reference time history can be generated based on the equivalent boundary input spectrum, and the single-channel reference time history conforms to the amplitude and frequency distribution defined by the equivalent boundary input spectrum. Since real vehicle vibration is not a single-direction translation, but rather a coupling of multi-dimensional rigid body motions including vertical sway, pitch about the lateral axis, and roll about the longitudinal axis, the orthogonality and symmetry of the vehicle's rigid body motion modes in space can be utilized to establish a mapping relationship from the single-channel signal to the multi-dimensional boundary excitation.

[0066] For example, pure vertical excitation can be simulated by assigning the reference time history in phase to all support points, roll excitation can be simulated by assigning it in opposite phase to the left and right support points, and pitch excitation can be simulated by assigning it in opposite phase to the front and rear support points. The phase coupling relationship between each degree of freedom can be reconstructed, so that the generated multidimensional boundary excitation can realistically drive the vehicle model to produce spatial attitude changes that conform to actual physical laws.

[0067] Step S140: Calculate the vibration signal of the pantograph base based on the multidimensional boundary excitation and transmission relationship.

[0068] In one embodiment of this application, multidimensional boundary excitation can be applied to multiple support corner points of the vehicle dynamics transfer model, and the vibration response of the pantograph base can be obtained through forward dynamics calculation. Since the pantograph base is usually not located at the vehicle's center of mass, the actual vibration of the pantograph base is a vector superposition of the translational motion of the center of mass and its rotation around the center of mass. Based on the positional parameters in the transfer relationship (such as the longitudinal and lateral distances of the pantograph base relative to the vehicle's center of mass), the vertical displacement and attitude angle of the center of mass can be converted into the vertical displacement, pitch angle, and roll angle at the pantograph base. These vibration signals are the final output pantograph base vibration signals, which can be directly used for subsequent pantograph-catenary coupling dynamics simulations.

[0069] The method for constructing pantograph base vibration signals based on measured power spectral density provided in this application can overcome the spectral distortion problem caused by the transmission characteristics of the vehicle system through frequency band compensation iteration. At the same time, it uses spatial phase mapping to map a single signal into multi-dimensional attitude vibration. The output pantograph base vibration signal not only conforms to the measured statistical characteristics but also has real spatial motion attributes, which can provide reliable boundary conditions for pantograph-catenary coupling simulation.

[0070] In one embodiment of this application, the frequency band compensation function includes a local compensation term and a broadband trend compensation term. The local compensation term can be used to correct the amplitude deviation between the simulated response spectrum calculated based on the transfer relationship and the target power spectral density within a local frequency band; the broadband trend compensation term can be used to correct the overall spectral amplitude deviation between the simulated response spectrum and the target power spectral density within a preset broadband frequency band.

[0071] The formula for calculating the frequency band compensation function may include:

[0072] ;

[0073] in, For the frequency band compensation function, This is the current frequency. The first part on the right side of the formula. For partial compensation terms, where The compensation amplitude for the j-th local frequency band is used to control the magnitude of the compensation within that frequency band. Let be the compensation center frequency of the j-th frequency band, corresponding to the frequency position of the resonant peak or valley value that needs to be corrected; The compensation bandwidth for the j-th frequency band determines the range of influence of the local correction. (The second part on the right side of the formula...) For broadband trend compensation term, where To compensate for the amplitude of broadband trend, The global maximum frequency, For exponential parameters.

[0074] For example, the exponential parameter A value greater than 1 can be used to focus on modifying values ​​in the mid-to-high frequency range. The value of r can be adaptively adjusted based on the specific vehicle model's suspension damping characteristics and the measured high-frequency slope of the PSD. For example, r can be set to 1.5.

[0075] In one embodiment of this application, the iterative correction process includes steps S201 to S204.

[0076] Step S201: Perform the superposition step, which includes superimposing the target spectrum envelope with the frequency band compensation function to obtain the equivalent boundary input spectrum.

[0077] Step S202: Perform the input step, which includes calculating the simulation response spectrum based on the equivalent boundary input spectrum and the transfer relationship. Specifically, the equivalent boundary input spectrum generated in the current round is used as the excitation source and input into the vehicle dynamics transfer model for forward solving to obtain the simulation response spectrum at the target measurement point.

[0078] Step S203: Perform adjustment steps. These steps include reducing the compensation amplitude or broadband trend compensation amplitude corresponding to the target frequency band if the simulated response spectrum is higher than the target power spectral density within the target frequency band; and increasing the compensation amplitude or broadband trend compensation amplitude corresponding to the target frequency band if the simulated response spectrum is lower than the target power spectral density within the target frequency band. For example, when a simulated peak value at 3.5Hz is detected to be 2dB higher than the measured target, the amplitude of the local compensation term at that frequency can be automatically reduced. Conversely, if the simulated value at 8Hz is too low, the bandwidth trend compensation amplitude will be increased. Or the local compensation amount for the corresponding frequency band.

[0079] Step S204: Repeat the superposition, input, and adjustment steps until the deviation between the simulated response spectrum and the target power spectral density meets the preset convergence condition. The preset convergence condition can be that the root mean square error across the entire frequency band is less than a set threshold, the maximum single-point deviation does not exceed the allowable range, or the preset maximum number of iterations is reached. Figure 2 As shown, this is a schematic diagram illustrating the target power spectral density of a pantograph base in an exemplary embodiment of this application, where the horizontal axis represents frequency in Hz and the vertical axis represents power spectral density in dB / Hz. Figure 3 As shown, this is a schematic diagram of the simulated response spectrum of a pantograph base according to an exemplary embodiment of this application, where the horizontal axis represents frequency in Hz and the vertical axis represents power spectral density in dB / Hz. After multiple iterations, the final simulated response spectrum is similar to the measured target power spectral density in terms of main peak positions, frequency band energy distribution, and overall attenuation trend.

[0080] In one embodiment of this application, the process of generating a single-channel reference time history based on the equivalent boundary input spectrum may include: discretizing the equivalent boundary input spectrum into multiple discrete frequency components; calculating the corresponding displacement amplitude based on the power spectral density value and frequency resolution of each discrete frequency component; and generating a single-channel reference time history by superimposing the displacement amplitude, discrete frequency components, and random phase.

[0081] The formula for calculating the single-channel reference time history is:

[0082] ;

[0083] in, This is the reference time history for a single channel; t represents time, in seconds. The total number of discrete frequency components participating in the synthesis; The displacement amplitude corresponding to the kth discrete frequency component is determined by the energy of the equivalent boundary input spectrum at that frequency. This represents the k-th discrete frequency component; The random phase corresponding to the k-th frequency component is typically an independent random variable uniformly distributed within the interval. Since actual vehicle vibration is a random process, if all frequency components are given a fixed phase (e.g., all zero), the synthesized signal will exhibit non-physical periodic pulses or excessively high peak factors in the time domain, leading to distortion of the simulated load. By assigning each frequency component an independent random phase, the coherence between harmonic components can be disrupted, allowing the synthesized signal to approximate a Gaussian distribution in amplitude distribution and exhibit the disordered fluctuation characteristics of real road surface excitation in the time domain waveform, thereby ensuring the statistical validity of the subsequent dynamic response.

[0084] ;

[0085] in, This represents the vehicle's equivalent boundary input spectrum value corresponding to the k-th discrete frequency. This indicates the frequency resolution, which can be set to 0.02Hz.

[0086] After obtaining the single-channel reference time history, it needs to be extended to boundary conditions that can drive the vehicle model to generate spatial motion. As one implementation method, multidimensional boundary excitation includes vertical excitation, roll excitation, and pitch excitation. These three excitation components correspond to the three mutually orthogonal basic modes in the rigid body motion of the vehicle: overall heave, roll about the longitudinal axis, and pitch about the lateral axis.

[0087] For vertical excitation, a single-channel reference time history is mapped to multiple support corners of the vehicle in an in-phase input manner to generate vertical excitation. For example, [the following is an example:] Simultaneously applied to four support points—front left, front right, rear left, and rear right—ensuring that the displacements of these four points remain equal in magnitude and direction at all times. This in-phase input only excites pure vertical translation of the vehicle body without generating any torque, and is used to simulate the overall lifting motion of a vehicle traversing a long-wave undulating road surface.

[0088] For roll excitation, a single-channel reference time history is mapped to multiple support corner points using a left-right inverted input method to generate roll excitation. For example, the left support point (e.g., front left, rear left) is used as the input. The input of the right-side support points (such as the front right and rear right) This excitation component is used to reproduce the vehicle body sway caused by the difference in the trajectories of the left and right wheels or the lateral slope of the road surface.

[0089] For pitch excitation, the single-channel reference time history is mapped to multiple support points using an inverted input method to generate pitch excitation. For example, the front axle support points (such as front left and front right) are used as inputs. The rear axle support points (such as rear left and rear right) are then input. This excitation component is used to simulate the pitch motion of a vehicle during acceleration / deceleration (nodding), braking / lifting, or driving over short-wave obstacles.

[0090] Through the mapping method described above, this embodiment successfully decouples and reconstructs a scalar time-history signal into a vector excitation field containing three independent degrees of freedom. This preserves the energy distribution characteristics of the single-channel signal obtained through precise inversion in the frequency domain, while also endowing the signal with correct geometric motion properties through deterministic spatial phase relationships.

[0091] In one embodiment of this application, the process of constructing a target spectral envelope based on a target power spectral density may include: extracting key frequency points from the curve of the target power spectral density, wherein the key frequency points include at least one of local peak points, local valley points, frequency band boundary points, and spectral line slope change points; and constructing a continuous target spectral envelope based on the key frequency points and their corresponding power spectral density values ​​using a piecewise interpolation method.

[0092] The measured target power spectral density typically contains numerous spikes and non-physical fluctuations caused by random noise or signal truncation effects. Using the target power spectral density as a benchmark for iterative correction can easily lead to the compensation function overfitting the noise, resulting in abnormal spikes or distorted energy distribution in the reconstructed excitation signal in the time domain. Therefore, the core characteristics of the spectrum can be characterized by extracting key frequency points with clear physical meaning. For example, such as... Figure 2 As shown, in the vibration spectrum of the pantograph base of an electrified highway truck, local peaks typically correspond to the natural modal frequencies of the vehicle body or suspension system (such as the cab suspension resonance peak at 3.5 Hz), local valleys reflect anti-resonance characteristics or the attenuation zone of the vibration isolator, frequency band boundary points define the effective excitation frequency range (such as 0 Hz to 10 Hz), and points where the spectral slope changes indicate the transition of the vibration energy transfer mechanism (such as the transition from the mid-to-low frequency plateau region to the high-frequency attenuation region). After obtaining these key control points, a continuous target spectral envelope is constructed using the piecewise cubic Hermite interpolation (PCHIP) isoform interpolation algorithm.

[0093] In one possible implementation, the vehicle dynamics transfer model can be a multi-degree-of-freedom coupled dynamics model, such as a seat-cab 4-degree-of-freedom coupled dynamics model. The vehicle dynamics transfer model can be used to establish a positive transfer relationship from the boundary input to the target measurement point response, serving as the physical basis for verifying the validity of the equivalent boundary input spectrum during iterative correction. It should be noted that step S202, which calculates the simulation response spectrum based on the equivalent boundary input spectrum and the transfer relationship, may include steps S202A to S202C.

[0094] Step S202A: Based on the transfer relationship, multidimensional boundary excitation is applied to multiple support corner points to calculate the vertical displacement of the vehicle's center of mass and the rotation angle around the preset coordinate axis. For example... Figure 4 The figure shown is a schematic diagram of a four-degree-of-freedom coupled dynamic model of a seat-cab, illustrating an exemplary embodiment of this application. In this figure, Seat represents the seat, Cab represents the cab, and Elastic connection represents the elastic connection between the seat and the base. The model treats the cab as a rigid body, connected to four support corner points (front left, front right, rear left, and rear right) via spring-damped elements. When vertical, roll, or pitch excitations are applied to these four corner points, the model calculates the vertical displacement of the cab's center of mass according to Newton's second law. Pitch angle about the transverse axis and the tilt angle about the longitudinal axis .

[0095] Vertical excitation can be expressed as: ;

[0096] The roll excitation can be expressed as: , ;

[0097] Pitch excitation can be expressed as: , ;

[0098] The equations of motion for the four-degree-of-freedom coupled dynamics model can be expressed as:

[0099] ;

[0100] ;

[0101] ;

[0102] ;

[0103] For example, with Figure 4 For example, this model uses the displacement of the four corner points. , , and The model has 100 degrees of freedom, which is the boundary condition. , , and . Let be the vertical displacement of the seat's equivalent mass block. This refers to the vertical displacement of the cab's center of gravity. and These are the rotation angles of the cab about the corresponding coordinate axes; where... It is the center of gravity of the cab system. The positive direction of the axis is the direction of vehicle travel. The positive direction of the axis is vertically upward. The positive direction of the axis is determined by the right-hand rule; , , and These represent the damping coefficients of the cab suspension at the four corners; , , and These represent the stiffness coefficients of the cab suspension at the four corners; and These represent the longitudinal distances from the center of gravity of the cab to the front and rear ends of the cab, respectively. , , and These represent the equivalent arm distances from the cab's center of gravity to the front left, front right, rear left, and rear right suspensions, respectively. and These are the distances in the longitudinal and lateral directions of the seat's elastic connection point relative to the center of gravity of the cab; and The model is around shaft and Moment of inertia of the shaft; and These refer to seat weight and cab weight, respectively. (Subscript) , , , , These represent the driver's cab, front, rear, left, and right, respectively. This indicates the vertical displacement of the seat's elastic connection point. , , , These represent the vertical displacements of the cab suspension at the four corners. The vertical displacement acceleration, pitch acceleration, and roll acceleration of the cab's center of gravity are calculated. Then, the vertical displacement of the cab's center of gravity is obtained by integrating these three accelerations twice. Pitch angle and roll angle Because the pitch and roll angles are relative to the overall model of the cab... shaft or Obtained by rotating the axis, for the center node of the pantograph base, its pitch and roll angles are equivalent to the pitch angle of the overall cab model. and roll angle .

[0104] Step S202B: Based on the vertical displacement and rotation angle of the vehicle's center of mass, and the position parameters from the vehicle's center of mass to the target measuring point, calculate the vertical displacement and attitude angle of the target measuring point. Since the target measuring point is usually not located at the vehicle's center of mass, its actual response is a vector superposition of the translation of the center of mass and the rotation about the center of mass.

[0105] The specific calculation formula is as follows:

[0106] ;

[0107] in, The vertical displacement of the target measuring point. This represents the vertical displacement of the vehicle's center of gravity. The vehicle's pitch angle, This refers to the vehicle's roll angle. and These are the longitudinal and lateral distances of the target measuring point relative to the vehicle's center of gravity, respectively, i.e., the aforementioned positional parameters. For the pantograph base installed at the rear top of the cab, its longitudinal distance... It can be 0.813, lateral offset It can be 0.013.

[0108] Step S202C determines the simulation response spectrum based on the vertical displacement and attitude angle of the target measurement point. Since step S220 outputs a time-domain signal (a sequence of vertical displacement and attitude angle changes over time), and the iterative correction process requires deviation comparison in the frequency domain (both the simulation response spectrum and the target power spectral density are power spectral density curves in the frequency domain), the time-domain response signal can be converted to a power spectral density in the frequency domain. The power spectral density of the time-domain response signal calculated in step S202B can be estimated to obtain the simulation response spectrum for the current iteration. This simulation response spectrum will be fed back into the iterative correction process and compared with the target power spectral density for parameter adjustment of the frequency band compensation function.

[0109] In one embodiment of this application, the calculation of the target power spectral density may include: segmenting the measured response signal to obtain multiple signal segments; applying a window function to each signal segment and then performing a Fast Fourier Transform; averaging the transform results of each signal segment to obtain the target power spectral density. A segmented averaging spectral estimation method (i.e., the Welch method) can be used for this process. During segmentation, a certain overlap rate (e.g., 50% or 75%) can be set between adjacent signal segments to increase the number of effective data segments and further smooth spectral fluctuations. Window functions can be used to suppress spectral leakage caused by signal truncation; Hanning, Hamming, Blackman, or Kaiser windows can be selected. The choice of the number of segments needs to strike a balance between frequency resolution and statistical smoothness: more segments result in smoother spectral estimation but lower frequency resolution; fewer segments result in higher frequency resolution but greater spectral noise. The operator can adaptively determine the segmentation strategy based on the total duration of the measured signal and the width of the target reconstructed bandwidth.

[0110] The formula for determining the target power spectral density can be expressed as:

[0111] ;

[0112] in, Indicates the target power spectral density. Indicates the number of segments. Indicates the sampling frequency. Represents the energy normalization coefficient. This refers to window functions (e.g., the Hanning window function). This represents the measured vibration signal. This represents the Fast Fourier Transform.

[0113] In one embodiment of this application, the equivalent boundary input spectrum is generated by: superimposing the target spectrum envelope and the frequency band compensation function in the logarithmic domain; and converting the superposition result from the logarithmic domain to the linear domain to obtain the equivalent boundary input spectrum.

[0114] The formula for calculating the vehicle equivalent boundary input spectrum may include:

[0115] ;

[0116] in, The input spectrum is the equivalent boundary of the transformed linear domain. Let be the logarithm of the target spectral envelope. This is the logarithm of the frequency band compensation function.

[0117] In one embodiment of this application, after obtaining the multidimensional boundary excitation, the method for constructing the pantograph base vibration signal based on the measured power spectral density may further include: applying the multidimensional boundary excitation to multiple support corner points of the vehicle dynamics model, calculating the time-domain response of the target measurement point; outputting the time-domain response at a fixed time step to generate a time-domain excitation file, which contains a time column and a corresponding response data column for importing into the subsequent dynamics simulation model.

[0118] Using pantograph-catenary coupling simulation of heavy-duty trucks on electrified highways as a typical application scenario, this paper demonstrates the process from measured data processing to final simulation loading. In this scenario, the target measurement point is set as the pantograph base. Vertical vibration signals of the pantograph base are collected when the vehicle is traveling on an actual operating road section, and the frequency band from 0Hz to 10Hz is selected as the target reconstruction frequency band. The equivalent boundary input spectrum obtained through iterative inversion, combined with the three types of multi-dimensional boundary excitations (vertical, roll, and pitch) generated by spatial phase mapping, are applied to the four support corners of the four-degree-of-freedom coupled dynamic model of the seat-cab. The longitudinal distance between the center of the pantograph base and the center of mass of the cab is also considered. The value is 0.813, representing the horizontal distance. The value is set to 0.013 to ensure the accuracy of the position parameter transmission relationship.

[0119] The system discretizes the calculated time-domain response of the pantograph base at a fixed time step (e.g., 0.001s or other step sizes set according to simulation requirements) and generates three independent text files: vertical.txt, pitch.txt, and roll.txt. Each file uses a two-column data format: the first column is the time series, and the second column is the corresponding physical quantity value. Specifically, vertical.txt records the vertical displacement (in meters) of the pantograph base center, pitch.txt records the pitch angle (in rad) about the vehicle's lateral axis, and roll.txt records the roll angle (in rad) about the vehicle's longitudinal axis.

[0120] In the subsequent pantograph-catenary dynamics simulation, the time-domain excitation files can be directly imported as boundary conditions. For example, in a general finite element analysis environment, the data in vertical.txt can be applied to the vertical translational degrees of freedom (such as the UY direction) of the center node of the pantograph base, and the data in pitch.txt and roll.txt can be applied to the corresponding rotational degrees of freedom (such as the ROTX and ROTZ directions), respectively. The originally complex random vibration environment of the vehicle is transformed into a deterministic boundary load that can be applied repeatedly, enabling the left and right pantograph bases to move synchronously under the same vehicle vibration reference, thereby realistically reproducing the dynamic behavior under dual-sided current collection conditions.

[0121] like Figure 5As shown, this is a schematic diagram illustrating the change of contact force under vertical excitation in an exemplary embodiment of this application. The blue line represents the original contact force, and the orange line represents the contact force under vertical excitation obtained using the pantograph base vibration signal construction method based on measured power spectral density provided in this application embodiment. The horizontal axis represents time in seconds, and the vertical axis represents contact force in N. Figure 6 As shown, this is a schematic diagram illustrating the change of contact force under tilting excitation, as presented in an exemplary embodiment of this application. The yellow line represents the original contact force, the blue line represents the right-side contact force under tilting excitation obtained using the pantograph base vibration signal construction method based on measured power spectral density provided in this application embodiment, and the orange line represents the left-side contact force under tilting excitation. The horizontal axis represents time in seconds (s), and the vertical axis represents contact force in nanometers (N). Figure 7 As shown, this is a schematic diagram illustrating the contact force variation under pitch excitation in an exemplary embodiment of this application. The blue line represents the original contact force, and the orange line represents the contact force under pitch excitation obtained using the pantograph base vibration signal construction method based on measured power spectral density provided in this application embodiment. The horizontal axis represents time in seconds, and the vertical axis represents contact force in N. The simulation results of pantograph-catenary contact force under traditional empirical spectral excitation and reconstructed excitation in this application are compared. Figures 5 to 7 It can be seen that under traditional empirical spectrum excitation, the contact force waveform is relatively smooth and the peak fluctuation range is narrow; however, the pantograph base vibration signal construction method based on measured power spectral density provided in this application shows that the contact force time history exhibits richer high-frequency components and greater amplitude transient impacts, and its statistical distribution characteristics are highly consistent with the measured data of the line.

[0122] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0123] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for constructing a pantograph base vibration signal based on measured power spectral density, characterized in that, include: Calculate the target power spectral density based on the measured response signal of the target measurement point; A target spectral envelope is constructed based on the target power spectral density. An equivalent boundary input spectrum is determined based on the target spectral envelope and the frequency band compensation function. The frequency band compensation function is iteratively corrected based on the simulation response spectrum calculated by the transfer relationship established by the vehicle dynamics transfer model. A single-channel reference time history is generated based on the equivalent boundary input spectrum, and the single-channel reference time history is mapped to a multi-dimensional boundary excitation by utilizing the spatial phase relationship of the vehicle rigid body motion modes. Based on the multidimensional boundary excitation and the transmission relationship, the vibration signal of the pantograph base is calculated.

2. The method for constructing pantograph base vibration signals based on measured power spectral density according to claim 1, characterized in that, The bandwidth compensation function includes a local compensation term and a broadband trend compensation term; The local compensation term is used to correct the amplitude deviation between the simulated response spectrum calculated based on the transfer relationship and the target power spectral density in the local frequency band; The broadband trend compensation term is used to correct the overall spectral amplitude deviation between the simulated response spectrum and the target power spectral density within a preset broadband band.

3. The method for constructing the pantograph base vibration signal based on measured power spectral density according to claim 2, characterized in that, The formula for calculating the frequency band compensation function is as follows: ； in, The frequency band compensation function is... For the current frequency, Let J be the compensation amplitude for the j-th local frequency band. Let j be the compensation center frequency of the j-th frequency band. The compensation bandwidth for the j-th frequency band is... For the aforementioned local compensation term, To compensate for the amplitude of broadband trend, For the maximum frequency, For exponential parameters, This is the broadband trend compensation term.

4. The method for constructing the pantograph base vibration signal based on measured power spectral density according to claim 2, characterized in that, The iterative correction process includes: Perform a superposition step, which includes superimposing the target spectral envelope with the frequency band compensation function to obtain the equivalent boundary input spectrum; The input step includes calculating the simulation response spectrum based on the equivalent boundary input spectrum and the transfer relationship; The adjustment steps include: if the simulated response spectrum is higher than the target power spectral density in the target frequency band, then reducing the compensation amplitude or the broadband trend compensation amplitude corresponding to the target frequency band; if the simulated response spectrum is lower than the target power spectral density in the target frequency band, then increasing the compensation amplitude or the broadband trend compensation amplitude corresponding to the target frequency band. Repeat the superposition step, the input step, and the adjustment step until the deviation between the simulated response spectrum and the target power spectral density meets the preset convergence condition.

5. The method for constructing the pantograph base vibration signal based on measured power spectral density according to claim 1, characterized in that, The multidimensional boundary excitation includes vertical excitation, roll excitation, and pitch excitation. The mapping of the single-channel reference time history to multidimensional boundary excitation using the spatial phase relationship of the vehicle rigid body motion modes includes: The single-channel reference time history is mapped to multiple support corner points of the vehicle in an in-phase input manner to generate the vertical excitation; The single-channel reference time history is mapped to the multiple support corner points in a left-right inverted input manner to generate the tilt excitation; The single-channel reference time history is mapped to the multiple support corner points in a forward-backward inverted input manner to generate the pitch excitation.

6. The method for constructing the pantograph base vibration signal based on measured power spectral density according to claim 1, characterized in that, The generation of a single-channel reference time history based on the equivalent boundary input spectrum includes: The equivalent boundary input spectrum is discretized into multiple discrete frequency components; Based on the power spectral density value and frequency resolution of each of the plurality of discrete frequency components, the corresponding displacement amplitude is calculated. Based on the displacement amplitude, the discrete frequency components, and the random phase, the single-channel reference time history is generated by superposition. The formula for calculating the single-channel reference time history is as follows: ； in, The single-channel reference time history, This represents the total number of the discrete frequency components involved in the synthesis. The displacement amplitude corresponds to the kth discrete frequency component. For the k-th discrete frequency component, The random phase.

7. The method for constructing the pantograph base vibration signal based on measured power spectral density according to claim 1, characterized in that, The construction of the target spectral envelope based on the target power spectral density includes: Key frequency points are extracted from the curve of the target power spectral density, and the key frequency points include at least one of local peak points, local valley points, frequency band boundary points, and points where the spectral slope changes. Based on the key frequency points and their corresponding power spectral density values, a continuous target spectral envelope is constructed using a piecewise interpolation method.

8. The method for constructing the pantograph base vibration signal based on measured power spectral density according to claim 4, characterized in that, The vehicle dynamics transfer model is a multi-degree-of-freedom coupled dynamics model. The simulation response spectrum is calculated based on the equivalent boundary input spectrum and the transfer relationship, including: Based on the aforementioned transfer relationship, the multidimensional boundary excitation is applied to multiple support corner points to calculate the vertical displacement of the vehicle's center of mass and the rotation angle around the preset coordinate axis. Based on the vertical displacement of the vehicle's center of gravity, the rotation angle, and the position parameters of the vehicle's center of gravity to the target measuring point, the vertical displacement and attitude angle of the target measuring point are calculated; The simulation response spectrum is determined based on the vertical displacement and attitude angle of the target measuring point.

9. The method for constructing the pantograph base vibration signal based on measured power spectral density according to claim 1, characterized in that, The target power spectral density is calculated using the following methods: The measured response signal is segmented to obtain multiple signal segments; After applying a window function to each signal segment, perform a Fast Fourier Transform. The target power spectral density is obtained by averaging the transformation results of each signal segment.

10. The method for constructing the pantograph base vibration signal based on measured power spectral density according to claim 1, characterized in that, The equivalent boundary input spectrum is generated in the following ways: The target spectrum envelope is superimposed on the frequency band compensation function in the logarithmic domain; The superposition result is transformed from the logarithmic domain to the linear domain to obtain the equivalent boundary input spectrum.

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