Railway compound curve automatic segmentation and parameter fitting method based on track measurement coordinates

Abstract

The application discloses a railway compound curve automatic segmentation and parameter fitting method based on track measurement coordinates, which comprises the following steps: S1, data preprocessing is performed on the obtained track measurement point sequence, and then a curvature point sequence is formed; S2, based on the curvature point sequence, initial segmentation and refinement are performed, and a boundary point index set is obtained; S3, compound curve parameters are initialized; S4, the coordinates of the center of a circle are coordinately corrected; S5, a preliminary fitting compound curve is obtained, a plane deviation is calculated, and a geometric line element type is marked; S6, based on the geometric line element type marking, a new boundary point index set is formed, an index change value is calculated, convergence judgment is performed, if the convergence is not obtained, the step S3 is returned according to the new boundary point index set, until the convergence is obtained, and the step S7 is executed; and S7, given easement curve length is taken as a constraint value, the compound curve parameters are optimized, and the compound curve fitting is completed. The method has high automation degree and fitting precision in the compound curve fitting.

Description

Technical Field

[0001] This invention relates to the field of railway engineering data processing, and in particular to a method for automatic segmentation and parameter fitting of railway complex curves based on track measurement coordinates. Background Technology

[0002] When railway lines require continuous turns and space is limited, using a single circular curve can significantly increase the workload and fail to meet requirements. Railway compound curves, by flexibly combining circular curves of different radii and utilizing incomplete transition curves to achieve curvature transitions, can better adapt to site conditions. This ensures a reasonable railway alignment while also considering the smoothness and comfort of train operation, and effectively reduces engineering waste. Railway compound curves are widely used in conventional railway operations, primarily in complex sections with strict terrain and feature constraints, such as mountainous areas and station bottlenecks.

[0003] When straightening railway tracks, it is necessary to accurately fit a curve based on the measured track coordinates to obtain the track deviation for guiding the correction work. However, due to the complex geometric characteristics of complex curves, the fitting process still faces the following problems:

[0004] 1. Low level of automation: Existing methods mostly rely on manual, repeated adjustments of complex curve parameters to ensure that the design coordinates match the measured coordinates. Complex curves have many parameters, making manual adjustments inefficient and difficult to guarantee accuracy.

[0005] 2. Strong parameter coupling: The parameters such as the tangent length, radius, and transition curve length of the complex curve influence each other and are strongly coupled, making the objective function exhibit strong nonlinearity and prone to getting trapped in local optima.

[0006] 3. Difficulty in meeting engineering constraints: In actual engineering, the length of the transition curve often needs to be rounded or consistent with the ledger data, which is a discrete constraint; while the intersection coordinates, center, radius, etc. are continuous variables; traditional optimization algorithms have difficulty in handling such "semi-discrete, semi-continuous" mixed constraints. Summary of the Invention

[0007] To address the problems existing in the prior art, this invention provides a robust, widely applicable, and highly accurate method for automatic segmentation and parameter fitting of railway complex curves based on track measurement coordinates.

[0008] Therefore, the present invention adopts the following technical solution:

[0009] An automatic segmentation and parameter fitting method for railway complex curves based on track measurement coordinates includes the following steps:

[0010] S1. Obtain the sequence of track measurement points, perform data preprocessing, and then number them according to the mileage to obtain a new sequence of track measurement points. Calculate the curvature point corresponding to each measurement point in the new sequence of track measurement points to form a curvature point sequence.

[0011] S2, perform median filtering on the curvature point sequence obtained in S1 to form a median-filtered curvature point sequence, classify the curvature points in the sequence, form initial segments and refine the segments, fit a curvature model to each refined segment, determine the boundary point mileage based on the curvature models of adjacent segments, and form a boundary point mileage set, which is used to divide the track measurement point sequence into seven measurement point subsets; obtain the boundary point index based on the set of the seven measurement point subsets, and form a boundary point index set;

[0012] S3 initializes the parameters of the complex curve through a fitting operation, obtaining the linear parameters of the preceding and following straight lines, the length of the first transition curve, the length of the middle transition curve, the length of the last transition curve, and the radius of the first circular curve. and the center of the circle, the radius of the second circular curve and the center of the circle, where the distance between the centers of the first circular curve and the second circular curve is... If the condition is met, execute S4; otherwise, execute S5.

[0013] S4, based on the given intermediate transition curve length, coordinate and correct the center coordinates of the first and second circular curves;

[0014] S5. Based on the initialized complex curve parameters, construct geometric line elements in the order of front straight line - front transition curve - first circular curve - middle transition curve - second circular curve - back transition curve - back straight line to obtain the fitted complex curve; calculate the plane deviation between each measurement point and its projection point, and mark the geometric line element type to which the corresponding projection point belongs.

[0015] S6: Based on the geometric element type markers obtained in S5, extract the numbers of the measurement points at the changes in geometric element type to form a new set of boundary point indices. Calculate the change value of each boundary point index. If the change value is less than the convergence threshold, convergence is determined, and S7 is executed. Otherwise, convergence is determined, and according to the new set of boundary point indices, return to step S3 and re-perform the convergence determination until convergence or the maximum number of iterations is reached. If convergence is still not achieved when the maximum number of iterations is reached, adjust the convergence threshold and return to step S3 until convergence is achieved.

[0016] S7 uses the length of the transition curve given by the ledger data as a constraint value to perform minimum deviation optimization on the center and radius of the first and second circular curves in the complex curve, thereby obtaining the parameters of the overall optimized complex curve and completing the complex curve fitting.

[0017] The specific operation of step S1 above is as follows:

[0018] Obtain the track measurement point sequence, including the mileage and plane coordinates of each measurement point, and sort them according to mileage. Perform data preprocessing operations on the measurement points in the track measurement point sequence, including outlier removal, duplicate point merging, equal mileage sampling, and thinning by mileage interval, with the mileage interval ranging from 0.5 to 5 meters. Then, number the measurement points according to mileage to obtain a new track measurement point sequence. , where each measurement point The mileage is The plane coordinates are , The measurement points are numbered; based on the sequence of track measurement points. The calculation yields the result for each measurement point. The curvature values ​​at each point form a sequence of curvature points. ,in, For measurement points The corresponding curvature point, , This represents the curvature value.

[0019] Step S2 above includes the following steps:

[0020] S21, the curvature point sequence obtained from S1 Perform median filtering: using the current curvature point Centered on the median, the curvature values ​​of all curvature points within the median filtering sliding window are sorted, and the median value after sorting is taken as the filtered curvature value of that point. The filtered curvature values ​​of all curvature points are obtained sequentially, forming a median-filtered sequence of curvature points. ;

[0021] S22, Dual-scale slope estimation: Curvature point sequence obtained from S21 after median filtering At each curvature point Centered on the mileage value, linear regressions were performed on the filtered curvature value with respect to the mileage value within both short and long sliding windows. The resulting slopes were used as local slope estimates for the short sliding window. Local slope estimates for long sliding windows ;

[0022] S23, Curvature point sequence after median filtering The curvature point in the curve is based on the short window slope threshold. With long window trend threshold Perform category determination: when or At that time, the curvature point Determine if a point is within the range of change; otherwise, determine if it is a point of curvature. Points identified as being within a stable segment;

[0023] S24, Initial Segmentation and Segment Refinement: Based on the category determination result of S23, consecutive curvature points of the same type are grouped together to form an initial segment. Then, segment refinement is performed on each initial segment to obtain the refined segment; the curvature point sequence obtained in S21 is... The set of curvature point subsequences is obtained by dividing the segments according to the refined segments. Each segment corresponds to a sequence of curvature points. ,in, For segment numbering, , The number of curvature points within each segment;

[0024] S25, firstly, for each segment refined in S24, based on its corresponding curvature point subsequence... The data at both ends of each segment is removed, with a removal ratio of 5% to 20%; then, the curvature is obtained by fitting using the least squares method. Regarding mileage By fitting the curvature model to the stable segment, a constant curvature model is obtained. By fitting the variation segment, a linear curvature model is obtained. ,in, The slope of the curvature model. The intercept is then calculated; next, the mileage of the boundary points between all adjacent piecewise curvature models is calculated. This forms a set of boundary point mileages. Boundary point mileage The calculation formula is:

[0025] ,

[0026] The slope of the stable segment is 0.

[0027] S26, Obtain the boundary point index set: Based on the boundary point mileage set obtained in S25. The orbit measurement point sequence obtained from S12 The measurement points in the data are divided into seven segments, resulting in a set of seven subsets of measurement points. Among them, the subset of measurement points , The subset index, , The number of measurement points within the subset; a set based on the seven-segment measurement point subset. Obtain the boundary point index This forms a set of boundary point indices. .

[0028] In step S2 above:

[0029] The median filtering sliding window radius The value range is 5~11m;

[0030] The radius of the short sliding window ranges from 2 to 5 m, and the radius of the long sliding window ranges from 8 to 15 m.

[0031] The short window slope threshold The value range is 4×10 -4 ~8×10 -4 , = , The value range is 0.1 to 0.5.

[0032] The specific operation of segmented refinement in step S24 above is as follows:

[0033] Let the minimum segment length be The value range is 10~50m;

[0034] When the length of the changed segment in the initial segment is less than If this happens, the segment will be identified as a noise segment and merged.

[0035] When the length of the stable segment in the initial segmentation is less than or equal to When the threshold is reached, the segment is identified as a noise segment and merged. Threshold = ;

[0036] When the curvature change of a segment is insufficient to characterize the slope of the transition curve, it is identified as a noise segment and merged.

[0037] The merging rule is as follows: a noise segment is merged with its adjacent noise segments of the same type; if necessary, adjacent noise segments of the same type are merged again to obtain a segmented sequence with alternating types and stable boundaries.

[0038] In step S3 above:

[0039] The complex curve comprises two sets of curves, divided according to their characteristics as follows: a first straight line, a first transition curve, a first circular curve, a middle transition curve, a second circular curve, a final transition curve, and a final straight line. The dividing point ZH1 is the transition point between the straight and transition curves of the first set of curves; HY1 is the transition point between the transition and circular curves of the first set of curves; YH1 is the transition point between the circular and transition curves of the first set of curves; HZ1 is the transition point between the straight and transition curves of the first set of curves; ZH2 is the transition point between the straight and transition curves of the second set of curves; HY2 is the transition point between the circular and transition curves of the second set of curves; YH2 is the transition point between the circular and transition curves of the second set of curves; HZ2 is the transition point between the straight and transition curves of the second set of curves; and the dividing point index set is based on S26. Obtain the coordinates of the dividing point.

[0040] The initialization of the complex curve parameters in step S3 above is as follows:

[0041] (1) Based on the plane coordinates of the measurement points in the front line and the back line, the corresponding line parameters are obtained by fitting: slope and intercept; based on the fitting results of the front line and the back line, the intersection point JD of the two lines is obtained.

[0042] (2) Based on the planar coordinates of the measurement points inside the first and second circular curves, the corresponding center and radius are obtained by fitting. The center of the first circular curve; The center of the second circular curve; The radius of the first circular curve; The radius of the second circular curve;

[0043] (3) Based on the results of the circular curve fitting and the coordinates of the dividing point, the inward displacement of the two sets of curves is calculated. and ; through inner displacement and The geometric relationship is used to obtain the length of the front transition curve. With the length of the subsequent easing curve :

[0044] The geometric relationship of the inner displacement satisfies the formula:

[0045] ,

[0046] in, To soften the curve length, Let be the radius of the corresponding circular curve. The slope of the corresponding line segment. For the intercept of the corresponding line segment, These are the coordinates of the center of the corresponding circular curve;

[0047] (4) Calculate the distance between the centers of the two circular curves. ,when At that time, based on the relative geometric relationship between the radii and centers of the two circular curves, the length of the intermediate transition curve between the two circular curves can be directly calculated. .

[0048] Step S4 above includes the following steps:

[0049] S41, based on the length of the intermediate transition curve given in the ledger. With the radius of the two circular curves Calculate the theoretical center distance Based on the tangent direction of the preceding straight line and the tangent direction of the endpoint of the subsequent transition curve, draw the current circle center of each of the two circular curves. Find two direction lines and their intersection point. Based on the aforementioned tangent directions, construct a unit direction vector. and , which serves as the direction of translation of the centers of the two circular curves;

[0050] S42, Establish and solve the objective function to obtain the translation amount that minimizes the total movement:

[0051] Based on translation , Establish the following constraints:

[0052] ,

[0053] in, and These are the centers of the two updated circular curves, respectively;

[0054] Establish the following objective function:

[0055] ,

[0056] Under the above constraints, optimize the objective function: [Calculate the translation amount]. As a variable, under the geometric constraints of fixed direction of movement and included angle, it satisfies the theoretical center distance. Furthermore, taking the minimum total movement as the criterion, a one-dimensional derivative-free optimization solution is performed to obtain the translation amount that minimizes the total movement. ;

[0057] S43, the translation amount that minimizes the total movement based on S42. Calculate the translation vector of the circle center. , Update the centers of the two circles. , And synchronize the corresponding boundary points.

[0058] The specific operation of step S7 above is as follows:

[0059] S71, based on the preliminary fitted complex curve obtained in S5, the measurement points are divided into a first half subset and a second half subset; the first half subset includes the measurement points within the range of the first straight line, the first transition curve, and the first circular curve; the second half subset includes the measurement points within the range of the second circular curve, the second transition curve, and the second straight line.

[0060] S72, construct the objective function based on the mean square of the plane deviation from the measurement point to the construction curve, which is the first half subset and the second half subset respectively:

[0061] ,

[0062] in, Let be the radius of the circular curve in the fitted curve of the corresponding subset. for or The distance moved tangentially, This represents the number of measurement points within the corresponding subset. For measurement points Distance to the current construction curve;

[0063] The construction curve is based on the current... , Given the lengths of the preceding and following transition curves, construct the first and second halves of the curves respectively using the line element method;

[0064] Using derivative-free two-dimensional optimization methods or the Nelder-Mead simplex method, the optimal parameters are obtained with the goal of making the measurement points closer to the constructed curve. and ;

[0065] S73, calculate the center coordinates of the first and second circular curves, and then, based on the center coordinates and radii of the first and second circular curves and the given intermediate transition curve length, execute the operation of step S4 to perform coordination correction on the center coordinates of the two circular curves, obtain the overall optimized parameters of the complex curve, and complete the complex curve fitting.

[0066] In step S7 above, the obtained transition curve length is rounded to a multiple of 10. If the rounded transition curve length does not match the ledger data, the ledger data shall prevail.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] 1. High degree of automation: The method of this invention starts from the measurement coordinates and automatically completes curvature calculation, segmentation, key point positioning and parameter solving, which significantly reduces the number of times manual interpretation and repeated parameter adjustment are required.

[0069] 2. Noise Resistance and Stability: This invention first filters the curvature data, then uses trend judgment at two scales to distinguish between stable and changing segments, and merges excessively short or invalid segments in the segmentation results, making the results less susceptible to measurement noise interference and resulting in more stable segmentation and fitting.

[0070] 3. High fitting accuracy: This invention improves the consistency of the overall fitting results of the complex curve by iteratively updating the boundary points, thus avoiding instability of the complex curve parameters caused by small differences in the segmented results.

[0071] 4. Good engineering adaptability: The method of this invention supports derivative-free optimization under given constraints such as gradient length, and performs center coordination correction by using the center distance constraint corresponding to the length of the intermediate incomplete transition curve, which ensures consistent geometric relationships and the fitting results are more in line with engineering needs. Attached Figure Description

[0072] Figure 1 This is a flowchart of the automatic segmentation and parameter fitting method for railway complex curves according to the present invention;

[0073] Figure 2 This is a schematic diagram illustrating the segmentation and boundary point extraction based on curvature according to the present invention;

[0074] Figure 3 This is a schematic diagram illustrating the construction of the geometric relationship of the complex curve in this invention;

[0075] Figure 4 This is a schematic diagram of the circle center distance correction method in this invention;

[0076] Figure 5 This is a schematic diagram of the circle center distance correction and optimization method in this invention;

[0077] Figure 6 This is a schematic diagram of fitting complex curve parameters to measurement points within a segmented subset in this invention;

[0078] Figure 7 This is a diagram illustrating the effect of automatic segmentation based on curvature point sequence in an embodiment of the present invention.

[0079] Figure 8 This is a graph showing the planar deviation values ​​of each measurement point in an embodiment of the present invention. Detailed Implementation

[0080] The technical solution of the invention will be clearly and completely described below with reference to the accompanying drawings and embodiments. Obviously, the following embodiments are only some embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0081] The present invention provides an automatic segmentation and parameter fitting method for railway complex curves based on track measurement coordinates, such as... Figure 1 As shown, it includes the following steps:

[0082] S1. Acquire track measurement data and generate a curvature point sequence, including the following steps:

[0083] S11, Data Acquisition: Obtain the sequence of track measurement points, including the mileage and planar coordinates of each measurement point, sorted according to mileage. When the obtained track measurement data is in other equivalent forms, such as mileage-coordinates or mileage-azimuth, it needs to be converted into the above-mentioned sequence of track measurement points.

[0084] S12, perform data preprocessing on the orbit measurement point sequence obtained in S11.

[0085] The measurement points in the track measurement point sequence undergo data preprocessing operations such as outlier removal, duplicate point merging, and equal-mileage sampling or thinning by mileage interval. Then, they are numbered according to mileage to obtain a new track measurement point sequence. , where each measurement point The mileage is The plane coordinates are , This is the number of the measurement point; the mileage interval can be 0.5~5m.

[0086] S13, the sequence of track measurement points obtained based on S12 The curvature calculation method, using discrete geometric approximation or local fitting-based curvature calculation, is used to calculate the curvature at each measurement point. The curvature values ​​at each point form a sequence of curvature points. ,in, For measurement points The corresponding curvature point, , This represents the curvature value.

[0087] S2, perform median filtering on the curvature point sequence obtained in S13 to obtain a median-filtered curvature point sequence, and then perform automatic segmentation to obtain a set of boundary point indices, including the following steps:

[0088] S21, perform median filtering on the curvature point sequence obtained in S13 to suppress outlier curvature points caused by measurement noise; the specific operation of the median filtering is as follows: using the current curvature point... Centered on a certain radius The median filtering sliding window sorts the curvature values ​​of all curvature points within the window and takes the median value after sorting as the filtered curvature value for that point. The filtered curvature values ​​of all curvature points are obtained sequentially, forming a median-filtered sequence of curvature points. The median filter sliding window radius The value range is 5~11m.

[0089] S22, Dual-Scale Slope Estimation: Based on Curvature Point Sequence After Median Filtering At each curvature point Centered on the filter, the curvature values ​​are analyzed within both short and long sliding windows. Regarding mileage Perform linear regression, and use the resulting slopes as local slope estimates for short sliding windows. Local slope estimates for long sliding windows The radius of the short sliding window ranges from 2 to 5 m, and the radius of the long sliding window ranges from 8 to 15 m.

[0090] In one embodiment of the present invention, the least squares method is used to perform the above-mentioned linear regression operation.

[0091] S23, Curvature point sequence after median filtering The curvature point in the curve is based on the short window slope threshold. (The value range is generally 4×10) -4 ~8×10 -4 ) and long window trend threshold To determine the category, the specific operation is as follows: when or At that time, the curvature point Points are classified as points in a transitional phase (RAMP); otherwise, they are classified as points in a stable phase (STABLE). = , The value range is 0.1 to 0.5. The stable segment represents the interval where the curvature is approximately constant, and is used to characterize straight line segments or circular curve segments; the changing segment represents the interval where the curvature changes approximately linearly with mileage, and is used to characterize transition curve segments.

[0092] S24, Initial Segmentation and Segmentation Refinement, the specific operations are as follows:

[0093] Based on the category determination result of S23, consecutive curvature points of the same type are grouped together to form an initial segment. Then, segmentation refinement is performed on each initial segment to obtain refined segments, thereby reducing fragmented segments and mis-segmented segments, wherein:

[0094] The specific operation of the segmented refinement is as follows:

[0095] Let the minimum segment length be The preferred value range is 10~50m;

[0096] When the length of the changed segment in the initial segment is less than If this happens, the segment is identified as a noise segment and merged.

[0097] When the length of the stable segment in the initial segmentation is less than or equal to Threshold (e.g.) If the condition is met, the segment is identified as a noise segment and merged to reduce the probability of the short circular curve being mistakenly deleted.

[0098] When the curvature change amplitude of a transition segment is insufficient to characterize the slope of the transition curve, it can be identified as a noise segment and merged. For example, when When this change segment is identified as a noise segment, it is considered invalid. This is the curvature value of the first curvature point within this segment of change. This refers to the curvature value of the last curvature point within this variation segment. To determine the threshold, A value of 1.0 to 3.0 is acceptable.

[0099] The merging rule is as follows: a noise segment is merged with its adjacent noise segments of the same type (changing segment, stable segment); if necessary, adjacent noise segments of the same type can be merged again to obtain a segmented sequence with alternating types and stable boundaries.

[0100] The curvature point sequence obtained from S21 The set of curvature point subsequences is obtained by dividing the segments according to the refined segments. Each segment corresponds to a sequence of curvature points. ,in, For segment numbering, , This represents the number of curvature points within each segment.

[0101] S25, Segmented Model Fitting and Boundary Point Extraction: Each refined segment is fitted to obtain multiple curvature models. The intersection mileage, i.e., the boundary point mileage, is determined based on the curvature models of adjacent segments. This forms a set of boundary point mileages. The specific steps are as follows:

[0102] First, for each segment refined by S24, based on its corresponding curvature point sequence... The data at both ends of each segment is removed, with a removal rate of 5% to 20%. Then, the least squares method is used for fitting to obtain the curvature. Regarding mileage The curvature model is obtained by fitting the stable segment to obtain a constant curvature model. Fitting the variation segment yields a linear curvature model. ,in, The slope of the curvature model. This is the intercept.

[0103] Next, calculate the mileage of the intersection points of all adjacent two piecewise curvature models, i.e., the mileage of the boundary points. This forms a set of boundary point mileages. The formula for calculating the mileage of the dividing point is:

[0104] ,

[0105] The slope of the stable segment is 0.

[0106] like Figure 2 As shown in the figure, the sequence of curvature points is calculated based on measured track data and then filtered using median filtering. The measured curvature curves were plotted, and the model fitting curves corresponding to the curvature models fitted to each segment and the boundary points between adjacent segments were displayed.

[0107] S26, Obtain the boundary point index set: Based on the boundary point mileage set obtained in S25. The orbit measurement point sequence obtained from S12 The measurement points in the data are divided into seven segments, resulting in a set of seven subsets of measurement points. Among them, the subset of measurement points , Subset index ( ), This represents the number of measurement points within the subset. It is a set based on a seven-segment measurement point subset. Obtain the boundary point index This forms a set of boundary point indices. .

[0108] S3, Initialize the parameters of the complex curve.

[0109] Complex curves consist of two sets of curves, such as Figure 3 As shown in Table 1, the curves can be divided according to their constituent characteristics into: the initial straight line, the initial transition curve, the first circular curve, the intermediate transition curve, the second circular curve, the subsequent transition curve, and the subsequent straight line; the coordinates of the dividing points can be based on the dividing point index set obtained in S26. get.

[0110] Table 1

[0111]

[0112] Wherein, ZH1 is the straight-to-curve point of the first group of curves; HY1 is the curve-to-round point of the first group of curves; YH1 is the curve-to-curve point of the first group of curves; HZ1 is the curve-to-straight point of the first group of curves; ZH2 is the straight-to-curve point of the second group of curves; HY2 is the curve-to-round point of the second group of curves; YH2 is the curve-to-curve point of the second group of curves; HZ2 is the curve-to-straight point of the second group of curves. Let be the center of the first circular curve; The center of the second circular curve; Let be the radius of the first circular curve; Let be the radius of the second circular curve; This represents the inner shift of the first set of curves; This represents the inner shift of the second set of curves; It is the distance between the centers of the circle.

[0113] The complex curve parameters include: the straight line parameters of the preceding and following straight lines, the length of the preceding transition curve, the length of the intermediate transition curve, the length of the following transition curve, the radius and center of the first circular curve, and the radius and center of the second circular curve. The specific steps for initializing the above complex curve parameters are as follows:

[0114] (1) Based on the planar coordinates of the measurement points within the front and rear lines, the corresponding line parameters are obtained by fitting: slope and intercept. Based on the fitting results of the front and rear lines, the intersection point JD of the two lines is obtained. In one embodiment of the present invention, the least squares method can be used for line fitting; in another embodiment of the present invention, the orthogonal least squares method is used for iterative fitting to obtain more accurate line parameters.

[0115] (2) Based on the planar coordinates of the measured points within the first and second circular curves, the corresponding center and radius are obtained by fitting. In one embodiment of the present invention, the least squares method can be used for fitting; in another embodiment of the present invention, the orthogonal least squares method is used for iterative fitting to obtain a more accurate center and radius.

[0116] (3) Based on the results of the circular curve fitting and the coordinates of the dividing point, the inward displacement of the two sets of curves can be calculated. and By shifting the distance inward and The geometric relationship yields the length of the pre-gradient curve. With the length of the subsequent easing curve :

[0117] The geometric relationship of the inner displacement satisfies the formula:

[0118] ,

[0119] in, To soften the curve length, Let be the radius of the corresponding circular curve. The slope of the corresponding line segment. For the intercept of the corresponding line segment, These are the coordinates of the center of the corresponding circular curve.

[0120] Solving the simultaneous geometric equations, we can obtain the lengths of the initial transition curves. With the length of the subsequent easing curve .

[0121] (4) Calculate the distance between the centers of the two circular curves obtained by fitting. ,when When the relative geometric relationship between the radii and centers of the two circular curves is established, the length of the intermediate transition curve between the two circular curves can be directly calculated. ;when At that time, execute S4.

[0122] S4, based on the given intermediate transition curve length The coordinates of the center curves are adjusted by coordinating the translations. This means that while keeping the inner displacement constant, the coordinates of the center curves of the two circular curves are translated in a coordinated manner to satisfy the given intermediate transition curve length. The theoretical center distance derived from the design data recorded in the ledger. Constraints include the following steps:

[0123] S41, Calculate the theoretical center distance Construct a unit direction vector.

[0124] Based on the length of the intermediate transition curve given in the ledger With the radius of the two circular curves Calculate the theoretical center distance .like Figure 4 As shown, based on the tangent direction of the preceding straight line (corresponding to the tangent at point ZH1) and the tangent direction of the endpoint of the subsequent transition curve (tangent at point HZ2), the current centers of the two circular curves are respectively drawn. Find two direction lines and their intersection point. The intersection point This serves as the geometric reference point for the coordinated translation of the circle's center. Based on the aforementioned tangent directions, construct the unit direction vector. and , respectively, serve as the translation directions of the centers of the two circular curves.

[0125] S42, as Figure 5 As shown, the objective function is established and solved to obtain the translation amount that minimizes the total movement.

[0126] Based on translation , Establish the following constraints:

[0127] ,

[0128] in, and These are the centers of the two updated circular curves.

[0129] Establish objective function :

[0130] ,

[0131] Under the above constraints, optimize the objective function, specifically: adjust the translation amount... As a variable, under the geometric constraints of fixed direction of movement and included angle, it satisfies the theoretical center distance. Furthermore, taking the minimum total movement as the criterion, a one-dimensional derivative-free optimization solution is performed to obtain the translation amount that minimizes the total movement. This reduces the perturbation to the existing fitting results.

[0132] In one embodiment of the present invention, the minimum perturbation solution that satisfies the constraints can be obtained by using a combination of coarse grid search and golden section search.

[0133] S43, center update and boundary point synchronization.

[0134] Translation based on S42 Calculate the translation vector of the circle center. , Update the centers of the two circles. , And synchronize the corresponding boundary points.

[0135] S5, initially fit the complex curve and calculate the plane deviation.

[0136] Based on the complex curve parameters obtained in steps S3 to S4, geometric line elements are constructed in the order of "first straight line - first transition curve - first circular curve - middle transition curve - second circular curve - last transition curve - last straight line" to obtain the preliminary fitted complex curve.

[0137] For each measurement point Determine the projection point (foot of the perpendicular) of the measurement point on the corresponding geometric element and calculate the plane deviation between each measurement point and its corresponding projection point. Record and mark the geometric element type (straight line, circular curve, transition curve) of the corresponding projection point of the measurement point for subsequent boundary point updates and convergence determination.

[0138] S6, convergence is determined by the change in the boundary point index:

[0139] Based on the geometric element type markers in S5, the numbers of the measurement points at the locations of geometric element type changes are extracted to form a new set of boundary point indexes. The old and new boundary point index sets are compared, and the change value of each boundary point index is calculated. If the change value is less than the convergence threshold, convergence is determined, and S7 is executed; otherwise, non-convergence is determined, and the boundary points are updated according to the new boundary point index set. Return to step S3 and re-perform the convergence determination. Set the maximum number of iterations (100 times) to avoid infinite loops. If convergence is still not achieved when the maximum number of iterations is reached, adjust the convergence threshold, continue to update the boundary point, and return to step S3 until convergence is achieved.

[0140] S7, Complex curve fitting under the constraint of transition curve length.

[0141] The lengths of the initial, intermediate, and final transition curves obtained through the above fitting operation may not meet the requirements of railway design specifications. Therefore, they need to be rounded to multiples of 10 and then compared with the design values ​​(given transition curve lengths) recorded in the ledger data. If they are the same, they are used directly as constraints; otherwise, the given transition curve length is used. For example, if the fitted initial transition curve length is 114.15m, it does not meet the requirement of rounding to multiples of 10 in the design specifications and needs to be rounded to 110m. If the ledger data records the initial transition curve length as 120m, then the value of 120m should be used. Therefore, the transition curve length given in the ledger data or the length obtained by rounding according to the specifications needs to be used as constraint values ​​to perform minimum deviation optimization on other parameters (center and radius) of the complex curve. The specific steps are as follows:

[0142] S71, the measurement points are divided into a first half subset and a second half subset based on the preliminary fitted curve obtained from the above fitting operation, and processed separately. Figure 6 The diagram shows the first half of the subset. The first half of the subset includes the measurement points within the range of the first straight line, the first transition curve, and the first circular curve; the second half of the subset includes the measurement points within the range of the second circular curve, the second transition curve, and the second straight line.

[0143] S72, construct the objective function based on the mean square of the plane deviation from the measurement point to the construction curve, which is the first half subset and the second half subset respectively:

[0144] ,

[0145] in, Let be the radius of the circular curve in the fitted curve of the corresponding subset. for (First half) or (The second half) The distance moved tangentially, This represents the number of measurement points within the corresponding subset. For measurement points Distance to the current construction curve.

[0146] The construction curve is based on the current... , Given the lengths of the first and second transition curves, the first and second halves of the curves are constructed using the line element method. Optimal parameters are obtained by employing a derivative-free two-dimensional optimization method or the Nelder-Mead simplex method, aiming to make the measurement points more closely approximate the constructed curves. and .

[0147] S73. After obtaining the optimal parameters, calculate the center coordinates of the first and second circular curves. Then, based on the center coordinates and radii of the two circular curves and the given intermediate transition curve length, perform the operation of step S4 to coordinate and correct the center coordinates of the two circular curves, thereby obtaining the overall optimized parameters of the complex curve.

[0148] Example

[0149] A complex curve exists within the range of K840+900-K806+700 on a certain railway line, and a total of 1800 measuring points were obtained in the field. For example... Figure 7 As shown, the curvature of each point is calculated and automatically segmented based on the curvature point sequence, dividing the complex curve into 7 segments according to "straight line - first transition curve - first circular curve - middle transition curve - second circular curve - last transition curve - straight line".

[0150] In this embodiment, the convergence threshold is set to 3. After 5 rounds of complex curve parameter initialization, convergence is achieved, and a stable fitted complex curve is obtained. The initial boundary point index and the boundary point indexes of the initially fitted complex curve after stabilization are shown in Table 2:

[0151] Table 2

[0152]

[0153] The parameters of the initial fitted complex curve after final stabilization are shown in Table 3:

[0154] Table 3

[0155]

[0156] The length of the initial transition curve in the ledger record is 80m, the length of the middle transition curve is 20m, and the length of the final transition curve is 80m. Based on this, a complex curve is fitted under the constraint of the transition curve length. The parameters of the fitted complex curve are shown in Table 4.

[0157] Table 4

[0158]

[0159] The plane deviation curves at each measurement point are as follows: Figure 8 As shown, the plane deviation range is [-23.3mm, 17.5mm], indicating that the fitted complex curve has a high degree of fit with the actual measured value.

Claims

1. A method for automatic segmentation and parameter fitting of railway complex curves based on track measurement coordinates, characterized in that, Includes the following steps: S1. Obtain the sequence of track measurement points, perform data preprocessing, and then number them according to the mileage to obtain a new sequence of track measurement points. Calculate the curvature point corresponding to each measurement point in the new sequence of track measurement points to form a curvature point sequence. S2, perform median filtering on the curvature point sequence obtained in S1 to form a median-filtered curvature point sequence, classify the curvature points in it, form initial segments and refine the segments, fit a curvature model for each refined segment, determine the boundary point mileage based on the curvature models of adjacent segments, and form a boundary point mileage set, which is used to divide the track measurement point sequence into seven measurement point subsets; The boundary point index is obtained based on the set of seven subsets of measurement points, forming a boundary point index set; S3 initializes the parameters of the complex curve through a fitting operation, obtaining the linear parameters of the preceding and following straight lines, the length of the first transition curve, the length of the middle transition curve, the length of the last transition curve, and the radius of the first circular curve. and the center of the circle, the radius of the second circular curve and the center of the circle, where the distance between the centers of the first circular curve and the second circular curve is... If the condition is met, execute S4; otherwise, execute S5. S4, based on the given intermediate transition curve length, coordinate and correct the center coordinates of the first and second circular curves; S5. Based on the initialized complex curve parameters, construct geometric line elements in the order of front straight line - front transition curve - first circular curve - middle transition curve - second circular curve - back transition curve - back straight line to obtain the fitted complex curve; calculate the plane deviation between each measurement point and its projection point, and mark the geometric line element type to which the corresponding projection point belongs. S6. Based on the geometric element type markers obtained in S5, extract the numbers of the measurement points at the change positions of the geometric element types to form a new set of boundary point indices, and calculate the change value of each boundary point index. When the change value is less than the convergence threshold, it is determined to be converged, and S7 is executed. Otherwise, it is determined to be non-converged, and according to the new set of boundary point indices, return to step S3 and re-perform the convergence determination until convergence or the maximum number of iterations is reached. If convergence is not achieved by the maximum number of iterations, adjust the convergence threshold and return to step S3 until convergence is achieved. S7 uses the length of the transition curve given by the ledger data as a constraint value to perform minimum deviation optimization on the center and radius of the first and second circular curves in the complex curve, thereby obtaining the parameters of the overall optimized complex curve and completing the complex curve fitting.

2. The method for automatic segmentation and parameter fitting of railway complex curves according to claim 1, characterized in that, The specific operation of step S1 is as follows: Obtain the track measurement point sequence, including the mileage and plane coordinates of each measurement point, and sort them according to mileage. Perform data preprocessing operations on the measurement points in the track measurement point sequence, including outlier removal, duplicate point merging, equal mileage sampling, and thinning by mileage interval, with the mileage interval ranging from 0.5 to 5 meters. Then, number the measurement points according to mileage to obtain a new track measurement point sequence. , where each measurement point The mileage is The plane coordinates are , The measurement points are numbered; based on the sequence of track measurement points. The calculation yields the result for each measurement point. The curvature values ​​at each point form a sequence of curvature points. ,in, For measurement points The corresponding curvature point, , This represents the curvature value.

3. The method for automatic segmentation and parameter fitting of railway complex curves according to claim 2, characterized in that, Step S2 includes the following steps: S21, the curvature point sequence obtained from S1 Perform median filtering: using the current curvature point Centered on the median, the curvature values ​​of all curvature points within the median filtering sliding window are sorted, and the median value after sorting is taken as the filtered curvature value of that point. The filtered curvature values ​​of all curvature points are obtained sequentially, forming a median-filtered sequence of curvature points. ; S22, Dual-scale slope estimation: Curvature point sequence obtained from S21 after median filtering For each curvature point Centered on the mileage value, linear regressions were performed on the filtered curvature value with respect to the mileage value within both short and long sliding windows. The resulting slopes were used as local slope estimates for the short sliding window. Local slope estimates for long sliding windows ; S23, Curvature point sequence after median filtering The curvature point in the curve is based on the short window slope threshold. With long window trend threshold Perform category determination: when or At that time, the curvature point Determine if a point is within the range of change; otherwise, determine if it is a point of curvature. Points identified as being within a stable segment; S24, Initial Segmentation and Segment Refinement: Based on the category determination result of S23, consecutive curvature points of the same type are grouped together to form an initial segment. Then, segment refinement is performed on each initial segment to obtain the refined segment; the curvature point sequence obtained in S21 is... The set of curvature point subsequences is obtained by dividing the segments according to the refined segments. Each segment corresponds to a sequence of curvature points. ,in, For segment numbering, , The number of curvature points within each segment; S25, firstly, for each segment refined in S24, based on its corresponding curvature point subsequence... The data at both ends of each segment is removed, with a removal ratio of 5% to 20%; then, the curvature is obtained by fitting using the least squares method. Regarding mileage The curvature model is obtained by fitting the stable segment to obtain a constant curvature model. By fitting the variation segment, a linear curvature model is obtained. ,in, The slope of the curvature model. The intercept is then calculated; next, the mileage of the boundary points between all adjacent piecewise curvature models is calculated. This forms a set of boundary point mileages. Boundary point mileage The calculation formula is: ， The slope of the stable segment is 0. S26, Obtain the boundary point index set: Based on the boundary point mileage set obtained in S25. The orbit measurement point sequence obtained from S12 The measurement points in the data are divided into seven segments, resulting in a set of seven subsets of measurement points. Among them, the subset of measurement points , The subset index, , The number of measurement points within the subset; a set based on the seven-segment measurement point subset. Obtain the boundary point index This forms a set of boundary point indices. .

4. The method for automatic segmentation and parameter fitting of railway complex curves according to claim 3, characterized in that, In step S2: The median filtering sliding window radius The value range is 5~11m; The radius of the short sliding window ranges from 2 to 5 m, and the radius of the long sliding window ranges from 8 to 15 m. The short window slope threshold The value range is 4×10 -4 ~8×10 -4 , = , The value range is 0.1 to 0.

5.

5. The method for automatic segmentation and parameter fitting of railway complex curves according to claim 4, characterized in that, The specific operations for segmented refinement in step S24 are as follows: Let the minimum segment length be The value range is 10~50m; When the length of the changed segment in the initial segment is less than If this happens, the segment will be identified as a noise segment and merged. When the length of the stable segment in the initial segmentation is less than or equal to When the threshold is reached, the segment is identified as a noise segment and merged. Threshold = ; When the curvature change of a segment is insufficient to characterize the slope of the transition curve, it is identified as a noise segment and merged. The merging rule is as follows: a noise segment is merged with its adjacent noise segments of the same type; if necessary, adjacent noise segments of the same type are merged again to obtain a segmented sequence with alternating types and stable boundaries.

6. The method for automatic segmentation and parameter fitting of railway complex curves according to claim 5, characterized in that, In step S3: The complex curve comprises two sets of curves, divided according to their characteristics as follows: a first straight line, a first transition curve, a first circular curve, a middle transition curve, a second circular curve, a final transition curve, and a final straight line. The dividing point ZH1 is the transition point between the straight and transition curves of the first set of curves; HY1 is the transition point between the transition and circular curves of the first set of curves; YH1 is the transition point between the circular and transition curves of the first set of curves; HZ1 is the transition point between the straight and transition curves of the first set of curves; ZH2 is the transition point between the straight and transition curves of the second set of curves; HY2 is the transition point between the circular and transition curves of the second set of curves; YH2 is the transition point between the circular and transition curves of the second set of curves; HZ2 is the transition point between the straight and transition curves of the second set of curves; and the dividing point index set is based on S26. Obtain the coordinates of the dividing point.

7. The method for automatic segmentation and parameter fitting of railway complex curves according to claim 6, characterized in that, The initialization of the complex curve parameters in step S3 is as follows: (1) Based on the plane coordinates of the measurement points in the front line and the back line, the corresponding line parameters are obtained by fitting: slope and intercept; based on the fitting results of the front line and the back line, the intersection point JD of the two lines is obtained. (2) Based on the planar coordinates of the measurement points inside the first and second circular curves, the corresponding center and radius are obtained by fitting. The center of the first circular curve; The center of the second circular curve; The radius of the first circular curve; The radius of the second circular curve; (3) Based on the results of the circular curve fitting and the coordinates of the dividing point, the inward displacement of the two sets of curves is calculated. and ; through inner displacement and The geometric relationship is used to obtain the length of the front transition curve. With the length of the subsequent easing curve : The geometric relationship of the inner displacement satisfies the formula: ， in, To soften the curve length, Let be the radius of the corresponding circular curve. The slope of the corresponding line segment. For the intercept of the corresponding line segment, These are the coordinates of the center of the corresponding circular curve; (4) Calculate the distance between the centers of the two circular curves. ,when At that time, based on the relative geometric relationship between the radii and centers of the two circular curves, the length of the intermediate transition curve between the two circular curves can be directly calculated. .

8. The method for automatic segmentation and parameter fitting of railway complex curves according to claim 7, characterized in that, Step S4 includes the following steps: S41, based on the length of the intermediate transition curve given in the ledger. With the radius of the two circular curves Calculate the theoretical distance between the centers Based on the tangent direction of the preceding straight line and the tangent direction of the endpoint of the subsequent transition curve, draw the current circle center of each of the two circular curves. Find two direction lines and their intersection point. Based on the aforementioned tangent directions, construct a unit direction vector. and , which serves as the direction of translation of the centers of the two circular curves; S42, Establish and solve the objective function to obtain the translation amount that minimizes the total movement: Based on translation , Establish the following constraints: ， in, and These are the centers of the two updated circular curves, respectively; Establish the objective function : ， Under the above constraints, optimize the objective function: [Calculate the translation amount]. As a variable, under the geometric constraints of fixed direction of movement and included angle, it satisfies the theoretical center distance. Furthermore, taking the minimum total movement as the criterion, a one-dimensional derivative-free optimization solution is performed to obtain the translation amount that minimizes the total movement. ; S43, the translation amount that minimizes the total movement based on S42. Calculate the translation vector of the circle center. , Update the centers of the two circles. , And synchronize the corresponding boundary points.

9. The method for automatic segmentation and parameter fitting of railway complex curves according to claim 8, characterized in that, The specific operation of step S7 is as follows: S71, based on the preliminary fitted complex curve obtained in S5, the measurement points are divided into a first half subset and a second half subset; the first half subset includes the measurement points within the range of the first straight line, the first transition curve, and the first circular curve; the second half subset includes the measurement points within the range of the second circular curve, the second transition curve, and the second straight line. S72, construct the objective function based on the mean square of the plane deviation from the measurement point to the construction curve, which is the first half subset and the second half subset respectively: ， in, Let be the radius of the circular curve in the fitted curve of the corresponding subset. for or The distance moved tangentially, This represents the number of measurement points within the corresponding subset. For measurement points Distance to the current construction curve; The construction curve is based on the current... , Given the lengths of the preceding and following transition curves, construct the first and second halves of the curves respectively using the line element method; Using derivative-free two-dimensional optimization methods or the Nelder-Mead simplex method, the optimal parameters are obtained with the goal of making the measurement points closer to the constructed curve. and ; S73, calculate the center coordinates of the first and second circular curves, and then, based on the center coordinates and radii of the first and second circular curves and the given intermediate transition curve length, execute the operation of step S4 to perform coordination correction on the center coordinates of the two circular curves, obtain the overall optimized parameters of the complex curve, and complete the complex curve fitting.

10. The method for automatic segmentation and parameter fitting of railway complex curves according to claim 9, characterized in that, In step S7, the obtained transition curve length is rounded to a multiple of 10. If the rounded transition curve length does not match the ledger data, the ledger data shall prevail.

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