A steel structure elevator shaft settlement prediction method based on LSTM model

Abstract

The present invention relates to the field of structural health monitoring technology, specifically a method for predicting the settlement of a steel structure elevator shaft based on an LSTM model, comprising the following steps: analyzing triaxial inclination data, screening effective sections of inclination changes, extracting three-dimensional displacement data to identify inclination linkage mode intervals, identifying offset amplitudes to construct a sample weight distribution table, detecting jump points, setting prediction paths to obtain settlement prediction information, and comparing residuals to identify time offsets to generate structural prediction offset trend data. In the present invention, by identifying inclination inflection points and combining the differences in triaxial change amplitudes, the extraction of effective data segments is achieved, the directional accuracy of structural trend judgment is enhanced by combining the identification of the main axis displacement direction, the training sample weights are adjusted in combination with the data offset amplitude, the model's learning ability for key deformation periods is optimized, the jump density is used to set the starting point of the prediction path, the behavioral responsiveness of trend prediction is improved, and the interpretation of the prediction results is enhanced by combining the translation state residual fluctuation analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of structural health monitoring, and in particular to a method for predicting settlement of a steel structure elevator shaft based on an LSTM model. Background Art

[0002] The field of structural health monitoring technology includes real-time or periodic monitoring, evaluation and early warning of the status of key load-bearing components such as building structures, bridges, tunnels, and elevator shafts. The core content is to collect physical change data of the structure during operation, such as inclination, displacement, strain, vibration, etc., through the deployment of sensor equipment, and to judge and predict the health status of the structure by establishing mathematical models, signal analysis and trend prediction methods. The systematic structural health monitoring covers multiple links such as data collection, status identification, model construction, threshold judgment and early warning issuance, aiming to provide a basis for structural maintenance and operation decisions, and avoid safety accidents caused by structural abnormalities or damage.

[0003] Among them, the steel structure elevator shaft settlement prediction method based on the LSTM model refers to a method for modeling and predicting the inclination angle and settlement displacement in the elevator shaft structure state based on the time series data processing characteristics and the use of a long short-term memory network model. It involves the inclination and settlement changes of the steel structure elevator shaft during long-term use, especially the prediction of small deformations caused by the environment, load and structural characteristics. Specifically, it includes collecting the inclination and displacement data of the elevator shaft by installing Beidou GNSS monitoring equipment, constructing a time series monitoring data set as the basis, inputting it into the LSTM neural network model, and using the internal input gate, forgetting gate and output gate structure to process historical data to form a predicted output for the subsequent time node state, and completing model optimization through multiple rounds of model training and error calculation.

[0004] Traditional steel structure elevator shaft settlement prediction technology uses a fixed threshold judgment method in the screening logic of inclination and settlement data, lacks fine-grained response judgment of continuous time evolution behavior, resulting in some small deformations cannot be effectively extracted in the preprocessing stage. The dynamic synergistic relationship between inclination and three-dimensional displacement is ignored in the spatial direction, causing the identified feature segments to have drift risks in the spatial direction. During the sample training process, weights are mostly adjusted based on mean difference or outlier degree, which cannot effectively identify and strengthen the focus on multiple high-amplitude deformation processes, causing the model to lose sensitivity to key periods of structural deformation during the training stage. The prediction path is started at a fixed time point, resulting in path starting point offset. There is a lack of a driving mechanism for structural state evolution, which reduces the structural stability and interpretability of the overall prediction chain. Summary of the Invention

[0005] In order to solve the technical problems existing in the prior art, an embodiment of the present invention provides a steel structure elevator shaft settlement prediction method based on the LSTM model, optimizes the model's learning ability for key deformation periods, uses jump density to set the starting point of the prediction path, improves the behavioral responsiveness of trend prediction, and combines the translation state residual fluctuation analysis to enhance the interpretability of the prediction results.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for predicting the settlement of a steel elevator shaft based on an LSTM model, comprising the following steps:

[0007] S1: Obtain the inclination data of the X, Y, and Z axes. According to the slope change direction of the inclination data of each axis at consecutive time points, identify the inflection point position, compare the inclination change amplitude of each axis in the same time period, analyze the distribution of the inclination difference over time, and select the effective inclination change section;

[0008] S2: Based on the effective section of the inclination change, obtain the three-dimensional displacement data of the structure, calculate the displacement vector angle and modulus change between adjacent time points, determine the consistency of the displacement direction, analyze the stability of the main axis direction, identify the time period with consistent displacement direction and inclination change trends, and generate the inclination linkage mode interval;

[0009] S3: calling the inclination linkage mode interval, extracting the corresponding inclination and settlement data, and calculating the change amplitude relative to the sample library mean, determining the degree of data deviation in each time period, and constructing a sample weight distribution table;

[0010] S4: According to the inclination linkage mode interval and sample weight distribution table, the inclination change sequence is analyzed and the slight jump points are detected. According to the distribution density of the slight jump points, the change frequency peak section is identified, the starting position of the trend prediction path is set, the settlement behavior of the elevator shaft is predicted, and settlement prediction information is generated.

[0011] As a further solution of the present invention, the effective section of the inclination change is specifically a multi-axis inclination joint change zone, a time series slope reversal zone, and a local amplitude difference aggregation zone; the inclination linkage mode interval includes a main axis direction continuous section, a displacement inclination coordination section, and a spatial displacement stable section; the sample weight allocation table includes data offset grouping items, sample priority labels, and training stage weight coefficients; the settlement prediction information is specifically a settlement trend path, a jump-intensive starting position, and a predicted target data sequence.

[0012] As a further solution of the present invention, the steps of obtaining the inclination data of the X, Y, and Z axes, identifying the inflection point position according to the slope change direction of the inclination data of each axis at consecutive time points, comparing the inclination change amplitudes of each axis in the same time period, analyzing the temporal distribution of the inclination differences, and screening the effective inclination change sections are specifically as follows:

[0013] S101: Obtain X, Y, and Z axis tilt data, identify the slope direction of multiple time points in each axis tilt sequence, extract the inflection point position in each tilt curve, calculate the time interval between adjacent inflection points in each curve and record the inflection point index, and generate a tilt change trend node group;

[0014] S102: Based on the tilt change trend node group, calling the tilt values ​​of the three axes X, Y, and Z in the same time period, comparing the tilt change amplitude of each axis in the same time period, analyzing the temporal distribution of the difference in the tilt change amplitude, and generating the tilt multi-axis difference change interval;

[0015] S103: According to the tilt multi-axis difference change interval and the temporal distribution of the difference in tilt change amplitude, a continuous change trend is identified and an effective tilt change section is selected.

[0016] As a further solution of the present invention, based on the effective section of the inclination change, the three-dimensional displacement data of the structure is obtained, the displacement vector angle and the modulus change between adjacent time points are calculated, the consistency of the displacement direction is determined, the stability of the main axis direction is analyzed, and the time period in which the displacement direction and the inclination change trend are consistent is identified. The steps of generating the inclination linkage mode interval are specifically as follows:

[0017] S201: Based on the effective section of the inclination change, obtain the X, Y, and Z three-dimensional displacement data within the corresponding time period, construct a spatial displacement vector group for each adjacent time point according to the time series order, calculate the angle and modulus change value of each group of vectors, and record the direction change trend and length change amplitude corresponding to each time point to generate a spatial displacement continuous change feature group;

[0018] S202: calling the spatial displacement continuous change feature group, performing consistency analysis on the direction of vector angle change in a continuous time period, analyzing the stability of the displacement main axis in the corresponding time period, extracting the direction stable section, and generating a main axis direction stable interval set;

[0019] S203: According to the main axis direction stable interval set, obtain the tilt angle change trend sequence in the corresponding time period, identify the time period in which the displacement direction and the tilt angle change trend are consistent, and generate the tilt angle linkage mode interval.

[0020] As a further solution of the present invention, the steps of calling the inclination linkage mode interval, extracting the corresponding inclination and settlement data, calculating the change amplitude relative to the sample library mean, determining the degree of deviation of the data in each time period, and constructing the sample weight distribution table are specifically as follows:

[0021] S301: calling the tilt linkage mode interval, extracting the tilt sequence and settlement sequence within the corresponding time period, calculating the difference between the tilt value at each time point and the corresponding tilt mean value in the sample library, calculating the difference between the settlement value and the settlement mean value in the sample library, and generating a tilt settlement offset amplitude group;

[0022] S302: Based on the tilt-settlement offset amplitude group, sort the relative positions of the fluctuation amplitudes of each time period in the sample set, and generate a sample offset level distribution label based on the offset degree of the data of each time period;

[0023] S303: According to the sample offset level distribution label and the offset degree, the training weight of the corresponding sample is adjusted to establish a sample weight distribution table.

[0024] As a further solution of the present invention, according to the inclination linkage mode interval and the sample weight distribution table, the inclination change sequence is analyzed and the slight jump point is detected. According to the distribution density of the slight jump point, the change frequency peak section is identified, the starting position of the trend prediction path is set, and the settlement behavior of the elevator shaft is predicted. The specific steps of generating settlement prediction information are as follows:

[0025] S401: extracting the tilt change sequence within the corresponding time period according to the tilt linkage mode interval and the sample weight distribution table, detecting the slight jump point by comparing it with the slight jump recognition threshold, and generating slight jump point information;

[0026] S402: Based on the information of the slight amplitude jump point, the distribution density of the slight amplitude jump point is analyzed, and according to the position of the jump point in the time series, the peak section of the change frequency is identified and set as the starting position of the trend prediction path, thereby generating trend path starting position parameters;

[0027] S403: Based on the starting position parameters of the trend path and in combination with the direction of inclination change at consecutive time points in the corresponding section, the settlement behavior of the elevator shaft is predicted to generate settlement prediction information.

[0028] As a further solution of the present invention, the specific formula for identifying the peak section of the frequency change is:

[0029] ;

[0030] Calculate the jump distribution density index;

[0031] in, For the The jump distribution density index within a time window is is the index of the transition point in the current time window, is the index of the time window, For the The original time index of the transition point, For the The original time index of the transition point, is the total time length of the current time window, For the The training sample weight value corresponding to the jump point, For the The normalized value of the inclination change amplitude of each jump point, is the residual stability correction term constant used to prevent division by zero operations, For the The total number of small amplitude jump points detected in a time window.

[0032] As a further embodiment of the present invention, the present invention further comprises:

[0033] S5: calling the settlement prediction information, obtaining a residual sequence between the predicted value and the actual value, analyzing the prediction error of each time step, adjusting the translation step size within the time window, calculating the error mean under each translation state, and by comparing the residual mean of each translation step, identifying the optimal translation state and the corresponding time offset distance based on the stability of the error and residual fluctuations, and generating structural prediction offset trend data;

[0034] The structural prediction offset trend data includes a model time response offset, a translation matching minimum residual value, and a trend error classification label.

[0035] As a further solution of the present invention, the steps of calling the settlement prediction information, obtaining a residual sequence between the predicted value and the actual value, analyzing the prediction error of each time step, adjusting the translation step size within the time window, calculating the error mean under each translation state, and identifying the optimal translation state and the corresponding time offset distance by comparing the residual mean of each translation step based on the stability of the error and residual fluctuations to generate the structural prediction offset trend data are specifically as follows:

[0036] S501: calling the settlement prediction information, obtaining a predicted value sequence and an actual value sequence, and constructing a difference sequence between the data sequences to generate a prediction error residual sequence;

[0037] S502: Calling the prediction error residual sequence, setting multiple continuous time windows, adjusting the translation step of the prediction data sequence relative to the actual monitoring data sequence, and calculating the residual mean value of the corresponding time window under each translation state to generate a translation state error mean value list;

[0038] S503: Call the translation state error mean list, identify the optimal translation state and the corresponding time offset distance by analyzing the error of each translation step and the stability of the residual fluctuation, mark them as the response offset predicted by the model, and generate structural prediction offset trend data.

[0039] As a further solution of the present invention, the specific formula for analyzing the stability of the error and residual fluctuation of each translation step is:

[0040] ;

[0041] Calculate the residual volatility score;

[0042] in, The translation step number is The normalized residual volatility score of The translation step number is The arithmetic mean of all forecast residual values ​​within the time window of The translation step number is And the time point index is The single prediction residual value of is the number of time points in the current time window, For all translation steps numbered The maximum absolute value of the residual mean of is the constant correction term value, represents the current translation step number used for analysis, Represents the discrete time point index within the current time window, Indicates the traversal index number of all translation steps to be compared.

[0043] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least:

[0044] By identifying the inflection point of the inclination angle and combining it with the difference in the amplitude of the three-axis change, the extraction of effective data segments is achieved. The directional accuracy of the structural trend judgment is enhanced by combining the identification of the main axis displacement direction. The training sample weight is adjusted in combination with the data offset amplitude to optimize the model's learning ability for key deformation periods. The jump density is used to set the starting point of the prediction path, which improves the behavioral responsiveness of the trend prediction. By identifying the fluctuation of the translation state residual, the interpretability of the model prediction results and the tolerance recognition ability are enhanced, the accuracy of structural state identification is improved, and the focus of model training and the rationality of prediction error tolerance are enhanced. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0046] Figure 1 Schematic diagram of the workflow of the present invention. DETAILED DESCRIPTION

[0047] The technical solution of the present invention is described below in conjunction with the accompanying drawings.

[0048] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as an "exemplary" in the present invention should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of the word "exemplary" is intended to present concepts in a concrete manner. Furthermore, in the embodiments of the present invention, "and / or" can mean both or either of the two.

[0049] In order to make the technical problems, technical solutions and advantages to be solved by the present invention clearer, a detailed description will be given below with reference to the accompanying drawings and specific embodiments.

[0050] See also Figure 1 The present invention provides a technical solution, a method for predicting the settlement of a steel structure elevator shaft based on an LSTM model, comprising the following steps:

[0051] S1: Obtain the inclination data of the X, Y, and Z axes. According to the slope change direction of the inclination data of each axis at consecutive time points, identify the inflection point position, compare the inclination change amplitude of each axis in the same time period, analyze the distribution of the inclination difference over time, and select the effective inclination change section;

[0052] S2: Based on the effective section of inclination change, obtain the three-dimensional displacement data of the structure, calculate the displacement vector angle and modulus change between adjacent time points, determine the consistency of the displacement direction, analyze the stability of the main axis direction, identify the time period with consistent displacement direction and inclination change trends, and generate the inclination linkage mode interval;

[0053] S3: Call the inclination linkage mode interval, extract the corresponding inclination and settlement data, calculate the change amplitude relative to the sample library mean, determine the degree of data deviation in each time period, and construct a sample weight distribution table;

[0054] S4: Based on the inclination linkage mode interval and sample weight distribution table, the inclination change sequence is analyzed and the slight jump points are detected. Based on the distribution density of the slight jump points, the change frequency peak section is identified, the starting position of the trend prediction path is set, the settlement behavior of the elevator shaft is predicted, and settlement prediction information is generated;

[0055] S5: Call the settlement prediction information, obtain the residual sequence between the predicted value and the actual value, analyze the prediction error of each time step, adjust the translation step size within the time window, calculate the error mean under each translation state, and by comparing the residual mean of each translation step, identify the optimal translation state and the corresponding time offset distance based on the stability of the error and residual fluctuations, and generate structural prediction offset trend data.

[0056] The effective sections of inclination change are specifically the multi-axis inclination joint change section, the time series slope reversal section, and the local amplitude difference aggregation section. The inclination linkage mode section includes the main axis direction continuous section, the displacement inclination coordination section, and the spatial displacement stable section. The sample weight allocation table includes data offset grouping items, sample priority labels, and training stage weight coefficients. The settlement prediction information is specifically the settlement trend path, the jump intensive starting position, and the predicted target data sequence. The structural prediction offset trend data includes the model time response offset, the minimum residual value of the translation matching, and the trend error classification label.

[0057] Obtain the X, Y, and Z axis inclination data, identify the inflection point based on the slope change direction of each axis's inclination data at consecutive time points, compare the inclination change amplitudes of each axis in the same time period, analyze the temporal distribution of the inclination differences, and select the effective inclination change sections as follows:

[0058] S101: Obtain X, Y, and Z axis tilt data, identify the slope direction of multiple time points in each axis tilt sequence, extract the inflection point position in each tilt curve, calculate the time interval between adjacent inflection points in each curve and record the inflection point index, and generate a tilt change trend node group;

[0059] After obtaining the X, Y, and Z axis tilt data, the three-axis tilt sequence is collected at equal time intervals and recorded as 、 、 ,in is the time point index, interval time Set to 30 seconds to form a time series array of inclination angles with time as the index. 、 、 The sequence performs slope direction judgment operation, that is, for each Calculate the inclination difference between the current and previous moments ,in, For the moment The inclination change of the current axis, is the inclination value at the current moment, is the inclination value at the previous moment, .like It is marked as an upward trend. The trend is marked as a downward trend. If the trend changes from rising to falling or from falling to rising at three consecutive points, it is identified as an inflection point. The inflection point time point is recorded as , which forms a sequence of inflection points on each axis 、 、 , and calculate the time interval between each adjacent inflection point ,in, is the time interval between adjacent inflection points, The time of the next turning point, The time of the previous inflection point. Record the inflection point time interval array , every turning point Corresponding to a label index , further integrated into a set of inclination change trend nodes. In actual testing, when the data at the elevator shaft inclination measurement point is as follows , then in Towards The change is the turning point of the downward trend. The sampling frequency is 30 seconds, corresponding to The judgment logic is executed according to the axis, and a node list is formed for each curve to form a complete trend node group.

[0060] S102: Based on the inclination change trend node group, the inclination values ​​of the three axes X, Y, and Z within the same time period are retrieved. By comparing the inclination change amplitude of each axis within the same time period, the temporal distribution of the difference in the inclination change amplitude is analyzed to generate the inclination multi-axis difference change interval;

[0061] Based on the node group with the trend of inclination change, the inclination value of the node in the time period is extracted from the X, Y and Z axes, and the inclination curve of each axis is plotted in the corresponding Extract a subsequence of 5 time points within the time period Calculate the maximum and minimum inclination values ​​within the section and take the difference ,in, For the Axis at the node The inclination fluctuation amplitude, The first The inclination value at a moment, Calculate in sequence 、 、 , the three constitute the inclination change amplitude group . Determine the maximum difference between the three-axis change amplitudes of the node ,in, Indicates the The maximum difference between the three-axis inclination changes at a time point, and are the maximum and minimum fluctuation amplitudes in the three axes respectively. degrees, it is marked as a multi-axis difference change. The system default difference threshold is The degree is determined by the equipment error tolerance and the structural deformation standard. For example: 、 、 ,but , marked as difference change segment, all satisfy The period of time constitutes the range of multi-axis difference variation of inclination.

[0062] S103: Based on the multi-axis tilt difference variation interval and the temporal distribution of the tilt variation amplitude difference, identify the continuous variation trend and select the effective tilt variation area;

[0063] According to the multi-axis difference variation range of the inclination angle, filter the continuous Time period, determine whether the number of nodes that continuously meet the conditions in each segment is greater than the continuous judgment benchmark If the number of nodes that continuously meet the condition is greater than or equal to 3, it is considered as a continuous effective change trend segment. Compare the overlapping range of the three-axis difference segments and take the time intersection of the three axes, which is recorded as ,in, Indicates the valid intersection segment of X, Y, and Z axes on the time axis. Check each segment Does the inclination sequence have at least two positive and negative reversals? That is, the product of the slopes of consecutive adjacent time points satisfies ,in, Indicates a time point Upper axis The slope of express If there are two or more point pairs that meet the product condition, the segment is included in the valid inclination change segment set. Example: An elevator shaft detects 6 consecutive For nodes with at least two direction reversals in X and Y, this period is recorded as the effective tilt angle change section.

[0064] Based on the effective section of inclination change, the three-dimensional displacement data of the structure is obtained, the displacement vector angle and modulus change between adjacent time points are calculated, the consistency of the displacement direction is determined, the stability of the main axis direction is analyzed, and the time period with consistent displacement direction and inclination change trends is identified. The specific steps for generating the inclination linkage mode interval are as follows:

[0065] S201: Based on the effective section of inclination change, obtain the X, Y, and Z three-dimensional displacement data within the corresponding time period, construct a spatial displacement vector group for each adjacent time point according to the time series order, calculate the angle and modulus change value of each group of vectors, and record the direction change trend and length change amplitude corresponding to each time point to generate a spatial displacement continuous change feature group;

[0066] Based on the effective section of the inclination change, the X, Y, and Z three-dimensional displacement data within the corresponding time period are obtained, and the displacement at each time point is expressed as a three-dimensional coordinate vector form. ,in Represents the time index, Respectively represent the spatial position values ​​in the three-axis directions at that moment, and the data is collected at an interval of 5 seconds. According to the time series order, a spatial displacement vector group is constructed for each two adjacent time points. , that is, by subtracting the three coordinate components respectively, we can get . Record the changes in the modulus length of each vector group, through Calculate the displacement amplitude of each segment of space; the direction change trend is calculated by calculating the angle between adjacent vectors, and the angle is calculated using the cosine formula The result is between If , it is judged that the direction is stable, if , it is judged as a sudden change in direction. Record the modulus and angle change values ​​at each time point as the spatial displacement feature of the point, forming a continuous change feature group of spatial displacement of the entire sequence. In the example, if there are three points 、 、 ,but 、 The angle between the two vectors is about 5.7 degrees, which is judged to be a stable change in direction.

[0067] S202: calling the spatial displacement continuous change feature group, performing consistency analysis on the direction of vector angle change in a continuous time period, analyzing the stability of the displacement main axis in the corresponding time period, extracting the direction stable section, and generating a main axis direction stable interval set;

[0068] Call the spatial displacement continuous change feature group, for all The angle values ​​between adjacent vectors represented by are traversed and analyzed, and the sections in the angle sequence with continuous changes less than the set angle difference are extracted as direction consistent intervals. The specific direction consistency threshold is set as , converted to cosine value is By continuously judging multiple time points Whether the condition is met continuously, if the direction consistency is met for more than 3 consecutive time points, the direction of this section is considered stable, and its start and end time are marked. Further analysis is made to see whether the vector modulus change in the direction stable section maintains a positive increasing or decreasing trend. If there are three consecutive sections of modulus length showing a monotonic change trend, it is recorded as the main axis offset direction is stable, and the time period index and the main vector axial direction of the vector change direction are recorded. For example, if there are five time points with an angle cosine value of , then the first three points meet the angle consistency condition, if at the same time their modulus lengths are , it is in an increasing state, forming a directional stable section, which is included in the main axis direction stable interval set.

[0069] S203: Based on the main axis direction stable interval set, obtain the tilt angle change trend sequence within the corresponding time period, identify the time period in which the displacement direction and the tilt angle change trend are consistent, and generate the tilt angle linkage mode interval;

[0070] According to the stable interval set of the main axis direction, the time index of each stable interval is extracted to obtain the inclination angle change trend sequence within the corresponding period. ,in , and further compare it with the direction of the current main vector of spatial displacement. Calculate the angle difference between the spatial displacement main axis direction vector and the tilt change direction of each axis. If the angle between the tilt change direction of a certain axis in the segment and the main axis direction is less than the set angle consistency threshold (for example, 15 degrees), then it is judged to be the tilt linkage trend direction in the segment. If there are at least two axes in the same segment that meet the convergence conditions of the tilt direction and the displacement direction, then the time index of the segment is recorded in the tilt linkage mode interval. In the example, if the main axis direction is the Z axis, and the tilt change sequence is continuously increasing on the Z axis, and the angle with the main axis is 9 degrees, then the segment can be identified as the linkage between the tilt and displacement directions, and the start and end times of the segment are marked into the tilt linkage mode interval set.

[0071] Call the dip linkage mode interval, extract the corresponding dip and settlement data, calculate the change amplitude relative to the sample library mean, determine the degree of data deviation in each time period, and construct the sample weight distribution table as follows:

[0072] S301: Calling the tilt linkage mode interval, extracting the tilt sequence and settlement sequence within the corresponding time period, calculating the difference between the tilt value at each time point and the corresponding tilt mean value in the sample library, and calculating the difference between the settlement value and the settlement mean value in the sample library, and generating a tilt settlement offset amplitude group;

[0073] Call the inclination linkage mode interval and extract the inclination value and settlement value at each moment in the interval, which are recorded as and ,in is the time point index, in seconds. The unit is degree, The unit is millimeter. Synchronously call the corresponding inclination angle and settlement reference mean of the period in the sample library, which are recorded as and For each time point , calculate the tilt offset as , the settlement offset is ,in, Indicates the change in the current inclination relative to the reference sample. Indicates the change of the current moment settlement relative to the reference sample. The offset difference sequence is formed for all time points in the entire section, which are and If you set the reference sample 、 , while the actual monitoring data is recorded at a certain moment as 、 , then the corresponding offset is 、 The offset amplitude set of the linkage section is constructed for all time points and recorded uniformly as the dip-settlement offset amplitude group.

[0074] S302: Based on the inclination and settlement offset amplitude group, the relative position of the fluctuation amplitude of each time period in the sample set is sorted, and the offset degree of the data in each time period is calculated to generate a sample offset level distribution label;

[0075] Based on the inclination-settlement offset amplitude group, the combined offset of inclination and settlement in each time period is recorded as a two-dimensional feature vector , sort the offset amplitudes of all labeled samples of the vector group in the overall sample set. The offset features in the sample set are classified according to the preset level standard, and the threshold is set according to the amplitude combination interval, for example: the inclination offset is less than And the settlement offset is less than is level one, the tilt offset is And the settlement offset is The second level, and the third level. The feature vectors are mapped to the above-mentioned level labels to form a sequence label group, which serves as the sample offset level distribution label for that time period. If the joint offset of five data points in a certain period of time is within the second-level interval, the entire period is labeled as "offset level 2".

[0076] S303: Distribute labels based on sample offset levels and adjust the training weights of corresponding samples according to the offset degree, and establish a sample weight distribution table;

[0077] According to the sample offset level distribution label, the training samples corresponding to each level are assigned different training weight values, and the weight of the first-level sample is set to , the second level is , the third level is , where the weight values ​​are taken from the recommended range for setting the gradient adjustment factor during network training. During the training data construction phase, all time points in the linkage interval are mapped to their corresponding level labels, with their weight values ​​then paired one-to-one with the original sample input data. This ultimately forms a mapping matrix between each sample moment and its training weight, outputting the sample weight distribution table. In this example, if the label sequence for a certain time period is {2, 2, 3, 1, 2}, the corresponding weight sequence is {1.0, 1.0, 1.5, 0.5, 1.0}. This sequence, combined with the original sample index, forms the complete training input template.

[0078] According to the inclination linkage mode interval and sample weight distribution table, the inclination change sequence is analyzed and the slight jump points are detected. Based on the distribution density of the slight jump points, the change frequency peak section is identified, the starting position of the trend prediction path is set, and the settlement behavior of the elevator shaft is predicted. The specific steps for generating settlement prediction information are as follows:

[0079] S401: Extracting the tilt change sequence within the corresponding time period based on the tilt linkage mode interval and the sample weight distribution table, detecting the slight jump point by comparing it with the slight jump recognition threshold, and generating slight jump point information;

[0080] According to the tilt linkage mode interval and sample weight distribution table, the tilt change sequence within the interval is extracted, and the tilt sequence is set as ,in As the index of continuous time points, the first-order difference processing is performed on the sequence to obtain the inclination change sequence ,in, Indicates the tilt angle change between two adjacent moments. The threshold for identifying slight jumps is defined as , used to determine the occurrence criteria of jump behavior. , if satisfied and Less than the large abnormal fluctuation identification threshold (set as ), then the point Recorded as a slight jump point. Further call the sample weight distribution table to mark and distinguish the jump points in the high weight segment, forming a structure of The triplet information of the slight jump point of is the weight of the training sample at the corresponding moment. In actual sampling, if ,but , where items 1, 2, and 4 all meet the slight jump conditions. These time points and corresponding weights are recorded to generate slight jump point information.

[0081] S402: Based on the information of the slight amplitude jump points, the distribution density of the slight amplitude jump points is analyzed. According to the position of the jump points in the time series, the peak segment of the change frequency is identified and set as the starting position of the trend prediction path, thereby generating the trend path starting position parameters;

[0082] The specific formula for identifying the peak segment of frequency change is:

[0083] ;

[0084] Calculate the jump distribution density index;

[0085] in, For the The jump distribution density index within a time window is is the index of the transition point in the current time window, is the index of the time window, For the The original time index of the transition point, For the The original time index of the transition point, is the total time length of the current time window, For the The training sample weight value corresponding to the jump point, For the The normalized value of the inclination change amplitude of each jump point, is the residual stability correction term constant used to prevent division by zero operations, For the The total number of small amplitude jump points detected in a time window.

[0086] formula:

[0087] ;

[0088] Detailed explanation of the formula and the process of formula calculation and derivation:

[0089] The formula used to calculate the Normalized density index of slight jump points in a time window ,This indicator is used to identify the time position where the frequency peak of the elevator shaft structure is concentrated in the micro-jump, and the result is used to set the starting time position of the trend prediction path;

[0090] Parameter meaning and setting value:

[0091] For the The original time index corresponding to the jump point, in seconds, is recorded by the Beidou GNSS high-frequency monitoring module to record the jump point timestamp, and the sequence value is set to ,Right now ;

[0092] The total time span of the current window, in seconds, is calculated by adding 1 to the difference between the maximum and minimum values ​​of the time index. ;

[0093] For the The tilt angle change amplitude of each jump point, in degrees, is obtained through the differential tilt angle change curve and is set to Spend;

[0094] is the maximum tilt angle change in the current time window, set to Spend;

[0095] is the normalized tilt angle variation, set to ;

[0096] is the sample weight, set to , which comes from the relationship between the tilt offset amplitude of each jump point and the training offset level;

[0097] is a numerical stability correction term, set to ;

[0098] Substitute the parameters into the formula for calculation:

[0099] ;

[0100] ;

[0101] ;

[0102] The result of 0.5457 indicates that the distribution of jump points in the current time window is relatively sparse, while their amplitude intensity is relatively concentrated. This indicates that the jump density of this section is medium, making it a candidate key section for the prediction starting path. This value will be sorted and used to identify the interval index corresponding to the minimum density index, which will serve as the starting point for the next sedimentation trend prediction path.

[0103] S403: Predicting the settlement behavior of the elevator shaft based on the trend path starting position parameters and the inclination change direction at consecutive time points within the corresponding section to generate settlement prediction information;

[0104] According to the trend path starting position parameters, locate the corresponding time point , extract the inclination value sequence in subsequent continuous time points , and perform direction trend judgment. Calculate the sign of the dip direction difference at each moment , count the length and direction of consecutive segments with the same symbol to determine whether the main change trend is rising or falling. Combined with this directional trend, find the behavioral characteristics of the historical settlement sequence in the same time period and build a mapping relationship model between the inclination trend and the settlement trend. Input the trend path into the mapping logic, perform the trend prediction calculation, and obtain the settlement trend output value sequence in the corresponding time period. The combined output is the settlement prediction information. If the inclination sequence direction is a continuous rising segment, and the corresponding settlement in the mapping history is an increasing trend, then the subsequent data in the output settlement prediction sequence will be a continuously increasing structure. Finally, the settlement prediction information is generated.

[0105] Call settlement prediction information, obtain the residual sequence between the predicted value and the actual value, analyze the prediction error of each time step, adjust the translation step size within the time window, calculate the error mean under each translation state, and by comparing the residual mean of each translation step, identify the optimal translation state and the corresponding time offset distance based on the stability of the error and residual fluctuations. The specific steps for generating structural prediction offset trend data are as follows:

[0106] S501: Calling settlement prediction information, obtaining the predicted value sequence and the actual value sequence, and constructing the difference sequence between the data sequences to generate the prediction error residual sequence;

[0107] Call settlement prediction information and extract the settlement prediction value sequence output by the model within a specific time range At the same time, the actual settlement monitoring value sequence within the same time period is retrieved from the structural health monitoring system ,in Represents the time point index in minutes or seconds, in millimeters. The two sets of time-synchronized numerical sequences are matched one-to-one, and for each time point Calculate the difference between the predicted value and the actual value and construct the residual sequence , which reflects the model’s prediction error for structural settlement at different time points. For example, if the sampling frequency at the bottom of the elevator shaft is set to once every 5 minutes, the prediction sequence for 4 consecutive time points is mm, corresponding to the actual monitoring sequence mm, then the difference sequence is The residuals are further stored as structured data by time index, recorded as , facilitating subsequent window analysis and trend identification. In actual engineering scenarios, this residual series will be used to identify problems such as systematic offsets, trend delays, or error anomalies in model predictions. For example, continuous negative deviations within a certain period of time may reflect a trend of lagged model predictions rather than a structural mutation.

[0108] S502: Call the prediction error residual sequence, set multiple continuous time windows, adjust the translation step size of the predicted data sequence relative to the actual monitoring data sequence, and calculate the residual mean value of the corresponding time window in each translation state to generate a translation state error mean list;

[0109] Call the forecast error residual series , set multiple fixed-length sliding windows for the entire time series, and the length of each window is set to time points, and a window is reconstructed each time it slides back a unit time point to form a sliding window set For each window , while maintaining the actual value sequence Under the condition of no change, the predicted value series Perform translation operation on the relative time axis, translation step The range is Time step, which means that the predicted value is adjusted forward or backward by up to 3 time points. In each translation state, the residual sequence in the window is recalculated. , and then the mean of the translation residual is calculated to obtain the average error value between the current window and the current translation state For example, in the window In the case where the translation step length is , the calculation result is , then the residual mean is mm. and the corresponding Pairing forms an error mean mapping list, which serves as the translation-error response data under the current window to provide support for subsequent step size optimization and trend delay identification.

[0110] S503: Calling the translation state error mean list, analyzing the error of each translation step and the stability of the residual fluctuation, identifying the optimal translation state and the corresponding time offset distance, marking them as the response offset predicted by the model, and generating structural prediction offset trend data;

[0111] The specific formula for analyzing the stability of the error and residual fluctuation of each translation step is:

[0112] ;

[0113] Calculate the residual volatility score;

[0114] in, The translation step number is The normalized residual volatility score of The translation step number is The arithmetic mean of all forecast residual values ​​within the time window of The translation step number is And the time point index is The single prediction residual value of is the number of time points in the current time window, For all translation steps numbered The maximum absolute value of the residual mean of is the constant correction term value, represents the current translation step number used for analysis, Represents the discrete time point index within the current time window, Indicates the traversal index number of all translation steps to be compared.

[0115] formula:

[0116] ;

[0117] Detailed explanation of the formula and the process of formula calculation and derivation:

[0118] The formula is used to calculate each predicted translation step The normalized residual volatility score of , the score value reflects the error level and stability of the model prediction results under different time offset states. The result is used to identify the optimal prediction time offset step as the basis for model response adjustment;

[0119] Parameter meaning and setting value:

[0120] is the translation step length The mean of all predicted residual values ​​in the time window under the state, in millimeters, is obtained by subtracting the predicted value from the measured value hour by hour and averaging it. The setting value is mm;

[0121] is the translation step length The time index in the state is The prediction residual value, in millimeters, comes from the difference sequence between the settlement monitoring data and the model prediction value, setting the current window length , for mm;

[0122] The number of time points in the current time window, which is determined by the monitoring frequency and the sliding window length, is currently set to 5;

[0123] is the maximum absolute mean of the residuals in all translation steps, set to mm;

[0124] It is a numerical stability correction term to ensure that the denominator is non-zero and is set to ;

[0125] Substitute the parameters into the formula for calculation:

[0126] ;

[0127] ;

[0128] ;

[0129] ;

[0130] Results show that the relative error strength of the model prediction residual level at the current translation step size across all candidate states is 0.6876, with lower values ​​indicating smaller errors and greater stability. This score is used to rank and compare the scores of other translation states, and the translation step size corresponding to the minimum value is used as the time correction for the model response offset, thereby generating structural prediction offset trend data. This process directly serves the model output time series alignment mechanism and is the core computational foundation for the error attribution feedback process.

[0131] The above embodiments can be implemented in whole or in part via software, hardware (e.g., circuits), firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product comprises one or more computer instructions or computer programs. When loaded or executed on a computer, the processes or functions described in accordance with the embodiments of the present invention are fully or partially performed. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired means (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server or data center that contains a collection of one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media. The semiconductor media can be a solid-state drive.

[0132] It should be understood that the term "and / or" as used herein simply describes a relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A alone, A and B together, or B alone. A and B can be singular or plural. Furthermore, the character " / " as used herein generally indicates an "or" relationship between the associated objects, but it may also indicate an "and / or" relationship. For specific understanding, please refer to the context.

[0133] In this disclosure, "at least one" means one or more, and "plurality" means two or more. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, "at least one of a, b, or c" can mean: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or plural.

[0134] It should be understood that in various embodiments of the present invention, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0135] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0136] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described equipment, devices and units can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0137] In the several embodiments provided by the present invention, it should be understood that the disclosed devices, apparatuses and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interface, indirect coupling or communication connection of the device or unit, which can be electrical, mechanical or other forms.

[0138] 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, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0139] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0140] If the functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or the portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media that can store program code, such as USB flash drives, mobile hard drives, read-only memories (ROM), random access memories (RAM), magnetic disks, or optical disks.

[0141] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A steel structure elevator shaft settlement prediction method based on LSTM model, characterized in that: include: S1: Obtain the inclination data of the X, Y, and Z axes. According to the slope change direction of the inclination data of each axis at consecutive time points, identify the inflection point position, compare the inclination change amplitude of each axis in the same time period, analyze the distribution of the inclination difference over time, and select the effective inclination change section; S2: Based on the effective section of the inclination change, obtain the three-dimensional displacement data of the structure, calculate the displacement vector angle and modulus change between adjacent time points, determine the consistency of the displacement direction, analyze the stability of the main axis direction, identify the time period with consistent displacement direction and inclination change trends, and generate the inclination linkage mode interval; S3: calling the inclination linkage mode interval, extracting the corresponding inclination and settlement data, and calculating the change amplitude relative to the sample library mean, determining the degree of data deviation in each time period, and constructing a sample weight distribution table; S4: According to the inclination linkage mode interval and sample weight distribution table, the inclination change sequence is analyzed and the slight jump points are detected. According to the distribution density of the slight jump points, the change frequency peak section is identified, the starting position of the trend prediction path is set, the settlement behavior of the elevator shaft is predicted, and settlement prediction information is generated.

2. The method for predicting settlement of a steel structure elevator shaft based on an LSTM model according to claim 1, characterized in that: The effective section of the inclination change is specifically the multi-axis inclination joint change area, the time series slope reversal area, and the local amplitude difference aggregation area. The inclination linkage mode interval includes the main axis direction continuous section, the displacement inclination coordination section, and the spatial displacement stable section. The sample weight allocation table includes data offset grouping items, sample priority labels, and training stage weight coefficients. The settlement prediction information is specifically the settlement trend path, the jump intensive starting position, and the predicted target data sequence.

3. The method for predicting settlement of a steel structure elevator shaft based on an LSTM model according to claim 1, characterized in that: Obtain the X, Y, and Z axis inclination data, identify the inflection point based on the slope change direction of each axis's inclination data at consecutive time points, compare the inclination change amplitudes of each axis in the same time period, analyze the temporal distribution of the inclination differences, and select the effective inclination change sections as follows: S101: Obtain X, Y, and Z axis tilt data, identify the slope direction of multiple time points in each axis tilt sequence, extract the inflection point position in each tilt curve, calculate the time interval between adjacent inflection points in each curve and record the inflection point index, and generate a tilt change trend node group; S102: Based on the tilt change trend node group, calling the tilt values ​​of the three axes X, Y, and Z in the same time period, comparing the tilt change amplitude of each axis in the same time period, analyzing the temporal distribution of the difference in the tilt change amplitude, and generating the tilt multi-axis difference change interval; S103: According to the tilt multi-axis difference change interval and the temporal distribution of the difference in tilt change amplitude, a continuous change trend is identified and an effective tilt change section is selected.

4. The method for predicting settlement of a steel structure elevator shaft based on an LSTM model according to claim 3 is characterized in that: Based on the effective section of the inclination change, the three-dimensional displacement data of the structure is obtained, the displacement vector angle and the modulus change between adjacent time points are calculated, the consistency of the displacement direction is determined, the stability of the main axis direction is analyzed, and the time period with consistent displacement direction and inclination change trends is identified. The steps of generating the inclination linkage mode interval are specifically as follows: S201: Based on the effective section of the inclination change, obtain the X, Y, and Z three-dimensional displacement data within the corresponding time period, construct a spatial displacement vector group for each adjacent time point according to the time series order, calculate the angle and modulus change value of each group of vectors, and record the direction change trend and length change amplitude corresponding to each time point to generate a spatial displacement continuous change feature group; S202: calling the spatial displacement continuous change feature group, performing consistency analysis on the direction of vector angle change in a continuous time period, analyzing the stability of the displacement main axis in the corresponding time period, extracting the direction stable section, and generating a main axis direction stable interval set; S203: According to the main axis direction stable interval set, obtain the tilt angle change trend sequence in the corresponding time period, identify the time period in which the displacement direction and the tilt angle change trend are consistent, and generate the tilt angle linkage mode interval.

5. The method for predicting settlement of a steel structure elevator shaft based on an LSTM model according to claim 4, characterized in that: The steps of calling the inclination linkage mode interval, extracting the corresponding inclination and settlement data, calculating the change amplitude relative to the sample library mean, determining the degree of data deviation in each time period, and constructing the sample weight distribution table are as follows: S301: calling the tilt linkage mode interval, extracting the tilt sequence and settlement sequence within the corresponding time period, calculating the difference between the tilt value at each time point and the corresponding tilt mean value in the sample library, calculating the difference between the settlement value and the settlement mean value in the sample library, and generating a tilt settlement offset amplitude group; S302: Based on the tilt-settlement offset amplitude group, sort the relative positions of the fluctuation amplitudes of each time period in the sample set, and generate a sample offset level distribution label based on the offset degree of the data of each time period; S303: According to the sample offset level distribution label and the offset degree, the training weight of the corresponding sample is adjusted to establish a sample weight distribution table.

6. The method for predicting settlement of a steel structure elevator shaft based on an LSTM model according to claim 5, characterized in that: According to the inclination linkage mode interval and the sample weight distribution table, the inclination change sequence is analyzed and the slight jump points are detected. According to the distribution density of the slight jump points, the change frequency peak section is identified, the starting position of the trend prediction path is set, and the settlement behavior of the elevator shaft is predicted. The specific steps of generating settlement prediction information are as follows: S401: extracting the tilt change sequence within the corresponding time period according to the tilt linkage mode interval and the sample weight distribution table, detecting the slight jump point by comparing it with the slight jump recognition threshold, and generating slight jump point information; S402: Based on the information of the slight amplitude jump point, the distribution density of the slight amplitude jump point is analyzed, and according to the position of the jump point in the time series, the peak section of the change frequency is identified and set as the starting position of the trend prediction path, thereby generating trend path starting position parameters; S403: Based on the starting position parameters of the trend path and in combination with the direction of inclination change at consecutive time points in the corresponding section, the settlement behavior of the elevator shaft is predicted to generate settlement prediction information.

7. The method for predicting settlement of a steel structure elevator shaft based on an LSTM model according to claim 6, characterized in that: The specific formula for identifying the peak section of the frequency change is: ； Calculate the jump distribution density index; in, For the The jump distribution density index within a time window is is the index of the transition point in the current time window, is the index of the time window, For the The original time index of the transition point, For the The original time index of the transition point, is the total time length of the current time window, For the The training sample weight value corresponding to the jump point, For the The normalized value of the inclination change amplitude of each jump point, is the residual stability correction term constant used to prevent division by zero operations, For the The total number of small amplitude jump points detected in a time window.

8. The method for predicting settlement of a steel structure elevator shaft based on an LSTM model according to claim 1, characterized in that: Also includes: S5: calling the settlement prediction information, obtaining a residual sequence between the predicted value and the actual value, analyzing the prediction error of each time step, adjusting the translation step size within the time window, calculating the error mean under each translation state, and by comparing the residual mean of each translation step, identifying the optimal translation state and the corresponding time offset distance based on the stability of the error and residual fluctuations, and generating structural prediction offset trend data; The structural prediction offset trend data includes a model time response offset, a translation matching minimum residual value, and a trend error classification label.

9. The method for predicting settlement of a steel structure elevator shaft based on an LSTM model according to claim 8, characterized in that: The steps of calling the settlement prediction information, obtaining the residual sequence between the predicted value and the actual value, analyzing the prediction error of each time step, adjusting the translation step size within the time window, calculating the error mean under each translation state, and identifying the optimal translation state and the corresponding time offset distance by comparing the residual mean of each translation step based on the stability of the error and residual fluctuations to generate the structural prediction offset trend data are as follows: S501: calling the settlement prediction information, obtaining a predicted value sequence and an actual value sequence, and constructing a difference sequence between the data sequences to generate a prediction error residual sequence; S502: Calling the prediction error residual sequence, setting multiple continuous time windows, adjusting the translation step of the prediction data sequence relative to the actual monitoring data sequence, and calculating the residual mean value of the corresponding time window under each translation state to generate a translation state error mean value list; S503: Call the translation state error mean list, identify the optimal translation state and the corresponding time offset distance by analyzing the error of each translation step and the stability of the residual fluctuation, mark them as the response offset predicted by the model, and generate structural prediction offset trend data.

10. The method for predicting settlement of a steel structure elevator shaft based on an LSTM model according to claim 9, characterized in that: The specific formula for analyzing the stability of the error and residual fluctuation of each translation step is: ； Calculate the residual volatility score; in, The translation step number is The normalized residual volatility score of The translation step number is The arithmetic mean of all forecast residual values ​​within the time window of The translation step number is And the time point index is The single prediction residual value of is the number of time points in the current time window, For all translation steps numbered The maximum absolute value of the residual mean of is the constant correction term value, represents the current translation step number used for analysis, Represents the discrete time point index within the current time window, Indicates the traversal index number of all translation steps to be compared.

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