Industrial equipment track error big data analysis and intelligent compensation method and system

Abstract

The invention provides an industrial equipment track error big data analysis and intelligent compensation method and system, and relates to the technical field of intelligent error compensation, and the method comprises the steps: collecting equipment operation state parameters, carrying out the segmentation processing, extracting motion features, generating feature fingerprints, comparing the feature fingerprints with a feature fingerprint database, and calculating the feature deviation; distributing the characteristic deviation to a multi-agent analysis area error characteristic, and constructing an error transfer chain; and constructing a layered compensation structure based on the error transfer chain, setting error representative points, calculating interlayer coupling constraints and intra-layer coordination constraints, and optimizing compensation components by adopting a hybrid iteration strategy to generate a compensation execution sequence. Accurate compensation of the motion trail of the industrial equipment can be realized, and the operation precision of the equipment is improved.

Description

Technical Field

[0001] The present invention relates to intelligent error compensation technology, and in particular to a method and system for big data analysis and intelligent compensation of industrial equipment trajectory errors. Background Art

[0002] The accuracy of the motion trajectory of industrial equipment during operation is directly related to product quality and equipment performance. However, due to factors such as sensor errors, actuator inaccuracies, and environmental disturbances, the actual operating trajectory of industrial equipment often exhibits significant deviations. Traditional error compensation methods often rely on static models or simple feedback control, which makes it difficult to dynamically identify error evolution patterns under complex operating conditions, resulting in limited compensation effectiveness.

[0003] With the development of industrial big data and intelligent algorithms, research has attempted to use data-driven methods to analyze equipment operating status and construct error models for correction. However, existing methods often ignore the dynamic transmission characteristics of errors in spatial and temporal dimensions, fail to fully utilize the coupling relationship between multi-source data, and fail to establish a hierarchical compensation structure, resulting in a lack of systematicity and adaptability in the overall compensation strategy.

[0004] At the same time, faced with high-dimensional feature data in complex industrial conditions, efficiently extracting error features and building a simplified and iterative error compensation mechanism remains a major challenge. Therefore, a trajectory error big data analysis and intelligent compensation method for industrial equipment is urgently needed to achieve higher-precision and more adaptable compensation effects. Summary of the Invention

[0005] The embodiments of the present invention provide a method and system for big data analysis and intelligent compensation of industrial equipment trajectory errors, which can solve the problems in the prior art.

[0006] A first aspect of an embodiment of the present invention provides a method for big data analysis and intelligent compensation of industrial equipment trajectory errors, comprising: Collect the operating status parameters of industrial equipment, segment them according to the time series, extract the motion characteristics of each segment of data, generate motion feature fingerprints, compare the motion feature fingerprints with the pre-established feature fingerprint library, and calculate the feature deviation data; The feature deviation data is distributed to multiple agents. Each agent analyzes the regional error characteristics based on the assigned feature deviation data. Adjacent agents exchange error feature information and evaluate the transmission strength of feature deviation to obtain error transmission weights. A probability graph structure is constructed based on the error transmission weights. The mutual information criterion is used to simplify the probability graph structure to obtain an error transmission chain. A hierarchical compensation structure is constructed based on the topological structure of the error transmission chain. Error representative points are set at each layer. The transmission influence coefficients between the error representative points of adjacent layers are calculated to obtain the inter-layer coupling constraints. The compensation coordination coefficients between the error representative points of the same layer are calculated to obtain the intra-layer coordination constraints. Based on the inter-layer coupling constraints and the intra-layer coordination constraints, a hybrid iterative strategy is used to optimize the compensation components and generate a compensation execution sequence. Error compensation of the motion trajectory of industrial equipment is achieved according to the compensation execution sequence.

[0007] In an optional embodiment, Collect the operating status parameters of industrial equipment, segment them according to the time series, extract the motion characteristics of each segment of data, and generate motion feature fingerprints including: Acquiring operating status parameters of industrial equipment, wherein the operating status parameters include motion parameters, working condition parameters, and environmental parameters; Extracting velocity data and acceleration data from the motion parameters; calculating velocity changes and acceleration changes of adjacent data points, marking points where both velocity changes and acceleration changes are greater than a preset velocity value as candidate segmentation points, and determining the segmentation points based on the consistency of the fluctuation trend; dividing the velocity data and acceleration data into multiple data segments based on the segmentation points; Combined with the working condition parameters and environmental parameters, the speed fluctuation value and acceleration fluctuation value of each data segment are calculated, and a fluctuation curve is constructed. Frequency domain feature data is obtained through Fourier transform. Waveform features and phase features are extracted from the frequency domain feature data and combined according to a preset mapping relationship to form a feature vector; Calculate the variance contribution value of each component of the eigenvector, perform dimensionality reduction processing on the eigenvector according to the variance contribution value, obtain the eigencomponents after dimensionality reduction, calculate the weight coefficients of the eigencomponents in combination with the working condition parameters, reorganize the eigencomponents after dimensionality reduction according to the weight coefficients, and generate a motion feature fingerprint.

[0008] In an optional embodiment, Compare the motion feature fingerprint with the pre-established feature fingerprint library and calculate the feature deviation data including: The motion feature fingerprint is divided into feature subsequences according to the sampling time window, the fluctuation trend of adjacent feature subsequences is calculated, the feature subsequences are merged according to the fluctuation trend to obtain waveform segments, and the amplitude sequence and phase sequence of the waveform segments are extracted; Normalizing the amplitude sequence and the phase sequence to obtain waveform features and phase features, respectively, combining the waveform features and the phase features to construct a feature vector, and calculating a weight coefficient based on the feature vector; Extracting fingerprint data from a pre-established feature fingerprint library, performing sequence division and feature extraction on the fingerprint data, constructing a reference feature vector, calculating the matching degree between the feature vector and the reference feature vector, and selecting the fingerprint data with the highest matching degree as the target fingerprint; Calculate the characteristic distance between the characteristic vector of the waveform segment and the reference characteristic vector of the waveform segment corresponding to the target fingerprint, calculate the weighted deviation value according to the characteristic distance and the weight coefficient, and calculate the time series distribution of the weighted deviation value to obtain the change pattern; The divergence trend of the weighted deviation value is determined according to the change rule; when a divergence trend occurs, the divergence rate and the divergence direction are calculated as characteristic deviation data.

[0009] In an optional embodiment, The feature deviation data is distributed to multiple agents. Each agent analyzes the regional error characteristics according to the assigned feature deviation data. Adjacent agents exchange error feature information and evaluate the transmission strength of feature deviation to obtain error transmission weights. A probability graph structure is constructed based on the error transmission weights. The mutual information criterion is used to simplify the probability graph structure to obtain the error transmission chain, which includes: Divide the motion space of the industrial equipment into grid units, each grid unit corresponds to an intelligent agent, calculate the Mahalanobis distance between the feature deviation data point and the center of the grid unit, calculate the allocation weight based on the Mahalanobis distance, and allocate the feature deviation data to the intelligent agent according to the allocation weight; Calculate the mean and standard deviation of the deviation within each agent region, extract the main direction of the deviation, and combine the mean, standard deviation and main direction to construct a regional error feature vector; Adjacent agents exchange regional error feature vectors, calculate feature vector similarity to construct feature similarity matrix, and calculate error gradients between adjacent agents; Combining the feature similarity matrix with the error gradient to obtain a transfer strength matrix, normalizing the transfer strength matrix to obtain an error transfer weight, and constructing an initial probability map based on the error transfer weight; The mutual information value between nodes in the initial probability graph is calculated, and the edges with mutual information values ​​less than a preset threshold are deleted to obtain a simplified probability graph. In the simplified probability graph, the error transfer weight is used as the objective function, and the maximum weight spanning tree algorithm is used to extract the optimal transfer path. The error transfer direction and transfer strength are determined according to the size relationship of the error transfer weights on the path, and an error transfer chain structure with transfer direction and transfer strength is constructed.

[0010] In an optional embodiment, In the simplified probability graph, the error transfer weight is used as the objective function, and the maximum weight spanning tree algorithm is used to extract the optimal transfer path. The error transfer direction and transfer strength are determined according to the size relationship of the error transfer weight on the path. The error transfer chain structure with transfer direction and transfer strength is constructed, including: Obtaining an error transfer weight of each edge in the simplified probability graph structure, and normalizing the error transfer weight to a preset interval based on a maximum weight and a minimum weight to obtain a normalized transfer weight of each edge; Sort the edges in the probability graph in descending order according to the normalized transfer weights, select the edges with the largest weights in turn, determine whether the edges form a loop and whether the error amplitudes of the nodes at both ends of the edges meet the size constraint, and add the edges that meet the constraint conditions to the edge set until the maximum weight spanning tree is constructed; In the maximum weight spanning tree, the local weight gradient is obtained by calculating the average value of the normalized transfer weights between the two end nodes of each edge and its adjacent nodes. The error propagation direction is determined based on the magnitude of the local weight gradients of the two end nodes, and the product of the difference between the local weight gradients and the normalized transfer weight is used as the transfer strength. The current transfer weight and transfer direction of each edge in the maximum weight spanning tree are periodically obtained, and the weight change and direction change are calculated; when the weight change is greater than the weight change threshold or the direction change is greater than the direction change threshold, the path extraction is re-executed for the edges in the changed area, and the local structure of the maximum weight spanning tree is updated to obtain an error transfer chain with dynamic update capability.

[0011] In an optional embodiment, A hierarchical compensation structure is constructed based on the topological structure of the error transmission chain. Error representative points are set at each layer. The transmission influence coefficients between the error representative points of adjacent layers are calculated to obtain the inter-layer coupling constraints. The compensation coordination coefficients between the error representative points of the same layer are calculated to obtain the intra-layer coordination constraints. Based on the inter-layer coupling constraints and the intra-layer coordination constraints, a hybrid iterative strategy is used to optimize the compensation components. The generated compensation execution sequence includes: Analyze the topological characteristics of the error transmission chain, determine the error source node, calculate the shortest transmission path length from each node to the error source node, assign nodes with the same transmission path length to the same level, and build a hierarchical compensation structure; In each layer of the hierarchical compensation structure, the amplitude characteristics and the rate of change characteristics of the error nodes are calculated, the amplitude characteristics and the rate of change characteristics are weightedly combined to obtain a node score, and the node with the highest score and the distance between adjacent nodes greater than a preset distance threshold is selected as the error representative point; For the error representative points of adjacent layers in the layered compensation structure, the projection component and the vertical component of the transfer direction are calculated, and a transfer influence coefficient is constructed based on the projection component and the vertical component. The transfer influence coefficient is corrected in combination with the spatial distance attenuation characteristic to obtain the interlayer coupling constraint; For the error representative points in the same layer of the layered compensation structure, the local variance and global variance of the error distribution are calculated, spatial adaptive weights are constructed based on the local variance and global variance, and the spatial adaptive weights are dynamically adjusted according to the compensation effect to obtain intra-layer coordination constraints; Based on inter-layer coupling constraints and intra-layer coordination constraints, a hybrid iterative strategy of inter-layer top-down alternation and intra-layer parallel optimization is adopted to optimize the compensation components. The iteration step size is dynamically adjusted according to the compensation residual. Historical compensation is introduced to construct an inertia correction term to suppress compensation oscillation until the compensation components converge, thus generating a compensation execution sequence.

[0012] In an optional embodiment, Based on inter-layer coupling constraints and intra-layer coordination constraints, a hybrid iterative strategy of inter-layer top-down alternation and intra-layer parallel optimization is adopted to optimize the compensation component. The iteration step size is dynamically adjusted according to the compensation residual. The historical compensation amount is introduced to construct the inertia correction term to suppress the compensation oscillation until the compensation component converges. The compensation execution sequence generated includes: Based on the inter-layer coupling constraints and intra-layer coordination constraints, iterate from the top layer downward layer by layer, use the upper layer compensation components as the constraints of the lower layer compensation, and use the parallel optimization method to calculate the compensation components of the same layer to obtain the compensation components of the current iteration; Calculating the compensation residual corresponding to the compensation component of the current iteration, comparing the compensation residual with the compensation residual of the previous iteration to obtain a residual change trend, dynamically adjusting the iteration step size based on the residual change trend, and updating the compensation component using the dynamically adjusted iteration step size; Recording the updated compensation component as the historical compensation amount of the current iteration, performing time-series weighting on the historical compensation amounts obtained from multiple consecutive iterations to obtain a compensation trend feature, constructing an inertia correction term based on the compensation trend feature, and combining the inertia correction term with the current compensation component to obtain a corrected compensation component; The change of the revised compensation component relative to the previous iteration is calculated, and when the change is less than a preset change threshold, a compensation execution sequence is generated; otherwise, the revised compensation component is used as the initial compensation component of the next iteration to continue the hybrid iterative optimization.

[0013] A second aspect of an embodiment of the present invention provides an industrial equipment trajectory error big data analysis and intelligent compensation system, comprising: The first unit is used to collect the operating status parameters of the industrial equipment, segment the operating status parameters according to the time series, extract the motion characteristics of each segment of data, generate a motion feature fingerprint, compare the motion feature fingerprint with a pre-established feature fingerprint library, and calculate the feature deviation data; The second unit is used to distribute feature deviation data to multiple agents. Each agent analyzes regional error characteristics based on the assigned feature deviation data. Adjacent agents exchange error feature information and evaluate the transmission strength of feature deviations to obtain error transmission weights. A probability graph structure is constructed based on the error transmission weights. The mutual information criterion is used to simplify the probability graph structure to obtain an error transmission chain. The third unit is used to construct a hierarchical compensation structure based on the topological structure of the error transmission chain. It sets error representative points at each layer, calculates the transmission influence coefficient between the error representative points of adjacent layers to obtain the inter-layer coupling constraint, calculates the compensation coordination coefficient between the error representative points of the same layer to obtain the intra-layer coordination constraint, and optimizes the compensation components using a hybrid iterative strategy based on the inter-layer coupling constraint and the intra-layer coordination constraint to generate a compensation execution sequence. The fourth unit is configured to implement error compensation of the motion trajectory of the industrial equipment according to the compensation execution sequence. A third aspect of the embodiment of the present invention provides an electronic device, including: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0014] According to a fourth aspect of an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0015] In this embodiment, motion feature fingerprint matching technology is used to process the operating status parameters of industrial equipment in a time-series and segmented manner, extract motion features and compare them with a pre-built feature library, which can quickly and accurately identify feature deviations in the motion trajectory of the equipment, and provide an accurate data basis for subsequent compensation. Through multi-agent collaborative analysis and probabilistic graph structure construction, the present invention achieves refined analysis of regional error features and accurate modeling of error transmission relationships, overcomes the limitations of traditional methods that are difficult to handle complex error transmission chains, and improves the systematic and comprehensive nature of error identification. Based on a hierarchical compensation structure and a hybrid iterative optimization strategy, the present invention establishes a compensation mechanism that takes into account both inter-layer coupling and intra-layer coordination, achieves precise and dynamic error compensation, effectively improves the motion accuracy and stability of industrial equipment, and is suitable for the error compensation needs of various types of high-precision industrial equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1Schematic diagram of the process of big data analysis and intelligent compensation method for industrial equipment trajectory errors according to an embodiment of the present invention; Figure 2 Schematic diagram of the characteristic subsequence fluctuation trend analysis and waveform segment merging process according to an embodiment of the present invention; Figure 3 This is a heat map of the effect of dynamic iterative step size adjustment in an embodiment of the present invention. DETAILED DESCRIPTION

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0018] The following specific embodiments are used to describe the technical solution of the present invention in detail. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0019] Figure 1 FIG. 1 is a flow chart of a method for analyzing big data and intelligently compensating industrial equipment trajectory errors according to an embodiment of the present invention. Figure 1 As shown, the method includes: Collect the operating status parameters of industrial equipment, segment them according to the time series, extract the motion characteristics of each segment of data, generate motion feature fingerprints, compare the motion feature fingerprints with the pre-established feature fingerprint library, and calculate the feature deviation data; The feature deviation data is distributed to multiple agents. Each agent analyzes the regional error characteristics based on the assigned feature deviation data. Adjacent agents exchange error feature information and evaluate the transmission strength of feature deviation to obtain error transmission weights. A probability graph structure is constructed based on the error transmission weights. The mutual information criterion is used to simplify the probability graph structure to obtain an error transmission chain. A hierarchical compensation structure is constructed based on the topological structure of the error transmission chain. Error representative points are set at each layer. The transmission influence coefficients between the error representative points of adjacent layers are calculated to obtain the inter-layer coupling constraints. The compensation coordination coefficients between the error representative points of the same layer are calculated to obtain the intra-layer coordination constraints. Based on the inter-layer coupling constraints and the intra-layer coordination constraints, a hybrid iterative strategy is used to optimize the compensation components and generate a compensation execution sequence. Error compensation of the motion trajectory of industrial equipment is achieved according to the compensation execution sequence.

[0020] In an optional embodiment, Collect the operating status parameters of industrial equipment, segment them according to the time series, extract the motion characteristics of each segment of data, and generate motion feature fingerprints including: Acquiring operating status parameters of industrial equipment, wherein the operating status parameters include motion parameters, working condition parameters, and environmental parameters; Extracting velocity data and acceleration data from the motion parameters; calculating velocity changes and acceleration changes of adjacent data points, marking points where both velocity changes and acceleration changes are greater than a preset velocity value as candidate segmentation points, and determining the segmentation points based on the consistency of the fluctuation trend; dividing the velocity data and acceleration data into multiple data segments based on the segmentation points; Combined with the working condition parameters and environmental parameters, the speed fluctuation value and acceleration fluctuation value of each data segment are calculated, and a fluctuation curve is constructed. Frequency domain feature data is obtained through Fourier transform. Waveform features and phase features are extracted from the frequency domain feature data and combined according to a preset mapping relationship to form a feature vector; Calculate the variance contribution value of each component of the eigenvector, perform dimensionality reduction processing on the eigenvector according to the variance contribution value, obtain the eigencomponents after dimensionality reduction, calculate the weight coefficients of the eigencomponents in combination with the working condition parameters, reorganize the eigencomponents after dimensionality reduction according to the weight coefficients, and generate a motion feature fingerprint.

[0021] Exemplarily, the operating status parameters of the industrial equipment are first obtained, including motion parameters, working condition parameters and environmental parameters. Taking a 3D printer as an example, the motion parameters include the position, speed and acceleration data of the print head in the X, Y and Z axes; the working condition parameters include printing temperature, printing speed setting value, extrusion amount, printing layer thickness, etc.; environmental parameters include ambient temperature, humidity, vibration, etc. The acquisition frequency is 100Hz, that is, 100 data points are collected per second to ensure the continuity and integrity of the data. From the collected motion parameters, velocity data and acceleration data are extracted. By calculating adjacent data points, the velocity change and acceleration change are obtained. Set the preset velocity threshold to 0.5mm / s and the acceleration threshold to 0.8mm / s 2 When the velocity change and acceleration change of adjacent data points are both greater than these preset values, the point is marked as a candidate segmentation point.

[0022] Perform a fluctuation trend consistency analysis on the marked candidate segmentation points. Fluctuation trend consistency refers to the changing trend of the data before and after the candidate segmentation point. This is achieved by calculating the rate of change of velocity and acceleration for 10 data points before and after the candidate segmentation point. If the sign of the rate of change flips and persists for more than 5 data points, the candidate point is confirmed as a valid segmentation point. For example, during the printing process of a 3D printer, when the print head switches from linear motion to curved motion, the velocity and acceleration changes will fluctuate significantly, resulting in a segmentation point.

[0023] According to the determined segmentation points, the velocity data and acceleration data are divided into multiple data segments. For a 3D printer to print a complex model, hundreds of data segments may be generated. Each data segment represents the operating status of the device in a specific motion mode. Combining the operating parameters and environmental parameters, the velocity fluctuation value and acceleration fluctuation value of each data segment are calculated. The velocity fluctuation value is the standard deviation of the velocity within the data segment, and the acceleration fluctuation value is the standard deviation of the acceleration within the data segment. In actual applications, when the printing temperature is 210°C and the ambient temperature is 25°C, the velocity fluctuation value of the X-axis in the linear motion segment is typically 0.3mm / s, and the acceleration fluctuation value is 0.5mm / s 2 In the curved motion section, the velocity fluctuation value can reach 0.8mm / s, and the acceleration fluctuation value can reach 1.2mm / s 2 .

[0024] A fluctuation curve is constructed based on the calculated fluctuation value, and the fluctuation curve is converted into frequency domain feature data through Fourier transform. In frequency domain analysis, waveform features and phase features are extracted. Waveform features include main frequency, frequency amplitude, harmonic ratio, etc.; phase features include phase angle, phase difference, etc. For example, when a 3D printer is operating normally, the main frequency of the X-axis movement is usually in the range of 2-5Hz, and the amplitude is between 0.1-0.3mm / s; when an abnormality occurs, abnormal frequency components may appear in the range of 10-15Hz, and the amplitude may increase to 0.5-0.8mm / s.

[0025] According to the preset mapping relationship, the waveform features and phase features are combined to form a feature vector. The preset mapping relationship refers to the weighted combination of different features according to their importance. In the 3D printer application, the weight of the main frequency is set to 0.4, the amplitude weight is set to 0.3, the harmonic ratio weight is set to 0.2, and the phase angle weight is set to 0.1. The dimension of the resulting feature vector may be very high, usually containing 30-50 feature components. The feature vector is subjected to dimensionality reduction processing, and the variance contribution value of each feature component is first calculated. The variance contribution value indicates the degree to which the component explains the overall variation. In practical applications, the variance contribution values ​​of the first 10 feature components usually account for more than 85% of the total variance. According to the calculation results, the feature components with a cumulative variance contribution value of 90% are retained, and the remaining components are discarded to achieve dimensionality reduction of the feature vector.

[0026] Calculate the weight coefficients of characteristic components based on the operating parameters. The importance of characteristic components varies under different operating conditions. For example, when the printing speed is 60 mm / s, the weight of the speed-related characteristic components should be increased; when the printing temperature is relatively high, the weight of the acceleration-related characteristic components should be increased. In practical applications, the weight coefficient can be set in the range of 0.6-1.4, and dynamically adjusted based on the degree of deviation of the operating parameters.

[0027] The reduced feature components are reorganized according to weight coefficients to generate a motion fingerprint. This fingerprint is a multidimensional vector, typically 8-12 dimensions, with each component representing an aspect of the device's motion characteristics. For 3D printers, this fingerprint can reflect characteristics such as the smoothness of the print head's motion, response speed, and trajectory accuracy. The resulting fingerprint can be used for anomaly detection, quality prediction, and trajectory error compensation.

[0028] In this embodiment, by extracting motion feature fingerprints, the characteristics and patterns of device trajectory errors can be accurately identified. The solution adopts a combination of time series segmentation processing and frequency domain feature extraction, which greatly improves the accuracy and stability of feature extraction. By analyzing the consistency of the fluctuation trend of velocity and acceleration data, accurate segmentation of the motion state is achieved, which solves the problem of inaccurate segmentation of traditional methods under complex working conditions. The introduction of working condition parameters and environmental parameters for feature weighting makes feature extraction more environmentally adaptable. The use of variance contribution value for dimensionality reduction reduces the computational complexity and improves the efficiency of the algorithm. This method can monitor the operating status of the equipment in real time, quickly identify abnormal trajectories, and perform intelligent compensation adjustments, significantly improving product accuracy and consistency.

[0029] In an optional embodiment, Compare the motion feature fingerprint with the pre-established feature fingerprint library and calculate the feature deviation data including: The motion feature fingerprint is divided into feature subsequences according to the sampling time window, the fluctuation trend of adjacent feature subsequences is calculated, the feature subsequences are merged according to the fluctuation trend to obtain waveform segments, and the amplitude sequence and phase sequence of the waveform segments are extracted; Normalizing the amplitude sequence and the phase sequence to obtain waveform features and phase features, respectively, combining the waveform features and the phase features to construct a feature vector, and calculating a weight coefficient based on the feature vector; Extracting fingerprint data from a pre-established feature fingerprint library, performing sequence division and feature extraction on the fingerprint data, constructing a reference feature vector, calculating the matching degree between the feature vector and the reference feature vector, and selecting the fingerprint data with the highest matching degree as the target fingerprint; Calculate the characteristic distance between the characteristic vector of the waveform segment and the reference characteristic vector of the waveform segment corresponding to the target fingerprint, calculate the weighted deviation value according to the characteristic distance and the weight coefficient, and calculate the time series distribution of the weighted deviation value to obtain the change pattern; The divergence trend of the weighted deviation value is determined according to the change rule; when a divergence trend occurs, the divergence rate and the divergence direction are calculated as characteristic deviation data.

[0030] In this embodiment, after acquiring the motion feature fingerprint, it is necessary to divide it into feature subsequences according to the sampling time window. The sampling time window is typically set to 5 seconds, that is, the continuously collected motion feature fingerprint data is divided into a feature subsequence every 5 seconds. For a processing task lasting 30 minutes, approximately 360 feature subsequences can be obtained. Each feature subsequence contains the complete motion feature information within that time window.

[0031] Calculate the fluctuation trend of adjacent feature subsequences. This process is achieved by analyzing the rate of change of the eigenvalues ​​of each dimension of adjacent feature subsequences. The fluctuation trend refers to the direction and magnitude of the change in the eigenvalues ​​over time. Specifically, the difference between each feature dimension in adjacent subsequences is calculated and smoothed to obtain the fluctuation trend data. When industrial equipment transitions from low-speed to high-speed motion, the rate of change of the speed-related feature dimensions of adjacent feature subsequences can reach 20%-30%. During stable motion, the rate of change is typically less than 5%.

[0032] Waveform segments are created by merging feature subsequences based on their fluctuation trends. The merging criterion is consistency of fluctuation trends. This is determined by setting a threshold. When the fluctuation trends of adjacent feature subsequences are less than this threshold, they are considered to belong to the same waveform segment. The fluctuation trend threshold is set to 8%, meaning that when the fluctuation rate of adjacent feature subsequences is less than 8%, they are merged into a single waveform segment. In this way, a 30-minute machining task can be merged into 20-30 waveform segments, each representing a relatively stable motion state.

[0033] Extract the amplitude sequence and phase sequence from the merged waveform segments. The amplitude sequence refers to the numerical size of each characteristic dimension in the waveform segment, and the phase sequence refers to the relative change time series relationship of each characteristic dimension. The amplitude sequence can reflect the intensity of the equipment's movement in different directions, while the phase sequence reflects the coordination and sequence of movement in different directions. The amplitude sequence and phase sequence are standardized separately to obtain waveform characteristics and phase characteristics. Standardization is the process of converting data of different dimensions into a unified numerical range. A common method is to subtract the mean and divide by the standard deviation. The numerical range of the standardized waveform characteristics and phase characteristics is usually between -3 and 3, which is convenient for subsequent comparison and analysis. Standardization can eliminate the absolute amplitude differences between different processing tasks and highlight the relative characteristics of the motion pattern.

[0034] Waveform and phase features are combined to construct a feature vector. This combination involves concatenating the standardized waveform and phase features in a predefined order to form a comprehensive feature vector. This feature vector typically contains 20-30 dimensions, with the first half representing waveform features and the second half representing phase features. This constructed feature vector comprehensively characterizes the operating status of the device during a specific motion phase.

[0035] The weight coefficient is calculated based on the eigenvector. The weight coefficient reflects the importance of each dimension of the eigenvector under the current working conditions. The calculation method is based on the fluctuation and differentiation of the eigenvector, with eigenvectors with greater fluctuation and higher differentiation being given higher weights. When machining complex contours, the weight of eigenvectors related to directional changes is increased; when machining fine structures, the weight of eigenvectors related to speed stability is increased. The weight coefficient typically ranges from 0.5 to 2.0.

[0036] Fingerprint data is extracted from a pre-established feature fingerprint library. This library contains a large amount of standard fingerprints generated from historical operating data, with each fingerprint corresponding to a typical operating state. The library may contain standard fingerprint data corresponding to various processing materials, processing speeds, and processing structure types, typically containing hundreds to thousands of standard fingerprint entries. The fingerprint data is sequenced and feature extracted to construct a reference feature vector. This step is consistent with the previous processing method for motion feature fingerprints, ensuring consistency in the processing of current and reference data, facilitating accurate comparison. The standard fingerprints extracted from the fingerprint library undergo the same sequence division, waveform segment merging, feature extraction, and normalization processes to form a reference feature vector.

[0037] Calculate the degree of match between the feature vector and the reference feature vector. The cosine similarity method is used to calculate the degree of match, that is, the cosine value of the angle between the two vectors is calculated. The closer the cosine value is to 1, the higher the degree of match. The threshold for a good match is usually set to 0.85, that is, when the cosine similarity is greater than 0.85, the two feature vectors are considered to have a high degree of similarity. The fingerprint data with the highest degree of match is selected as the target fingerprint. If the matching degree of multiple fingerprint data exceeds the threshold, the one with the highest degree of match is selected as the target fingerprint. The matching degree is usually between 0.80 and 0.95. A lower matching degree may mean that there is a certain difference between the current operating status and the historical data, which requires further analysis.

[0038] Calculate the characteristic distance between the waveform segment's feature vector and the reference feature vector of the corresponding waveform segment of the target fingerprint. The characteristic distance is calculated using the Euclidean distance, which is the square root of the sum of the squared differences in each dimension. A smaller characteristic distance indicates that the current operating state is closer to the standard state. The characteristic distance for normal operation is typically less than 0.5. A characteristic distance exceeding 1.0 may indicate an abnormal state.

[0039] The weighted deviation value is calculated based on the feature distance and the weight coefficient. The weighted deviation value is the weighted result obtained by multiplying the feature distance by the weight coefficient. It reflects the actual deviation degree after considering the importance of the current working condition. When machining fine structures, even small feature distances can produce large weighted deviation values ​​due to the high weight, indicating the need for higher precision control.

[0040] The time series distribution of weighted deviation values ​​is statistically analyzed to determine the pattern of change. Time series distribution refers to the change in weighted deviation values ​​over time. By analyzing the weighted deviation values ​​over multiple consecutive time windows, the trend of deviation change can be identified. The pattern of deviation value change can exhibit various patterns, including stable, fluctuating, increasing, or cyclical. Based on this pattern of change, the divergence trend of the weighted deviation values ​​is determined. A divergence trend refers to a continuous increase in the deviation value at an accelerating rate, indicating that the equipment's operating status is deviating from the normal range. The criterion for this is a monotonically increasing deviation value over multiple consecutive time windows with an increasing rate of growth. When machine tool bearings wear, the weighted deviation values ​​may exhibit a divergent trend, with slow growth initially and accelerated growth later.

[0041] When a divergence trend emerges, the divergence rate and direction are calculated as characteristic deviation data. The divergence rate represents the acceleration of the deviation value, while the divergence direction represents the direction of the main component of the deviation in each dimension of the characteristic vector. When the screw becomes loose, the divergence direction is mainly reflected in the characteristic dimension of the relevant axis. The divergence rate may reach 0.05-0.1 / hour, indicating that the problem is accelerating and requires timely intervention. By identifying the divergence trend and calculating the divergence rate and direction, it is possible to predict potential trajectory error issues in the equipment and provide a basis for subsequent compensation adjustments.

[0042] In this embodiment, by systematically comparing the motion feature fingerprint with a pre-established feature fingerprint library, accurate identification and analysis of the trajectory error of industrial equipment is achieved. The time window division and fluctuation trend merging method are adopted to effectively solve the accuracy problem of feature extraction in different motion stages. Through standardization processing and feature vector construction, the technical difficulty of data incomparability under different working conditions is overcome. The introduction of the weight coefficient calculation mechanism enables the system to adaptively adjust the importance of each feature dimension according to the current working conditions, thereby improving the pertinence of the analysis. Divergence trend judgment and divergence rate calculation realize early warning of the development of trajectory error, and transform equipment maintenance from passive response to active prevention. This method can identify minor motion anomalies, realize early prediction of trajectory error change trends, and significantly reduce processing defects caused by trajectory errors. At the same time, this method reduces the dependence on the experience of professionals and realizes the intelligence and standardization of trajectory error analysis.

[0043] Figure 2 FIG. 1 is a schematic diagram of the characteristic subsequence fluctuation trend analysis and waveform segment merging process according to an embodiment of the present invention. Figure 2As shown in the figure, the horizontal axis represents the time window number (a total of 300 windows, approximately 25 minutes), and the vertical axis represents the fluctuation rate. This technical solution (solid line) more accurately captures changes in motion state, particularly at the low-to-high-speed transition points (fluctuation rate of 22.0%) and the high-to-low-speed transition points (fluctuation rate of 12.0%). The horizontal dashed line represents the 8% merging threshold. When the fluctuation rate of adjacent feature subsequences is less than this threshold, they are merged into the same waveform segment. Five waveform segments are identified in the figure, representing different motion states. Compared with traditional fixed-threshold merging methods (short-dashed line) and sliding window methods (dotted-dashed line), this technical solution demonstrates higher sensitivity at inflection points in the changing trend. It can more accurately identify feature changes during the transition from low-speed to high-speed motion (fluctuation rate of up to 22.0%) and during stable operation (fluctuations of approximately 15.0% and 3.5%). This enables more precise segmentation of waveforms, laying the foundation for subsequent feature extraction and anomaly detection.

[0044] In an optional embodiment, The feature deviation data is distributed to multiple agents. Each agent analyzes the regional error characteristics according to the assigned feature deviation data. Adjacent agents exchange error feature information and evaluate the transmission strength of feature deviation to obtain error transmission weights. A probability graph structure is constructed based on the error transmission weights. The mutual information criterion is used to simplify the probability graph structure to obtain the error transmission chain, which includes: Divide the motion space of the industrial equipment into grid units, each grid unit corresponds to an intelligent agent, calculate the Mahalanobis distance between the feature deviation data point and the center of the grid unit, calculate the allocation weight based on the Mahalanobis distance, and allocate the feature deviation data to the intelligent agent according to the allocation weight; Calculate the mean and standard deviation of the deviation within each agent region, extract the main direction of the deviation, and combine the mean, standard deviation and main direction to construct a regional error feature vector; Adjacent agents exchange regional error feature vectors, calculate feature vector similarity to construct feature similarity matrix, and calculate error gradients between adjacent agents; Combining the feature similarity matrix with the error gradient to obtain a transfer strength matrix, normalizing the transfer strength matrix to obtain an error transfer weight, and constructing an initial probability map based on the error transfer weight; The mutual information value between nodes in the initial probability graph is calculated, and the edges with mutual information values ​​less than a preset threshold are deleted to obtain a simplified probability graph. In the simplified probability graph, the error transfer weight is used as the objective function, and the maximum weight spanning tree algorithm is used to extract the optimal transfer path. The error transfer direction and transfer strength are determined according to the size relationship of the error transfer weights on the path, and an error transfer chain structure with transfer direction and transfer strength is constructed.

[0045] For example, after acquiring characteristic deviation data, the motion space of the industrial equipment is divided into grid cells. The granularity of the grid division depends on the equipment's motion accuracy requirements and the size of its workspace. Generally, the space can be divided into a 10×10×5 three-dimensional grid, corresponding to the working range of the X, Y, and Z axes of motion. Each grid cell corresponds to an intelligent agent, which is responsible for analyzing the error characteristics within that area. The grid cell size is typically 10-30 mm to ensure sufficient spatial resolution.

[0046] Calculate the Mahalanobis distance between the characteristic deviation data point and the grid cell center. The Mahalanobis distance takes into account the covariance structure of the data and can more accurately represent the proximity of the data point to the grid center. It is calculated by multiplying the difference vector between the characteristic deviation data point and the grid center point by the inverse of the covariance matrix, and then multiplying it by the transpose of the difference vector. When the difference vector is zero, the Mahalanobis distance is zero; the larger the difference vector and the further it deviates from the main eigenvector of the covariance matrix, the larger the Mahalanobis distance. In practical applications, the calculated Mahalanobis distance is typically between 0 and 10.

[0047] The weights are calculated based on the Mahalanobis distance. The weights are assigned using an exponential decay function, where the weight is equal to the negative power of the Mahalanobis distance divided by a preset bandwidth parameter. The bandwidth parameter controls the rate at which the weight decays with distance and is typically set to 2.0-3.0. Closer distances result in greater weights, while greater distances result in smaller weights. This ensures that each feature deviation data point contributes to all grid cells, but contributes more to neighboring grid cells.

[0048] Feature deviation data is assigned to agents based on the weights. The assignment process distributes the information of feature deviation data points to each agent in proportion to their weights. For each feature deviation data point, the Mahalanobis distance between it and the center of all grid cells and the corresponding weight are calculated. The deviation information of this data point is then distributed to each agent in proportion to the weights. This soft assignment method can handle data points located at grid boundaries and avoids the discontinuities that can result from hard assignment.

[0049] Calculate the mean and standard deviation of the deviation within each agent's region. The mean deviation is the weighted average of all assigned feature deviation data within the region, while the standard deviation is the dispersion of the deviation data around the mean. The assignment weight is used as a weighting factor to ensure that data points closer to the center of the grid have greater influence. In industrial equipment movement, the mean deviation reflects the systematic error within the region, while the standard deviation reflects the magnitude of random error.

[0050] Extract the main direction of the deviation. The main direction of the deviation refers to the main direction of change of the characteristic deviation data in the region. It is determined by calculating the covariance matrix of the characteristic deviation data and solving the eigenvector corresponding to its maximum eigenvalue. The main direction of the deviation reflects the main trend of the error in the region and is of great significance for understanding the error transmission path. In practical applications, the main direction of the deviation is usually represented by a three-dimensional unit vector, indicating the main distribution direction of the error in space. The mean deviation, standard deviation and main direction are combined to construct the regional error feature vector. The regional error feature vector is a multidimensional vector that comprehensively characterizes the regional error characteristics and contains information such as the mean deviation, standard deviation and main direction. The dimension of the feature vector is usually 5-7 dimensions, which can comprehensively describe the size, distribution and directional characteristics of the error in the region.

[0051] Neighboring agents exchange regional error feature vectors. Communication between agents is based on grid-level neighbor relationships. Each agent may have up to 26 neighboring agents. During the exchange process, an agent sends its own regional error feature vector to a neighboring agent and simultaneously receives feature vectors from its neighbors. Through feature vector exchange, the agent obtains information about the error characteristics of the surrounding area, providing a foundation for subsequent analysis of error transmission.

[0052] Calculate eigenvector similarity to construct a feature similarity matrix. Eigenvector similarity is calculated using cosine similarity, which is the dot product of two eigenvectors divided by the product of their respective moduli. Similarity values ​​range from -1 to 1, with values ​​closer to 1 indicating more similar error characteristics between the two regions. The feature similarity matrix is ​​a symmetric matrix whose elements represent the degree of feature similarity between the corresponding agents. Calculate the error gradient between adjacent agents. The error gradient is the rate of change of the error magnitude between two adjacent regions. It is calculated as the difference in the mean deviations of the two regions divided by the distance between the two region centers. The error gradient reflects the spatial trend of the error, with the gradient pointing in the direction of increasing error. In practical applications, the error gradient is typically represented by a vector, containing both magnitude and direction information. Combine the feature similarity matrix with the error gradient to obtain the transfer strength matrix. The transfer strength is calculated by taking the scalar product of the feature similarity and the error gradient as the transfer strength. When the error characteristics of two regions are similar and a significant error gradient exists, the transfer strength is high, indicating that error propagation is likely along that direction. When the characteristics are dissimilar or the gradient is small, the transfer strength is low. The transfer strength matrix describes the possible paths and strengths of error propagation in space.

[0053] The error propagation weights are obtained by normalizing the transfer strength matrix. Normalization involves dividing the elements of the transfer strength matrix by the sum of the matrix elements, so that the sum of all elements equals 1. The normalized matrix elements are the error propagation weights, which reflect the relative importance of each propagation path. A larger error propagation weight indicates a higher probability of error propagation along that path.

[0054] An initial probability graph is constructed based on the error propagation weights. The initial probability graph is a weighted undirected graph in which nodes represent agents, edges represent connections between agents, and edge weights are the corresponding error propagation weights. While the initial probability graph describes all possible error propagation paths, it contains many weak connections and requires further simplification. Mutual information is calculated between nodes in the initial probability graph. Mutual information measures the interdependence between two random variables and is calculated as the joint entropy of the two nodes minus the sum of their individual entropies. A larger mutual information value indicates a stronger dependency between the two nodes; a smaller mutual information value indicates a weaker relationship. In practical applications, mutual information is calculated based on historical node error data and obtained through statistical analysis. Edges with mutual information values ​​below a preset threshold are removed to obtain a simplified probability graph. The preset threshold is typically set to the median or a specific percentile of the mutual information distribution, such as the 70th percentile of all mutual information values. Removing edges with low mutual information values ​​and retaining those with high values ​​reduces the graph complexity and highlights the main error propagation paths. The simplified probability graph contains the most important error propagation relationships, making it easier to analyze and understand.

[0055] In the simplified probability graph, the maximum weight spanning tree algorithm is used to extract the optimal error propagation path, using the error propagation weight as the objective function. The maximum weight spanning tree algorithm selects a spanning tree from the graph such that the sum of the weights of all edges in the tree is maximized. The algorithm starts with the edge with the highest weight and gradually adds edges with the next highest weight until a tree is formed that encompasses all nodes while avoiding loops. The maximum weight spanning tree contains the most likely error propagation paths, providing a skeletal structure for error propagation analysis.

[0056] The error propagation direction and strength are determined based on the error propagation weights along the path. The propagation direction points from nodes with smaller error propagation weights to nodes with larger weights, indicating that errors may propagate from areas with smaller weights to areas with larger weights. The propagation strength is represented by the error propagation weight of the corresponding edge; larger weights indicate greater propagation strength. By analyzing the propagation direction and strength, the source of the error and the primary propagation path can be identified, providing a basis for subsequent error compensation. An error propagation chain structure with propagation direction and strength is constructed. The error propagation chain is a directed, weighted tree structure, where nodes represent agents, edges represent error propagation paths, edge directions indicate propagation directions, and edge weights indicate propagation strength. The error propagation chain intuitively illustrates the propagation patterns of errors in industrial equipment, helping to understand the generation and propagation mechanisms of errors and laying the foundation for accurate error compensation.

[0057] In this embodiment, a multi-agent collaborative analysis mechanism is used to accurately identify and evaluate the spatial distribution characteristics and propagation patterns of industrial equipment trajectory errors. Existing technologies primarily use a single global error model or simple region partitioning method to analyze trajectory errors, which makes it difficult to accurately characterize the local characteristics and propagation relationships of errors in complex spaces, resulting in insufficient error compensation accuracy. This solution, using a soft assignment mechanism based on Mahalanobis distance, overcomes the limitations of traditional hard boundary partitioning, enabling smooth and transitional allocation of feature deviation data to multiple agents, effectively avoiding discontinuities caused by boundary effects. The inter-agent feature vector exchange and similarity analysis mechanism, combined with error gradient calculation, innovatively constructs a propagation intensity matrix, achieving a probabilistic description of error propagation paths. The mutual information criterion is introduced to simplify the probability graph, retaining key propagation paths and significantly reducing computational complexity. The maximum weight spanning tree algorithm is used to extract the optimal propagation path, accurately identifying the error source and propagation direction, providing a theoretical basis for precise error compensation. This solution not only improves the accuracy of trajectory error analysis but also significantly reduces the resource consumption of compensation calculations, enabling high-precision motion control of complex industrial equipment and significantly improving processing quality and production efficiency.

[0058] In an optional embodiment, In the simplified probability graph, the error transfer weight is used as the objective function, and the maximum weight spanning tree algorithm is used to extract the optimal transfer path. The error transfer direction and transfer strength are determined according to the size relationship of the error transfer weight on the path. The error transfer chain structure with transfer direction and transfer strength is constructed, including: Obtaining an error transfer weight of each edge in the simplified probability graph structure, and normalizing the error transfer weight to a preset interval based on a maximum weight and a minimum weight to obtain a normalized transfer weight of each edge; Sort the edges in the probability graph in descending order according to the normalized transfer weights, select the edges with the largest weights in turn, determine whether the edges form a loop and whether the error amplitudes of the nodes at both ends of the edges meet the size constraint, and add the edges that meet the constraint conditions to the edge set until the maximum weight spanning tree is constructed; In the maximum weight spanning tree, the local weight gradient is obtained by calculating the average value of the normalized transfer weights between the two end nodes of each edge and its adjacent nodes. The error propagation direction is determined based on the magnitude of the local weight gradients of the two end nodes, and the product of the difference between the local weight gradients and the normalized transfer weight is used as the transfer strength. The current transfer weight and transfer direction of each edge in the maximum weight spanning tree are periodically obtained, and the weight change and direction change are calculated; when the weight change is greater than the weight change threshold or the direction change is greater than the direction change threshold, the path extraction is re-executed for the edges in the changed area, and the local structure of the maximum weight spanning tree is updated to obtain an error transfer chain with dynamic update capability.

[0059] In this embodiment, the error propagation weight of each edge in the simplified probabilistic graph structure is first obtained. The error propagation weight reflects the probability of error propagation between two regions. The weight value is typically between 0 and 1, but the distribution may be uneven. For example, in a probabilistic graph containing 200 nodes and approximately 800 edges, the error propagation weight may be distributed between 0.05 and 0.95, with the majority of edge weights concentrated between 0.3 and 0.7.

[0060] Based on the maximum and minimum weights, the error propagation weights are normalized to a preset interval to obtain the normalized propagation weights for each edge. Normalization linearly maps the original weights to a preset interval, typically between 0.1 and 1.0. Normalization subtracts the minimum weight from the original weight, then divides it by the difference between the maximum and minimum weights, multiplies it by the range of the preset interval, and finally adds the minimum value of the preset interval. Through normalization, error propagation weights across different regions and time periods can be compared and analyzed on a unified scale, improving the stability and interpretability of the algorithm.

[0061] The edges in the probability graph are sorted in descending order based on their normalized transfer weights. This sorting process arranges all edges from highest to lowest normalized transfer weights, forming an ordered list of edges. This sorting facilitates the subsequent execution of the greedy algorithm, ensuring that edges with higher weights are prioritized. In industrial equipment trajectory error analysis, edges with higher weights typically correspond to paths with more pronounced error propagation, which is crucial for understanding the error propagation mechanism.

[0062] The edges with the largest weight are selected in sequence to determine whether adding them forms a loop and whether the error amplitudes of the nodes at both ends of the edge meet the magnitude constraint. Loop determination ensures that the final structure is a tree without loops. This determination is done by checking whether the two endpoints of the edge are already in the same connected component. If so, adding the edge will form a loop. The error amplitude magnitude constraint ensures the rationality of the error propagation direction. The constraint condition is that the error amplitude of the node at one end of the edge must be smaller than the error amplitude of the node at the other end, or the difference must be within an allowable range. The error amplitude refers to the error size of the area represented by the node and is usually expressed as the root mean square error.

[0063] Edges that satisfy the constraints are added to the edge set until a maximum-weight spanning tree is constructed. The edge set is initially empty, and as the algorithm executes, additional edges that satisfy the constraints are added. When the number of edges in the edge set reaches the number of nodes minus one, a tree containing all nodes has been constructed, known as the maximum-weight spanning tree. The maximum-weight spanning tree contains the most likely paths for error propagation, providing a skeletal structure for error propagation analysis. In industrial equipment trajectory error analysis, a maximum-weight spanning tree containing 200 nodes has 199 edges, representing the most important error propagation paths.

[0064] The local weight gradient is calculated by averaging the normalized transfer weights between the two end nodes of each edge and its adjacent nodes in the maximum weight spanning tree. This local weight gradient reflects the change in the weight of a node within its local region. It is calculated by averaging the normalized transfer weights between a node and all of its adjacent nodes. Each node has a local weight gradient value; a larger value indicates a stronger transfer effect in the local region. In industrial equipment trajectory error analysis, local weight gradients typically range from 0.2 to 0.8, reflecting the strength of the error transfer effect of different regions.

[0065] The error propagation direction is determined based on the magnitude of the local weight gradients at the two end nodes. The propagation direction is from the node with the smaller local weight gradient to the node with the larger local weight gradient. This definition is based on the physical law that errors typically propagate from low-gradient regions to high-gradient regions. In industrial equipment trajectory error analysis, the propagation direction is typically from the fixed end of the equipment to the moving end, reflecting the process of error accumulation. The product of the difference in local weight gradients and the normalized propagation weight is used as the propagation strength. The propagation strength reflects the strength of error propagation along that direction. It is calculated by multiplying the difference in local weight gradients between the two end nodes of an edge by the normalized propagation weight of that edge. A higher propagation strength indicates a higher probability of error propagation along that path, and a greater impact on the overall accuracy of the equipment. In industrial equipment trajectory error analysis, the propagation strength typically ranges from 0.05 to 0.5, and the difference in propagation strength across different paths reflects the unevenness of error propagation.

[0066] Periodically obtain the current transfer weight and direction of each edge in the maximum weight spanning tree. Periodic acquisition recalculates the transfer weight and direction of each edge at regular intervals (such as 1 or 5 minutes) during device operation. This periodic acquisition monitors the dynamic changes in error propagation patterns and provides a basis for timely adjustment of compensation strategies. In industrial equipment trajectory error analysis, transfer weights and directions may change with factors such as device operating status, workload, and ambient temperature.

[0067] Calculate the weight change and direction change. The weight change is the absolute value of the difference between the current transfer weight and the previous cycle's transfer weight, while the direction change is the angle between the current transfer direction and the previous cycle's transfer direction. This calculation is used to determine whether the error propagation pattern has significantly changed. In industrial equipment trajectory error analysis, weight change is typically expressed as a relative rate of change, such as 10% or 20%, while direction change is typically expressed as an angle, such as 15 degrees or 30 degrees.

[0068] When the weight change exceeds the weight change threshold or the direction change exceeds the direction change threshold, path extraction is re-executed for the edges in the changed region, and the local structure of the maximum weight spanning tree is updated. The weight change threshold and direction change threshold are preset judgment criteria used to determine when the error propagation chain needs to be updated. Re-executing path extraction for the edges in the changed region means re-applying the maximum weight spanning tree algorithm only to areas with significant changes, rather than recalculating the entire graph, thereby reducing computational complexity. In industrial equipment trajectory error analysis, the weight change threshold is typically set to 15%, and the direction change threshold is typically set to 25 degrees.

[0069] By updating the local structure of the maximum-weight spanning tree, a dynamically updated error propagation chain is generated. This local structural update replaces only the edges in regions with significant changes, leaving all other regions unchanged. By using local updates rather than global reconstruction, computational resources can be significantly reduced while maintaining accuracy. This dynamically updated error propagation chain can adapt to changes in the device's operating state and reflect the dynamic characteristics of the error propagation pattern in real time.

[0070] In this embodiment, an error propagation chain structure constructed based on a maximum weighted spanning tree algorithm enables precise characterization and analysis of the error propagation patterns of industrial equipment trajectories. Existing techniques primarily use static error models or simple accumulation methods to analyze trajectory error propagation, which struggles to accurately capture the dynamic characteristics and directionality of error propagation, resulting in limited compensation effectiveness. This solution innovatively introduces a normalized propagation weight mechanism to address the incomparable error propagation strengths across different regions, making weight assessment more objective and accurate. An edge selection strategy combining loop judgment with error amplitude constraints ensures that the constructed propagation paths are physically meaningful and conform to the actual laws of error propagation. The introduction of local weight gradients eliminates the reliance on simple error magnitude comparisons for propagation direction determination, basing it on the overall propagation trend within the region, significantly improving directional accuracy. The propagation strength calculation method considers the combined influence of gradient differences and weights, providing a more comprehensive characterization of error propagation capabilities. The core advantage of this solution lies in its dynamic update mechanism. By periodically monitoring weight and direction changes, it enables adaptive updates of the propagation chain, enabling the system to respond to dynamic factors such as operating conditions and temperature drift. This dynamically adaptive error transfer chain structure significantly improves the accuracy and stability of trajectory error compensation, enabling complex industrial equipment to maintain high-precision motion control performance during long-term operation, providing a strong guarantee for high-quality processing.

[0071] In an optional embodiment, A hierarchical compensation structure is constructed based on the topological structure of the error transmission chain. Error representative points are set at each layer. The transmission influence coefficients between the error representative points of adjacent layers are calculated to obtain the inter-layer coupling constraints. The compensation coordination coefficients between the error representative points of the same layer are calculated to obtain the intra-layer coordination constraints. Based on the inter-layer coupling constraints and the intra-layer coordination constraints, a hybrid iterative strategy is used to optimize the compensation components. The generated compensation execution sequence includes: Analyze the topological characteristics of the error transmission chain, determine the error source node, calculate the shortest transmission path length from each node to the error source node, assign nodes with the same transmission path length to the same level, and build a hierarchical compensation structure; In each layer of the hierarchical compensation structure, the amplitude characteristics and the rate of change characteristics of the error nodes are calculated, the amplitude characteristics and the rate of change characteristics are weightedly combined to obtain a node score, and the node with the highest score and the distance between adjacent nodes greater than a preset distance threshold is selected as the error representative point; For the error representative points of adjacent layers in the layered compensation structure, the projection component and the vertical component of the transfer direction are calculated, and a transfer influence coefficient is constructed based on the projection component and the vertical component. The transfer influence coefficient is corrected in combination with the spatial distance attenuation characteristic to obtain the interlayer coupling constraint; For the error representative points in the same layer of the layered compensation structure, the local variance and global variance of the error distribution are calculated, spatial adaptive weights are constructed based on the local variance and global variance, and the spatial adaptive weights are dynamically adjusted according to the compensation effect to obtain intra-layer coordination constraints; Based on inter-layer coupling constraints and intra-layer coordination constraints, a hybrid iterative strategy of inter-layer top-down alternation and intra-layer parallel optimization is adopted to optimize the compensation components. The iteration step size is dynamically adjusted according to the compensation residual. Historical compensation is introduced to construct an inertia correction term to suppress compensation oscillation until the compensation components converge, thus generating a compensation execution sequence.

[0072] For example, the error source nodes are first identified. Error source nodes are the source of errors and are typically characterized by having no incoming edges or low incoming edge weights but large outgoing edge weights. The method for determining error source nodes is to calculate the in-degree and out-degree ratio of each node, that is, the sum of the outgoing edge weights divided by the sum of the incoming edge weights. The node with the largest ratio is generally the error source node. For example, in a 3D printer system, the error source node is often located at the base or the starting point of the transmission system. The structural rigidity and positioning accuracy of these locations have a decisive influence on the overall error.

[0073] Calculate the shortest path length from each node to the error source node. The shortest path length refers to the minimum number of edges required to reach the target node from the error source node. This calculation uses a breadth-first search algorithm, starting from the error source node and expanding outward layer by layer until all nodes are visited. For each node, the shortest path length from the error source node is recorded. In industrial equipment error analysis, path length reflects the number of stages of error transmission. The longer the path, the more links the error accumulates, making compensation more difficult.

[0074] Nodes with the same transmission path length are assigned to the same level to construct a hierarchical compensation structure. This structure organizes nodes in the error transmission chain into layers based on their distance from the error source node. Nodes with the same distance belong to the same level, starting from the error source node and progressing to level 0, level 1, level 2, and so on. This hierarchical compensation structure reflects the hierarchical nature of error transmission and provides an organizational framework for subsequent compensation strategies. In complex industrial equipment, the hierarchical structure typically consists of three to seven levels, with each level containing several nodes representing the error characteristics of different regions in the motion space.

[0075] At each layer of the hierarchical compensation structure, the amplitude and rate-of-change characteristics of the error node are calculated. The amplitude characteristic refers to the absolute magnitude of the node error, typically expressed as the root mean square error (RMS); the rate-of-change characteristic refers to the degree of change in the node error over time, typically expressed as the ratio of the error standard deviation to the mean. The amplitude characteristic reflects the severity of the node error, while the rate-of-change characteristic reflects the stability of the node error. The amplitude and rate-of-change characteristics are weighted and combined to obtain a node score. This weighted combination multiplies the amplitude characteristic by a first weight coefficient and the rate-of-change characteristic by a second weight coefficient, and the sum of the two results is used to obtain the node score. The weight coefficients are set based on application requirements. When compensation stability is high, the weight of the rate-of-change characteristic can be increased; when compensation accuracy is high, the weight of the amplitude characteristic can be increased. Typically, the first weight coefficient is set between 0.6 and 0.8, and the second weight coefficient is set between 0.2 and 0.4. A higher node score indicates a more significant error characteristic of the node and a greater impact on overall accuracy.

[0076] Nodes with the highest scores and adjacent distances greater than a preset distance threshold are selected as error representative points. Error representative points are key nodes in each layer, used to represent the error characteristics of that layer and calculate compensation. The selection method is to sort the nodes in descending order of score and select the nodes with the highest scores. At the same time, the distance between the selected nodes must be greater than a preset threshold to ensure uniform and representative distribution of the representative points. The preset distance threshold is typically set to 5%-10% of the workspace size.

[0077] For representative error points in adjacent layers of a layered compensation structure, the projected and perpendicular components of the transfer direction are calculated. The transfer direction is a unit vector pointing from the upper-layer node to the lower-layer node. The projected component is the projection of the transfer direction onto the principal error direction, while the perpendicular component is the projection of the transfer direction onto a plane perpendicular to the principal error direction. The projected and perpendicular components reflect the directional characteristics of error transfer and influence the direction and magnitude of compensation. In a 3D printer system, errors in the Z-axis transmission system may be primarily transmitted along the Z-axis direction, in which case the projected component is larger and the perpendicular component is smaller.

[0078] The transfer influence coefficient is constructed based on the projected and perpendicular components. The transfer influence coefficient indicates the degree of influence of the upper-level node error on the lower-level nodes. This coefficient is constructed by multiplying the projected component by the first coefficient and the perpendicular component by the second coefficient, and then summing the results to obtain the transfer influence coefficient. Typically, the first coefficient is greater than the second coefficient, reflecting a greater influence along the main direction of the error. In practical applications, the first coefficient is typically set to 0.7-0.9, and the second coefficient is set to 0.1-0.3. A larger transfer influence coefficient indicates a greater influence of the upper-level node on the lower-level node, and a stronger coupling effect that needs to be considered during compensation.

[0079] The interlayer coupling constraint is obtained by modifying the transfer influence coefficient in combination with the spatial distance attenuation characteristic. The spatial distance attenuation characteristic refers to the property that the error influence decreases with increasing distance. The correction method is to multiply the transfer influence coefficient by a distance attenuation factor, which decreases as the distance between the two nodes increases. The distance attenuation factor typically uses an exponential decay function, that is, a negative exponential power, where the exponent is the distance between the two nodes divided by the characteristic length. The characteristic length is a parameter that characterizes the range of influence and is usually set to 15%-25% of the workspace size. The modified transfer influence coefficient is the interlayer coupling constraint, which is used to describe the mutual influence of error compensation between different layers.

[0080] For the error representative points on the same layer in the layered compensation structure, the local variance and global variance of the error distribution are calculated. The local variance refers to the degree of dispersion of the error in the area near the representative point, and the global variance refers to the degree of dispersion of the error for all nodes in the entire layer. The calculation method is to select nodes within a certain radius around the representative point to calculate the local variance, and select all nodes in the layer to calculate the global variance. The local variance reflects the local consistency of the error, while the global variance reflects the overall distribution characteristics of the error. For example, a small local variance and a large global variance indicate that the errors are similar within the local area but vary significantly between different regions, and a regionalized compensation strategy is needed.

[0081] Spatially adaptive weights are constructed based on local and global variances. Spatially adaptive weights represent the degree of coordination between different representative points in the same layer. They are constructed by calculating the ratio of the local variance to the global variance and then converting it into a weight using a mapping function. When the local variance is much smaller than the global variance, the weight is large, indicating that the representative point can well represent the local area and a high degree of independence should be maintained during compensation. When the local variance is close to the global variance, the weight is small, indicating that the error characteristics of the representative point and other areas are similar and that greater coordination should be achieved during compensation. The mapping function typically uses a sigmoid function to ensure that the weight value varies smoothly between 0 and 1. In error compensation systems, the sigmoid function is often used to smoothly map one numerical range to another, while having high sensitivity in the middle region and relatively gentle changes at the ends. Typical sigmoid functions include the sigmoid function and the hyperbolic tangent function.

[0082] The spatial adaptive weights are dynamically adjusted based on the compensation effect to create an intra-layer coordination constraint. The compensation effect refers to the residual error after applying the current compensation. The dynamic adjustment method adjusts the spatial adaptive weights based on the ratio of the residual error after compensation to the initial error. When the compensation effect is good, the weights are slightly increased to enhance the independence of the representative points. When the compensation effect is poor, the weights are reduced to enhance coordination between the representative points. The adjusted spatial adaptive weights are the intra-layer coordination constraints, which describe the coordination relationship between compensation between different representative points in the same layer.

[0083] Based on inter-layer coupling constraints and intra-layer coordination constraints, a hybrid iterative strategy combining inter-layer top-down alternation and intra-layer parallelism is used to optimize the compensation components. This hybrid iterative strategy combines the advantages of both inter-layer and intra-layer iterations. Inter-layer top-down alternation involves calculating the compensation components of each layer sequentially, starting from layer 0, while taking into account the impact of the compensation values ​​determined in the previous layer on the current layer. Intra-layer parallelism involves simultaneously calculating the compensation components of all representative points in the same layer, taking into account the intra-layer coordination constraints. This strategy not only considers the hierarchical nature of error propagation but also improves computational efficiency. In practical applications, 3-5 rounds of iteration are typically performed, meaning the calculation process from layer 0 to the bottom layer is repeated 3-5 times.

[0084] The iteration step size is dynamically adjusted based on the compensation residual. The compensation residual refers to the remaining error after applying the current compensation. Dynamic adjustment adjusts the iteration step size based on the trend of the compensation residual. When the residual decreases rapidly, the step size is increased to accelerate convergence; when the residual decreases slowly or fluctuates, the step size is reduced to improve stability. Step size adjustment typically uses an adaptive method, determining the next iteration step size based on the ratio of the residuals from two consecutive iterations.

[0085] Historical compensation values ​​are introduced to construct an inertia correction term to suppress compensation oscillations until the compensation components converge. This inertia correction term is an additional term calculated based on historical compensation values. It is used to smooth changes in the compensation value and prevent oscillations during the compensation process. This term is constructed by taking the weighted average of the compensation values ​​from previous iterations and using it as the correction term for the current iteration. The weight typically decreases over time, with more recent historical compensation values ​​receiving a greater weight. The inclusion of the inertia correction term makes the compensation process smoother and avoids system instability caused by overcompensation. The convergence criterion for the compensation component is that the change in compensation value between two consecutive iterations is less than a preset threshold, typically set at 1%-3% of the initial error.

[0086] Generate a compensation execution sequence. A compensation execution sequence is a set of compensation operation instructions arranged in a specific order, used to guide industrial equipment in implementing error compensation. This generation method converts the converged compensation components into an instruction format executable by the equipment and arranges them in a topologically sorted order starting from the error source node. The generation of the compensation execution sequence takes into account the hierarchical and directional nature of error propagation, ensuring that compensation starts at the root cause, gradually eliminating errors at each layer, and ultimately achieving accurate compensation for the overall trajectory error.

[0087] In this embodiment, accurate compensation of the trajectory error of industrial equipment is achieved by constructing a hierarchical compensation structure and adopting a hybrid iterative strategy to generate a compensation execution sequence. The hierarchical structure constructed based on the error transfer chain makes the compensation and error formation mechanism highly matched, and the error representative point scoring mechanism ensures that the key areas are fully compensated. The inter-layer coupling constraint accurately characterizes the influence relationship between errors at different levels, and the intra-layer coordination constraint achieves a balance between local characteristics and overall coordination through spatial adaptive weights. The hybrid iterative strategy combined with dynamic step size and inertia correction improves computational efficiency and stability, making the compensation process more reliable. This hierarchical and adaptive compensation method not only improves trajectory accuracy, but also has good environmental adaptability and long-term stability, providing strong support for high-precision manufacturing.

[0088] In an optional embodiment, Based on inter-layer coupling constraints and intra-layer coordination constraints, a hybrid iterative strategy of inter-layer top-down alternation and intra-layer parallel optimization is adopted to optimize the compensation component. The iteration step size is dynamically adjusted according to the compensation residual. The historical compensation amount is introduced to construct the inertia correction term to suppress the compensation oscillation until the compensation component converges. The compensation execution sequence generated includes: Based on the inter-layer coupling constraints and intra-layer coordination constraints, iterate from the top layer downward layer by layer, use the upper layer compensation components as the constraints of the lower layer compensation, and use the parallel optimization method to calculate the compensation components of the same layer to obtain the compensation components of the current iteration; Calculating the compensation residual corresponding to the compensation component of the current iteration, comparing the compensation residual with the compensation residual of the previous iteration to obtain a residual change trend, dynamically adjusting the iteration step size based on the residual change trend, and updating the compensation component using the dynamically adjusted iteration step size; Recording the updated compensation component as the historical compensation amount of the current iteration, performing time-series weighting on the historical compensation amounts obtained from multiple consecutive iterations to obtain a compensation trend feature, constructing an inertia correction term based on the compensation trend feature, and combining the inertia correction term with the current compensation component to obtain a corrected compensation component; The change of the revised compensation component relative to the previous iteration is calculated, and when the change is less than a preset change threshold, a compensation execution sequence is generated; otherwise, the revised compensation component is used as the initial compensation component of the next iteration to continue the hybrid iterative optimization.

[0089] In this embodiment, based on the inter-layer coupling constraints and the intra-layer coordination constraints, the upper layer compensation components are iterated downward from the top layer to the bottom layer. The hierarchical compensation structure consists of multiple levels, starting from the top layer (0th layer) where the error source node is located, and extending downward to the bottom layer. The inter-layer coupling constraint describes the degree of influence of the upper layer compensation on the lower layer compensation, which is represented by a transfer influence coefficient matrix. The layer-by-layer iteration process starts from the 0th layer and calculates the compensation components of each layer in turn. When calculating the compensation components of a certain layer, it is necessary to consider the influence of the compensation components determined by the upper layer on the current layer. The specific method is to multiply the upper layer compensation component by the corresponding transfer influence coefficient to obtain the influence of the upper layer on the current layer, and then use this influence as the constraint condition for the current layer compensation calculation.

[0090] The compensation components of the same layer are calculated using a parallel optimization method to obtain the compensation components of the current iteration. Parallel optimization means that all error representative points in the same layer calculate their respective compensation components simultaneously, rather than sequentially. The intra-layer coordination constraint describes the coordination relationship between different representative points in the same layer and is represented by a spatially adaptive weight matrix. The parallel optimization method is to construct an optimization objective function for each representative point based on its error characteristics and intra-layer coordination constraints, and simultaneously solve for the optimal compensation components of all representative points. The optimization objective function comprehensively considers factors such as error elimination, compensation smoothness, and energy consumption. The solution process usually uses gradient descent or conjugate gradient method.

[0091] Calculate the compensation residual corresponding to the compensation component of the current iteration. The compensation residual refers to the error that remains after applying the current compensation and reflects the effectiveness of the compensation. It is calculated by subtracting the compensation amount from the original error to obtain the residual error. The root mean square value of this residual error is then calculated as the compensation residual. Smaller compensation residuals indicate better compensation effectiveness; larger compensation residuals indicate poor compensation effectiveness and require further optimization.

[0092] The compensation residual is compared with the compensation residual from the previous iteration to obtain the residual trend. This residual trend reflects the convergence of the compensation optimization process. The comparison method is to calculate the ratio of the current residual to the residual from the previous iteration to obtain the residual change rate. A residual change rate less than 1 indicates that the residual is decreasing and the compensation effect is improving; a rate of change equal to 1 indicates that the residual remains unchanged and the compensation effect is stagnant; a rate of change greater than 1 indicates that the residual is increasing and the compensation effect is deteriorating. The residual change rates of multiple consecutive iterations constitute the residual trend.

[0093] The iteration step size is dynamically adjusted based on the residual error trend. The iteration step size controls the magnitude of the compensation component update in each iteration and directly affects the convergence speed and stability. The dynamic adjustment method adaptively increases or decreases the step size based on the residual error trend. When the residual error decreases rapidly (the rate of change is far less than 1), the step size is appropriately increased to accelerate convergence; when the residual error decreases slowly (the rate of change is close to 1), the current step size is maintained; when the residual error begins to increase (the rate of change is greater than 1), the step size is reduced to improve stability. Step size adjustment typically uses a mapping function to map the residual error rate of change to a step size adjustment coefficient.

[0094] The compensation component is updated using the dynamically adjusted iteration step size. The compensation component is updated by adding the current compensation component to the compensation increment to obtain a new compensation component. The compensation increment is calculated based on the optimization direction and step size, and the calculation method is to multiply the optimization direction vector by the iteration step size. The updated compensation component is closer to the optimal solution, which helps to further reduce the error. The updated compensation component is recorded as the historical compensation amount of the current iteration. The historical compensation amount refers to the sequence of compensation components generated during multiple iterations, which is used to analyze the changing trend of the compensation. The recording method is to store the compensation component of each iteration in a historical queue. The queue length is usually 3-5, that is, the compensation components of the last 3-5 iterations are retained. The historical compensation amount records the evolution process of the compensation component and provides a data basis for subsequent inertia correction.

[0095] The compensation trend characteristic is obtained by applying time-series weighting to the historical compensation values ​​obtained from multiple consecutive iterations. Time-series weighting assigns different weights based on chronological order, typically giving larger weights to recent compensation values ​​and smaller weights to distant compensation values. Weighting is achieved by multiplying the historical compensation values ​​by the corresponding time-series weights and then summing them to obtain a weighted average. Time-series weights typically use an exponential decay scheme, where the weights are raised to a power of a base number less than 1, with the exponent being the time distance. The weighted average reflects the changing trend of the compensation component and is called the compensation trend characteristic. An inertia correction term is constructed based on the compensation trend characteristic. The inertia correction term is an additional compensation adjustment used to smooth compensation changes and prevent oscillation. The inertia correction term is constructed by multiplying the difference between the current compensation component and the compensation trend characteristic by an inertia coefficient. The inertia coefficient controls the strength of the correction and is typically set between 0.1 and 0.3. When the current compensation component deviates significantly from the trend, the inertia correction term pulls the compensation component back in line with the overall trend. When the compensation component changes gradually, the inertia correction term has less impact. The inertia correction term is combined with the current compensation component to obtain the corrected compensation component. The combination method is to add the current compensation component to the inertia correction term to obtain the corrected compensation component.

[0096] Calculate the change in the revised compensation component relative to the previous iteration. This change reflects the degree of convergence of the compensation component and is an important indicator for determining whether the iteration has terminated. This change is calculated by subtracting the revised compensation component from the previous iteration's compensation component and then calculating the norm of the difference (such as the Euclidean norm or the maximum absolute value norm) as the change. A smaller change indicates that the compensation component is closer to convergence; a larger change indicates that the compensation component is still changing rapidly and requires further iteration.

[0097] When the variation is less than a preset variation threshold, a compensation execution sequence is generated. The variation threshold serves as a criterion for determining whether the compensation component has converged and is typically set to 1%-3% of the norm of the initial compensation component. When the variation falls below the threshold multiple times (e.g., three times) in a row, the compensation component is considered converged, and the iterations are terminated, generating the final compensation execution sequence. A compensation execution sequence is a set of compensation operation instructions arranged in a specific order, used to guide industrial equipment in implementing error compensation. This generation method converts the converged compensation components into an executable instruction format for the device and arranges them in a topologically sorted order starting from the error source node.

[0098] If the change is greater than the preset change threshold, the corrected compensation component is used as the initial compensation component for the next iteration, and hybrid iterative optimization continues. This iterative method ensures that the compensation component can gradually converge to the optimal solution. At the same time, through dynamic step size adjustment and inertia correction, the convergence speed and stability are improved. In practical applications, hybrid iterative optimization usually requires 10-30 iterations to reach convergence conditions. The specific number of iterations depends on the complexity of the error distribution and the setting of the convergence threshold. The compensation component optimized in this way can effectively eliminate the trajectory error of industrial equipment and improve processing accuracy and product quality.

[0099] In this embodiment, a hierarchical error compensation structure is constructed, combining the coupling relationship between upper and lower layers with the coordination mechanism within the same layer to achieve global collaborative optimization of error information. The introduction of a hybrid iterative strategy and inertia correction mechanism enables dynamic adjustment of the compensation strategy, suppressing oscillations, accelerating convergence, and improving the adaptability and convergence efficiency of the compensation process. The resulting compensation execution sequence can directly drive the device to achieve trajectory correction, improving manufacturing quality and control system robustness.

[0100] Figure 3 This is a heat map of the dynamic iterative step size adjustment effect of the embodiment of the present invention, such as Figure 3The figure shows the relationship between the rate of change of the compensation residual and the iteration step size, and their impact on the compensation residual. The heatmap uses color to represent the size of the compensation residual, with darker colors corresponding to compensation residuals ranging from 7.5μm to 0μm. The data shows that when the rate of change of the compensation residual is 1.4 and the iteration step size is 0.45-0.55, the minimum compensation residual of 1.6μm is achieved (marked by the red dashed box in the upper right corner). However, when the rate of change of the compensation residual is 0.8 and the iteration step size is 0.25, a suboptimal region is reached, with a compensation residual of 3.2μm (marked by the green dashed box in the middle). The data also shows that with increasing the iteration step size, the compensation residual first decreases and then increases. For example, when the rate of change of the compensation residual is 0.8, the compensation residual decreases from 5.1μm to 2.4μm as the iteration step size increases from 0.05 to 0.45. However, when the step size is further increased to 0.55, the compensation residual remains essentially stable. At the same time, the greater the rate of change of the compensation residual, the higher the compensation accuracy achieved at the same step size. For example, at a step size of 0.25, the rate of change increases from 0.4 to 1.4, and the compensation residual decreases from 5.8μm to 2.3μm. This fully demonstrates that the dynamic step size adjustment strategy of this technical solution can adaptively adjust the iterative step size based on the changing trend of the compensation residual, effectively balancing convergence speed and stability to achieve the best compensation effect.

[0101] A second aspect of an embodiment of the present invention provides a system for big data analysis and intelligent compensation of industrial equipment trajectory errors, the system comprising: The first unit is used to collect the operating status parameters of the industrial equipment, segment the operating status parameters according to the time series, extract the motion characteristics of each segment of data, generate a motion feature fingerprint, compare the motion feature fingerprint with a pre-established feature fingerprint library, and calculate the feature deviation data; The second unit is used to distribute feature deviation data to multiple agents. Each agent analyzes regional error characteristics based on the assigned feature deviation data. Adjacent agents exchange error feature information and evaluate the transmission strength of feature deviations to obtain error transmission weights. A probability graph structure is constructed based on the error transmission weights. The mutual information criterion is used to simplify the probability graph structure to obtain an error transmission chain. The third unit is used to construct a hierarchical compensation structure based on the topological structure of the error transmission chain. It sets error representative points at each layer, calculates the transmission influence coefficient between the error representative points of adjacent layers to obtain the inter-layer coupling constraint, calculates the compensation coordination coefficient between the error representative points of the same layer to obtain the intra-layer coordination constraint, and optimizes the compensation components using a hybrid iterative strategy based on the inter-layer coupling constraint and the intra-layer coordination constraint to generate a compensation execution sequence. The fourth unit is configured to implement error compensation of the motion trajectory of the industrial equipment according to the compensation execution sequence. A third aspect of the embodiment of the present invention provides an electronic device, including: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0102] According to a fourth aspect of an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0103] The present invention may be a method, an apparatus, a system and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for executing various aspects of the present invention.

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. Big data analysis and intelligent compensation method for industrial equipment trajectory errors, characterized by: include: Collect the operating status parameters of industrial equipment, segment them according to the time series, extract the motion characteristics of each segment of data, generate motion feature fingerprints, compare the motion feature fingerprints with the pre-established feature fingerprint library, and calculate the feature deviation data; The feature deviation data is distributed to multiple agents. Each agent analyzes the regional error characteristics based on the assigned feature deviation data. Adjacent agents exchange error feature information and evaluate the transmission strength of feature deviation to obtain error transmission weights. A probability graph structure is constructed based on the error transmission weights. The mutual information criterion is used to simplify the probability graph structure to obtain an error transmission chain. A hierarchical compensation structure is constructed based on the topological structure of the error transmission chain. Error representative points are set at each layer. The transmission influence coefficients between the error representative points of adjacent layers are calculated to obtain the inter-layer coupling constraints. The compensation coordination coefficients between the error representative points of the same layer are calculated to obtain the intra-layer coordination constraints. Based on the inter-layer coupling constraints and the intra-layer coordination constraints, a hybrid iterative strategy is used to optimize the compensation components and generate a compensation execution sequence. Error compensation of the motion trajectory of industrial equipment is achieved according to the compensation execution sequence.

2. The method according to claim 1, characterized in that Collect the operating status parameters of industrial equipment, segment them according to the time series, extract the motion characteristics of each segment of data, and generate motion feature fingerprints including: Acquiring operating status parameters of industrial equipment, wherein the operating status parameters include motion parameters, working condition parameters, and environmental parameters; Extracting velocity data and acceleration data from the motion parameters; calculating velocity changes and acceleration changes of adjacent data points, marking points where both velocity changes and acceleration changes are greater than a preset velocity value as candidate segmentation points, and determining the segmentation points based on the consistency of the fluctuation trend; dividing the velocity data and acceleration data into multiple data segments based on the segmentation points; Combined with the working condition parameters and environmental parameters, the speed fluctuation value and acceleration fluctuation value of each data segment are calculated, and a fluctuation curve is constructed. Frequency domain feature data is obtained through Fourier transform. Waveform features and phase features are extracted from the frequency domain feature data and combined according to a preset mapping relationship to form a feature vector; Calculate the variance contribution value of each component of the eigenvector, perform dimensionality reduction processing on the eigenvector according to the variance contribution value, obtain the eigencomponents after dimensionality reduction, calculate the weight coefficients of the eigencomponents in combination with the working condition parameters, reorganize the eigencomponents after dimensionality reduction according to the weight coefficients, and generate a motion feature fingerprint.

3. The method according to claim 1, characterized in that Compare the motion feature fingerprint with the pre-established feature fingerprint library and calculate the feature deviation data including: The motion feature fingerprint is divided into feature subsequences according to the sampling time window, the fluctuation trend of adjacent feature subsequences is calculated, the feature subsequences are merged according to the fluctuation trend to obtain waveform segments, and the amplitude sequence and phase sequence of the waveform segments are extracted; Normalizing the amplitude sequence and the phase sequence to obtain waveform features and phase features, respectively, combining the waveform features and the phase features to construct a feature vector, and calculating a weight coefficient based on the feature vector; Extracting fingerprint data from a pre-established feature fingerprint library, performing sequence division and feature extraction on the fingerprint data, constructing a reference feature vector, calculating the matching degree between the feature vector and the reference feature vector, and selecting the fingerprint data with the highest matching degree as the target fingerprint; Calculate the characteristic distance between the characteristic vector of the waveform segment and the reference characteristic vector of the waveform segment corresponding to the target fingerprint, calculate the weighted deviation value according to the characteristic distance and the weight coefficient, and calculate the time series distribution of the weighted deviation value to obtain the change pattern; The divergence trend of the weighted deviation value is determined according to the change rule; when a divergence trend occurs, the divergence rate and the divergence direction are calculated as characteristic deviation data.

4. The method according to claim 1, wherein The feature deviation data is distributed to multiple agents. Each agent analyzes the regional error characteristics according to the assigned feature deviation data. Adjacent agents exchange error feature information and evaluate the transmission strength of feature deviation to obtain error transmission weights. A probability graph structure is constructed based on the error transmission weights. The mutual information criterion is used to simplify the probability graph structure to obtain the error transmission chain, which includes: Divide the motion space of the industrial equipment into grid units, each grid unit corresponds to an intelligent agent, calculate the Mahalanobis distance between the feature deviation data point and the center of the grid unit, calculate the allocation weight based on the Mahalanobis distance, and allocate the feature deviation data to the intelligent agent according to the allocation weight; Calculate the mean and standard deviation of the deviation within each agent region, extract the main direction of the deviation, and combine the mean, standard deviation and main direction to construct a regional error feature vector; Adjacent agents exchange regional error feature vectors, calculate feature vector similarity to construct feature similarity matrix, and calculate error gradients between adjacent agents; Combining the feature similarity matrix with the error gradient to obtain a transfer strength matrix, normalizing the transfer strength matrix to obtain an error transfer weight, and constructing an initial probability map based on the error transfer weight; The mutual information value between nodes in the initial probability graph is calculated, and the edges with mutual information values ​​less than a preset threshold are deleted to obtain a simplified probability graph. In the simplified probability graph, the error transfer weight is used as the objective function, and the maximum weight spanning tree algorithm is used to extract the optimal transfer path. The error transfer direction and transfer strength are determined according to the size relationship of the error transfer weights on the path, and an error transfer chain structure with transfer direction and transfer strength is constructed.

5. The method according to claim 4, characterized in that In the simplified probability graph, the error transfer weight is used as the objective function, and the maximum weight spanning tree algorithm is used to extract the optimal transfer path. The error transfer direction and transfer strength are determined according to the size relationship of the error transfer weight on the path. The error transfer chain structure with transfer direction and transfer strength is constructed, including: Obtaining an error transfer weight of each edge in the simplified probability graph structure, and normalizing the error transfer weight to a preset interval based on a maximum weight and a minimum weight to obtain a normalized transfer weight of each edge; Sort the edges in the probability graph in descending order according to the normalized transfer weights, select the edges with the largest weights in turn, determine whether the edges form a loop and whether the error amplitudes of the nodes at both ends of the edges meet the size constraint, and add the edges that meet the constraint conditions to the edge set until the maximum weight spanning tree is constructed; In the maximum weight spanning tree, the local weight gradient is obtained by calculating the average value of the normalized transfer weights between the two end nodes of each edge and its adjacent nodes. The error propagation direction is determined based on the magnitude of the local weight gradients of the two end nodes, and the product of the difference between the local weight gradients and the normalized transfer weight is used as the transfer strength. The current transfer weight and transfer direction of each edge in the maximum weight spanning tree are periodically obtained, and the weight change and direction change are calculated; when the weight change is greater than the weight change threshold or the direction change is greater than the direction change threshold, the path extraction is re-executed for the edges in the changed area, and the local structure of the maximum weight spanning tree is updated to obtain an error transfer chain with dynamic update capability.

6. The method according to claim 1, characterized in that A hierarchical compensation structure is constructed based on the topological structure of the error transmission chain. Error representative points are set at each layer. The transmission influence coefficients between the error representative points of adjacent layers are calculated to obtain the inter-layer coupling constraints. The compensation coordination coefficients between the error representative points of the same layer are calculated to obtain the intra-layer coordination constraints. Based on the inter-layer coupling constraints and the intra-layer coordination constraints, a hybrid iterative strategy is used to optimize the compensation components. The generated compensation execution sequence includes: Analyze the topological characteristics of the error transmission chain, determine the error source node, calculate the shortest transmission path length from each node to the error source node, assign nodes with the same transmission path length to the same level, and build a hierarchical compensation structure; In each layer of the hierarchical compensation structure, the amplitude characteristics and the rate of change characteristics of the error nodes are calculated, the amplitude characteristics and the rate of change characteristics are weightedly combined to obtain a node score, and the node with the highest score and the distance between adjacent nodes greater than a preset distance threshold is selected as the error representative point; For the error representative points of adjacent layers in the layered compensation structure, the projection component and the vertical component of the transfer direction are calculated, and a transfer influence coefficient is constructed based on the projection component and the vertical component. The transfer influence coefficient is corrected in combination with the spatial distance attenuation characteristic to obtain the interlayer coupling constraint; For the error representative points in the same layer of the layered compensation structure, the local variance and global variance of the error distribution are calculated, spatial adaptive weights are constructed based on the local variance and global variance, and the spatial adaptive weights are dynamically adjusted according to the compensation effect to obtain intra-layer coordination constraints; Based on inter-layer coupling constraints and intra-layer coordination constraints, a hybrid iterative strategy of inter-layer top-down alternation and intra-layer parallel optimization is adopted to optimize the compensation components. The iteration step size is dynamically adjusted according to the compensation residual. Historical compensation is introduced to construct an inertia correction term to suppress compensation oscillation until the compensation components converge, thus generating a compensation execution sequence.

7. The method according to claim 6, characterized in that Based on inter-layer coupling constraints and intra-layer coordination constraints, a hybrid iterative strategy of inter-layer top-down alternation and intra-layer parallel optimization is adopted to optimize the compensation component. The iteration step size is dynamically adjusted according to the compensation residual. The historical compensation amount is introduced to construct the inertia correction term to suppress the compensation oscillation until the compensation component converges. The compensation execution sequence generated includes: Based on the inter-layer coupling constraints and intra-layer coordination constraints, iterate from the top layer downward layer by layer, use the upper layer compensation components as the constraints of the lower layer compensation, and use the parallel optimization method to calculate the compensation components of the same layer to obtain the compensation components of the current iteration; Calculating the compensation residual corresponding to the compensation component of the current iteration, comparing the compensation residual with the compensation residual of the previous iteration to obtain a residual change trend, dynamically adjusting the iteration step size based on the residual change trend, and updating the compensation component using the dynamically adjusted iteration step size; Recording the updated compensation component as the historical compensation amount of the current iteration, performing time-series weighting on the historical compensation amounts obtained from multiple consecutive iterations to obtain a compensation trend feature, constructing an inertia correction term based on the compensation trend feature, and combining the inertia correction term with the current compensation component to obtain a corrected compensation component; The change of the revised compensation component relative to the previous iteration is calculated, and when the change is less than a preset change threshold, a compensation execution sequence is generated; otherwise, the revised compensation component is used as the initial compensation component of the next iteration to continue the hybrid iterative optimization.

8. Industrial equipment trajectory error big data analysis and intelligent compensation system, used to implement the method described in any one of claims 1 to 7, characterized in that: include: The first unit is used to collect the operating status parameters of the industrial equipment, segment the operating status parameters according to the time series, extract the motion characteristics of each segment of data, generate a motion feature fingerprint, compare the motion feature fingerprint with a pre-established feature fingerprint library, and calculate the feature deviation data; The second unit is used to distribute feature deviation data to multiple agents. Each agent analyzes regional error characteristics based on the assigned feature deviation data. Adjacent agents exchange error feature information and evaluate the transmission strength of feature deviations to obtain error transmission weights. A probability graph structure is constructed based on the error transmission weights. The mutual information criterion is used to simplify the probability graph structure to obtain an error transmission chain. The third unit is used to construct a hierarchical compensation structure based on the topological structure of the error transmission chain. It sets error representative points at each layer, calculates the transmission influence coefficient between the error representative points of adjacent layers to obtain the inter-layer coupling constraint, calculates the compensation coordination coefficient between the error representative points of the same layer to obtain the intra-layer coordination constraint, and optimizes the compensation components using a hybrid iterative strategy based on the inter-layer coupling constraint and the intra-layer coordination constraint to generate a compensation execution sequence. The fourth unit is used to realize error compensation of the motion trajectory of the industrial equipment according to the compensation execution sequence.

9. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the method according to any one of claims 1 to 7.

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

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