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

Abstract

The application provides an industrial equipment trajectory error big data analysis and intelligent compensation method and system, relates to the technical field of intelligent error compensation, and comprises collecting equipment operation state parameters and processing in sections, extracting motion characteristics to generate characteristic fingerprints and comparing the characteristic fingerprints with a characteristic fingerprint library to calculate characteristic deviations; the characteristic deviations are distributed to multi-agent analysis area error characteristics to construct an error transmission chain; a hierarchical compensation structure is constructed based on the error transmission chain, error representative points are set, interlayer coupling constraints and intralayer coordination constraints are calculated, a mixed iteration strategy is used to optimize compensation components to generate a compensation execution sequence. The application can realize accurate compensation of industrial equipment motion trajectories and improve equipment operation precision.

Description

TECHNICAL FIELD

[0001] The present application relates to intelligent error compensation technology, and in particular to an industrial equipment trajectory error big data analysis and intelligent compensation method and system. BACKGROUND

[0002] The accuracy of the motion trajectory of an industrial equipment directly relates to product quality and equipment performance during operation. However, due to factors such as sensor error, insufficient actuator precision, and environmental disturbance, the actual running trajectory of the industrial equipment often has an unavoidable deviation. Traditional error compensation methods rely on static models or simple feedback control, and are difficult to dynamically identify error evolution laws under complex working conditions, so the compensation effect is limited.

[0003] With the development of industrial big data and intelligent algorithms, existing research attempts to use data-driven methods to analyze the equipment running state and build an error model for correction. However, the existing methods ignore the dynamic transmission characteristics of the error in the space and time dimensions, do not fully utilize the coupling relationship between multi-source data, and do not establish a hierarchical compensation structure, resulting in a lack of systematicness and adaptability of the overall compensation strategy.

[0004] At the same time, in the face of high-dimensional feature data under complex industrial working conditions, how to efficiently extract error features and build a simplified and iterative error compensation mechanism is still a major challenge. Therefore, there is an urgent need for an industrial equipment trajectory error big data analysis and intelligent compensation method to achieve higher precision and stronger adaptability of the compensation effect. SUMMARY

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

[0006] In a first aspect, the embodiments of the present application provide an industrial equipment trajectory error big data analysis and intelligent compensation method, comprising:

[0007] Collecting industrial equipment running state parameters, segmenting the running state parameters according to time series, extracting motion features of each segment of data, generating motion feature fingerprints, comparing the motion feature fingerprints with a pre-established feature fingerprint library, and calculating feature deviation data;

[0008] The feature deviation data is distributed to a plurality of agents, each agent analyzes regional error features according to the distributed feature deviation data, adjacent agents exchange error feature information and evaluate the transmission strength of the feature deviation to obtain error transmission weights, a probability graph structure is constructed based on the error transmission weights, and the probability graph structure is simplified to obtain an error transmission chain using the mutual information criterion;

[0009] According to the topology structure of the error transmission chain, a hierarchical compensation structure is constructed, error representative points are arranged at each layer, a transmission influence coefficient between adjacent error representative points is calculated to obtain inter-layer coupling constraints, a compensation coordination coefficient between error representative points in the same layer is calculated to obtain intra-layer coordination constraints, a hybrid iteration strategy is adopted based on the inter-layer coupling constraints and the intra-layer coordination constraints to optimize compensation components, and a compensation execution sequence is generated;

[0010] According to the compensation execution sequence, error compensation of the motion trajectory of the industrial equipment is realized.

[0011] In an optional embodiment,

[0012] An industrial equipment running state parameter is collected, the running state parameter is segmented according to a time sequence, a motion feature of each segment of data is extracted, and a motion feature fingerprint is generated, including:

[0013] An industrial equipment running state parameter is collected, the running state parameter includes a motion parameter, a working condition parameter, and an environment parameter;

[0014] Velocity data and acceleration data are extracted from the motion parameter, a velocity change amount and an acceleration change amount of adjacent data points are calculated, a point position where the velocity change amount and the acceleration change amount are both greater than a preset velocity value is marked as a candidate segmentation point, a segmentation point is determined according to fluctuation consistency, and the velocity data and the acceleration data are divided into a plurality of data segments according to the segmentation point;

[0015] Combining the working condition parameter and the environment parameter, a velocity fluctuation value and an acceleration fluctuation value of each data segment are calculated, a fluctuation curve is constructed, frequency domain feature data are obtained through Fourier transform, waveform features and phase features are extracted from the frequency domain feature data, and a feature vector is formed by combining the waveform features and the phase features according to a preset mapping relationship;

[0016] The variance contribution values of the components of the feature vector are calculated, the feature vector is processed by dimension reduction according to the variance contribution values, the feature components after dimension reduction are obtained, the weight coefficients of the feature components are calculated in combination with the working condition parameter, the feature components after dimension reduction are recombined according to the weight coefficients, and a motion feature fingerprint is generated.

[0017] In an optional embodiment,

[0018] The motion feature fingerprint is compared with a pre-established feature fingerprint library, and feature deviation data are calculated, including:

[0019] The motion feature fingerprint is divided into feature subsequences according to a sampling time window, fluctuation change trends of adjacent feature subsequences are calculated, waveform segments are obtained by merging the feature subsequences according to the fluctuation change trends, and an amplitude sequence and a phase sequence of the waveform segments are extracted;

[0020] The amplitude sequence and the phase sequence are respectively normalized to obtain waveform features and phase features, the waveform features and the phase features are combined to construct a feature vector, and a weight coefficient is calculated according to the feature vector;

[0021] Fingerprint data is extracted from a pre-established feature fingerprint library, sequence division and feature extraction are performed on the fingerprint data, a reference feature vector is constructed, a matching degree between the feature vector and the reference feature vector is calculated, and fingerprint data with the highest matching degree is selected as a target fingerprint;

[0022] The feature distance between the feature vector of the waveform segment and the reference feature vector of the corresponding waveform segment of the target fingerprint is calculated, a weighted deviation value is calculated according to the feature distance and the weight coefficient, and a change rule is obtained by statistically analyzing the time sequence distribution of the weighted deviation value;

[0023] The divergence trend of the weighted deviation value is determined according to the change rule; when the divergence trend occurs, the divergence rate and the divergence direction are calculated as feature deviation data.

[0024] In an optional embodiment,

[0025] The feature deviation data is distributed to a plurality of agents, each agent analyzes regional error features according to the distributed feature deviation data, adjacent agents exchange error feature information and evaluate the transmission strength of the feature deviation to obtain an error transmission weight, a probability graph structure is constructed based on the error transmission weight, and the probability graph structure is simplified to obtain an error transmission chain using the mutual information criterion, including:

[0026] The motion space of the industrial equipment is divided into grid cells, each grid cell corresponds to an agent, the Mahalanobis distance between the feature deviation data point and the center of the grid cell is calculated, the distribution weight is calculated based on the Mahalanobis distance, and the feature deviation data is distributed to the agent according to the distribution weight;

[0027] The deviation mean and standard deviation in each agent region are calculated, the main direction of the deviation is extracted, and the deviation mean, standard deviation and main direction are combined to construct a regional error feature vector;

[0028] Adjacent agents exchange regional error feature vectors, calculate the feature vector similarity to construct a feature similarity matrix, and calculate the error gradient between adjacent agents;

[0029] The feature similarity matrix and the error gradient are combined to obtain a transmission strength matrix, the transmission strength matrix is normalized to obtain an error transmission weight, and an initial probability graph is constructed based on the error transmission weight;

[0030] Calculate mutual information values between nodes in the initial probability graph, delete edges with mutual information values less than a preset threshold to obtain a simplified probability graph, in the simplified probability graph, extract an optimal transmission path by using a maximum weight spanning tree algorithm with error transmission weights as an objective function, determine error transmission direction and transmission strength according to the size relationship of error transmission weights on the path, and construct an error transmission chain structure with the transmission direction and the transmission strength.

[0031] In an alternative embodiment,

[0032] In the simplified probability graph, extract an optimal transmission path by using a maximum weight spanning tree algorithm with error transmission weights as an objective function, determine error transmission direction and transmission strength according to the size relationship of error transmission weights on the path, and construct an error transmission chain structure with the transmission direction and the transmission strength, comprising:

[0033] Obtain error transmission weights of edges in the simplified probability graph structure, normalize the error transmission weights to a preset interval based on maximum and minimum weights to obtain normalized transmission weights of the edges;

[0034] Sort the edges in the probability graph in descending order according to the normalized transmission weights, select the edges with the largest weights in turn, judge whether the edges form a loop and whether the error amplitudes of the nodes at both ends of the edges satisfy the size relationship constraint, add the edges that satisfy the constraint conditions to an edge set, and construct a maximum weight spanning tree until the construction is completed;

[0035] Calculate the average value of the normalized transmission weights between the nodes at both ends of each edge and their adjacent nodes in the maximum weight spanning tree to obtain a local weight gradient, determine the error transmission direction based on the size of the local weight gradient of the nodes at both ends, and take the product of the difference value of the local weight gradient and the normalized transmission weight as the transmission strength;

[0036] Periodically obtain the current transmission weights and transmission directions of the edges in the maximum weight spanning tree, calculate the weight change and the direction change; when the weight change is greater than a weight change threshold or the direction change is greater than a direction change threshold, re-execute the path extraction on the edges in the changed area, update the local structure of the maximum weight spanning tree, and obtain an error transmission chain with dynamic updating capability.

[0037] In an alternative embodiment,

[0038] Construct a hierarchical compensation structure according to the topology of the error transmission chain, set error representative points at each layer, calculate the transmission influence coefficient between the error representative points of adjacent layers to obtain inter-layer coupling constraints, calculate the compensation coordination coefficient between the error representative points of the same layer to obtain intra-layer coordination constraints, and optimize the compensation components based on the inter-layer coupling constraints and the intra-layer coordination constraints using a hybrid iteration strategy to generate a compensation execution sequence, comprising:

[0039] The topology characteristics of the error propagation chain are analyzed, an error source node is determined, the shortest propagation path length from each node to the error source node is calculated, nodes with the same propagation path length are attributed to the same level, and a hierarchical compensation structure is constructed;

[0040] In each level of the hierarchical compensation structure, the amplitude characteristics and the change rate characteristics of the error nodes are calculated, the amplitude characteristics and the change rate characteristics are combined by weighting to obtain node scores, and nodes with the highest scores and distances between adjacent nodes greater than a preset distance threshold are selected as error representative points;

[0041] For the error representative points of adjacent levels in the hierarchical compensation structure, the projection component and the vertical component of the propagation direction are calculated, the propagation influence coefficient is constructed based on the projection component and the vertical component, and the inter-layer coupling constraint is obtained by modifying the propagation influence coefficient combined with the spatial distance attenuation characteristics;

[0042] For the error representative points of the same level in the hierarchical compensation structure, the local variance and the global variance of the error distribution are calculated, the spatial adaptive weight is constructed based on the local variance and the global variance, and the intra-layer coordination constraint is obtained by dynamically adjusting the spatial adaptive weight according to the compensation effect;

[0043] Based on the inter-layer coupling constraint and the intra-layer coordination constraint, a hybrid iterative strategy of inter-layer top-down alternation and intra-layer parallel is adopted to optimize the compensation component, the iteration step is dynamically adjusted according to the compensation residual, the inertial correction term is constructed by introducing the historical compensation amount to suppress the compensation oscillation until the compensation component converges, and the compensation execution sequence is generated.

[0044] In an alternative embodiment,

[0045] Based on the inter-layer coupling constraint and the intra-layer coordination constraint, a hybrid iterative strategy of inter-layer top-down alternation and intra-layer parallel is adopted to optimize the compensation component, the iteration step is dynamically adjusted according to the compensation residual, the inertial correction term is constructed by introducing the historical compensation amount to suppress the compensation oscillation until the compensation component converges, and the compensation execution sequence is generated.

[0046] Based on the inter-layer coupling constraint and the intra-layer coordination constraint, the iteration is performed layer by layer from the topmost layer down, the compensation component of the upper layer is taken as the constraint condition for the compensation of the lower layer, the compensation component of the same layer is calculated by using the parallel optimization method, and the compensation component of the current iteration is obtained;

[0047] The compensation residual corresponding to the compensation component of the current iteration is calculated, the compensation residual is compared with the compensation residual of the previous iteration to obtain the residual change trend, the iteration step is dynamically adjusted based on the residual change trend, and the compensation component is updated by using the iteration step after dynamic adjustment;

[0048] record the updated compensation component as a history compensation amount of the current iteration, time-weight the history compensation amounts obtained in continuous multiple iterations to obtain a compensation trend feature, construct an inertia correction term based on the compensation trend feature, combine the inertia correction term with the current compensation component to obtain a corrected compensation component;

[0049] calculate a change amount of the corrected compensation component relative to the last iteration, generate a compensation execution sequence when the change amount is less than a preset change amount threshold, otherwise continue to execute the hybrid iterative optimization by taking the corrected compensation component as an initial compensation component of the next iteration.

[0050] In a second aspect of the embodiment of the present application, an industrial equipment trajectory error big data analysis and intelligent compensation system is provided, comprising:

[0051] A first unit is configured to collect industrial equipment operation state parameters, segment the operation state parameters according to time sequences, extract motion features of each segment of data, generate motion feature fingerprints, compare the motion feature fingerprints with a pre-established feature fingerprint library, and calculate feature deviation data;

[0052] A second unit is configured to distribute the feature deviation data to multiple agents, each agent analyzes regional error features according to the distributed feature deviation data, adjacent agents exchange error feature information and evaluate the transmission strength of the feature deviation to obtain error transmission weights, construct a probability graph structure based on the error transmission weights, and simplify the probability graph structure using a mutual information criterion to obtain an error transmission chain;

[0053] A third unit is configured to construct a hierarchical compensation structure according to the topological structure of the error transmission chain, set error representative points at each layer, calculate transmission influence coefficients between error representative points of adjacent layers to obtain inter-layer coupling constraints, calculate compensation coordination coefficients between error representative points of the same layer to obtain intra-layer coordination constraints, optimize compensation components using a hybrid iterative strategy based on the inter-layer coupling constraints and the intra-layer coordination constraints, and generate a compensation execution sequence;

[0054] A fourth unit is configured to implement error compensation of the motion trajectory of the industrial equipment according to the compensation execution sequence. In a third aspect of the embodiment of the present application, an electronic device is provided, comprising:

[0055] a processor;

[0056] a memory for storing processor-executable instructions;

[0057] The processor is configured to invoke the instructions stored in the memory to execute the method described above.

[0058] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0059] In this embodiment, motion feature fingerprinting technology is employed to process the operating status parameters of industrial equipment in a time-series manner, extract motion features, and compare them with a pre-built feature library. This enables rapid and accurate identification of feature deviations in the equipment's motion trajectory, providing an accurate data foundation for subsequent compensation. Through multi-agent collaborative analysis and probabilistic graph structure construction, this invention achieves refined analysis of regional error features and accurate modeling of error propagation relationships, overcoming the limitations of traditional methods in handling complex error propagation chains and improving the systematicness and comprehensiveness of error identification. Based on a hierarchical compensation structure and a hybrid iterative optimization strategy, this invention establishes a compensation mechanism that balances inter-layer coupling and intra-layer coordination, achieving precise and dynamic error compensation. This effectively improves the motion accuracy and stability of industrial equipment and is suitable for the error compensation needs of various high-precision industrial equipment. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating the big data analysis and intelligent compensation method for trajectory errors of industrial equipment according to an embodiment of the present invention.

[0061] Figure 2 This is a schematic diagram illustrating the process of characteristic subsequence fluctuation trend analysis and waveform segment merging in an embodiment of the present invention;

[0062] Figure 3 This is a heatmap showing the effect of dynamic iteration step size adjustment in an embodiment of the present invention. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0065] Figure 1 This is a flowchart illustrating the big data analysis and intelligent compensation method for industrial equipment trajectory errors according to an embodiment of the present invention. Figure 1 As shown, the method includes:

[0066] Collecting industrial equipment running state parameters, segmenting the running state parameters according to time sequence, extracting motion features of each segment of data, generating motion feature fingerprints, comparing the motion feature fingerprints with a pre-established feature fingerprint library, and calculating feature deviation data;

[0067] Assigning the feature deviation data to multiple agents, each agent analyzing regional error features according to the assigned feature deviation data, adjacent agents exchanging error feature information and evaluating the transmission strength of the feature deviation to obtain error transmission weights, constructing a probabilistic graph structure based on the error transmission weights, and simplifying the probabilistic graph structure using mutual information criteria to obtain an error transmission chain;

[0068] Constructing a hierarchical compensation structure according to the topological structure of the error transmission chain, setting error representative points at each layer, calculating the transmission influence coefficient between adjacent layer error representative points to obtain inter-layer coupling constraints, calculating the compensation coordination coefficient between error representative points in the same layer to obtain intra-layer coordination constraints, and using a hybrid iteration strategy to optimize compensation components based on inter-layer coupling constraints and intra-layer coordination constraints to generate a compensation execution sequence;

[0069] According to the compensation execution sequence, error compensation of the motion trajectory of the industrial equipment is realized.

[0070] In an alternative embodiment,

[0071] Collecting industrial equipment running state parameters, segmenting the running state parameters according to time sequence, extracting motion features of each segment of data, generating motion feature fingerprints, including:

[0072] Obtaining industrial equipment running state parameters, the running state parameters including motion parameters, working condition parameters and environmental parameters;

[0073] Extracting velocity data and acceleration data from the motion parameters; calculating the velocity change and acceleration change of adjacent data points, marking the points where the velocity change and acceleration change are both greater than a preset velocity value as candidate segmentation points, and determining the segmentation points according to the consistency of fluctuation trend; dividing the velocity data and acceleration data into multiple data segments according to the segmentation points;

[0074] Combining the working condition parameters and environmental parameters, calculating the velocity fluctuation value and acceleration fluctuation value of each data segment, constructing a fluctuation curve, obtaining frequency domain feature data through Fourier transform, extracting waveform features and phase features from the frequency domain feature data, and combining the waveform features and phase features to form a feature vector according to a preset mapping relationship;

[0075] The variance contribution values of components of the feature vector are calculated, the feature vector is processed in dimension reduction according to the variance contribution values, feature components after dimension reduction are obtained, weight coefficients of the feature components are calculated in combination with the working condition parameters, the feature components after dimension reduction are recombined according to the weight coefficients, and a motion feature fingerprint is generated.

[0076] Exemplarily, first, the running state parameters of the industrial equipment are acquired, including motion parameters, working condition parameters and environment parameters. Taking a three-dimensional printer as an example, the motion parameters include position, speed and acceleration data of the print head in X, Y and Z three axes; the working condition parameters include printing temperature, printing speed setting value, extrusion amount, printing layer thickness and the like; and the environment parameters include environment temperature, humidity, vibration and the like. The collection frequency is 100 Hz, that is, 100 data points are collected per second, so as to ensure the continuity and integrity of the data. From the collected motion parameters, the speed data and acceleration data are extracted. By calculating adjacent data points, the speed variation and acceleration variation are obtained. The preset speed threshold is set to 0.5 mm / s, and the acceleration threshold is set to 0.8 mm / s 2 When the speed variation and acceleration variation of adjacent data points are greater than the preset values at the same time, the point is marked as a candidate segmentation point.

[0077] The marked candidate segmentation points are analyzed for fluctuation trend consistency. The fluctuation trend consistency refers to the change trend of data before and after the candidate segmentation point. The specific implementation manner is to calculate the speed and acceleration variation rates of 10 data points before and after the candidate segmentation point, and if the sign of the variation rate appears to flip and the duration exceeds 5 data points, the candidate point is confirmed as an effective segmentation point. For example, in the printing process of a three-dimensional printer, when the print head switches from straight line motion to curve motion, the speed and acceleration variation will produce obvious fluctuation, and at this time, a segmentation point will be generated.

[0078] According to the determined segmentation points, the speed data and acceleration data are divided into a plurality of data segments. For a three-dimensional printer to print a complex model, there can be hundreds of data segments. Each data segment represents the running state of the equipment under a specific motion mode. In combination with the working condition parameters and the environment parameters, the speed fluctuation value and the acceleration fluctuation value of each data segment are calculated. The speed fluctuation value is the standard deviation of the speed in the data segment, and the acceleration fluctuation value is the standard deviation of the acceleration in the data segment. In actual application, when the printing temperature is 210℃ and the environment temperature is 25℃, the typical value of the speed fluctuation value of the X-axis in the straight line motion segment is 0.3 mm / s, and the acceleration fluctuation value is 0.5 mm / s 2 ; while in the curve motion segment, the speed fluctuation value can reach 0.8 mm / s, and the acceleration fluctuation value can reach 1.2 mm / s 2 .

[0079] A fluctuation curve is constructed according to the calculated fluctuation values, and the fluctuation curve is converted into frequency domain characteristic data by Fourier transform. In frequency domain analysis, waveform features and phase features are extracted. The waveform features include main frequency, frequency amplitude, harmonic ratio, etc.; the phase features include phase angle, phase difference, etc. For example, under normal operation of the three-dimensional printer, the main frequency of the X-axis movement is usually in the range of 2-5 Hz, and the amplitude is between 0.1-0.3 mm / s; when an anomaly occurs, an abnormal frequency component may appear in the range of 10-15 Hz, and the amplitude may increase to 0.5-0.8 mm / s.

[0080] The waveform features and phase features are combined to form a feature vector according to a preset mapping relationship. The preset mapping relationship means that different features are combined according to their importance. In the application of three-dimensional printers, the weight of the main frequency is set to 0.4, the weight of the amplitude is set to 0.3, the weight of the harmonic ratio is set to 0.2, and the weight of the phase angle is set to 0.1. The dimension of the formed feature vector may be high, usually containing 30-50 feature components. Dimensionality reduction processing is performed on the feature vector. First, the variance contribution value of each feature component is calculated. The variance contribution value represents the degree of explanation of the component to 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 result, the feature components whose cumulative variance contribution value reaches 90% are retained, and the remaining components are discarded, realizing dimensionality reduction of the feature vector.

[0081] The weight coefficients of the feature components are calculated in combination with the working condition parameters. In different working conditions, the importance of the feature components is different. For example, when the printing speed is 60 mm / s, the weight of the speed-related feature components should be increased; when the printing temperature is too high, the weight of the acceleration-related feature components should be increased. In practical applications, the weight coefficient range can be set to 0.6-1.4, and dynamically adjusted according to the deviation degree of the working condition parameters.

[0082] The dimensionally reduced feature components are recombined according to the weight coefficients to generate a motion feature fingerprint. The motion feature fingerprint is a multi-dimensional vector, and the typical dimension is 8-12. Each component represents an aspect of the motion characteristics of the equipment. For three-dimensional printers, the motion feature fingerprint can reflect the smoothness, response speed, trajectory accuracy and other characteristics of the print head movement. The generated motion feature fingerprint can be used for anomaly detection, quality prediction and trajectory error compensation.

[0083] In this embodiment, the characteristics and rules of device trajectory error can be accurately identified by extracting motion characteristic fingerprints. The scheme combines time series segmentation processing and frequency domain feature extraction, significantly improving the accuracy and stability of feature extraction. Through the consistency analysis of the fluctuation trend of speed and acceleration data, the motion state is accurately segmented, solving the problem of inaccurate segmentation in complex working conditions in traditional methods. The introduction of working condition parameters and environmental parameters for feature weighting makes the feature extraction more environmentally adaptable. The use of variance contribution value for dimension reduction reduces the computational complexity and improves the algorithm running efficiency. This method can monitor the device running state in real time, quickly identify abnormal trajectories, and intelligently compensate and adjust, significantly improving product precision and consistency.

[0084] In an alternative embodiment,

[0085] Comparing the motion characteristic fingerprint with the pre-established characteristic fingerprint library to calculate the characteristic deviation data includes:

[0086] Divide the motion characteristic fingerprint into characteristic subsequences according to the sampling time window, calculate the fluctuation trend of adjacent characteristic subsequences, and combine the characteristic subsequences according to the fluctuation trend to obtain waveform segments, and extract the amplitude sequence and phase sequence of the waveform segments;

[0087] Standardize the amplitude sequence and phase sequence respectively to obtain waveform features and phase features, combine the waveform features and phase features to construct a feature vector, and calculate a weight coefficient according to the feature vector;

[0088] Extract fingerprint data from the pre-established characteristic fingerprint library, perform sequence division and feature extraction on the fingerprint data, construct a reference feature vector, calculate the matching degree of the feature vector and the reference feature vector, and select the fingerprint data with the highest matching degree as the target fingerprint;

[0089] Calculate the feature distance between the feature vector of the waveform segment and the reference feature vector of the corresponding waveform segment of the target fingerprint, calculate the weighted deviation value according to the feature distance and the weight coefficient, and calculate the change rule by statistically analyzing the time sequence distribution of the weighted deviation value;

[0090] According to the change rule, judge the divergence trend of the weighted deviation value; when the divergence trend appears, calculate the divergence rate and divergence direction as the characteristic deviation data.

[0091] In this embodiment, after obtaining the motion characteristic fingerprint, it needs to be divided into characteristic subsequences according to the sampling time window. The sampling time window is usually set to 5 seconds, that is, the continuously collected motion characteristic fingerprint data is divided into a characteristic subsequence every 5 seconds. For a 30-minute processing task, about 360 characteristic subsequences can be obtained. Each characteristic subsequence contains complete motion characteristic information within the time window.

[0092] The fluctuation change trend of adjacent feature subsequences is calculated, which is achieved by analyzing the change rate of each dimension feature value of adjacent feature subsequences. The fluctuation change trend refers to the change direction and amplitude of the feature value in the time dimension. In specific implementation, the difference between each feature dimension in adjacent subsequences is calculated, and the difference is smoothed to obtain the fluctuation change trend data. When the industrial equipment changes from low-speed motion to high-speed motion, the change rate of the speed-related feature dimension of adjacent feature subsequences may reach 20%-30%, while in the stable motion stage, the change rate is usually less than 5%.

[0093] The feature subsequences are merged according to the fluctuation change trend to obtain the waveform segment. The merging standard is the consistency of the fluctuation change trend, and the specific judgment method is to set a threshold value. When the fluctuation change trend of adjacent feature subsequences is less than the threshold value, they are considered to belong to the same waveform segment. The fluctuation change trend threshold is set to 8%, that is, when the fluctuation change rate of adjacent feature subsequences is less than 8%, they are merged into one waveform segment. In this way, a 30-minute processing task may be merged into 20-30 waveform segments, each representing a relatively stable motion state.

[0094] The amplitude sequence and the phase sequence are extracted from the merged waveform segment. The amplitude sequence refers to the numerical value of each feature dimension in the waveform segment, and the phase sequence refers to the relative change time sequence relationship of each feature dimension. The amplitude sequence can reflect the motion intensity of the equipment in different directions, and the phase sequence reflects the coordination and sequence of motion in different directions. The amplitude sequence and the phase sequence are standardized respectively to obtain the waveform feature and the phase feature. Standardization processing is to convert data of different dimensions to a unified numerical range. A commonly used method is to subtract the mean value and divide by the standard deviation. The standardized waveform feature and phase feature value range is usually between -3 and 3, which is convenient for subsequent comparison and analysis. Standardization processing can eliminate the absolute amplitude difference between different processing tasks and highlight the relative characteristics of the motion pattern.

[0095] The waveform feature and the phase feature are combined to construct a feature vector. The combination method is to splice the standardized waveform feature and phase feature according to a predefined order to form a comprehensive feature vector. The feature vector usually contains 20-30 dimensions, of which the first half is the waveform feature and the second half is the phase feature. The constructed feature vector can fully represent the running state characteristics of the equipment in a specific motion stage.

[0096] The weight coefficient is calculated according to the feature vector. The weight coefficient reflects the importance of each dimension of the feature vector in the current working condition. The calculation method is based on the fluctuation degree and the discrimination degree of the feature dimension. The feature dimension with high fluctuation degree and high discrimination degree is given a higher weight. When processing complex contours, the weight of the feature dimension related to direction change will increase; when processing fine structures, the weight of the feature dimension related to speed stability will increase. The value range of the weight coefficient is usually 0.5-2.0.

[0097] The fingerprint data is extracted from the pre-established feature fingerprint library. The feature fingerprint library contains a large number of standard fingerprints generated from historical operation data, and each fingerprint corresponds to a typical operating state. The fingerprint library may contain standard fingerprint data corresponding to various processing materials, processing speeds, and processing structure types, and usually contains hundreds to thousands of standard fingerprint entries. The fingerprint data is divided into sequences and features are extracted to construct a reference feature vector. This step is consistent with the processing method of the motion feature fingerprint described above, ensuring that the processing methods of the current data and the reference data are consistent, facilitating accurate comparison. The standard fingerprints extracted from the fingerprint library are subjected to the same sequence division, waveform segment merging, feature extraction, and standardization processing to form a reference feature vector.

[0098] The matching degree of the feature vector and the reference feature vector is calculated. The matching degree is calculated using the cosine similarity method, i.e., the cosine value of the included angle between the two vectors is calculated. The closer the cosine value is to 1, the higher the matching degree. The threshold for good matching is usually set to 0.85, i.e., when the cosine similarity is greater than 0.85, it is considered that the two feature vectors have high similarity. Select the fingerprint data with the highest matching degree as the target fingerprint. If there are multiple fingerprint data with matching degrees exceeding the threshold, select the one with the highest matching degree as the target fingerprint. The matching degree is usually between 0.80 and 0.95, and a lower matching degree may indicate that the current operating state differs from the historical data, which needs to be further analyzed.

[0099] The feature distance between the feature vector of the waveform segment and the reference feature vector of the corresponding waveform segment of the target fingerprint is calculated. The feature distance is calculated using the Euclidean distance, i.e., the square root of the sum of the squares of the differences in each dimension. The smaller the feature distance, the closer the current operating state is to the standard state. The feature distance of the normal operating state is usually less than 0.5, and when the feature distance exceeds 1.0, it may indicate an abnormal state.

[0100] The weighted deviation value is calculated according to 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, which reflects the actual deviation degree considering the importance of the current working condition. When processing fine structures, even a small feature distance may result in a large weighted deviation value due to high weight, indicating the need for higher precision control.

[0101] The time sequence distribution of the statistical weighted deviation value is obtained to obtain a change rule. The time sequence distribution refers to the change of the weighted deviation value with time. By analyzing the weighted deviation values of a plurality of continuous time windows, the change trend of the deviation can be identified. The change rule of the deviation value can present a plurality of modes such as stability, fluctuation, increment, or periodic change. The divergence trend of the weighted deviation value is judged according to the change rule. The divergence trend refers to that the deviation value continuously increases and the growth rate accelerates, indicating that the running state of the equipment is deviating from the normal range. The judgment standard is that the deviation values of a plurality of continuous time windows monotonically increase and the growth rate continuously increases. When the machine tool bearing wears, the divergence trend of the weighted deviation value can occur, and the growth is slow at the initial stage and accelerates at the later stage.

[0102] When the divergence trend occurs, the divergence rate and the divergence direction are calculated as the characteristic deviation data. The divergence rate is the acceleration of the growth of the deviation value, and the divergence direction is the main component direction of the deviation of each dimension of the characteristic vector. When the lead screw loosens, the divergence direction is mainly reflected in the characteristic dimension of the related shaft, and the divergence rate can reach 0.05-0.1 / hour, indicating that the problem is accelerating and needs to be intervened in time. By identifying the divergence trend and calculating the divergence rate and direction, the trajectory error problem that can occur in the equipment can be predicted, and a basis for subsequent compensation adjustment is provided.

[0103] In the embodiment, by systematically comparing the motion characteristic fingerprint with the pre-established characteristic fingerprint library, the accurate identification and analysis of the trajectory error of the industrial equipment are realized. The time window division and the fluctuation trend merging are adopted, and the accuracy of the feature extraction in different motion stages is effectively solved. Through the standardization processing and the characteristic vector construction, the technical difficulty of the incomparable data under different working conditions is overcome. The weight coefficient calculation mechanism is introduced, so that the system can adaptively adjust the importance of each characteristic dimension according to the current working condition, and the pertinence of the analysis is improved. The divergence trend judgment and the divergence rate calculation realize the early warning of the development of the trajectory error, so that the equipment maintenance is changed from passive response to active prevention. The method can identify the slight motion abnormality, realize the early prediction of the change trend of the trajectory error, and greatly reduce the processing defects caused by the trajectory error. At the same time, the method reduces the dependence on the experience of professionals, realizes the intelligentization and standardization of the trajectory error analysis.

[0104] Figure 2 A feature subsequence fluctuation change trend analysis and waveform segment merging process schematic diagram for the embodiment of the application is shown in FIG. 6. Figure 2As shown, the horizontal axis of the graph represents the time window number (a total of 300 windows, about 25 minutes), and the vertical axis represents the fluctuation rate. The present technical solution (solid line) can more accurately capture the changes in the motion state, especially at the low-to-high speed transition point (fluctuation rate 22.0%) and the high-to-low speed transition point (fluctuation rate 12.0%). The horizontal dashed line represents the merging threshold of 8%, when the fluctuation rates of adjacent feature subsequences are less than the threshold, they are merged into the same waveform segment. Five waveform segments are identified in the figure, representing different motion states. Compared with the traditional fixed threshold merging method (short dashed line) and the sliding window method (dotted line), the present technical solution shows higher sensitivity at the trend turning point, can more accurately identify the feature changes of the device from low-speed motion to high-speed motion (fluctuation rate reaches 22.0%) and the stable running stage (fluctuation rate is about 15.0% and 3.5%), thereby realizing more accurate waveform segment division, laying a foundation for subsequent feature extraction and anomaly detection.

[0105] In an alternative embodiment,

[0106] The feature deviation data is distributed to a plurality of agents, each agent analyzes the regional error features according to the distributed feature deviation data, adjacent agents exchange error feature information and evaluate the transmission strength of the feature deviation to obtain an error transmission weight, a probability graph structure is constructed based on the error transmission weight, and the probability graph structure is simplified to obtain an error transmission chain using a mutual information criterion, including:

[0107] The motion space of the industrial equipment is divided into grid cells, each grid cell corresponds to an agent, the Mahalanobis distance between the feature deviation data point and the center of the grid cell is calculated, the distribution weight is calculated based on the Mahalanobis distance, and the feature deviation data is distributed to the agent according to the distribution weight;

[0108] The mean and standard deviation of the deviation in each agent region are calculated, the main direction of the deviation is extracted, and the mean, standard deviation and main direction of the deviation are combined to construct a regional error feature vector;

[0109] Adjacent agents exchange regional error feature vectors, calculate the feature vector similarity to construct a feature similarity matrix, and calculate the error gradient between adjacent agents;

[0110] The feature similarity matrix and the error gradient are combined to obtain a transmission strength matrix, the transmission strength matrix is normalized to obtain an error transmission weight, and an initial probability graph is constructed based on the error transmission weight;

[0111] The mutual information values between nodes in the initial probability graph are calculated, edges with mutual information values less than a preset threshold are deleted, and a simplified probability graph is obtained. In the simplified probability graph, the maximum weight spanning tree algorithm is used to extract the optimal transmission path by taking the error transmission weight as the objective function. The error transmission direction and transmission strength are determined according to the size relationship of the error transmission weight on the path, and the error transmission chain structure with the transmission direction and the transmission strength is constructed.

[0112] Exemplarily, after obtaining the feature deviation data, the motion space of the industrial equipment is divided into grid units. The granularity of grid division depends on the motion accuracy requirement and the size of the working space of the equipment. Generally, the space can be divided into a 10x10x5 three-dimensional grid, corresponding to the working range of the X, Y and Z three motion axes. Each grid unit corresponds to an agent, which is responsible for analyzing the error characteristics in the region. The size of the grid unit is usually 10-30 mm to ensure sufficient spatial resolution.

[0113] The Mahalanobis distance between the feature deviation data points and the center of the grid unit is calculated. The Mahalanobis distance takes into account the covariance structure of the data, and can more accurately represent the closeness of the data points to the grid center. The calculation method is to multiply the difference vector between the feature deviation data point and the grid center point by the inverse matrix of the covariance matrix, and then multiply by the transpose of the difference vector. When the difference vector is zero, the Mahalanobis distance is zero; when the difference vector is larger and deviates farther along the principal eigenvector direction of the covariance matrix, the Mahalanobis distance is larger. In practical applications, the calculation result of the Mahalanobis distance is usually between 0-10.

[0114] The distribution weight is calculated based on the Mahalanobis distance. The distribution weight adopts an exponential decay function, that is, the weight is equal to the negative exponential power, where the index is the Mahalanobis distance divided by a preset bandwidth parameter. The bandwidth parameter controls the rate of weight decay with distance, and is usually set to 2.0-3.0. The closer the distance, the greater the weight; the farther the distance, the smaller the weight. In this way, each feature deviation data point contributes to all grid units, but contributes more to the neighboring grid units.

[0115] The feature deviation data is distributed to the agent according to the distribution weight. The distribution process is to distribute the information of the feature deviation data point to each agent according to the weight proportion. For a feature deviation data point, the Mahalanobis distance and the corresponding distribution weight of all grid unit centers are calculated, and then the deviation information of the data point is distributed to each agent according to the weight proportion. This soft distribution method can handle the case where the data point is located at the grid boundary, avoiding the discontinuity that may be caused by hard distribution.

[0116] The mean and standard deviation of the bias in each agent region are calculated. The mean of the bias is the weighted average of all the assigned feature bias data in the region, and the standard deviation is the degree of dispersion of the bias data around the mean. When calculating, the assignment weight is used as the weighting coefficient to ensure that data points closer to the grid center have more influence. In industrial equipment motion, the mean of the bias reflects the systematic error of the region, and the standard deviation reflects the size of the random error.

[0117] The main direction of the bias is extracted. The main direction of the bias refers to the main change direction of the feature bias data in the region, which is determined by calculating the covariance matrix of the feature bias data and solving the eigenvector corresponding to the maximum eigenvalue. The main direction of the bias reflects the main trend of the error in the region, which is important for understanding the error transmission path. In practical applications, the main direction of the bias is usually represented by a three-dimensional unit vector, indicating the main distribution direction of the error in space. The mean, standard deviation and main direction of the bias are combined to construct the regional error feature vector. The regional error feature vector is a multi-dimensional vector that comprehensively represents the error characteristics of the region, containing information such as the mean, standard deviation and main direction. The dimension of the feature vector is usually 5-7, which can fully describe the size, distribution and direction characteristics of the error in the region.

[0118] Adjacent agents exchange regional error feature vectors. Communication between agents is based on the adjacency relationship of the grid, and each agent can have up to 26 adjacent agents. During the exchange process, the agent sends its own regional error feature vector to the adjacent agents, and receives the feature vectors of the adjacent agents. Through the exchange of feature vectors, the agent obtains the error characteristic information of the surrounding region, providing a basis for subsequent analysis of error transmission.

[0119] The feature vector similarity is calculated to construct a feature similarity matrix. The feature vector similarity is calculated using cosine similarity, which is the dot product of two feature vectors divided by the product of their respective magnitudes. The similarity value is between -1 and 1, with a value closer to 1 indicating that the error characteristics of the two regions are more similar. The feature similarity matrix is a symmetric matrix, with matrix elements representing the degree of feature similarity between corresponding agents. The error gradient between adjacent agents is calculated. The error gradient is the rate of change of the error between two adjacent regions, calculated as the difference between the mean deviations of the two regions divided by the distance between their center points. The error gradient reflects the trend of error change along the space, with the gradient direction pointing to the direction of increasing error. In practical applications, the error gradient is usually represented as a vector, containing both magnitude and direction information. The feature similarity matrix and the error gradient are combined to obtain a transfer strength matrix. The combination method is to take 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 there is a significant error gradient, the transfer strength is larger, indicating that the error may be transmitted in that direction; when the characteristics are not similar or the gradient is small, the transfer strength is smaller. The transfer strength matrix describes the possible transmission paths and strengths of the error in space.

[0120] The transfer strength matrix is normalized to obtain the error transmission weight. The normalization process is to divide the elements of the transfer strength matrix by the sum of the matrix elements, so that the sum of all elements is 1. The normalized matrix elements are the error transmission weights, reflecting the relative importance of each transmission path. The larger the error transmission weight, the higher the likelihood of error transmission along that path.

[0121] Based on the error transmission weight, an initial probability graph is constructed. The initial probability graph is a weighted undirected graph, with nodes representing agents and edges representing the connection between agents, with edge weights corresponding to the error transmission weight. The initial probability graph describes all possible error transmission paths, but contains many weak connections that need to be further simplified. The mutual information value between nodes in the initial probability graph is calculated. Mutual information is an indicator of the dependence between two random variables, calculated as the sum of the entropies of the two nodes minus the joint entropy. The larger the mutual information value, the stronger the dependence between the two nodes; the smaller the mutual information value, the weaker the relationship between the two nodes. In practical applications, mutual information is calculated based on historical error data of the nodes, obtained through statistical analysis. Edges with mutual information values less than a pre-set threshold are deleted to obtain a simplified probability graph. The pre-set threshold is usually set to the median or a specific percentile of the mutual information value distribution, for example, set to the 70th percentile of all mutual information values. Deleting edges with small mutual information values and retaining edges with large mutual information values can reduce the complexity of the graph and highlight the main error transmission paths. The simplified probability graph contains the main error transmission relationships, making it easier to analyze and understand.

[0122] In the simplified probability graph, the error propagation weight is taken as the objective function, and the maximum weight spanning tree algorithm is used to extract the optimal propagation path. 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 maximum. The algorithm starts with the edge with the largest weight, and gradually adds edges with smaller weights until a tree containing all nodes is formed, while avoiding forming loops. The maximum weight spanning tree contains the most likely error propagation path, providing a skeletal structure for error propagation analysis.

[0123] The error propagation direction and intensity are determined according to the size relationship of the error propagation weight on the path. The propagation direction points from the node with smaller error propagation weight to the node with larger weight, indicating that the error may propagate from the area with smaller weight to the area with larger weight. The propagation intensity is represented by the error propagation weight of the corresponding edge, and the larger the weight, the greater the propagation intensity. By analyzing the propagation direction and intensity, the source of the error and the main propagation path can be identified, providing a basis for subsequent error compensation. The error propagation chain structure with propagation direction and intensity is constructed. The error propagation chain is a directed and weighted tree structure, where nodes represent agents and edges represent error propagation paths. The direction of the edge represents the propagation direction, and the weight of the edge represents the propagation intensity. The error propagation chain intuitively shows the propagation law of the error in the industrial equipment, helping to understand the generation mechanism and propagation process of the error, and laying a foundation for precise error compensation.

[0124] In this embodiment, through the multi-agent collaborative analysis mechanism, the spatial distribution characteristics and propagation law of the industrial equipment trajectory error are accurately identified and evaluated. The existing technology mainly uses a single global error model or a simple region division method to analyze the trajectory error, which is difficult to accurately represent the local characteristics and propagation relationship of the error in complex space, resulting in insufficient error compensation accuracy. The soft assignment mechanism based on Mahalanobis distance breaks through the limitations of traditional hard boundary division, allowing feature deviation data to be smoothly assigned to multiple agents, effectively avoiding the discontinuity problem caused by boundary effects. The feature vector exchange and similarity analysis mechanism between agents, combined with error gradient calculation, innovatively constructs the propagation intensity matrix, realizing the probabilistic description of the error propagation path. The mutual information criterion is introduced to simplify the probability graph, retaining the key propagation path and significantly reducing the 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 scheme not only improves the accuracy of trajectory error analysis, but also significantly reduces the resource consumption of compensation calculation, making high-precision motion control of complex industrial equipment possible, which is of great significance to improving processing quality and production efficiency.

[0125] In an alternative embodiment,

[0126] In the simplified probability graph, the error propagation weight is taken as the objective function, and the maximum weight spanning tree algorithm is used to extract the optimal propagation path. According to the size relationship of the error propagation weight on the path, the error propagation direction and propagation strength are determined, and the error propagation chain structure with propagation direction and propagation strength is constructed, including:

[0127] The error propagation weight of each edge in the simplified probability graph structure is obtained, and the error propagation weight is normalized to a preset interval based on the maximum weight and the minimum weight, to obtain the normalized propagation weight of each edge.

[0128] The edges in the probability graph are sorted in descending order according to the normalized propagation weight, and the edge with the maximum weight is selected in turn. It is judged whether the edge forms a loop and whether the error amplitude of the nodes at both ends of the edge satisfies the size relationship constraint. The edge that satisfies the constraint condition is added to the edge set, and the maximum weight spanning tree is constructed until the construction is completed.

[0129] The average value of the normalized propagation weight between the two end nodes and their adjacent nodes of each edge in the maximum weight spanning tree is calculated to obtain the local weight gradient. Based on the size of the local weight gradient of the two end nodes, the error propagation direction is determined, and the product of the difference value of the local weight gradient and the normalized propagation weight is taken as the propagation strength.

[0130] The current propagation weight and propagation 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 edges in the changed area are re-executed for path extraction, and the local structure of the maximum weight spanning tree is updated to obtain an error propagation chain with dynamic updating capability.

[0131] In this embodiment, first, the error propagation weight of each edge in the simplified probability graph structure is obtained. The error propagation weight reflects the possibility of error propagation between two regions, and the weight value is usually between 0 and 1, but there may be uneven distribution. For example, in a probability graph containing 200 nodes and about 800 edges, the error propagation weight may be distributed between 0.05 and 0.95, and most of the edges have a weight between 0.3 and 0.7.

[0132] The error propagation weight is normalized to a preset interval based on the maximum weight and the minimum weight, to obtain the normalized propagation weight of each edge. The normalization process is to linearly map the original weight to the preset interval, and the preset interval is usually 0.1 to 1.0. The normalization method is to subtract the minimum weight from the original weight, then divide by the difference between the maximum weight and the minimum weight, multiply by the range of the preset interval, and finally add the minimum value of the preset interval. Through normalization, the error propagation weights of different regions and different time periods can be compared and analyzed on a unified scale, improving the stability and interpretability of the algorithm.

[0133] The edges in the probability graph are sorted in descending order according to the normalized transmission weight. The sorting process is to arrange all edges in descending order of normalized transmission weight to form an ordered edge list. The sorting result facilitates the subsequent execution of the greedy algorithm and ensures that edges with larger weights are selected first. In industrial equipment trajectory error analysis, edges with larger weights usually correspond to paths with more obvious error transmission, which is of great significance to understanding the error transmission mechanism.

[0134] The edge with the largest weight is selected in turn, and it is determined whether the edge forms a loop and whether the error amplitudes of the two end nodes satisfy the size relationship constraint. The loop judgment is to ensure that the finally constructed structure is a tree without loops. The judgment method is to check 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 size relationship constraint is to ensure the rationality of the error transmission direction. The constraint condition is that the error amplitude of one end node of the edge should be less than that of the other end node, or the difference should be within the allowed range. The error amplitude refers to the error size of the region represented by the node, usually represented by the root mean square error.

[0135] The edges that satisfy the constraint condition are added to the edge set until the maximum weight spanning tree is constructed. The edge set is initially empty, and edges that satisfy the condition are added gradually as the algorithm executes. When the number of edges in the edge set reaches the number of nodes minus one, it means that a tree containing all nodes has been constructed, i.e., a maximum weight spanning tree. The maximum weight spanning tree contains the most likely paths of error transmission, providing a skeletal structure for error transmission analysis. In industrial equipment trajectory error analysis, a maximum weight spanning tree containing 200 nodes has 199 edges, which represent the most important error transmission paths.

[0136] The average value of the normalized transmission weight between the two end nodes of each edge and its adjacent nodes in the maximum weight spanning tree is calculated to obtain the local weight gradient. The local weight gradient reflects the change of the weight of the node in its local area. The calculation method is to average the normalized transmission weight between the node and all its adjacent nodes. Each node has a local weight gradient value, and the larger the value, the stronger the transmission effect of the node in the local area. In industrial equipment trajectory error analysis, the local weight gradient is usually distributed between 0.2 and 0.8, reflecting the strength of the different regions in error transmission.

[0137] The error propagation direction is determined based on the local weight gradient size of the two end nodes. The propagation direction is from the node with smaller local weight gradient to the node with larger local weight gradient. This definition is based on the physical law that error usually propagates from low gradient area to high gradient area. In industrial equipment trajectory error analysis, the propagation direction usually propagates from the fixed end to the moving end of the equipment, reflecting the process of error accumulation. The product of the difference value of the local weight gradient and the normalized propagation weight is taken as the propagation strength. The propagation strength reflects the strength of error propagation along this direction. The calculation method is to multiply the difference value of the local weight gradient of the two end nodes of the edge by the normalized propagation weight of the edge. The larger the propagation strength, the higher the possibility of error propagation along this path, and the greater the impact on the overall accuracy of the equipment. In industrial equipment trajectory error analysis, the propagation strength usually distributes between 0.05 and 0.5, and the difference in propagation strength of different paths reflects the unevenness of error propagation.

[0138] The current propagation weight and propagation direction of each edge in the maximum weight spanning tree are periodically acquired. Periodic acquisition means that the propagation weight and propagation direction of each edge are recalculated every certain time (such as 1 minute or 5 minutes) during the operation of the equipment. Through periodic acquisition, the dynamic changes of error propagation law can be monitored, providing basis for timely adjustment of compensation strategy. In industrial equipment trajectory error analysis, the propagation weight and propagation direction may change with factors such as equipment operating state, workload, and environmental temperature.

[0139] The weight change amount and direction change amount are calculated. The weight change amount is the absolute value of the difference between the current propagation weight and the last period propagation weight, and the direction change amount is the included angle between the current propagation direction and the last period propagation direction. The calculation of change amount is used to judge whether the error propagation law has changed significantly. In industrial equipment trajectory error analysis, the weight change amount is usually represented by relative change rate, such as 10% or 20%; the direction change amount is usually represented by angle, such as 15 degrees or 30 degrees.

[0140] When the weight change amount is greater than the weight change threshold or the direction change amount is greater than the direction change threshold, the edges in the changed area are re-executed for path extraction, and the local structure of the maximum weight spanning tree is updated. The weight change threshold and the direction change threshold are preset judgment criteria for determining when to update the error propagation chain. Re-executing path extraction for the edges in the changed area means reapplying the maximum weight spanning tree algorithm only to the area that has changed significantly, rather than recalculating the entire graph, thereby reducing the computational complexity. In industrial equipment trajectory error analysis, the weight change threshold is usually set to 15%, and the direction change threshold is usually set to 25 degrees.

[0141] The local structure of the maximum weight spanning tree is updated to obtain an error propagation chain with dynamic updating capability. The local structure updating refers to replacing only the edges of the area that has changed significantly and keeping other areas unchanged. Through local updating instead of global reconstruction, the calculation resource consumption can be significantly reduced while ensuring the accuracy. The error propagation chain with dynamic updating capability can adapt to the changes in the running state of the equipment and reflect the dynamic characteristics of the error propagation law in real time.

[0142] In the embodiment, the error propagation chain structure is constructed based on the maximum weight spanning tree algorithm to realize accurate characterization and analysis of the trajectory error propagation law of the industrial equipment. The prior art mainly uses a static error model or a simple accumulation method to analyze the trajectory error propagation, which is difficult to accurately capture the dynamic characteristics and directionality of the error propagation, resulting in limited compensation effect. The normalized propagation weight mechanism is innovatively introduced to solve the problem of incomparable error propagation intensity in different areas, making the weight evaluation more objective and accurate. The edge selection strategy combining loop judgment and error amplitude constraint ensures that the constructed propagation path has clear physical meaning and conforms to the actual law of error propagation. The introduction of local weight gradient makes the propagation direction judgment no longer rely on simple error size comparison, but based on the overall propagation trend in the area, greatly improving the accuracy of direction judgment. The propagation intensity calculation method considers the comprehensive influence of gradient difference and weight, more comprehensively characterizing the error propagation ability. The core advantage of the scheme lies in the dynamic updating mechanism, which realizes adaptive updating of the propagation chain through periodic monitoring of weight and direction changes, enabling the system to respond to dynamic factors such as working condition changes and temperature drift. This dynamic and adaptive error propagation 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.

[0143] In an alternative embodiment,

[0144] A hierarchical compensation structure is constructed according to the topological structure of the error propagation chain, error representative points are set at each layer, the propagation influence coefficient between adjacent layer error representative points is calculated to obtain inter-layer coupling constraints, the compensation coordination coefficient between error representative points in the same layer is calculated to obtain intra-layer coordination constraints, and a hybrid iteration strategy is used based on the inter-layer coupling constraints and the intra-layer coordination constraints to optimize the compensation components and generate a compensation execution sequence, including:

[0145] The topological characteristics of the error propagation chain are analyzed, the error source node is determined, the shortest propagation path length from each node to the error source node is calculated, nodes with the same propagation path length are attributed to the same level, and a hierarchical compensation structure is constructed;

[0146] In each layer of the hierarchical compensation structure, an amplitude feature and a change rate feature of an error node are calculated, the amplitude feature and the change rate feature are combined by weighting to obtain a node score, and a node with the highest score and a distance between adjacent nodes greater than a preset distance threshold is selected as an error representative point;

[0147] For the error representative points of adjacent layers in the hierarchical compensation structure, a projection component and a perpendicular component of a transmission direction are calculated, a transmission influence coefficient is constructed based on the projection component and the perpendicular component, and the transmission influence coefficient is corrected based on a spatial distance decay characteristic to obtain an inter-layer coupling constraint;

[0148] For the error representative points of the same layer in the hierarchical compensation structure, a local variance and a global variance of error distribution are calculated, a spatial adaptive weight is constructed based on the local variance and the global variance, and the spatial adaptive weight is dynamically adjusted according to a compensation effect to obtain an intra-layer coordination constraint;

[0149] Based on the inter-layer coupling constraint and the intra-layer coordination constraint, a hybrid iterative strategy of inter-layer top-down alternation and intra-layer parallelism is adopted to optimize the compensation component, an iteration step is dynamically adjusted according to a compensation residual, an inertia correction term is constructed by introducing a historical compensation amount to suppress compensation oscillation until the compensation component converges, and a compensation execution sequence is generated.

[0150] Illustratively, first, an error source node is determined. The error source node is the source of error, which is usually represented by a node without an incoming edge or with a small incoming edge weight but a large outgoing edge weight. The method of determining the error source node is to calculate the out-in degree ratio of each node, that is, the sum of the outgoing edge weight divided by the sum of the incoming edge weight. The node with the largest ratio is usually the error source node. For example, in a three-dimensional printer system, the error source node is usually located at the starting position of the base or the transmission system. The structural rigidity and positioning accuracy of these positions have a decisive influence on the overall error.

[0151] The shortest transmission path length of each node to the error source node is calculated. The shortest transmission path length refers to the minimum number of edges from the error source node to the target node. The calculation method uses the breadth-first search algorithm, which starts from the error source node and expands outward layer by layer until all nodes are visited. For each node, record its shortest path length to the error source node. In industrial equipment error analysis, the path length reflects the number of stages of error transmission. The longer the path, the more links the error accumulates, and the more difficult the compensation is.

[0152] Nodes with the same error propagation length are attributed to the same level, and a hierarchical compensation structure is constructed. The hierarchical compensation structure is a structure in which nodes in the error propagation chain are hierarchically organized according to the distance to the error source node. Nodes with the same distance belong to the same level, and the levels are sequentially the 0th level, the 1st level, the 2nd level, and so on from the error source node. The hierarchical compensation structure reflects the hierarchical nature of error propagation and provides an organizational framework for subsequent compensation strategies. In complex industrial equipment, the hierarchical structure usually has 3-7 levels, and each level contains several nodes representing the error characteristics of different regions in the motion space.

[0153] In each level of the hierarchical compensation structure, the amplitude feature and the rate of change feature of the error node are calculated. The amplitude feature refers to the absolute size of the node error, usually represented by the root mean square error; the rate of change feature refers to the degree of change of the node error over time, usually represented by the ratio of the standard deviation to the mean of the error. The amplitude feature reflects the severity of the node error, and the rate of change feature reflects the stability of the node error. The amplitude feature and the rate of change feature are combined by weighting to obtain the node score. The way of weighted combination is to multiply the amplitude feature by a first weight coefficient, multiply the rate of change feature by a second weight coefficient, and then sum to obtain the node score. The weight coefficients are set according to application requirements, when the compensation stability requirement is high, the weight of the rate of change feature can be increased; when the compensation precision requirement is high, the weight of the amplitude feature can be increased. Usually the first weight coefficient is set to 0.6-0.8, and the second weight coefficient is set to 0.2-0.4. The higher the node score, the more significant the error characteristics of the node, and the greater the impact on the overall accuracy.

[0154] The node with the highest score and a distance between adjacent nodes greater than a preset distance threshold is selected as the error representative point. The error representative point is a key node in each level, which is used to represent the error characteristics of the level and calculate the compensation amount. The selection method is to arrange the nodes in descending order of node score, and select the node with the highest score in turn, while ensuring that the distance between the selected nodes is greater than the preset threshold, to ensure the uniformity and representativeness of the representative point distribution. The preset distance threshold is usually set to 5%-10% of the size of the working space.

[0155] For the error representative points of adjacent layers in the hierarchical compensation structure, the projection component and the perpendicular component of the transmission direction are calculated. The transmission direction is a unit vector from the upper layer node to the lower layer node. The projection component is the projection of the transmission direction in the error main direction, and the perpendicular component is the projection of the transmission direction in the plane perpendicular to the error main direction. The projection component and the perpendicular component reflect the directional characteristics of error propagation, which affect the direction and size of compensation. In a three-dimensional printer system, the error of the Z-axis transmission system may mainly propagate along the Z-axis direction, at this time the projection component is larger and the perpendicular component is smaller.

[0156] The transfer influence coefficient is constructed based on the projection component and the vertical component. The transfer influence coefficient represents the influence degree of the error of the upper layer node on the lower layer node. The construction method is to multiply the projection component by a first coefficient, multiply the vertical component by a second coefficient, and then sum to obtain the transfer influence coefficient. Generally, the first coefficient is greater than the second coefficient, reflecting that the influence along the main direction of error transmission is greater. In practical applications, the first coefficient is usually set to 0.7-0.9, and the second coefficient is set to 0.1-0.3. The greater the transfer influence coefficient, the greater the influence of the upper layer node on the lower layer node, and the stronger the coupling effect that needs to be considered in compensation.

[0157] 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 characteristic that the error influence decreases with the increase of distance. The modification method is to multiply the transfer influence coefficient by a distance attenuation factor, which decreases with the increase of the distance between the two nodes. The distance attenuation factor usually adopts an exponential decay function, that is, a negative exponential power, where the index is the distance between the two nodes divided by the characteristic length. The characteristic length is a parameter representing the influence range, which is usually set to 15%-25% of the size of the working space. The modified transfer influence coefficient is the interlayer coupling constraint, which is used to describe the mutual influence of error compensation between different levels.

[0158] The local variance and the global variance of the error distribution are calculated for the error representative points in the same layer of the hierarchical compensation structure. The local variance refers to the dispersion degree of the error in the region around the representative point, and the global variance refers to the dispersion degree of the error of all nodes in the layer. The calculation method is to select the nodes within a certain radius around the representative point to calculate the local variance, and to select all nodes in the layer to calculate the global variance. The local variance reflects the local consistency of the error, and the global variance reflects the overall distribution characteristics of the error. For example, if the local variance is small and the global variance is large, it indicates that the error is similar in the local region but significantly different in different regions, and a regionalized compensation strategy needs to be adopted.

[0159] The spatial adaptive weight is constructed based on the local variance and the global variance. The spatial adaptive weight represents the coordination degree between different representative points in the same layer. The construction method is to calculate the ratio of the local variance to the global variance, and then convert it to a weight value through a mapping function. When the local variance is much smaller than the global variance, the weight value is larger, indicating that the representative point can well represent the local region, and higher independence should be maintained during compensation; when the local variance is close to the global variance, the weight value is smaller, indicating that the error characteristics of the representative point are similar to those of other regions, and coordination should be strengthened during compensation. The mapping function usually adopts an S-shaped function to ensure that the weight value changes smoothly between 0 and 1. In the error compensation system, the S-shaped function is commonly used to smoothly map one numerical range to another, while having higher sensitivity in the middle region and relatively gentle change in the two end regions. Typical S-shaped functions include Sigmoid function, hyperbolic tangent function, etc.

[0160] The layer-in coordination constraint is obtained by dynamically adjusting the spatial adaptive weight according to the compensation effect. The compensation effect refers to the size of the residual error after applying the current compensation. The dynamic adjustment method is to adjust the size of the spatial adaptive weight according to the ratio of the residual error after compensation to the initial error. When the compensation effect is good, the weight value is slightly increased to enhance the independence of the representative points; when the compensation effect is poor, the weight value is reduced to strengthen the coordination between the representative points. The adjusted spatial adaptive weight is the layer-in coordination constraint, which is used to describe the coordination relationship between the compensation of different representative points in the same layer.

[0161] Based on the inter-layer coupling constraint and the layer-in coordination constraint, a hybrid iterative strategy of inter-layer top-down alternation and layer-in parallel is adopted to optimize the compensation component. The hybrid iterative strategy combines the advantages of inter-layer iteration and layer-in iteration. The inter-layer top-down alternation refers to starting from the 0th layer, calculating the compensation component of each layer in turn, and considering the influence of the compensation amount of the upper layer on the current layer during calculation; the layer-in parallel refers to all representative points in the same layer simultaneously calculating their respective compensation components, and considering the layer-in coordination constraint during calculation. This strategy not only considers the hierarchy of error transmission, but also improves the calculation efficiency. In practical application, usually 3-5 rounds of iteration are performed, that is, the calculation process from the 0th layer to the bottom layer is repeated 3-5 times.

[0162] The iteration step size is dynamically adjusted according to the compensation residual error. The compensation residual error refers to the remaining error after applying the current compensation. The dynamic adjustment method is to adjust the size of the iteration step size according to the trend of the compensation residual error. When the residual error decreases rapidly, the step size is increased to speed up the convergence; when the residual error decreases slowly or fluctuates, the step size is reduced to improve the stability. The adjustment of the step size usually adopts an adaptive method, which determines the step size of the next iteration according to the residual error ratio of the last two iterations.

[0163] The historical compensation amount is introduced to construct an inertia correction term to suppress compensation oscillation until the compensation component converges. The inertia correction term is an additional term calculated based on the historical compensation amount, which is used to smooth the change of the compensation amount and prevent oscillation in the compensation process. The construction method is to weight and average the compensation amounts of the previous iterations as the correction term of the current iteration. The weight usually decreases over time, that is, the weight of the more recent historical compensation amount is larger. The addition of the inertia correction term makes the compensation process more stable, avoiding system instability caused by excessive compensation. The convergence judgment standard of the compensation component is that the change of the compensation amount of the last two iterations is less than the preset threshold, which is usually set to 1%-3% of the initial error.

[0164] A compensation execution sequence is generated. The compensation execution sequence is a compensation operation instruction arranged in a specific order, used to guide the industrial equipment to implement error compensation. The generation method is to convert the converged compensation component into an instruction format executable by the equipment, and arrange it in the topological order starting from the error source node. The generation of the compensation execution sequence considers the hierarchy and directionality of error propagation, ensuring that the compensation starts from the root source and gradually eliminates the errors of each layer, ultimately achieving accurate compensation of the overall trajectory error.

[0165] In this embodiment, by constructing a hierarchical compensation structure and using a hybrid iteration strategy to generate a compensation execution sequence, accurate compensation of the trajectory error of the industrial equipment is achieved. The hierarchical structure constructed based on the error propagation chain makes the compensation highly matched with the error formation mechanism, and the error representative point scoring mechanism ensures that the key areas are fully compensated. The inter-layer coupling constraint accurately represents the influence relationship between different levels, and the intra-layer coordination constraint realizes the balance between local characteristics and overall coordination through spatial adaptive weight. The hybrid iteration strategy combines dynamic step size and inertia correction to improve the calculation efficiency and stability, making the compensation process more reliable. This hierarchical and adaptive compensation method not only improves the trajectory accuracy, but also has good environmental adaptability and long-term stability, providing strong support for high-precision manufacturing.

[0166] In an alternative embodiment,

[0167] Based on the inter-layer coupling constraint and the intra-layer coordination constraint, a hybrid iteration strategy of inter-layer top-down alternation and intra-layer parallelism is used to optimize the compensation component, the iteration step size is dynamically adjusted according to the compensation residual error, and a history compensation amount is introduced to construct an inertia correction term to suppress compensation oscillation until the compensation component converges, and a compensation execution sequence is generated, including:

[0168] Based on the inter-layer coupling constraint and the intra-layer coordination constraint, starting from the topmost layer, iterates layer by layer downward, taking the upper layer compensation component as the constraint condition for the lower layer compensation, and calculates the compensation component of the same layer in parallel to obtain the compensation component of the current iteration;

[0169] The compensation residual error corresponding to the compensation component of the current iteration is calculated, the residual error change trend is obtained by comparing the compensation residual error with the compensation residual error of the previous iteration, the iteration step size is dynamically adjusted based on the residual error change trend, and the compensation component is updated using the dynamically adjusted iteration step size;

[0170] The updated compensation component is recorded as the history compensation amount of the current iteration, the history compensation amount obtained by continuous multiple iterations is time-weighted to obtain a compensation trend feature, and an inertia correction term is constructed based on the compensation trend feature, and the inertia correction term is combined with the current compensation component to obtain a corrected compensation component;

[0171] The change of the modified compensation component relative to the last iteration is calculated, and when the change is less than a preset change threshold, a compensation execution sequence is generated, otherwise the modified compensation component is taken as the initial compensation component for the next iteration to continue the hybrid iterative optimization.

[0172] In the embodiment, based on the inter-layer coupling constraint and the intra-layer coordination constraint, the compensation component is iterated layer by layer from the top layer to the bottom layer, and the compensation component of the upper layer is taken as the constraint condition for the compensation of the lower layer. The hierarchical compensation structure is composed of multiple layers, and extends from the top layer (0th layer) where the error source node is located to the bottom layer. The inter-layer coupling constraint describes the influence degree of the upper layer compensation on the lower layer compensation, and is expressed by a transfer influence coefficient matrix. The process of the layer-by-layer iteration is to calculate the compensation component of each layer in turn from the 0th layer. When calculating the compensation component of a layer, the influence of the determined compensation component of the upper layer on the current layer needs to be considered. The specific method is to multiply the compensation component of the upper layer by the corresponding transfer influence coefficient to obtain the influence amount of the upper layer on the current layer, and then take the influence amount as the constraint condition for the compensation calculation of the current layer.

[0173] The compensation component of the same layer is calculated by using a parallel optimization method to obtain the compensation component of the current iteration. The parallel optimization refers to that all error representative points in the same layer calculate their respective compensation components at the same time, rather than sequentially. The intra-layer coordination constraint describes the coordination relationship between different representative points in the same layer, and is expressed by a spatial adaptive weight matrix. The parallel optimization method is to construct an optimization objective function for each representative point based on its error characteristics and the intra-layer coordination constraint, and to simultaneously solve the optimal compensation component of all representative points. The optimization objective function comprehensively considers factors such as error elimination degree, compensation smoothness and energy consumption, and the solving process usually adopts gradient descent or conjugate gradient method.

[0174] The compensation residual corresponding to the compensation component of the current iteration is calculated. The compensation residual refers to the error that still exists after the application of the current compensation, and reflects the effectiveness of the compensation. The calculation method is to subtract the compensation amount from the original error to obtain the remaining error, and then to calculate the root mean square value of the remaining error as the compensation residual. The smaller the compensation residual is, the better the compensation effect is; the larger the compensation residual is, the poorer the compensation effect is, and further optimization is needed.

[0175] The residual change trend is obtained by comparing the compensation residual with the compensation residual of the previous iteration. The residual change trend reflects the convergence of the compensation optimization process. The comparison method is to calculate the ratio of the current residual to the residual of the previous iteration to obtain the residual change rate. The residual change rate less than 1 indicates that the residual is decreasing and the compensation effect is improving; the change rate equal to 1 indicates that the residual remains unchanged and the compensation effect is stagnant; the change rate greater than 1 indicates that the residual is increasing and the compensation effect is deteriorating. The residual change rates of continuous multiple iterations constitute the residual change trend.

[0176] The iteration step size is dynamically adjusted based on the residual change trend. The iteration step size controls the update amplitude of the compensation component in each iteration, directly affecting the convergence speed and stability. The dynamic adjustment method is to adaptively increase or decrease the step size according to the residual change trend. When the residual decreases rapidly (change rate is much less than 1), the step size is appropriately increased to speed up the convergence; when the residual decreases slowly (change rate is close to 1), the current step size is maintained; when the residual starts to increase (change rate is greater than 1), the step size is decreased to improve stability. The step size adjustment usually uses a mapping function to map the residual change rate to the step size adjustment coefficient.

[0177] The compensation component is updated using the dynamically adjusted iteration step size. The update of the compensation component is to add the current compensation component and the compensation increment to obtain the new compensation component. The compensation increment is calculated based on the optimization direction and the 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 of the current iteration. The historical compensation refers to the sequence of compensation components generated in the process of multiple iterations, which is used to analyze the change trend of the compensation. The recording method is to store the compensation component of each iteration in the historical queue, and the queue length is usually 3-5, that is, the compensation components of the last 3-5 iterations are retained. The historical compensation records the evolution process of the compensation component, providing a data basis for subsequent inertia correction.

[0178] The historical compensation obtained by continuous multiple iterations is time-weighted to obtain the compensation trend feature. Time weighting refers to giving different weights according to the time sequence, usually the recent compensation weight is larger and the long-term compensation weight is smaller. The weighting method is to multiply the historical compensation by the corresponding time weight, and then sum to obtain the weighted average value. The time weight usually adopts an exponential decay method, that is, the weight is equal to the power of a base less than 1, and the power index is the time distance. The weighted average value reflects the change trend of the compensation component, which is called the compensation trend feature. The inertia correction term is constructed based on the compensation trend feature. The inertia correction term is an additional compensation adjustment, which is used to smooth the compensation change and prevent oscillation. The construction method is to multiply the difference between the current compensation component and the compensation trend feature by an inertia coefficient to obtain the inertia correction term. The inertia coefficient controls the strength of the correction, which is usually set to 0.1-0.3. When the current compensation component deviates from the trend, the inertia correction term will pull back the compensation component, making it closer to the overall trend; when the compensation component changes smoothly, the inertia correction term has less impact. The inertia correction term and the current compensation component are combined to obtain the corrected compensation component. The combination method is to add the current compensation component and the inertia correction term to obtain the corrected compensation component.

[0179] The change amount of the modified compensation component relative to the last iteration is calculated. The change amount reflects the convergence degree of the compensation component, which is an important indicator for judging whether the iteration is terminated. The calculation method is to subtract the modified compensation component from the compensation component of the last iteration, and then calculate the norm (such as Euclidean norm or maximum absolute value norm) of the difference value as the change amount. The smaller the change amount, the closer the compensation component is to convergence; the larger the change amount, the faster the compensation component is still changing, and the iteration needs to continue.

[0180] The compensation execution sequence is generated when the change amount is less than the preset change amount threshold. The change amount threshold is a standard for judging whether the compensation component converges, and is usually set to 1%-3% of the norm of the initial compensation component. When the change amount is continuously lower than the threshold for multiple times (such as 3 times), it is considered that the compensation component has converged, and the iteration can be terminated to generate the final compensation execution sequence. The compensation execution sequence is a compensation operation instruction arranged in a specific order, which is used to guide the industrial equipment to implement error compensation. The generation method is to convert the converged compensation component into an instruction format executable by the equipment, and arrange it in the topological order starting from the error source node.

[0181] If the change amount is greater than the preset change amount threshold, the modified compensation component is taken as the initial compensation component for the next iteration to continue the hybrid iterative optimization. This iteration method ensures that the compensation component can gradually converge to the optimal solution, and at the same time, through dynamic step adjustment and inertia correction, it improves the convergence speed and stability. In practical applications, hybrid iterative optimization usually needs 10-30 iterations to reach the convergence condition, and the specific number of iterations depends on the complexity of error distribution and the setting of convergence threshold. Through this way of optimization, the compensation component can effectively eliminate the trajectory error of the industrial equipment, improve the machining precision and product quality.

[0182] In this embodiment, by constructing a hierarchical error compensation structure, combining the coupling relationship between upper and lower layers and the coordination mechanism within the same layer, global collaborative optimization of error information is realized. The introduction of hybrid iteration strategy and inertia correction mechanism can dynamically adjust the compensation strategy, suppress oscillation, speed up convergence, and improve the adaptive ability and convergence efficiency of the compensation process. The finally generated compensation execution sequence can directly drive the equipment to realize trajectory correction, and improve the manufacturing quality and robustness of the control system.

[0183] Figure 3 The dynamic iteration step adjustment effect heat map of the embodiment of the present application is as follows: Figure 3As shown in the figure, the figure shows the relationship between the compensation residual rate of change and the iteration step and its influence on the compensation residual. The heat map uses color depth to represent the size of the compensation residual, and the color from deep to shallow corresponds to the compensation residual of 7.5 μm to 0 μm. From the data, when the compensation residual rate of change is 1.4 and the iteration step is 0.45-0.55, the smallest compensation residual 1.6 μm can be obtained (the upper right corner of the red dashed line frame marked area); while the compensation residual rate of change is 0.8 and the iteration step is 0.25, a suboptimal area is formed, and the compensation residual is 3.2 μm (the middle green dashed line frame marked area). The data also shows that with the increase of the iteration step, the compensation residual presents a trend of first decreasing and then increasing, for example, when the compensation residual rate of change is 0.8, the iteration step increases from 0.05 to 0.45, and the compensation residual decreases from 5.1 μm to 2.4 μm; while the step continues to increase to 0.55, the compensation residual basically remains stable. At the same time, the greater the compensation residual rate of change, the higher the compensation accuracy that can be obtained at the same step, such as at the step of 0.25, the rate of change from 0.4 to 1.4, the compensation residual from 5.8 μm to 2.3 μm. This fully proves that the dynamic step adjustment strategy of the technical scheme can adaptively adjust the iteration step according to the change trend of the compensation residual, effectively balance the convergence speed and stability, and thus obtain the best compensation effect.

[0184] In a second aspect of the embodiments of the present application, an industrial equipment trajectory error big data analysis and intelligent compensation system is provided, the system comprising:

[0185] A first unit is configured to collect industrial equipment operation state parameters, segment the operation state parameters according to time sequence, extract the motion characteristics of each segment of data, generate motion characteristic fingerprints, compare the motion characteristic fingerprints with a pre-established characteristic fingerprint library, and calculate characteristic deviation data;

[0186] A second unit is configured to distribute the characteristic deviation data to a plurality of agents, each agent analyzes regional error characteristics according to the distributed characteristic deviation data, adjacent agents exchange error characteristic information and evaluate the transmission strength of the characteristic deviation to obtain error transmission weights, construct a probability graph structure based on the error transmission weights, and simplify the probability graph structure using mutual information criteria to obtain an error transmission chain;

[0187] A third unit is configured to construct a hierarchical compensation structure according to the topological structure of the error transmission chain, set error representative points at each layer, calculate the transmission influence coefficient between adjacent layer error representative points to obtain interlayer coupling constraints, calculate the compensation coordination coefficient between error representative points in the same layer to obtain intralayer coordination constraints, optimize compensation components based on the interlayer coupling constraints and the intralayer coordination constraints using a hybrid iteration strategy, and generate a compensation execution sequence;

[0188] A fourth unit is configured to compensate for errors in the motion trajectory of the industrial equipment according to the compensation execution sequence. In a third aspect, the present application provides an electronic device, comprising:

[0189] a processor;

[0190] a memory for storing processor-executable instructions;

[0191] The processor is configured to invoke the instructions stored in the memory to execute the method described above.

[0192] In a fourth aspect, the present application provides a computer-readable storage medium having stored thereon computer program instructions, which, when executed by a processor, implement the method described above.

[0193] The present application can be a method, device, system and / or computer program product. The computer program product can include a computer-readable storage medium having stored thereon computer-readable program instructions that, when executed by a computer, cause the computer to carry out the various aspects of the present application.

[0194] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for big data analysis and intelligent compensation of trajectory errors in industrial equipment, characterized in that, include: The operating status parameters of industrial equipment are collected, and the operating status parameters are segmented according to the time series. The motion features of each segment are extracted to generate motion feature fingerprints. The motion feature fingerprints are compared with the pre-established feature fingerprint database to calculate the feature deviation data. Feature bias data is distributed to multiple agents. Each agent analyzes the regional error characteristics based on the assigned feature bias data. Adjacent agents exchange error feature information and evaluate the propagation strength of feature bias to obtain error propagation weights. Based on the error propagation weights, a probabilistic graph structure is constructed. The mutual information criterion is used to simplify the probabilistic graph structure to obtain the error propagation chain. Analyze the topological characteristics of the error propagation chain, identify the error source node, calculate the shortest propagation path length from each node to the error source node, assign nodes with the same propagation path length to the same level, and construct a hierarchical compensation structure. In each layer of the hierarchical compensation structure, the magnitude characteristics and rate of change characteristics of the error nodes are calculated. The magnitude characteristics and rate of change characteristics are weighted and combined to obtain the node score. The node with the highest score and the distance between adjacent nodes is 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 vertical component of the transmission direction are calculated. Based on the projection component and vertical component, the transmission influence coefficient is constructed. The transmission influence coefficient is corrected by combining the spatial distance attenuation characteristics to obtain the interlayer coupling constraint. For the error representative points in the same layer of the hierarchical compensation structure, the local variance and global variance of the error distribution are calculated. Based on the local variance and global variance, spatial adaptive weights are constructed. The spatial adaptive weights are dynamically adjusted according to the compensation effect to obtain the intra-layer coordination constraints. Based on inter-layer coupling constraints and intra-layer coordination constraints, a hybrid iterative strategy of top-down alternation between inter-layers and parallel intra-layers is adopted to optimize the compensation components. The iteration step size is dynamically adjusted according to the compensation residual. Historical compensation amounts are introduced to construct an inertial correction term to suppress compensation oscillations until the compensation components converge, and a compensation execution sequence is generated. Error compensation for the motion trajectory of industrial equipment is achieved based on the compensation execution sequence.

2. The method according to claim 1, characterized in that, Industrial equipment operating status parameters are collected, and these parameters are segmented according to a time series. Motion features of each segment are extracted to generate motion feature fingerprints, including: Acquire the operating status parameters of industrial equipment, including motion parameters, operating condition parameters, and environmental parameters; Velocity and acceleration data are extracted from the motion parameters; the velocity and acceleration changes of adjacent data points are calculated, and points where the velocity and acceleration changes are both greater than a preset velocity value are marked as candidate segmentation points. Segmentation points are determined based on the consistency of the fluctuation trend; the velocity and acceleration data are divided into multiple data segments based on the segmentation points. By combining operating condition parameters and environmental parameters, the velocity fluctuation value and acceleration fluctuation value of each data segment are calculated, a fluctuation curve is constructed, and 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 feature vector, perform dimensionality reduction on the feature vector based on the variance contribution value, obtain the dimensionality-reduced feature components, calculate the weight coefficient of the feature components in combination with the working condition parameters, and reorganize the dimensionality-reduced feature components based on the weight coefficient to generate motion feature fingerprint.

3. The method according to claim 1, characterized in that, The motion feature fingerprint is compared with a pre-established feature fingerprint database, and the feature deviation data is calculated, 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. Based on the fluctuation trend, the feature subsequences are merged to obtain waveform segments. The amplitude sequence and phase sequence of the waveform segments are extracted. The amplitude sequence and phase sequence are standardized to obtain waveform features and phase features, respectively. The waveform features and phase features are combined to construct a feature vector, and the weighting coefficients are calculated based on the feature vector. Fingerprint data is extracted from a pre-established feature fingerprint database, the fingerprint data is divided into sequences and features are extracted, a reference feature vector is constructed, the matching degree between the feature vector and the reference feature vector is calculated, and the fingerprint data with the highest matching degree is selected as the target fingerprint. Calculate the feature distance between the feature vector of the waveform segment and the reference feature vector of the corresponding waveform segment of the target fingerprint; calculate the weighted deviation value based on the feature distance and weighting coefficient; and statistically analyze the temporal distribution of the weighted deviation value to obtain the variation pattern. The divergence trend of the weighted deviation value is determined based on the changing pattern; when a divergence trend occurs, the divergence rate and divergence direction are calculated as characteristic deviation data.

4. The method according to claim 1, characterized in that, Feature bias data is distributed to multiple agents. Each agent analyzes the regional error characteristics based on its assigned feature bias data. Neighboring agents exchange error feature information and evaluate the propagation strength of the feature bias to obtain error propagation weights. A probabilistic graph structure is constructed based on the error propagation weights. The mutual information criterion is used to simplify the probabilistic graph structure to obtain the error propagation chain, which includes: The motion space of industrial equipment is divided into grid cells, each grid cell corresponds to an intelligent agent. The Mahalanobis distance between the feature deviation data points and the center of the grid cell is calculated. Based on the Mahalanobis distance, the allocation weight is calculated, and the feature deviation data is allocated to the intelligent agent according to the allocation weight. Calculate the mean and standard deviation of the deviation within each agent's region, extract the principal direction of the deviation, and combine the mean, standard deviation, and principal direction of the deviation to construct a region error feature vector; Neighboring agents exchange regional error feature vectors, calculate the feature vector similarity to construct a feature similarity matrix, and calculate the error gradient between neighboring agents. The feature similarity matrix is ​​combined with the error gradient to obtain the propagation strength matrix. The propagation strength matrix is ​​normalized to obtain the error propagation weights. An initial probability map is constructed based on the error propagation weights. Calculate the mutual information value between nodes in the initial probability graph, delete edges with mutual information values ​​less than a preset threshold to obtain a simplified probability graph. In the simplified probability graph, with the error propagation weight as the objective function, use the maximum weight spanning tree algorithm to extract the optimal propagation path. Determine the propagation direction and propagation intensity of the error based on the relationship between the error propagation weights on the path, and construct an error propagation chain structure with propagation direction and propagation intensity.

5. The method according to claim 4, characterized in that, In the simplified probability graph, using the error propagation weight as the objective function, the maximum weight spanning tree algorithm is employed to extract the optimal propagation path. The propagation direction and intensity of the error are determined based on the magnitude relationship of the error propagation weights along the path. The resulting error propagation chain structure with both propagation direction and intensity includes: Obtain the error propagation weights of each edge in the simplified probability graph structure, and normalize the error propagation weights to a preset interval based on the maximum and minimum weights to obtain the normalized propagation weights of each edge. The edges in the probability graph are sorted in descending order according to the normalized transfer weights. The edges with the largest weights are selected in turn. It is determined whether the addition of the edge forms a loop and whether the error magnitudes of the nodes at both ends of the edge meet the size relationship constraint. The edges that meet the constraint conditions are added to the edge set until the maximum weight spanning tree is constructed. In the calculation of the maximum weight spanning tree, the average value of the normalized propagation weights between the two endpoints of each edge and its adjacent nodes is used to obtain the local weight gradient. The error propagation direction is determined based on the magnitude of the local weight gradients of the two endpoints. The product of the difference in local weight gradients and the normalized propagation weights is used as the propagation strength. The current propagation weight and propagation 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 on the edges of the changed region, the local structure of the maximum weight spanning tree is updated, and an error propagation chain with dynamic update capability is obtained.

6. The method according to claim 1, characterized in that, Based on inter-layer coupling constraints and intra-layer coordination constraints, a hybrid iterative strategy of top-down alternation between inter-layer components and parallel intra-layer components is adopted to optimize the compensation components. The iteration step size is dynamically adjusted according to the compensation residual. Historical compensation amounts are introduced to construct an inertial correction term to suppress compensation oscillations until the compensation components converge. The generated compensation execution sequence includes: Based on inter-layer coupling constraints and intra-layer coordination constraints, the algorithm iterates layer by layer from the top layer downwards, using the compensation components of the upper layer as constraints for the compensation of the lower layer, and calculates the compensation components of the same layer in parallel to obtain the compensation components of the current iteration. Calculate the compensation residual corresponding to the compensation component of the current iteration, compare the compensation residual with the compensation residual of the previous iteration to obtain the residual change trend, dynamically adjust the iteration step size based on the residual change trend, and update the compensation component using the dynamically adjusted iteration step size. The updated compensation component is recorded as the historical compensation amount of the current iteration. The historical compensation amounts obtained from multiple consecutive iterations are time-weighted to obtain the compensation trend characteristics. An inertial correction term is constructed based on the compensation trend characteristics. The inertial correction term is combined with the current compensation component to obtain the corrected compensation component. Calculate the change of the corrected compensation component relative to the previous iteration. If the change is less than a preset change threshold, generate a compensation execution sequence; otherwise, use the corrected compensation component as the initial compensation component for the next iteration to continue performing hybrid iterative optimization.

7. A big data analysis and intelligent compensation system for industrial equipment trajectory errors, used to implement the method described in any one of claims 1-6, characterized in that, include: The first unit is used to collect the operating status parameters of industrial equipment, process the operating status parameters into segments according to the time series, extract the motion features of each segment of data, generate motion feature fingerprints, compare the motion feature fingerprints with the pre-established feature fingerprint database, and calculate the feature deviation data. The second unit is used to distribute feature deviation data to multiple agents. Each agent analyzes the regional error characteristics based on the distributed feature deviation data. Adjacent agents exchange error feature information and evaluate the propagation strength of feature deviation to obtain error propagation weights. Based on the error propagation weights, a probabilistic graph structure is constructed. The mutual information criterion is used to simplify the probabilistic graph structure to obtain the error propagation chain. The third unit is used to construct a hierarchical compensation structure based on the topology of the error propagation chain. In each layer, error representative points are set, and the propagation influence coefficient between adjacent error representative points is calculated to obtain inter-layer coupling constraints. The compensation coordination coefficient between error representative points in the same layer is calculated to obtain intra-layer coordination constraints. Based on the inter-layer coupling constraints and intra-layer coordination constraints, a hybrid iterative strategy is adopted to optimize the compensation components and generate a compensation execution sequence. The fourth unit is used to perform error compensation for the motion trajectory of industrial equipment based on the compensation execution sequence.

8. An electronic device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 6.

Images