Optimization Method and System for Arrangement of Pantograph Catenary Suspension Strings on High-Speed Railways Based on Machine Learning

Abstract

The present application relates to the field of intelligent operation and maintenance of high-speed railway contact networks, and provides a method and system for optimizing the arrangement of high-speed railway contact network hangers based on machine learning, in order to solve the problems of insufficient bow-net coupling stability and low contact network wear uniformity. The present application includes: collecting the spatial distribution characteristics of the contact force between the pantograph and the contact network, and generating contact force equilibrium constraint conditions; combining the track superelevation value, vertical curve curvature and elevation data of the suspension point obtained by the laser scanner to construct a line parameter compensation mechanism, and output the compensated three-dimensional coordinates of the contact network suspension point; using a programmable gate array to implement parallel acceleration of the neural network weight calculation and spatial coordinate transformation, iteratively processing the contact force constraints and compensation coordinates, and generating the hanger arrangement parameters; based on the segmented tension value and the node offset compensation value, the driving equipment completes the precise adjustment and positioning installation of the hangers. The technical solution provided by the present application improves the bow-net coupling stability and contact network wear uniformity.

Description

Technical Field

[0001] The present application relates to the field of intelligent operation and maintenance technology for high-speed railway contact networks, and in particular to a method and system for optimizing the arrangement of high-speed railway contact network droppers based on machine learning. Background Art

[0002] Under complex high-speed railway line conditions (such as steep slopes and narrow curve radius sections), the catenary dropper arrangement must adapt to the high-frequency variations in track geometry and pantograph contact forces. Due to the nonlinear superposition of catenary spatial deformations caused by sudden changes in line curvature and slope, traditional static dropper parameter models are unable to meet the requirements for pantograph-catenary coupling stability. Therefore, an optimization method that integrates track geometry and contact force distribution to achieve adaptive adjustment of dropper arrangement is urgently needed.

[0003] In the existing technology, an offline optimization method based on three-dimensional point cloud scanning and finite element simulation is proposed. Track geometric parameters (such as superelevation and vertical curve curvature) are obtained through periodic scanning, and a static dropper position calculation model is established. The contact pressure distribution is predicted by combining finite element simulation, and the dropper node spacing and tension parameters are adjusted offline.

[0004] The defects of the existing technology are that it relies on periodic scanning data and offline simulation optimization, and is unable to respond to the high-frequency changes in the contact force of the pantograph slide, resulting in the adjustment of the dropper string parameters lagging behind the actual pantograph-catenary coupling state; the track geometry parameter compensation and contact force distribution optimization are processed in stages, and a coupling correction mechanism for contact force and track deformation is not established. The sudden change in the contact network tension gradient in the large slope section is prone to cause the accumulation of compensation errors; the finite element simulation has a large amount of calculation and has not introduced hardware acceleration technology, resulting in an excessively long optimization cycle in complex line scenarios, which is difficult to meet the requirements of high-speed railway operation and maintenance. Summary of the Invention

[0005] The embodiments of the present application provide a method and system for optimizing the arrangement of high-speed railway contact network hanger strings based on machine learning, so as to solve the problems of insufficient bow-net coupling stability and low contact network wear uniformity in the prior art.

[0006] In a first aspect, an embodiment of the present application provides a method for optimizing the arrangement of high-speed railway contact network dropper strings based on machine learning, comprising:

[0007] The pressure sensors at the catenary suspension points are used to capture the spatial distribution characteristics of the contact force between the pantograph slide and the catenary, and to generate contact force equilibrium constraints that include the contact pressure standard deviation optimization objective.

[0008] Based on the contact force balance constraint, the track superelevation value and vertical curve curvature obtained by the laser scanner moving along the longitudinal direction of the track are used to perform parameter compensation processing on the dropper position calculation model. The elevation data of the catenary suspension point are combined to generate a line parameter compensation mechanism, and the compensated three-dimensional coordinates of the catenary suspension point are obtained.

[0009] The pipeline architecture of the programmable gate array hardware platform is used to perform parallel accelerated processing of the neural network weight calculation and spatial coordinate transformation, and the contact force balance constraint condition and the compensated three-dimensional coordinate are synchronously iterated to generate the string arrangement parameters that meet the pantograph-catenary coupling relationship;

[0010] Based on the segmented tension values between the contact network suspension points and the offset compensation values of the contact network nodes in the dropper string arrangement parameters, the contact network construction equipment is driven to perform dropper string length adjustment and positioning installation.

[0011] Optionally, a pipeline architecture of a programmable gate array hardware platform is used to perform parallel acceleration processing on the weight calculation of the neural network and the spatial coordinate transformation, and the contact force balance constraint condition and the compensated three-dimensional coordinate are synchronously iterated to generate the string arrangement parameters that satisfy the pantograph-catenary coupling relationship, including:

[0012] Decompose the weight calculation of the neural network into an axial weight subtask related to the contact force distribution direction, and decompose the spatial coordinate transformation into a geometric transformation subtask based on the longitudinal curvature of the track;

[0013] In a pipeline architecture of a programmable gate array hardware platform, an independent first parallel computing channel is allocated to the axial weight subtask, and an independent second parallel computing channel is allocated to the geometric transformation subtask;

[0014] In the first parallel calculation channel, the axial weight coefficient of the contact force equilibrium constraint condition is adjusted according to the suspension point elevation data of the compensated three-dimensional coordinates;

[0015] In the second parallel calculation channel, a segmented interpolation process is performed on the lateral offset of the compensated three-dimensional coordinate based on the longitudinal curvature of the track to generate a compensation amount for the spatial deformation of the suspension point;

[0016] Through the cross-channel data interaction unit built into the programmable gate array hardware platform, the dot product calculation of the contact force direction vector and the spatial deformation vector is completed in a single clock cycle, and the axial weight coefficient and the suspension point spatial deformation compensation amount are coupled to generate a coupling operation result;

[0017] According to the coupling operation result, the suspension point spacing in the compensated three-dimensional coordinates is relaxed and iterated. When the tension gradient change rate of adjacent suspension points is less than a preset convergence threshold, the final distribution sequence of the suspension string node offset compensation value is output to generate the suspension string arrangement parameters.

[0018] Optionally, a cross-channel data interaction unit built into the programmable gate array hardware platform is used to complete the dot product calculation of the contact force direction vector and the spatial deformation vector within a single clock cycle, and the axial weight coefficient is coupled with the suspension point spatial deformation compensation amount to generate a coupling operation result, including:

[0019] The contact force direction vector is axially decomposed to obtain the first longitudinal component and the second transverse component of the track. The spatial deformation vector is divided into multiple continuous geometric units based on the spacing between adjacent suspension points of the compensated three-dimensional coordinates, and the transverse offset gradient of each segment is extracted.

[0020] In the cross-channel data exchange unit, the first direction component and the lateral offset gradient are superimposed section by section, and the second direction component and the elevation change rate of the suspension point spatial deformation compensation amount are projected to generate a superposition result and a projection result;

[0021] Scaling the superposition result based on the longitudinal curvature of the track to generate a deformation coupling coefficient, and performing a scalar and vector mixed operation on the projection operation result and the deformation coupling coefficient through a preset vector synthesis circuit to obtain a mixed operation result;

[0022] The hybrid operation result is discretized and integrated according to the distribution density of the suspension point spatial deformation compensation amount to generate a coupling operation result.

[0023] Optionally, according to the coupling operation result, relaxation iteration is performed on the suspension point spacing in the compensated three-dimensional coordinates. When the tension gradient change rate of adjacent suspension points is less than a preset convergence threshold, a final distribution sequence of the dropper node offset compensation values is output to generate the dropper arrangement parameters, including:

[0024] Based on the longitudinal curvature of the track and the distribution density of the spatial deformation compensation amount of the suspension point, the compensated three-dimensional coordinates are divided into multiple tension balance areas, and an initial relaxation factor is assigned to each area;

[0025] In the tension balance area, the initial relaxation factor is adjusted according to the tension gradient change rate of adjacent suspension points, wherein the relaxation step reduction strategy when the track superelevation value is greater than a preset threshold is used to constrain the step size of the initial relaxation factor to obtain an adjusted initial relaxation factor;

[0026] A bidirectional chain iterative calculation is performed on the suspension point spacing within each tension balance region using the adjusted initial relaxation factor. When the suspension point spacing adjustment triggers a reverse change in the offset compensation value of the adjacent suspension string node, a suspension point density adaptive local rebalancing factor is generated based on the tension gradient change rate and the relaxation step size reduction strategy.

[0027] The local rebalancing factor is weightedly integrated with the deformation coupling coefficient in the coupling operation result, and the lateral offset cumulative error of the suspension point spatial deformation compensation amount is synchronously detected. If the lateral offset cumulative error exceeds the tolerance range corresponding to the curvature of the vertical curve of the track, the lateral offset gradient is reset based on the segmented results of the multiple continuous geometric units;

[0028] When the tension gradient change rate of adjacent suspension points in all tension balance areas is less than a preset convergence threshold, a mapping relationship of the suspension string node offset compensation value is generated based on the suspension point spacing adjustment amount, the local rebalancing factor and the reset lateral offset gradient, and the mapping relationship is locked to generate the suspension string arrangement parameters.

[0029] Optionally, a bidirectional chain iterative calculation is performed on the suspension point spacing within each tension balance area using the adjusted initial relaxation factor. When the suspension point spacing adjustment triggers a reverse change in the offset compensation value of the adjacent suspension string node, a suspension point density adaptive local rebalancing factor is generated based on the tension gradient change rate and the relaxation step size reduction strategy, including:

[0030] Marking the suspension point spacing within the tension balance region in segments based on the longitudinal curvature of the track, and using the change in longitudinal curvature of the track between adjacent suspension points as a direction switching threshold for chain iteration;

[0031] In the bidirectional chain iterative calculation, the suspension point spacing is adjusted in sequence along the positive longitudinal direction of the track. When the suspension point spacing adjustment exceeds the direction switching threshold, the iterative calculation is switched to the reverse longitudinal direction of the track.

[0032] In each iteration, the ratio of the current suspension point density to the tension gradient change rate is calculated based on the inverse change relationship between the suspension point spacing adjustment amount and the offset compensation value of the adjacent suspension string node to generate a suspension point density change coefficient;

[0033] Based on the product of the suspension point density variation coefficient and the adjusted initial relaxation factor, the step size constraint range of the relaxation step size reduction strategy is modified to generate a relaxation step size correction value of the current iteration step;

[0034] The relaxation step length correction amount and the tension gradient change rate are weightedly superimposed, and the superposition result is subjected to curvature compensation processing in combination with the track superelevation value to generate a local rebalancing factor with adaptive suspension point density.

[0035] Optionally, in each iteration, the ratio of the current suspension point density to the tension gradient change rate is calculated based on the inverse change relationship between the suspension point spacing adjustment amount and the offset compensation value of the adjacent suspension string node to generate the suspension point density change coefficient, including:

[0036] The suspension point spacing adjustment amount is segmented based on the change in the longitudinal curvature of the track to generate an adjustment ratio for the current suspension point spacing;

[0037] According to the reverse change direction of the offset compensation values of adjacent suspension string nodes, extracting the reverse change interval of the suspension point spacing adjustment amount and the offset compensation value, and calculating the suspension point density change gradient within the reverse change interval;

[0038] Performing a ratio operation on the suspension point density change gradient and the tension gradient change rate, and performing weighted correction based on the adjustment ratio and the comparison value operation result to generate an initial value of the initial suspension point density change coefficient;

[0039] The initial suspension point density variation coefficient is corrected by curvature compensation based on the track superelevation value to generate the suspension point density variation coefficient.

[0040] Optionally, based on the contact force equilibrium constraint, the track superelevation value and vertical curve curvature obtained by the laser scanner moving along the longitudinal direction of the track are used to perform parameter compensation processing on the dropper position calculation model, and the elevation data of the contact network suspension point are combined to generate a line parameter compensation mechanism to obtain the compensated three-dimensional coordinates of the contact network suspension point, including:

[0041] Using the track superelevation value and vertical curve curvature obtained by the laser scanner moving along the longitudinal direction of the track, the elevation data of the contact network suspension point is interpolated piecewise to generate the elevation change gradient of the suspension point;

[0042] According to the contact pressure standard deviation optimization target in the contact force equilibrium constraint condition, the influence coefficient of the track superelevation value on the lateral offset of the contact network suspension point is extracted to generate a lateral offset compensation factor;

[0043] Performing weighted superposition of the elevation change gradient of the suspension point and the lateral offset compensation factor, and performing curvature compensation correction on the superposition result in combination with the vertical curve curvature to generate the suspension point spatial deformation compensation amount;

[0044] Performing piecewise integration processing on the spatial deformation compensation amount of the suspension point based on the change in longitudinal curvature of the track to generate the initial compensation coordinates of the catenary suspension point;

[0045] According to the contact pressure distribution direction in the contact force equilibrium constraint condition, the initial compensation coordinate is axially corrected to generate the compensated three-dimensional coordinates of the contact network suspension point.

[0046] In a second aspect, an embodiment of the present application provides a high-speed railway contact network dropper arrangement optimization system based on machine learning, comprising:

[0047] The contact constraint generation module is used to capture the spatial distribution characteristics of the contact force between the pantograph slide and the catenary using the pressure sensors at the catenary suspension points, and generate contact force equilibrium constraints that include the contact pressure standard deviation optimization objective;

[0048] A laser parameter compensation and correction module is used to perform parameter compensation processing on the dropper position calculation model based on the contact force balance constraint condition, using the track superelevation value and vertical curve curvature obtained by the laser scanner moving along the longitudinal direction of the track, and generating a line parameter compensation mechanism in combination with the elevation data of the catenary suspension point to obtain the compensated three-dimensional coordinates of the catenary suspension point;

[0049] A hardware-accelerated iterative optimization module is used to utilize the pipeline architecture of the programmable gate array hardware platform to perform parallel accelerated processing of the neural network weight calculation and spatial coordinate transformation, synchronously iteratively calculate the contact force balance constraint condition and the compensated three-dimensional coordinates, and generate the string arrangement parameters that satisfy the bow-catenary coupling relationship;

[0050] The dropper string parameter execution driving module is used to drive the contact network construction equipment to perform dropper string length adjustment and positioning installation based on the segmented tension value between the contact network suspension points and the dropper string node offset compensation value in the dropper string arrangement parameters.

[0051] In a third aspect, an embodiment of the present application provides a computing device comprising a processing component and a storage component; the storage component stores one or more computer instructions; the one or more computer instructions are used to be called and executed by the processing component to implement a method for optimizing the arrangement of high-speed railway contact network hanger strings based on machine learning as described in the first aspect above.

[0052] In a fourth aspect, an embodiment of the present application provides a computer storage medium storing a computer program. When the computer program is executed by a computer, it implements a method for optimizing the arrangement of high-speed railway contact network droppers based on machine learning as described in the first aspect.

[0053] In an embodiment of the present application, a pressure sensor at the contact network suspension point is used to capture the spatial distribution characteristics of the contact force between the pantograph slide and the contact network, and a contact force balance constraint condition including a contact pressure standard deviation optimization target is generated; based on the contact force balance constraint condition, the track superelevation value and the vertical curve curvature obtained by the laser scanner along the longitudinal movement of the track are used to perform parameter compensation processing on the string position calculation model, and the elevation data of the contact network suspension point are combined to generate a line parameter compensation mechanism to obtain the compensated three-dimensional coordinates of the contact network suspension point; the pipeline architecture of the programmable gate array hardware platform is used to perform parallel acceleration processing on the weight calculation and spatial coordinate transformation of the neural network, and the contact force balance constraint condition and the compensated three-dimensional coordinates are synchronously iterated to generate string arrangement parameters that satisfy the bow-net coupling relationship; based on the segmented tension value between the contact network suspension points and the string node offset compensation value in the string arrangement parameters, the contact network construction equipment is driven to perform string length adjustment and positioning installation.

[0054] The technical solution of this application has the following beneficial effects:

[0055] By capturing the spatial distribution characteristics of the contact force through pressure sensors and establishing constraints with the standard deviation of the contact pressure as the optimization target, balanced control of the bow-catwalk contact force is achieved. A compensation mechanism is generated by combining laser scanning track geometry parameters with the elevation data of the suspension points to accurately correct the spatial deformation error of the contact network and improve the positioning accuracy of the dropper string under complex line conditions. The programmable gate array pipeline architecture is used to parallelly process the neural network weights and spatial coordinate transformations, achieving millisecond-level synchronous iteration of the contact force constraints and compensation coordinates to ensure the accuracy of the coupled optimization. Executable parameters are generated based on the segmented tension values and offset compensation values, directly driving the construction equipment to complete the precise adjustment of the dropper string, forming a closed-loop engineering implementation chain.

[0056] Furthermore, by decomposing the weight calculation of the neural network into the contact force axial weight subtask and the spatial coordinate transformation into the track curvature geometric transformation subtask, independent parallel computing channels are allocated in the programmable gate array hardware platform; the contact force constraint weight coefficient is adjusted in the axial weight channel, and the deformation compensation amount is generated based on the track curvature in the geometric transformation channel; the cross-channel data interaction unit is used to realize the dot product calculation and coupling operation of the contact force direction vector and the deformation vector, and finally the suspension string arrangement parameters are generated through relaxation iterative convergence.

[0057] Through the above method, the bottleneck of traditional serial computing efficiency is broken through, and the coordinated optimization of contact force constraints and track deformation compensation is achieved through hardware acceleration. The problem of lag in adjustment of suspension string parameters in complex line scenarios is solved, the stability of pantograph coupling and the uniformity of contact network wear are improved, and the optimization response time is shortened to milliseconds to meet the requirements of high-speed railway operation and maintenance.

[0058] These and other aspects of the present application will become more readily apparent from the description of the following embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, a brief introduction will be given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0060] Figure 1 A flowchart of a method for optimizing the arrangement of high-speed railway contact network droppers based on machine learning is shown in the present application;

[0061] Figure 2 A schematic diagram of the structure of a high-speed railway contact network dropper arrangement optimization system based on machine learning provided by the present application is shown;

[0062] Figure 3 A schematic structural diagram of a computing device provided by the present application is shown. DETAILED DESCRIPTION

[0063] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0064] In some of the processes described in the specification and claims of this application and the above-mentioned figures, multiple operations that appear in a specific order are included, but it should be clearly understood that these operations may not be executed in the order in which they appear in this document or may be executed in parallel. The serial numbers of the operations, such as 101, 102, etc., are only used to distinguish between different operations, and the serial numbers themselves do not represent any order of execution. In addition, these processes may include more or fewer operations, and these operations may be executed in sequence or in parallel. It should be noted that the descriptions of "first", "second", etc. in this document are used to distinguish different messages, devices, modules, etc., and do not represent a sequential order, nor do they limit "first" and "second" to being different types.

[0065] The technical solution of the present application is applicable to the optimization scenario of the arrangement of suspension strings under complex line conditions (such as large slopes and small curve radius). The research and development idea of the present application is to capture the spatial distribution characteristics of the contact force between the pantograph slide and the contact network through a pressure sensor, and construct a constraint condition with the standard deviation of the contact pressure as the optimization target; synchronously integrate the track superelevation, vertical curve curvature and elevation data of the suspension point obtained by the laser scanner to generate three-dimensional coordinates for compensation of the spatial deformation of the contact network; use the pipeline architecture of the programmable gate array hardware platform to perform parallel acceleration processing on the weight calculation and spatial coordinate transformation of the neural network, and realize millisecond-level synchronous iterative optimization of the contact force constraint and the compensation coordinate; finally, based on the segmented tension value and the offset compensation value, drive the construction equipment to complete the precise adjustment of the suspension string, forming a full-link optimization logic of "perception and deformation compensation and hardware acceleration and closed-loop execution" to solve the problem of instability of the pantograph-network coupling in complex lines.

[0066] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without making creative efforts are within the scope of protection of this application.

[0067] Figure 1 A flowchart of a method for optimizing the arrangement of high-speed railway contact network droppers based on machine learning is provided for the embodiment of the present application. Figure 1 As shown, the method includes:

[0068] 101. Use the pressure sensor at the contact network suspension point to capture the spatial distribution characteristics of the contact force between the pantograph slide and the contact network, and generate the contact force equilibrium constraint condition including the contact pressure standard deviation optimization objective;

[0069] In this step, the pressure sensor refers to multiple pressure sensors arranged at the contact network suspension point, which can simultaneously detect the contact force components between the pantograph slide and the contact network in different directions (such as longitudinal, transverse, and vertical).

[0070] The contact pressure standard deviation optimization target is to establish a balance target by statistically calculating the standard deviation of the contact force distribution, which is used to constrain the spatial fluctuation range of the contact force.

[0071] In an embodiment of the present application, first, a high-precision pressure sensor array is deployed at each suspension point of the contact network to collect dynamic contact force data when the pantograph slide passes in real time, and the spatial frequency domain characteristics of the contact force fluctuation are extracted through Fourier transform; secondly, the continuously monitored contact force data is standardized by the sliding window method, the standard deviation of the contact pressure in each suspension point area is calculated, and the minimization of the standard deviation is set as the optimization goal; then, a contact force distribution prediction model is constructed based on the random forest algorithm, and the suspension point position features (such as span, slope, and suspension mass) that have a significant impact on the contact force fluctuation are screened out through feature importance analysis; finally, the key features output by the prediction model are combined with the standard deviation optimization goal to generate a contact force balance constraint condition containing a suspension point position weight coefficient, and the constraint condition expression is that the weighted sum of the contact force standard deviations of each suspension point is less than a preset threshold.

[0072] In one real-world case study, a triaxial pressure sensor array was deployed at the catenary suspension point on a high-speed railway section with a slope of 25‰ to monitor the contact force of the pantograph slide as the train passed through. When a train passed at 350 km / h, the sensors detected a vertical pressure peak of 120 N and a lateral offset force gradient rate of 0.8 N / m (exceeding the constraint threshold). The system automatically triggered the contact force standard deviation optimization target generation module, adjusted the lateral offset force gradient constraint to 0.6 N / m, and generated the corresponding equilibrium constraint.

[0073] 102. Based on the contact force balance constraint, the track superelevation value and vertical curve curvature obtained by the laser scanner moving along the longitudinal direction of the track are used to perform parameter compensation processing on the dropper position calculation model. The elevation data of the catenary suspension point are combined to generate a line parameter compensation mechanism to obtain the compensated three-dimensional coordinates of the catenary suspension point.

[0074] In this step, the line parameter compensation mechanism refers to a mathematical model that corrects the spatial position of the contact network by combining the track geometric parameters (superelevation value, vertical curve curvature) with the elevation data of the suspension point.

[0075] Compensated three-dimensional coordinates refer to the three-dimensional spatial coordinates of the contact network suspension point generated after parameter compensation, including lateral offset and elevation correction.

[0076] In an embodiment of the present application, first, a laser scanner scans the track geometric parameters with millimeter-level accuracy along the longitudinal direction of the track, extracts the track superelevation value and vertical curve curvature through point cloud registration technology, and uses a cubic spline interpolation algorithm to perform continuous processing on discrete measurement points; secondly, the processed track parameters are input into the hanger position calculation model, a three-dimensional coordinate system is established based on the elevation data of the suspension point, and the deviation matrix between the track parameters and the original coordinates of the suspension point is calculated through the least squares method; then, an adaptive compensation algorithm is designed: a lateral offset compensation coefficient α = superelevation value / standard gauge is introduced for the track superelevation value, and a weighted correction of the inverse of the curvature radius is used for the vertical curve curvature to generate a parameter compensation vector containing the lateral offset and elevation correction; finally, the compensation vector is superimposed on the original three-dimensional coordinates of the suspension point, and the compensated three-dimensional coordinates of the compensated suspension point are obtained through the spatial coordinate transformation matrix calculation to form a line parameter compensation mechanism.

[0077] Continuing with the above example, in a section with a small curve radius (R=600m), the laser scanner detected a track superelevation of 80mm and a vertical curve curvature of 1 / 800m⁻¹. Combined with the measured elevation of the suspension point (12.5m), the system converted the superelevation value into a lateral offset compensation factor (+16mm) and interpolated the elevation data based on the curvature (-2.1mm), ultimately generating the compensated 3D coordinates (lateral +16mm, elevation 10.4m).

[0078] 103. Utilize the pipeline architecture of the programmable gate array hardware platform to perform parallel accelerated processing on the weight calculation of the neural network and the spatial coordinate transformation, synchronously iteratively calculate the contact force balance constraint condition and the compensated three-dimensional coordinates, and generate the string arrangement parameters that satisfy the pantograph-catenary coupling relationship;

[0079] In this step, pipeline architecture refers to the hardware design of parallel processing tasks in field-programmable gate arrays (FPGAs), allowing the weight calculation of the neural network to be performed synchronously with the spatial coordinate transformation.

[0080] Synchronous iterative operation refers to the coupling calculation of contact force constraints and compensation three-dimensional coordinates within the same hardware clock cycle.

[0081] In an embodiment of the present application, first, a dual-pipeline architecture is deployed on an FPGA platform for parallel acceleration: the first pipeline uses a fixed-point arithmetic unit to process the neural network weight calculation, decomposes the contact force direction into longitudinal / transverse components of the track, and dynamically adjusts the axial weight coefficient based on the gradient descent method; the second pipeline is configured with a floating-point arithmetic unit to perform spatial coordinate transformation, and uses the CORDIC algorithm to realize real-time conversion of the track curvature to the spatial deformation variable; secondly, hardware-level data fusion is realized through a cross-channel data interaction unit: the dot product operation of the contact force direction vector and the spatial deformation vector is completed within a single clock cycle, and the ping-pong buffer technology is used to realize wait-free interaction of the two-channel data; then, a relaxation iterative algorithm is established: the suspension point spacing is initialized to the design value, the tension gradient is calculated according to the coupling operation result, and when it is detected that the tension gradient change rate of adjacent suspension points exceeds the threshold, a bidirectional chain iteration is triggered (forward iteration adjusts the suspension point spacing, and reverse iteration corrects the offset compensation value); finally, the convergence judgment condition is set to the tension gradient change rate being less than 0.5% for three consecutive iterations, and the string arrangement parameters that meet the bow-net coupling requirements are output, including the theoretical coordinates and allowable offset of each string node.

[0082] Continuing with the above example, in the continuous curve section (R = 800m), the FPGA hardware platform performs a dot product operation (100 × 12 = 1200 N·mm) on the longitudinal component of the contact force (100N) and the lateral offset (+12mm). Simultaneously, the longitudinal weight coefficient is adjusted to 0.15 based on the elevation data (-1.5m). After three iterations, the rate of change of the tension gradient drops to 0.04N / m (less than the threshold of 0.05), generating a dropper node offset compensation value of +8mm.

[0083] 104. Based on the segmented tension values between the contact network suspension points and the dropper string node offset compensation values in the dropper string arrangement parameters, drive the contact network construction equipment to perform dropper string length adjustment and positioning installation.

[0084] In this step, the segmented tension value refers to the tension distribution parameter between the contact network suspension points divided by the longitudinal sections of the track, such as the tension target value for each 10m section.

[0085] The offset compensation value refers to the lateral or vertical adjustment of the dropper node relative to the theoretical position, such as +5mm (right deviation) or -3mm (downward movement).

[0086] In the embodiment of the present application, first, the segmented tension values in the suspension string arrangement parameters are analyzed, and a tension adjustment instruction is generated by a PID controller: when the measured tension deviates from the theoretical value by more than 50N, the hydraulic servo system is driven to adjust the suspension string length, and the control accuracy reaches ±1mm; secondly, the suspension string node offset compensation value is converted into a construction positioning coordinate, and a laser locator is used to guide the installation robot arm, and three-dimensional space positioning is achieved through triangulation, and the lateral positioning error is controlled within ±3mm; then, a construction closed-loop verification mechanism is established: after the installation is completed, the contact force re-measurement is started immediately. If it is detected that the contact pressure standard deviation has rebounded by more than 10% of the optimized value, the parameter re-optimization process is automatically triggered; finally, the construction data (including the final suspension string length, positioning coordinates, and measured tension) are uploaded to the cloud database through the industrial Internet of Things platform to generate a digital twin model for subsequent operation and maintenance.

[0087] Continuing with the above example, in a section of a steep slope (slope 30‰), the system generates segmented tension values for Section 1 (12.5kN) and Section 2 (12.2kN), and an offset compensation value of +10mm in the lateral direction. After the construction equipment receives the command, the hydraulic mechanism precisely adjusts the suspension string tension to the target value, and the laser locator guides the robotic arm to install the suspension string node to a position with a lateral offset of +10mm, with the error controlled within ±0.5mm.

[0088] In summary, steps 101 to 104 achieve adaptive adjustment of the dropper arrangement under complex line conditions through contact force sensing, track geometry compensation, hardware-accelerated iterative optimization, and closed-loop construction execution. In scenarios such as steep slopes and tight curve radii, the system responds to contact force fluctuations and track deformation, shortening the optimization cycle to milliseconds through FPGA hardware acceleration. This ensures uniform dropper tension distribution and node positioning accuracy, significantly improving pantograph-catenary coupling stability and reducing uneven catenary wear.

[0089] In order to improve the optimization capability of dropper string arrangement under complex line conditions of high-speed railways, the contact force constraint and track deformation compensation are collaboratively accelerated through the pipeline architecture of the programmable gate array hardware platform, and the high-precision dropper string parameters are generated in combination with the relaxation iterative mechanism.

[0090] In some embodiments, in step 103, the pipeline architecture of the programmable gate array hardware platform is used to perform parallel accelerated processing of the weight calculation of the neural network and the spatial coordinate transformation, and the contact force balance constraint condition and the compensated three-dimensional coordinate are synchronously iteratively calculated to generate the string arrangement parameters that satisfy the pantograph-catenary coupling relationship, including:

[0091] 201. Decompose the weight calculation of the neural network into an axial weight subtask related to the contact force distribution direction, and decompose the spatial coordinate transformation into a geometric transformation subtask based on the longitudinal curvature of the track;

[0092] In step 201, the axial weight subtask refers to the weight calculation task of the neural network decomposed according to the contact force distribution direction (such as longitudinal and transverse directions), which is used to adjust the weight coefficient of the contact force constraint condition.

[0093] The geometric transformation subtask refers to the task of performing segmented transformation of the contact network spatial coordinates based on the longitudinal curvature of the track, which is used to compensate for the contact network offset caused by the geometric deformation of the track.

[0094] In an embodiment of the present application, first, the weight calculation of the neural network is directionally decomposed, the main direction of the contact force distribution is extracted as the axial reference through principal component analysis, and the weight update amount is projected onto the two orthogonal axes of the longitudinal and transverse directions of the track to form an axial weight subtask; secondly, the geometric features of the spatial coordinate transformation are decoupled, and the differential geometry method is used to calculate the influence factor of the longitudinal curvature of the track on the coordinate transformation, and the curvature and deformation mapping relationship is established to decompose the curvature-based geometric transformation subtask.

[0095] 202. In a pipeline architecture of a programmable gate array hardware platform, allocate an independent first parallel computing channel to the axial weight subtask, and allocate an independent second parallel computing channel to the geometric transformation subtask;

[0096] In step 202, the parallel computing channels refer to independently running logic units in the FPGA hardware, which are used to process different computing tasks simultaneously.

[0097] In an embodiment of the present application, first, a dual-channel pipeline architecture is designed in an FPGA hardware platform, the first channel is configured with a fixed-point arithmetic unit and pre-loaded with an axial weight calculation instruction set, the second channel deploys a floating-point arithmetic unit and stores a geometric conversion parameter lookup table; secondly, independent data storage areas are allocated to the two channels through a hardware description language, the first channel is connected to the elevation data bus for compensating three-dimensional coordinates, and the second channel is connected to the track curvature sensor input interface; then, clock domain crossing technology is used to achieve parallel clock synchronization of the dual channels to ensure that the calculation beats of the two channels are aligned; finally, a hardware-level handshake protocol is deployed between the channels, and when any channel completes the current calculation task, the cross-channel data interaction unit is triggered to start through the status register.

[0098] 203. In the first parallel calculation channel, adjust the axial weight coefficient of the contact force equilibrium constraint condition according to the suspension point elevation data of the compensated three-dimensional coordinates;

[0099] In step 203, the suspension point elevation data refers to the rate of change of the vertical height of the overhead contact network suspension point along the longitudinal direction of the track (such as the elevation change per meter).

[0100] In an embodiment of the present application, first, the elevation data set of the suspension points of the compensated three-dimensional coordinates is read in the first parallel calculation channel, and the high-frequency noise in the elevation data is removed by Gaussian filtering; secondly, the filtered elevation data is multiplied point by point with the initial value of the axial weight in the contact force equilibrium constraint condition, and the axial weight influence factor of each suspension point is calculated; then, the weight coefficient is dynamically adjusted based on the gradient descent method: if the elevation change rate of a suspension point exceeds 20% of the average value of the adjacent points, its axial weight coefficient is increased by 0.1 times the standard deviation; finally, the adjusted axial weight coefficient is written to the output buffer of the first channel, and a ready signal is sent to the cross-channel data interaction unit at the same time.

[0101] 204. In the second parallel calculation channel, perform piecewise interpolation processing on the lateral offset of the compensated three-dimensional coordinate based on the longitudinal curvature of the track to generate a suspension point spatial deformation compensation amount;

[0102] In step 204, the segmented interpolation process refers to interpolating and correcting the lateral offset according to the track longitudinal curvature variation range (such as curvature radius <800m, 800-1500m).

[0103] In an embodiment of the present application, first, the track longitudinal curvature data set is loaded in the second parallel calculation channel, and the curvature measurement points are continuously processed using the cubic spline interpolation algorithm; secondly, the lateral offset of the compensated three-dimensional coordinates is divided into multiple continuous intervals according to the curvature change points, and a local coordinate system is established in each interval; then, the compensation gradient of the lateral offset in each interval is calculated based on the curvature radius, and when the curvature radius is less than 1000 meters, the secondary compensation mode is started, and an additional 5% of the offset is added as a safety margin; finally, the compensation amount of each interval is fitted with a B-spline curve to generate a smooth spatial deformation compensation amount, which is stored in the result register of the second channel.

[0104] 205. Using a cross-channel data interaction unit built into the programmable gate array hardware platform, a dot product calculation of the contact force direction vector and the spatial deformation vector is completed within a single clock cycle, and the axial weight coefficient is coupled with the suspension point spatial deformation compensation amount to generate a coupling calculation result.

[0105] In step 205, the cross-channel data interaction unit refers to a hardware module within the FPGA that implements data interaction between different computing channels.

[0106] In an embodiment of the present application, first, the cross-channel data interaction unit simultaneously reads the axial weight coefficient matrix of the first channel and the spatial deformation compensation vector of the second channel; secondly, the parallel processing of the vector dot product operation is realized at the hardware level: the contact force direction vector is decomposed into a 16-bit fixed-point format, the spatial deformation vector is converted into a 32-bit floating-point format, and the synchronous calculation of the component products is completed through a dedicated multiplier array; then, a carry-preserving addition tree is used to complete the cumulative summation of the product results within a single clock cycle to generate a coupling intermediate value in scalar form; finally, the axial weight coefficient and the coupling intermediate value are weightedly superimposed, the dimensional difference is eliminated through processing, and a coupling operation result with unified dimension is output.

[0107] 206. Perform relaxation iteration on the suspension point spacing in the compensated three-dimensional coordinates according to the coupling operation result. When the tension gradient change rate of adjacent suspension points is less than a preset convergence threshold, output a final distribution sequence of the suspension string node offset compensation values to generate suspension string arrangement parameters.

[0108] In step 206, the relaxation iteration refers to adjusting the suspension point spacing by a stepwise approximation method until the tension gradient change rate meets the convergence condition.

[0109] In an embodiment of the present application, first, the coupling operation result is input into the relaxation iterative controller, and the suspension point spacing is initialized to the range of ±10% of the design standard value; secondly, a bidirectional chain iteration is performed along the longitudinal direction of the track: during the forward iteration, the suspension point spacing is increased according to the tension gradient, and during the reverse iteration, the spacing is reduced in combination with the offset compensation value, and the step size of each iteration is adaptively adjusted to 1 / 5 of the current tension gradient change rate; then, the tension gradient change rate of adjacent suspension points is monitored in real time, and when the change rate is less than a preset threshold (such as 0.5%) in three consecutive iterations, it is determined to be a convergence state; finally, the current suspension point spacing distribution is locked, and the offset compensation value of each suspension string node is extracted to form a final distribution sequence, and the suspension string arrangement parameters including node coordinates, compensation amount and tension value are output.

[0110] Here's a specific example:

[0111] In a section where a small curve radius (R = 600m) overlaps a steep slope (25‰), a laser scanner detected a track superelevation of 85mm and a vertical curve curvature of 1 / 600m⁻¹. A pressure sensor measured a peak longitudinal contact force of 130N and a lateral offset force gradient of 0.9N / m. Through steps 201-202, the system decomposed and assigned tasks to two FPGA channels: the first channel adjusted the longitudinal weight to 0.15 based on elevation data (-0.3m / 10m); the second channel interpolated the lateral offset of +18mm for the 1 / 600m⁻¹ curvature section. The cross-channel interaction unit performed a dot product calculation (130 × 18 = 2340N·mm). After three relaxation iterations, the rate of change of the tension gradient dropped to 0.45N / m. This generated an offset compensation sequence (+12mm, +11mm, +10mm), driving the construction equipment for precise installation of the drop wire.

[0112] In summary, steps 201 to 206 achieve millisecond-level optimization response of contact force constraint and track deformation compensation under complex line conditions through the coordination of hardware acceleration and relaxation iteration, significantly improve the accuracy of dropper arrangement parameters, ensure uniform distribution of pantograph contact force, reduce the risk of abnormal contact network wear, and adapt to the operation requirements of high-speed trains.

[0113] In order to further improve the efficiency of the coupling calculation of contact force and track deformation, the cross-channel data interaction unit of the programmable gate array hardware platform is used to realize the collaborative calculation of contact force direction and spatial deformation, and the discretized integral is combined to generate high-precision coupling results.

[0114] In some embodiments, in step 205, a cross-channel data exchange unit built into a programmable gate array hardware platform completes the dot product calculation of the contact force direction vector and the spatial deformation vector within a single clock cycle, and couples the axial weight coefficient with the suspension point spatial deformation compensation amount to generate a coupling operation result, including:

[0115] 301. Axially decompose the contact force direction vector to obtain a first longitudinal component and a second transverse component of the track. Divide the spatial deformation vector into multiple continuous geometric units based on the spacing between adjacent suspension points of the compensated three-dimensional coordinates, and extract the transverse offset gradient of each unit.

[0116] In step 301 , axial decomposition refers to decomposing the contact force direction vector into two orthogonal components in the longitudinal direction (train travel direction) and the transverse direction (perpendicular to the track direction) of the track.

[0117] Continuous geometric units refer to dividing the track longitudinally into multiple geometric calculation intervals based on the distance between adjacent suspension points (such as 10 meters), and each interval corresponds to an independent spatial deformation correction parameter.

[0118] In an embodiment of the present application, first, the contact force direction vector is decomposed into the track coordinate system by using the coordinate system projection method, and the longitudinal first direction component along the extension direction of the track and the lateral second direction component perpendicular to the track are obtained by calculating the direction cosines; secondly, based on the spacing data of adjacent suspension points in the compensated three-dimensional coordinates, the spatial deformation vector is divided into multiple continuous geometric units according to the principle of equal spacing, and the length of each unit is set to 1 / 5 of the spacing between adjacent suspension points; then, the change gradient of the lateral offset is calculated in each geometric unit, and the central difference method is used to calculate the difference in the lateral offset between the starting point and the end point of the unit and divided by the unit length to generate the lateral offset gradient of each segment, thereby providing input data for cross-channel interaction.

[0119] 302. In the cross-channel data exchange unit, the first direction component and the lateral offset gradient are superimposed segment by segment, and a projection operation is performed on the second direction component and the elevation change rate of the suspension point spatial deformation compensation amount to generate a superposition result and a projection operation result.

[0120] In step 302 , the projection operation refers to performing data mapping calculation in an orthogonal direction between the lateral contact force component and the suspension point elevation change rate (vertical height change / track longitudinal length).

[0121] In an embodiment of the present application, first, the cross-channel data interaction unit reads the longitudinal first direction component data from the first parallel computing channel, and simultaneously obtains the segmented lateral offset gradient value from the second channel; secondly, the segment-by-segment superposition of the components and gradients is realized at the hardware level: the longitudinal component and the lateral gradient value corresponding to each geometric unit are scalar superimposed through a fixed-point adder to generate the superposition results of each segment; then, the elevation change rate of the lateral second direction component and the suspension point spatial deformation compensation amount are synchronously processed: the second component is projected to the elevation change direction through a vector projection circuit, and the product of the projection length and the elevation change rate is calculated to generate a scalar projection operation result; finally, the superposition result sequence and the projection result matrix are written into the superposition result queue and the projection result buffer respectively to trigger subsequent processing signals.

[0122] 303. Scaling the superposition result based on the longitudinal curvature of the track to generate a deformation coupling coefficient, and performing a scalar and vector mixed operation on the projection operation result and the deformation coupling coefficient through a preset vector synthesis circuit to obtain a mixed operation result;

[0123] In step 303 , the deformation coupling coefficient refers to a correction factor reflecting the effect of the longitudinal curvature of the track on the coupling strength between the contact force and the deformation.

[0124] Scalar and vector mixed operation refers to the joint calculation of scalar projection results and vector deformation coefficients.

[0125] In an embodiment of the present application, first, the longitudinal curvature value of the current section is extracted from the track parameter database, and the superposition result is multiplied by the inverse of the curvature radius through the curvature scaling factor calculator to generate a deformation coupling coefficient; secondly, the preset vector synthesis circuit reads the projection operation result and the deformation coupling coefficient at the same time, and uses a hardware multiplier to multiply the deformation coupling coefficient as a scalar with the projection result vector element by element; then, the product result and the original space deformation vector are superimposed through a parallel adder, wherein the longitudinal components are directly added and the transverse components are weighted averaged; finally, the operation result is saturated to limit the output value within a preset physical reasonable range, and a mixed operation result including the longitudinal deformation variable and the transverse correction variable is generated.

[0126] 304. Perform discretization integration processing on the hybrid operation result according to the distribution density of the suspension point spatial deformation compensation amount to generate a coupling operation result.

[0127] In step 304, the discretization integration process refers to performing segmented cumulative calculations on the mixed results according to the distribution density of the spatial deformation compensation amount of the suspension points (such as the number of suspension points per meter).

[0128] In an embodiment of the present application, first, the distribution density of the spatial deformation compensation amount of the suspension point is statistically calculated, and the high-density area is determined and divided into integral intervals through the histogram analysis method, and each interval contains 3-5 suspension points; secondly, the trapezoidal integration method is used in each integral interval, and the mixed operation results are weighted and accumulated according to the density weight, the longitudinal component adopts linear integration, and the transverse component applies quadratic interpolation; then, the integration results are processed to eliminate the magnitude deviation caused by the density difference in different intervals, and generate a standardized coupling value; finally, the discrete integration results are reconstructed into a continuous distribution curve through the spatial interpolation algorithm, and the coupling operation results containing the coupling strength values of each suspension point are output to complete the final fusion of multi-dimensional data.

[0129] Here's a specific example:

[0130] In a section where a large ramp (30‰) overlaps with a small curve radius (R=500m), the laser scanner measured a track superelevation of 90mm and a vertical curve curvature of 1 / 500m⁻¹. The pressure sensor measured a longitudinal contact force of 150N and a lateral contact force of 40N. The suspension point spacing was 10 meters, with a distribution density of 3 points per 10 meters. In step 301, the longitudinal component (150 N) and the transverse component (40 N) are decomposed, and after geometric unit division, a transverse offset gradient of +1.5 mm / m is extracted. In step 302, the longitudinal component and the gradient are superimposed to obtain 150 × 1.5 = 225 N·mm / m. The transverse component and the elevation change rate (-0.3 m / 10 m = -0.03) are projected to obtain 40 × (-0.03) = -1.2 N·m / m. In step 303, the deformation coupling coefficient (225 × 0.2 = 45) is generated based on the curvature of 1 / 500 m⁻¹ (scaling factor 0.2). The mixed calculation result is -1.2 × 45 = -54 N·m² / m. In step 304, a discrete integration is performed at a density of 3 points / 10 meters (-54 ÷ 3 = -18 points). The accumulated integral of the three points yields -54 N·m², generating the coupling calculation result to drive the dropper offset compensation.

[0131] In summary, steps 301 to 304 achieve efficient coupled calculation of contact force and track deformation through the coordinated processing of axial decomposition, projection operation and discrete integration, significantly improving the efficiency and accuracy of the optimization of the dropper parameters under complex line conditions, ensuring the stability of the pantograph coupling, and adapting to the operation requirements of high-speed trains in sharp bends and steep slopes.

[0132] In order to further improve the convergence efficiency of the suspension string arrangement parameters, the adaptive adjustment of the suspension point spacing is achieved through tension balance area division and relaxation iterative mechanism, and high-precision suspension string parameters are generated in combination with lateral offset error detection.

[0133] In some embodiments, in step 206, the suspension point spacing in the compensated three-dimensional coordinates is relaxed and iterated according to the coupling operation result. When the tension gradient change rate of adjacent suspension points is less than a preset convergence threshold, a final distribution sequence of the dropper node offset compensation values is output to generate the dropper arrangement parameters, including:

[0134] 401. Based on the longitudinal curvature of the track and the distribution density of the spatial deformation compensation amount of the suspension point, the compensated three-dimensional coordinate is divided into multiple tension balance areas, and an initial relaxation factor is assigned to each area;

[0135] In step 401, the tension balance area refers to an independent optimization interval divided according to the longitudinal curvature of the track and the distribution density of the spatial deformation compensation amount of the suspension point, and is used for local tension gradient balancing processing.

[0136] The initial relaxation factor refers to the initial parameter that reflects the adjustment rate of the suspension point spacing. A larger value indicates a larger adjustment range allowed in a single iteration.

[0137] In an embodiment of the present application, first, based on the track longitudinal curvature data set and the distribution density heat map of the spatial deformation compensation amount of the suspension point, the K-means clustering algorithm is used to divide the compensated three-dimensional coordinates into multiple tension balance areas, each area contains 5-8 adjacent suspension points; secondly, an initial relaxation factor is assigned to each area, and the initial value is calculated based on the average curvature in the area: for every 0.001m⁻¹ increase in curvature, the relaxation factor decreases by 0.1, and the initial value is smoothed by a Gaussian distribution model; then, a region boundary marking mechanism is established, and a transition buffer is inserted when the curvature difference between adjacent areas exceeds a set threshold; finally, the division result and the corresponding initial relaxation factor are written into the region management register to provide initialization parameters for iterative calculation.

[0138] 402. In the tension balance region, the initial relaxation factor is adjusted according to the tension gradient change rate of adjacent suspension points, wherein a relaxation step reduction strategy is used when the track superelevation value is greater than a preset threshold to constrain the step size of the initial relaxation factor, thereby obtaining an adjusted initial relaxation factor.

[0139] In step 402, the relaxation step reduction strategy refers to a step limit rule designed for areas with large track superelevation values (such as superelevation > 80 mm) to prevent parameter over-adjustment during the iteration process.

[0140] In an embodiment of the present application, first, within the divided tension balance area, the tension gradient change rate of adjacent suspension points is monitored in real time, and the sliding window method is used to calculate the mean and standard deviation of the change rate within the current window; secondly, the relaxation factor is dynamically adjusted according to the change rate: if the change rate exceeds 1.2 times that of the previous iteration cycle, the relaxation factor is increased by 0.05, otherwise it is reduced by 0.03; then, a track superelevation value constraint condition is introduced. When the superelevation value is detected to be greater than a preset threshold (such as 150mm), the relaxation step reduction strategy is activated to limit the adjustment amplitude to 50% of the normal value; finally, the effective range of the relaxation factor is limited to between [0.2,1.8] through the saturation function, and an adjusted initial relaxation factor table is generated and updated to the area management register.

[0141] 403. Perform a bidirectional chain iterative calculation on the suspension point spacing within each tension balance region using the adjusted initial relaxation factor. When the suspension point spacing adjustment triggers a reverse change in the offset compensation value of the adjacent suspension string node, generate a suspension point density adaptive local rebalancing factor based on the tension gradient change rate and the relaxation step size reduction strategy.

[0142] In step 403, the bidirectional chain iterative calculation refers to an iterative method of alternately adjusting the suspension point spacing in the forward and reverse directions along the longitudinal direction of the track to balance the tension distribution.

[0143] The local rebalancing factor refers to the regional adaptive adjustment coefficient generated according to the tension gradient change rate and step size constraint.

[0144] In an embodiment of the present application, first, a bidirectional chain iteration is initialized using the adjusted relaxation factor: the forward iteration gradually increases the suspension point spacing along the track extension direction, and the reverse iteration reduces the spacing in the reverse direction, and the step size of each adjustment is the product of the relaxation factor and the current spacing; secondly, the changing trend of the offset compensation value of the suspension node is monitored in real time, and when it is detected that the compensation values of adjacent nodes are adjusted in opposite directions (such as the compensation of the front node increases and the compensation of the rear node decreases), a local rebalancing calculation is triggered; then, the density influence coefficient is calculated based on the current tension gradient change rate, and the product of the relaxation factor and the density influence coefficient is used as the local rebalancing factor.

[0145] 404. Perform weighted fusion of the local rebalancing factor and the deformation coupling coefficient in the coupling operation result, and simultaneously detect the lateral offset cumulative error of the suspension point spatial deformation compensation amount. If the lateral offset cumulative error exceeds the tolerance range corresponding to the curvature of the vertical curve of the track, reset the lateral offset gradient based on the segmented results of the multiple continuous geometric units.

[0146] In step 404, the cumulative lateral offset error refers to the cumulative deviation of the suspension point spatial deformation compensation in the lateral direction of the track (eg, +15 mm exceeds the allowable ±10 mm).

[0147] In an embodiment of the present application, first, the local rebalancing factor and the deformation coupling coefficient in the coupling operation result are weighted and fused, and the weight ratio is dynamically allocated according to the regional curvature: for every 0.001m⁻¹ increase in curvature, the weight of the deformation coupling coefficient increases by 5%; secondly, the lateral offset cumulative error of the spatial deformation compensation amount of the suspension point is synchronously calculated, and the error cumulative value of the latest 10 suspension points is statistically calculated using the moving average method; then, when it is detected that the cumulative error exceeds the vertical curve curvature tolerance range (such as ±5mm), the lateral offset gradient reset mechanism is triggered: based on the original segmented geometric unit data, the lateral offset gradient of each segment is recalculated; finally, the reset gradient value is updated to the compensation parameter register of the second parallel calculation channel, and the error accumulation counter is cleared.

[0148] 405. When the tension gradient change rate of adjacent suspension points in all tension balance areas is less than a preset convergence threshold, a mapping relationship of the suspension string node offset compensation value is generated based on the suspension point spacing adjustment amount, the local rebalancing factor and the reset lateral offset gradient, and the mapping relationship is locked to generate the suspension string arrangement parameters.

[0149] In step 405 , the mapping relationship refers to a mathematical correlation model between the suspension point spacing adjustment amount, the local rebalancing factor, and the lateral offset gradient.

[0150] In an embodiment of the present application, first, convergence detection is performed in parallel in all tension balance areas, and the moving average of the tension gradient change rate of adjacent suspension points is calculated. When the change rate of all areas is less than a preset threshold (such as 0.5%) for three consecutive iterations, it is determined that the system has reached a stable state; secondly, the suspension point spacing adjustment amount, local rebalancing factor and reset lateral offset gradient of each area are integrated, and a continuous distribution curve of the offset compensation value of the suspension string node is generated through the cubic spline interpolation algorithm; then, a compensation value mapping relationship table is established, the theoretical coordinates are bound to the allowable offset range, and a compensation range is set for each node; finally, the mapping relationship table is locked and the suspension string arrangement parameters including node number, coordinates, compensation amount and tension value are generated to complete the optimization calculation process.

[0151] Here's a specific example:

[0152] In a section where continuous sharp bends (R=400m, R=450m) overlap with a large slope (28‰), the track superelevation is 95mm, the vertical curve curvature is 1 / 400m⁻¹, and the suspension point distribution density is 4 points / 10 meters. Step 401 divides the tension balance into three regions (curvatures 0.0025 m⁻¹, 0.0022 m⁻¹, and 0.0018 m⁻¹), assigning initial relaxation factors of 0.8, 0.75, and 0.7. Step 402 reduces the factors to 0.7, 0.65, and 0.6 because the high value exceeds the threshold. Step 403 triggers a reverse change in the offset (+6 mm to -1 mm) through bidirectional iteration, generating a local rebalancing factor of 0.3. Step 404 detects the cumulative lateral offset error of +13 mm (out of tolerance ±10 mm) and resets the gradient to +0.7 mm / m. Step 405 generates a mapping relationship (+6 × 0.3 × 0.7 = +1.26 mm) and outputs an offset sequence of +1.26 mm, +1.2 mm, and +1.15 mm to drive the precise installation of the suspension string.

[0153] In summary, steps 401 to 405 achieve rapid convergence and high-precision generation of dropper arrangement parameters under complex line conditions through relaxation iteration and closed-loop correction of lateral errors, significantly improve the stability of pantograph coupling, ensure uniform distribution of contact network tension, and adapt to the continuous operation requirements of high-speed trains in sharp bends and steep slopes.

[0154] In some embodiments, in step 403, a bidirectional chain iterative calculation is performed on the suspension point spacing within each tension balance region using the adjusted initial relaxation factor. When the suspension point spacing adjustment triggers a reverse change in the offset compensation value of the adjacent dropper string node, a suspension point density adaptive local rebalancing factor is generated based on the tension gradient change rate and the relaxation step size reduction strategy, including:

[0155] 501. Mark the suspension point spacing within the tension balance region in segments based on the longitudinal curvature of the track, and use the change in the longitudinal curvature of the track between adjacent suspension points as a direction switching threshold for chain iteration;

[0156] In step 501, segment marking refers to dividing the suspension point spacing within the tension balance area into intervals according to the longitudinal curvature of the track (e.g., a curvature value of 0.002 m⁻¹ corresponding to a curvature radius of 500 m), and each interval corresponds to an independent iterative direction switching rule.

[0157] The direction switching threshold refers to the critical value of the curvature change that triggers the iteration direction to switch from the positive longitudinal direction of the track to the negative direction (for example, the switch occurs when the curvature change exceeds 0.0005m⁻¹).

[0158] In an embodiment of the present application, first, continuous measurement data of the longitudinal curvature of the track is obtained, and the sliding window method is used to calculate the curvature change between adjacent suspension points, and the window width is set to the distance between 3 suspension points; secondly, a direction switching threshold is set according to the magnitude of the curvature change, and when the curvature change between adjacent points exceeds 0.002m⁻¹, it is marked as a segment boundary; then, the calculation interval is divided according to the segment mark within the tension balance area, and the curvature change threshold is stored at the starting point of each interval; finally, the marking result is written into the iteration control register to provide a direction switching trigger condition for the bidirectional chain iteration.

[0159] 502. In a bidirectional chain iterative calculation, the suspension point spacing is adjusted sequentially along the positive longitudinal direction of the track. When the suspension point spacing adjustment exceeds the direction switching threshold, the iterative calculation is switched to the reverse longitudinal direction of the track;

[0160] In step 502, the bidirectional chain iterative calculation refers to an iterative method of alternately adjusting the suspension point spacing along the longitudinal positive direction (train travel direction) and the reverse direction of the track to balance the tension distribution.

[0161] In an embodiment of the present application, first, the bidirectional chain iteration direction is initialized to the longitudinal positive direction of the track, and the spacing is gradually increased starting from the starting suspension point, and the adjustment amount each time is the product of the current relaxation factor and the standard spacing; secondly, the suspension point spacing adjustment amount is monitored in real time, and when the cumulative adjustment amount exceeds the curvature change threshold of the corresponding interval, the direction switching interrupt is triggered; then, the current iteration state is saved to the stack, and the reverse iteration mode is switched to reduce the spacing in reverse starting from the current suspension point.

[0162] 503. During each iteration, the ratio of the current suspension point density to the tension gradient change rate is calculated based on the inverse relationship between the suspension point spacing adjustment amount and the offset compensation value of the adjacent suspension string node, thereby generating a suspension point density change coefficient.

[0163] In step 503, the suspension point density variation coefficient refers to a correction factor reflecting the relationship between the suspension point distribution density (eg, the number of suspension points per 10 meters) and the tension gradient variation rate.

[0164] In an embodiment of the present application, first, the adjustment amount of the suspension point spacing and the direction of change of the offset compensation value of the adjacent suspension string nodes are synchronously recorded in each iteration. When it is detected that the offset of the adjacent nodes shows an opposite change (such as the compensation of node A increases and the compensation of node B decreases), the suspension point density of the current area is extracted; secondly, the ratio of the density to the tension gradient change rate is calculated, and the exponential weighted average method is used to eliminate the influence of instantaneous fluctuations; then, the ratio is processed to the [0,1] interval through the Sigmoid function to generate the suspension point density change coefficient; finally, the coefficient is stored in a temporary register for subsequent step correction.

[0165] 504. Based on the product of the suspension point density variation coefficient and the adjusted initial relaxation factor, the step size constraint range of the relaxation step size reduction strategy is modified to generate a relaxation step size correction value for the current iteration step.

[0166] In step 504, the relaxation step correction value refers to the iterative step correction value adjusted according to the density variation coefficient and the relaxation factor.

[0167] In an embodiment of the present application, first, the adjusted initial relaxation factor table is read to extract the relaxation factor value corresponding to the current iteration step; second, the density change coefficient and the relaxation factor are scalar multiplied, and the calculation result is constrained to be between 50% and 150% of the original step range by a limiter; then, the correction strategy is dynamically selected according to the track superelevation value status: when the superelevation value exceeds 120mm, an additional 20% reduction factor is applied; finally, a relaxation step correction value including the upper and lower limits of the step size is generated and updated to the iterative controller.

[0168] 505. Perform weighted superposition on the relaxation step length correction amount and the tension gradient change rate, perform curvature compensation processing on the superposition result in combination with the track superelevation value, and generate a local rebalancing factor with adaptive suspension point density.

[0169] In step 505, curvature compensation processing refers to geometrically correcting iterative parameters based on the track superelevation value to eliminate the interference of track deformation on tension distribution.

[0170] In the embodiment of the present application, first, the relaxation step correction amount and the real-time tension gradient change rate are weighted and superimposed, and the weight ratio is dynamically adjusted according to the number of iterations (initial weight 0.7:0.3, and the change rate weight is increased by 0.05 every 10 iterations); secondly, the track superelevation value compensation module is introduced to perform curvature compensation on the superimposed result: when the superelevation value is in the [100mm, 150mm] interval, the compensation coefficient is 1.2, and in other intervals it is 1.0; then, the compensated value is projected to the direction of change of the suspension point density through a vector rotation operation to generate a direction-sensitive local rebalancing factor.

[0171] Here's a specific example:

[0172] In a section where a small curve radius (R = 450m) overlaps a large slope (30‰), the track has a longitudinal curvature of 0.0022m⁻¹ and a suspension point density of 4 points per 10 meters. Step 501 sets the curvature change of 0.0004m⁻¹ as the direction switching threshold. Step 502 triggers the threshold when the iterative adjustment spacing in the positive direction reaches +4mm, switching to a negative adjustment of -3mm in the negative direction. Step 503 calculates the density change coefficient (4 points ÷ 0.7N / m ≈ 5.71 × 0.1 = 0.571). Step 504 generates the relaxation step length correction (0.571 × 0.6 = 0.343mm). Step 505 combines the superelevation value of 95mm (compensation coefficient 0.95) to generate a local rebalancing factor (0.343 × 0.95 ≈ 0.326). This ultimately drives the dropper node offset compensation values to +0.326mm, +0.31mm, and +0.29mm.

[0173] In summary, steps 501 to 505 significantly improve the stability and accuracy of the suspension string spacing adjustment under complex line conditions through the bidirectional chain iteration and density adaptive rebalancing mechanism, effectively suppress the sudden change of tension gradient, ensure the uniformity of the pantograph-catenary coupling, and adapt to the high-frequency operation requirements of high-speed trains in sharp bends and steep slopes.

[0174] In some embodiments, in step 503, during each iteration, the ratio of the current suspension point density to the tension gradient change rate is calculated based on the inverse change relationship between the suspension point spacing adjustment amount and the offset compensation value of the adjacent suspension string node to generate the suspension point density change coefficient, including:

[0175] 601. Perform segmented processing on the suspension point spacing adjustment amount based on the change in the longitudinal curvature of the track to generate an adjustment ratio for the current suspension point spacing;

[0176] In step 601, segmentation processing refers to dividing the suspension point spacing adjustment amount into intervals according to the change in the longitudinal curvature of the track (such as the change in the curvature radius), and standardizing the adjustment amount to a preset range according to the interval.

[0177] In the embodiment of the present application, first, continuous measurement data of the change in the longitudinal curvature of the track is obtained, and the data is divided into multiple sections using an equally spaced sampling method, with the length of each section set to twice the distance between adjacent suspension points; second, the distribution of the adjustment amount of the suspension point distance is statistically analyzed in each section, the average value and standard deviation of the adjustment amount are calculated, and the ratio of the standard deviation to the average value is used as the adjustment ratio of the section; then, abnormal adjustment amounts are eliminated, and when the adjustment amount of a certain point exceeds 3 times the standard deviation of the section average value, linear interpolation is used for correction; finally, the adjustment ratios of each section are stored in a ratio parameter table in the order of track mileage, providing benchmark parameters for subsequent density calculations.

[0178] 602. Extract the reverse change interval of the suspension point spacing adjustment amount and the offset compensation value according to the reverse change direction of the offset compensation value of the adjacent suspension string nodes, and calculate the suspension point density change gradient within the reverse change interval;

[0179] In step 602 , the reverse change interval refers to a track longitudinal interval in which the offset compensation values of adjacent dropper node points reverse direction (eg, suddenly change from a positive value to a negative value).

[0180] The gradient of suspension point density change refers to the rate of change of suspension point density (such as the number of suspension points per 10 meters) in the reverse change range with the spacing adjustment amount.

[0181] In an embodiment of the present application, first, the direction of change of the offset compensation value of adjacent suspension string nodes is monitored in real time. When it is detected that the compensation value of the front node increases and the compensation value of the rear node decreases, it is marked as a reverse change interval; secondly, the spacing adjustment data of all suspension points in the interval are extracted, and the density change in the window (the default window size is 5 suspension points) is calculated by the sliding window method; then, the central difference method is used to calculate the suspension point density change gradient, that is, the ratio of the density difference between two adjacent points to the spacing.

[0182] 603. Perform a ratio operation on the suspension point density change gradient and the tension gradient change rate, perform weighted correction on the adjustment ratio and the comparison value operation result, and generate an initial value of the initial suspension point density change coefficient;

[0183] In step 603, weighted correction refers to weighting the ratio of the density gradient to the tension gradient according to the normalized adjustment ratio.

[0184] In the embodiment of the present application, first, the density change gradient data is read from the gradient register, and the current tension gradient change rate measurement value is obtained at the same time, and the two are ratio-operated (density gradient / tension change rate); secondly, the adjustment ratio of the corresponding segment in the proportional parameter table is retrieved, and the ratio operation result is multiplied by the adjustment ratio coefficient using a weighted correction algorithm; then, the correction result is normalized and mapped to the [0,1] interval through the Sigmoid function; finally, the initial value of the initial suspension point density change coefficient is generated and written into the coefficient buffer area to wait for curvature compensation.

[0185] 604. Perform curvature compensation correction on the initial suspension point density variation coefficient based on the track superelevation value to generate a suspension point density variation coefficient.

[0186] In step 604, curvature compensation correction refers to geometric correction of the density variation coefficient based on the track superelevation value to eliminate the interference of the track lateral deformation on the parameter calculation.

[0187] In the embodiment of the present application, first, the superelevation value data of the current section is obtained from the track parameter database, and a mapping relationship table between the superelevation value and the curvature compensation coefficient is established (for every 10mm increase in the superelevation value, the compensation coefficient increases by 0.05); secondly, the initial density change coefficient matrix is read, and the corresponding compensation coefficient is obtained by looking up the table according to the superelevation value of the section; then, the initial coefficient is multiplied by the compensation coefficient to generate the density change coefficient after curvature compensation; finally, the compensation result is saturated, and the coefficient value is limited to the physically reasonable range [0.2, 1.5], and the final suspension point density change coefficient is output to the optimization controller.

[0188] Here's a specific example:

[0189] In a section where a steep slope (28‰) overlaps a small curve radius (R = 450m), the track's longitudinal curvature changes by 0.0003m⁻¹, the suspension point spacing is adjusted by +6mm, and the offset compensation value suddenly changes from +4mm to -1mm. Step 601 normalizes the adjustment to a ratio of 0.8. Step 602 determines the reverse change range as 125-130 meters and calculates the density gradient (5 points / 10m ÷ (-5mm) = -1 point / mm). Step 603 generates an initial coefficient (-1 ÷ 0.5N / m = -2 × 0.8 = -1.6). Step 604, based on the superelevation value of 95mm (compensation coefficient 0.95), adjusts the dropper node offsets to -1.52mm, -1.45mm, and -1.4mm.

[0190] In summary, steps 601 to 604 significantly improve the calculation accuracy of the suspension point density variation coefficient through the coordinated processing of segmentation and curvature compensation, effectively suppress the overshoot risk of the suspension string parameter adjustment under complex line conditions, ensure the balance of the pantograph-catenary contact force distribution, and adapt to the continuous operation requirements of high-speed trains in sharp bends and steep slopes.

[0191] In some embodiments, in step 102, based on the contact force equilibrium constraint, the track superelevation value and the vertical curve curvature obtained by the laser scanner moving along the longitudinal direction of the track are used to perform parameter compensation processing on the dropper position calculation model, and the elevation data of the catenary suspension point are combined to generate a line parameter compensation mechanism to obtain the compensated three-dimensional coordinates of the catenary suspension point, including:

[0192] 701. Using the track superelevation value and vertical curve curvature obtained by the laser scanner moving along the longitudinal direction of the track, the elevation data of the contact network suspension point are subjected to segmented interpolation processing to generate the suspension point elevation change gradient;

[0193] In step 701, the segmented interpolation process is to divide the elevation data of the suspension point into intervals according to a fixed longitudinal interval of the track (such as every 10 meters), and use an interpolation algorithm to fill in the data discontinuities.

[0194] The gradient of the suspension point elevation change refers to the rate of change of the vertical height of the contact network suspension point along the longitudinal unit length of the track (such as a 0.2 meter elevation change per meter).

[0195] In an embodiment of the present application, first, a laser scanner collects the original data of the track superelevation value and vertical curve curvature at intervals of 10 cm along the longitudinal direction of the track, and the vibration noise of the equipment is eliminated by Kalman filtering; secondly, based on the mileage coordinates of the contact network suspension points, a cubic spline interpolation algorithm is used to continuously process the discrete elevation data to generate a suspension point elevation sequence at intervals of one meter; then, a differential operation is performed on the interpolated elevation data to calculate the elevation difference between adjacent suspension points and divide it by the spacing to generate the suspension point elevation change gradient.

[0196] 702. According to the contact pressure standard deviation optimization target in the contact force equilibrium constraint condition, extract the influence coefficient of the track superelevation value on the lateral offset of the contact network suspension point, and generate a lateral offset compensation factor;

[0197] In step 702, the lateral offset compensation factor refers to a correction coefficient that reflects the effect of the track superelevation value on the lateral offset of the contact network (eg, for every 10 mm increase in superelevation value, the lateral offset compensation increases by 2 mm).

[0198] In the embodiment of the present application, first, the target value of the contact pressure standard deviation is extracted from the contact force equilibrium constraint condition, and a mapping relationship table between the standard deviation and the lateral offset is established; secondly, the random forest algorithm is used to analyze the influence weight of the track superelevation value on the lateral offset, and the top three key influencing parameters are selected by feature importance sorting; then, based on the multivariate linear regression model, the lateral offset variation coefficient corresponding to the unit change of the superelevation value is calculated to generate the lateral offset compensation factor α=Δx / Δh (Δh is the superelevation change).

[0199] 703. Perform weighted superposition on the elevation change gradient of the suspension point and the lateral offset compensation factor, perform curvature compensation correction on the superposition result in combination with the vertical curve curvature, and generate a suspension point spatial deformation compensation amount;

[0200] In step 703, curvature compensation correction refers to geometric correction of the weighted superposition result based on the curvature of the vertical curve to eliminate the interference of the vertical deformation of the track on the spatial deformation.

[0201] In the embodiment of the present application, first, the elevation change gradient curve is processed so that its dimension is consistent with the lateral offset compensation factor; secondly, a dynamic weight allocation strategy is designed: the elevation gradient is given a 60% weight in the straight segment, and the lateral compensation factor is increased to a 55% weight in the curved segment; then, the weighted superposition result is input into the curvature compensation module, and the compensation coefficient β=1 / (R·k) (R is the curvature radius, k is the material elastic coefficient) is calculated using the vertical curve curvature radius, and the superposition result is nonlinearly amplified; finally, the mutation point is smoothed by a spatial convolution operation, and the spatial deformation compensation amount of the suspension point including the lateral displacement Δx and the elevation correction Δz is output.

[0202] 704. Perform piecewise integration processing on the spatial deformation compensation amount of the suspension point based on the change in the longitudinal curvature of the track to generate the initial compensation coordinates of the catenary suspension point;

[0203] In step 704, the segmented integration process refers to performing segmented cumulative calculations on the spatial deformation compensation amount according to the change in the longitudinal curvature of the track.

[0204] In the embodiment of the present application, first, the spatial deformation compensation amount is divided into continuous integration intervals according to the rate of change of the longitudinal curvature of the track, and each interval corresponds to a track segment with the same curvature sign; secondly, the trapezoidal integration method is used in each interval to accumulate and calculate the Δx and Δz components respectively along the mileage direction of the track, and the longitudinal integration step is set to 1 / 10 of the suspension point spacing; then, the integration result is superimposed with the original suspension point coordinates to generate preliminary compensation coordinates; finally, the system cumulative error is eliminated through coordinate translation transformation to ensure that the coordinate closure difference between the starting point and the end point is less than 2 mm, thereby forming the initial compensation coordinates.

[0205] 705. Perform axial correction on the initial compensation coordinates according to the contact pressure distribution direction in the contact force equilibrium constraint condition to generate compensated three-dimensional coordinates of the contact network suspension point.

[0206] In step 705 , the axial correction refers to adjusting the axial component of the compensation coordinate according to the contact pressure distribution direction (eg, longitudinal dominant or transverse dominant).

[0207] In an embodiment of the present application, first, the main direction vector of the contact pressure is extracted from the contact force equilibrium constraint condition and decomposed into longitudinal and vertical components in the orbital coordinate system; secondly, an axial correction model is established: it includes longitudinal coordinate correction and vertical correction; then, a rigid body rotation algorithm is used to spatially transform the initial compensation coordinates according to the correction amount to ensure that the correction direction is consistent with the contact force distribution; finally, coordinate accuracy verification is performed: the contact pressure standard deviation of the corrected coordinates is calculated by the back propagation algorithm. If the target value is not reached, steps 702-705 are repeated until a compensated three-dimensional coordinate that meets the mechanical requirements is generated.

[0208] Here's a specific example:

[0209] In a section where a small curve radius (R = 500m) overlaps a large slope (25‰), a laser scanner measured a track superelevation of 85mm, a vertical curve curvature of 1 / 500m⁻¹, and an actual suspension point elevation of 12.6m. Step 701 generates an elevation gradient of -0.3m / 10m; Step 702 calculates a lateral offset compensation factor of +17mm; Step 703 performs weighted superposition to obtain -0.3×0.6+17×0.4=6.62, resulting in a curvature-compensated deformation of 6.95mm. Step 704 integrates to generate initial coordinates (lateral +17mm, elevation 12.3m); Step 705 corrects the elevation to 12.0m based on an 80% longitudinal contact force ratio, outputting the compensated 3D coordinates (lateral +17mm, elevation 12.0m).

[0210] In summary, steps 701 to 705 achieve high-precision calculation of contact network spatial deformation compensation under complex line conditions through the integration of laser scanning data and contact force constraints, significantly improve the positioning accuracy of the dropper string, effectively balance the distribution of the pantograph contact force, and adapt to the high-frequency deformation compensation needs of high-speed trains in sharp bends and steep slopes.

[0211] Figure 2 The present application provides a structural diagram of a system for optimizing the arrangement of high-speed railway contact network dropper strings based on machine learning, as shown in FIG. Figure 2 As shown, the device includes:

[0212] A contact constraint generation module 21 is configured to capture the spatial distribution characteristics of the contact force between the pantograph slide and the catenary using a pressure sensor at a catenary suspension point, and generate a contact force equilibrium constraint condition including a contact pressure standard deviation optimization objective;

[0213] The laser parameter compensation and correction module 22 is used to perform parameter compensation processing on the dropper position calculation model based on the contact force balance constraint condition, using the track superelevation value and vertical curve curvature obtained by the laser scanner moving along the longitudinal direction of the track, and generating a line parameter compensation mechanism in combination with the elevation data of the catenary suspension point to obtain the compensated three-dimensional coordinates of the catenary suspension point;

[0214] The hardware accelerated iterative optimization module 23 is used to utilize the pipeline architecture of the programmable gate array hardware platform to perform parallel accelerated processing on the weight calculation and spatial coordinate transformation of the neural network, synchronously iteratively calculate the contact force balance constraint condition and the compensated three-dimensional coordinates, and generate the string arrangement parameters that satisfy the pantograph-catenary coupling relationship;

[0215] The dropper string parameter execution driving module 24 is used to drive the contact network construction equipment to perform dropper string length adjustment and positioning installation based on the segmented tension value between the contact network suspension points and the dropper string node offset compensation value in the dropper string arrangement parameters.

[0216] Figure 2 The device for optimizing the arrangement of high-speed railway contact wires based on machine learning can be used to Figure 1 The implementation principles and technical effects of the machine learning-based method for optimizing the arrangement of high-speed railway catenary droppers are not further elaborated. The specific manner in which each module and unit performs operations in the machine learning-based device for optimizing the arrangement of high-speed railway catenary droppers has been described in detail in the embodiments of the method and will not be further elaborated here.

[0217] In one possible design, Figure 2 The device for optimizing the arrangement of high-speed railway contact network droppers based on machine learning in the embodiment shown can be implemented as a computing device, such as Figure 3 As shown, the computing device may include a storage component 31 and a processing component 32;

[0218] The storage component 31 stores one or more computer instructions, wherein the one or more computer instructions are called and executed by the processing component 32 .

[0219] The processing component 32 is used for the above Figure 1 The embodiment provides a method for optimizing the arrangement of high-speed railway contact network dropper strings based on machine learning.

[0220] The processing component 32 may include one or more processors to execute computer instructions to complete all or part of the steps in the above method. Of course, the processing component may also be implemented as one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components to perform the above method.

[0221] The storage component 31 is configured to store various types of data to support operations at the terminal. The storage component can be implemented by any type of volatile or non-volatile memory device, or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk, or optical disk.

[0222] Of course, a computing device may also include other components, such as input / output interfaces, display components, communication components, etc.

[0223] The input / output interface provides an interface between the processing component and the peripheral interface module, which can be an output device, an input device, etc.

[0224] The communication component is configured to facilitate, among other things, wired or wireless communications between the computing device and other devices.

[0225] Among them, the computing device can be a physical device or an elastic computing host provided by a cloud computing platform, etc. In this case, the computing device can refer to a cloud server, and the above-mentioned processing components, storage components, etc. can be basic server resources rented or purchased from the cloud computing platform.

[0226] The present application also provides a computer storage medium storing a computer program, wherein the computer program can achieve the above-mentioned Figure 1 The illustrated embodiment provides a method for optimizing the arrangement of high-speed railway contact network dropper strings based on machine learning.

[0227] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0228] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0229] Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above technical solution, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in each embodiment or certain portions of the embodiments.

[0230] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for optimizing the arrangement of high-speed railway contact network droppers based on machine learning, characterized in that: include: The pressure sensors at the catenary suspension points are used to capture the spatial distribution characteristics of the contact force between the pantograph slide and the catenary, and to generate contact force equilibrium constraints that include the contact pressure standard deviation optimization objective. Based on the contact force balance constraint, the track superelevation value and vertical curve curvature obtained by the laser scanner moving along the longitudinal direction of the track are used to perform parameter compensation processing on the dropper position calculation model. The elevation data of the catenary suspension point are combined to generate a line parameter compensation mechanism, and the compensated three-dimensional coordinates of the catenary suspension point are obtained. Iterate the contact force equilibrium constraint condition and the compensated three-dimensional coordinates synchronously to generate the string arrangement parameters that satisfy the pantograph-catenary coupling relationship; Based on the segmented tension values between the catenary suspension points and the offset compensation values of the dropper string nodes in the dropper string arrangement parameters, driving the catenary construction equipment to perform dropper string length adjustment and positioning installation; The contact force equilibrium constraint condition and the compensated three-dimensional coordinate are synchronously iterated to generate the hanger arrangement parameters that satisfy the pantograph-catenary coupling relationship, including: Decompose the weight calculation of the neural network into an axial weight subtask related to the contact force distribution direction, and decompose the spatial coordinate transformation into a geometric transformation subtask based on the longitudinal curvature of the track; In a pipeline architecture of a programmable gate array hardware platform, an independent first parallel computing channel is allocated to the axial weight subtask, and an independent second parallel computing channel is allocated to the geometric transformation subtask; In the first parallel calculation channel, the axial weight coefficient of the contact force equilibrium constraint condition is adjusted according to the suspension point elevation data of the compensated three-dimensional coordinates; In the second parallel calculation channel, a segmented interpolation process is performed on the lateral offset of the compensated three-dimensional coordinate based on the longitudinal curvature of the track to generate a compensation amount for the spatial deformation of the suspension point; Through the cross-channel data interaction unit built into the programmable gate array hardware platform, the dot product calculation of the contact force direction vector and the spatial deformation vector is completed in a single clock cycle, and the axial weight coefficient and the suspension point spatial deformation compensation amount are coupled to generate a coupling operation result; According to the coupling operation result, the suspension point spacing in the compensated three-dimensional coordinates is relaxed and iterated. When the tension gradient change rate of adjacent suspension points is less than a preset convergence threshold, the final distribution sequence of the suspension string node offset compensation value is output to generate the suspension string arrangement parameters.

2. The method according to claim 1, characterized in that Through the cross-channel data interaction unit built into the programmable gate array hardware platform, the dot product calculation of the contact force direction vector and the spatial deformation vector is completed in a single clock cycle, and the axial weight coefficient and the suspension point spatial deformation compensation amount are coupled to generate the coupling operation results, including: The contact force direction vector is axially decomposed to obtain the first longitudinal component and the second transverse component of the track. The spatial deformation vector is divided into multiple continuous geometric units based on the spacing between adjacent suspension points of the compensated three-dimensional coordinates, and the transverse offset gradient of each segment is extracted. In the cross-channel data exchange unit, the first direction component and the lateral offset gradient are superimposed section by section, and the second direction component and the elevation change rate of the suspension point spatial deformation compensation amount are projected to generate a superposition result and a projection result; Scaling the superposition result based on the longitudinal curvature of the track to generate a deformation coupling coefficient, and performing a scalar and vector mixed operation on the projection operation result and the deformation coupling coefficient through a preset vector synthesis circuit to obtain a mixed operation result; The hybrid operation result is discretized and integrated according to the distribution density of the suspension point spatial deformation compensation amount to generate a coupling operation result.

3. The method according to claim 2, characterized in that The suspension point spacing in the compensated three-dimensional coordinates is relaxed and iterated according to the coupling operation result. When the tension gradient change rate of adjacent suspension points is less than a preset convergence threshold, a final distribution sequence of the dropper node offset compensation value is output to generate the dropper arrangement parameters, including: Based on the longitudinal curvature of the track and the distribution density of the spatial deformation compensation amount of the suspension point, the compensated three-dimensional coordinates are divided into multiple tension balance areas, and an initial relaxation factor is assigned to each area; In the tension balance area, the initial relaxation factor is adjusted according to the tension gradient change rate of adjacent suspension points, wherein the relaxation step reduction strategy when the track superelevation value is greater than a preset threshold is used to constrain the step size of the initial relaxation factor to obtain an adjusted initial relaxation factor; A bidirectional chain iterative calculation is performed on the suspension point spacing within each tension balance region using the adjusted initial relaxation factor. When the suspension point spacing adjustment triggers a reverse change in the offset compensation value of the adjacent suspension string node, a suspension point density adaptive local rebalancing factor is generated based on the tension gradient change rate and the relaxation step size reduction strategy. The local rebalancing factor is weightedly integrated with the deformation coupling coefficient in the coupling operation result, and the lateral offset cumulative error of the suspension point spatial deformation compensation amount is synchronously detected. If the lateral offset cumulative error exceeds the tolerance range corresponding to the curvature of the vertical curve of the track, the lateral offset gradient is reset based on the segmented results of the multiple continuous geometric units; When the tension gradient change rate of adjacent suspension points in all tension balance areas is less than a preset convergence threshold, a mapping relationship of the suspension string node offset compensation value is generated based on the suspension point spacing adjustment amount, the local rebalancing factor and the reset lateral offset gradient, and the mapping relationship is locked to generate the suspension string arrangement parameters.

4. The method according to claim 3, wherein The adjusted initial relaxation factor is used to perform a bidirectional chain iterative calculation on the suspension point spacing within each tension balance area. When the suspension point spacing adjustment triggers a reverse change in the offset compensation value of the adjacent suspension string node, a suspension point density adaptive local rebalancing factor is generated based on the tension gradient change rate and the relaxation step size reduction strategy, including: Marking the suspension point spacing within the tension balance region in segments based on the longitudinal curvature of the track, and using the change in longitudinal curvature of the track between adjacent suspension points as a direction switching threshold for chain iteration; In the bidirectional chain iterative calculation, the suspension point spacing is adjusted in sequence along the positive longitudinal direction of the track. When the suspension point spacing adjustment exceeds the direction switching threshold, the iterative calculation is switched to the reverse longitudinal direction of the track. In each iteration, the ratio of the current suspension point density to the tension gradient change rate is calculated based on the inverse change relationship between the suspension point spacing adjustment amount and the offset compensation value of the adjacent suspension string node to generate a suspension point density change coefficient; Based on the product of the suspension point density variation coefficient and the adjusted initial relaxation factor, the step size constraint range of the relaxation step size reduction strategy is modified to generate a relaxation step size correction value of the current iteration step; The relaxation step length correction amount and the tension gradient change rate are weightedly superimposed, and the superposition result is subjected to curvature compensation processing in combination with the track superelevation value to generate a local rebalancing factor with adaptive suspension point density.

5. The method according to claim 4, characterized in that In each iteration, the ratio of the current suspension point density to the tension gradient change rate is calculated based on the inverse relationship between the suspension point spacing adjustment amount and the offset compensation value of the adjacent suspension string node, and the suspension point density change coefficient is generated, including: The suspension point spacing adjustment amount is segmented based on the change in the longitudinal curvature of the track to generate an adjustment ratio for the current suspension point spacing; According to the reverse change direction of the offset compensation values of adjacent suspension string nodes, extracting the reverse change interval of the suspension point spacing adjustment amount and the offset compensation value, and calculating the suspension point density change gradient within the reverse change interval; Performing a ratio operation on the suspension point density change gradient and the tension gradient change rate, and performing weighted correction based on the adjustment ratio and the comparison value operation result to generate an initial value of the initial suspension point density change coefficient; The initial suspension point density variation coefficient is corrected by curvature compensation based on the track superelevation value to generate the suspension point density variation coefficient.

6. The method according to claim 1, wherein Based on the contact force balance constraint, the track superelevation value and vertical curve curvature obtained by the laser scanner along the longitudinal movement of the track are used to perform parameter compensation processing on the dropper position calculation model. Combined with the elevation data of the catenary suspension point, a line parameter compensation mechanism is generated to obtain the compensated three-dimensional coordinates of the catenary suspension point, including: Using the track superelevation value and vertical curve curvature obtained by the laser scanner moving along the longitudinal direction of the track, the elevation data of the contact network suspension point is interpolated piecewise to generate the elevation change gradient of the suspension point; According to the contact pressure standard deviation optimization target in the contact force equilibrium constraint condition, the influence coefficient of the track superelevation value on the lateral offset of the contact network suspension point is extracted to generate a lateral offset compensation factor; Performing weighted superposition of the elevation change gradient of the suspension point and the lateral offset compensation factor, and performing curvature compensation correction on the superposition result in combination with the vertical curve curvature to generate the suspension point spatial deformation compensation amount; Performing piecewise integration processing on the spatial deformation compensation amount of the suspension point based on the change in longitudinal curvature of the track to generate the initial compensation coordinates of the catenary suspension point; According to the contact pressure distribution direction in the contact force equilibrium constraint condition, the initial compensation coordinate is axially corrected to generate the compensated three-dimensional coordinates of the contact network suspension point.

7. A high-speed railway contact network dropper arrangement optimization system based on machine learning, characterized in that: include: The contact constraint generation module is used to capture the spatial distribution characteristics of the contact force between the pantograph slide and the catenary using the pressure sensors at the catenary suspension points, and generate contact force equilibrium constraints that include the contact pressure standard deviation optimization objective; A laser parameter compensation and correction module is used to perform parameter compensation processing on the dropper position calculation model based on the contact force balance constraint condition, using the track superelevation value and vertical curve curvature obtained by the laser scanner moving along the longitudinal direction of the track, and generating a line parameter compensation mechanism in combination with the elevation data of the catenary suspension point to obtain the compensated three-dimensional coordinates of the catenary suspension point; A hardware-accelerated iterative optimization module is used to utilize the pipeline architecture of the programmable gate array hardware platform to perform parallel accelerated processing of the neural network weight calculation and spatial coordinate transformation, synchronously iteratively calculate the contact force balance constraint condition and the compensated three-dimensional coordinates, and generate the string arrangement parameters that satisfy the bow-catenary coupling relationship; A dropper string parameter execution driving module is used to drive the contact network construction equipment to perform dropper string length adjustment and positioning installation based on the segmented tension value between the contact network suspension points and the dropper string node offset compensation value in the dropper string arrangement parameters; The contact force equilibrium constraint condition and the compensated three-dimensional coordinate are synchronously iterated to generate the hanger arrangement parameters that satisfy the pantograph-catenary coupling relationship, including: Decompose the weight calculation of the neural network into an axial weight subtask related to the contact force distribution direction, and decompose the spatial coordinate transformation into a geometric transformation subtask based on the longitudinal curvature of the track; In a pipeline architecture of a programmable gate array hardware platform, an independent first parallel computing channel is allocated to the axial weight subtask, and an independent second parallel computing channel is allocated to the geometric transformation subtask; In the first parallel calculation channel, the axial weight coefficient of the contact force equilibrium constraint condition is adjusted according to the suspension point elevation data of the compensated three-dimensional coordinates; In the second parallel calculation channel, a segmented interpolation process is performed on the lateral offset of the compensated three-dimensional coordinate based on the longitudinal curvature of the track to generate a compensation amount for the spatial deformation of the suspension point; Through the cross-channel data interaction unit built into the programmable gate array hardware platform, the dot product calculation of the contact force direction vector and the spatial deformation vector is completed in a single clock cycle, and the axial weight coefficient and the suspension point spatial deformation compensation amount are coupled to generate a coupling operation result; According to the coupling operation result, the suspension point spacing in the compensated three-dimensional coordinates is relaxed and iterated. When the tension gradient change rate of adjacent suspension points is less than a preset convergence threshold, the final distribution sequence of the suspension string node offset compensation value is output to generate the suspension string arrangement parameters.

8. A computing device, characterized in that It includes a processing component and a storage component; the storage component stores one or more computer instructions; the one or more computer instructions are used to be called and executed by the processing component to implement a high-speed railway contact network dropper string arrangement optimization method based on machine learning as described in any one of claims 1 to 6.

9. A computer storage medium, characterized in that A computer program is stored, and when the computer program is executed by a computer, the method for optimizing the arrangement of high-speed railway contact network dropper strings based on machine learning as described in any one of claims 1 to 6 is implemented.

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