Precise detection method and device for lead screw module based on multi-parameter recursive optimization

Abstract

The invention relates to a multi-parameter recursive optimization lead screw module precision detection method and device. The method comprises the following steps: carrying out motion trail and load detection on a screw rod module to obtain displacement error data and load response data; constructing a three-dimensional error parameter model according to the displacement error data and the load response data, and calculating initial error characteristics through the three-dimensional error parameter model; performing working condition adaptive analysis on the initial error features to obtain a multi-dimensional compression error matrix; inputting the multi-dimensional compression error matrix into a recursive optimization algorithm for hierarchical parameter iteration to obtain an error compensation parameter; and thin plate spline fitting is carried out on the error compensation parameters to obtain a space error mapping function, the position compensation amount is calculated according to the space error mapping function, and a lead screw module accurate positioning control instruction is generated. According to the method, the error characteristics of the lead screw module under different working conditions are comprehensively captured, so that the lead screw module can keep stable high-precision performance under the standard working condition, the limit working condition and the variable working condition.

Description

Technical Field

[0001] The present invention relates to the field of precision detection technology, and particularly to a precision detection method and device for a lead screw module with multi-parameter recursive optimization. Background Art

[0002] As a core component for achieving high-precision displacement control and motion transmission in the field of industrial automation, the accuracy performance of the lead screw module directly affects the performance of the overall system. With the continuous improvement of the precision requirements in modern manufacturing, the traditional lead screw module detection methods are difficult to meet the requirements in complex application scenarios. The existing detection technologies mainly rely on single-parameter monitoring and static error compensation, and do not fully consider the dynamic error characteristics of the lead screw module under various working conditions, such as radial offset, vertical displacement, and angular rotation error, resulting in under-compensation or over-compensation in actual applications.

[0003] The main problem faced in the current field of precision detection of lead screw modules lies in the accurate perception and processing of error data. Traditional detection methods often regard the lead screw module as an ideal motion system, ignoring the non-linear errors generated by load changes, temperature fluctuations, and high-speed operation, resulting in distorted reference data containing many measured values beyond the standard range. In addition, the error processing algorithms in the existing technologies have a large amount of calculation and a slow response speed, and it is difficult to adapt to complex working conditions with uneven error distribution using a fixed grid method, making it difficult to minimize errors in a high-dynamic environment, thus resulting in accuracy deviation problems. Summary of the Invention

[0004] The main object of the present invention is to provide a precision detection method and device for a lead screw module with multi-parameter recursive optimization. The present invention comprehensively captures the error characteristics of the lead screw module under different working conditions, enabling the lead screw module to maintain stable high-precision performance under standard working conditions, extreme working conditions, and variable working conditions.

[0005] To achieve the above object, the present invention provides a precision detection method for a lead screw module with multi-parameter recursive optimization, including the following steps:

[0006] Perform motion trajectory and load detection on the lead screw module to obtain displacement error data and load response data;

[0007] Construct a three-dimensional error parameter model based on the displacement error data and the load response data, and calculate initial error characteristics through the three-dimensional error parameter model;

[0008] Perform working condition adaptive analysis on the initial error characteristics to obtain a multi-dimensional compressed error matrix;

[0009] Input the multi-dimensional compressed error matrix into a recursive optimization algorithm for hierarchical parameter iteration to obtain error compensation parameters;

[0010] Perform thin plate spline fitting on the error compensation parameters to obtain a spatial error mapping function, and calculate the position compensation amount according to the spatial error mapping function to generate a precise positioning control instruction for the lead screw module.

[0011] The present invention also provides a precise detection device for a lead screw module with multi-parameter recursive optimization, including:

[0012] A detection module for detecting the motion trajectory and load of the lead screw module to obtain displacement error data and load response data;

[0013] A construction module for constructing a three-dimensional error parameter model according to the displacement error data and the load response data, and calculating initial error characteristics through the three-dimensional error parameter model;

[0014] An analysis module for performing working condition adaptive analysis on the initial error characteristics to obtain a multi-dimensional compressed error matrix;

[0015] An iteration module for inputting the multi-dimensional compressed error matrix into a recursive optimization algorithm for hierarchical parameter iteration to obtain error compensation parameters;

[0016] A generation module for performing thin plate spline fitting on the error compensation parameters to obtain a spatial error mapping function, and calculating the position compensation amount according to the spatial error mapping function to generate a precise positioning control instruction for the lead screw module.

[0017] In summary, the technical solution provided by the present invention simultaneously senses error information from two dimensions of the motion trajectory and the load, constructs a cascaded recursive optimization estimation hybrid architecture, and comprehensively captures the error characteristics of the lead screw module under different working conditions. The introduced adaptive error sensing mechanism improves the system's ability to identify error characteristics in various operating states. At the same time, the error dimension compression technology reduces the computational complexity, improves the processing efficiency while retaining key error information. The multi-parameter recursive optimization algorithm realizes the comprehensive optimization of global and local error characteristics through hierarchical parameter iteration, ensuring the accuracy and continuity of error compensation. The thin plate spline fitting algorithm is used to replace the traditional multi-point grid error processing method, combined with the block fitting strategy and the adaptive grid refinement mechanism, providing a continuous and smooth error mapping function, significantly improving the system response speed and optimizing the resource utilization efficiency. The real-time error compensation mechanism combining feed-forward compensation and feedback adjustment enables the lead screw module to maintain stable high-precision performance under standard working conditions, extreme working conditions, and variable working conditions. Description of the Drawings

[0018] Figure 1 is a schematic diagram of the steps of a precise detection method for a lead screw module with multi-parameter recursive optimization in an embodiment of the present invention;

[0019] Figure 2 It is a structural block diagram of a precision detection device for a lead screw module with multi-parameter recursive optimization in an embodiment of the present invention.

[0020] The realization of the purpose of the present invention, its functional characteristics and advantages will be further described in conjunction with the embodiments with reference to the accompanying drawings. Specific embodiments

[0021] In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0022] Referring to Figure 1 , this embodiment provides a precision detection method for a lead screw module with multi-parameter recursive optimization, including the following steps:

[0023] S1. Detect the motion trajectory and load of the lead screw module to obtain displacement error data and load response data;

[0024] Among them, displacement sensors are installed at both ends, the slider connection, and the middle position of the lead screw module to collect the original displacement data generated during the operation of the lead screw module in real time. These displacement sensors work based on precise optical or electromagnetic principles, and their sampling frequency is reasonably set according to the response speed of the system. The collected displacement data accurately reflects the motion trajectory and its error conditions of the lead screw module under different loads. To monitor the axial force and radial force borne by the lead screw module, a strain gauge load sensor is installed at the slider connection. The strain gauge sensor measures the mechanical load borne by the lead screw module during operation to obtain load mechanical data, which helps the system identify the performance changes under different load conditions. An angle encoder is used to record the rotational speed, acceleration, and deceleration of the lead screw module to obtain rotational dynamic parameters. When performing the above detections, multiple tests need to be carried out under different working conditions to ensure comprehensive operation data is obtained. This includes performing full-stroke reciprocating motion, segmented motion of the lead screw module, and tests under different speed conditions. During these tests, the lead screw module works in multiple operation modes, and the generated error and response data reflect various situations encountered in actual applications. At the same time, temperature sensors are used during the test to monitor the temperature changes in the test environment and the temperature changes of each component of the lead screw module. Temperature changes will cause thermal expansion and contraction of the materials of the lead screw module, thereby affecting its accuracy. The temperature drift compensation data provided by the temperature sensors can effectively correct the errors caused by temperature changes. Time synchronization tags and data fusion are performed on the original displacement data, load mechanical data, rotational dynamic parameters, multi-condition operation data sets, and temperature drift compensation data. The purpose of time synchronization tags is to ensure that the data collected by different sensors is aligned on the time axis to avoid data offset caused by time differences. Data fusion is to comprehensively process data from different sources. By fusing the observation results of different sensors, more comprehensive and accurate displacement error data and load response data are obtained.

[0025] S2. Construct a three-dimensional error parameter model based on the displacement error data and the load response data, and calculate the initial error characteristics through the three-dimensional error parameter model;

[0026] Specifically, the displacement error data is compared and calculated with the theoretical displacement value of the lead screw module. The theoretical displacement value is obtained through an ideal model or simulation calculation, representing the ideal motion trajectory of the lead screw module under perfect conditions. By comparing the actually collected displacement error data with these theoretical values, a displacement error sequence is obtained, reflecting the accuracy deviation of the lead screw module during actual operation. Perform spectral analysis on the load response data, transform the load data from the time domain to the frequency domain, revealing the periodic characteristics of the load change and the impact on the system performance at different frequencies. Through spectral analysis, the dynamic changes under different load conditions are reflected, and the correlation data between the load change and the displacement error is obtained. Establish a three-dimensional error parameter model based on the displacement error sequence and the correlation data. The three-dimensional error parameter model includes an axial distance error coefficient, a radial offset error coefficient, a vertical displacement error coefficient, an angular rotation error coefficient, an installation spacing error coefficient, a detection aperture error coefficient, and a temperature drift compensation coefficient, etc. These coefficients are obtained through previous data analysis, and there is a certain coupling relationship between them, reflecting the comprehensive impact of each error source on the overall error. Perform recursive least squares algorithm calculation on the three-dimensional error parameter model to calculate the initial values of each error coefficient. The recursive least squares algorithm is an adaptive algorithm that obtains a relatively accurate error coefficient estimate in fewer calculation steps through continuous iterative optimization. Each time an iteration is performed, the algorithm updates the error coefficient according to the actual displacement error data and the load response data, gradually approaching the optimal solution. The recursive calculation method enables the model to be adjusted in real time under dynamic working conditions, continuously improving the accuracy. Construct a coupling relationship matrix between parameters based on the initial values of each error coefficient, reflecting the interaction between each error coefficient. Through the coupling relationship matrix, create an error compensation function, which calculates the error amount to be compensated according to the current working conditions and parameter settings. Through the calculation of the error compensation function, the initial error characteristics are obtained.

[0027] S3. Perform a working condition adaptive analysis on the initial error characteristics to obtain a multi-dimensional compressed error matrix;

[0028] It should be noted that according to the operating speed of the lead screw module, the load state, and the temperature changes of the environment and the system, a weight function is constructed. This weight function maps these working condition parameters into dynamic weight factors, which are used to adjust the importance weights of the displacement error and the load error in the initial error characteristics. For example, when the lead screw module is moving at high speed, the inertial force and centrifugal effect caused by the rotational speed change lead to a significant increase in the displacement error. At this time, the weight function correspondingly increases the weight of the displacement error. Under heavy load conditions, the influence of the load response on the system accuracy is more prominent, so the weight of the load error will increase accordingly. The dynamic weight allocation method can flexibly adapt to the changes in error characteristics under different working conditions, making the weighted error data reflect the error performance of the system during actual operation. Perform multi-scale analysis on the weighted error data. Multi-scale analysis is a method of decomposing data through different frequencies and time scales, decomposing the complex error signal into multiple frequency band characteristic components, which respectively represent the change characteristics of the error in different time or frequency ranges. For example, through techniques such as wavelet transform or empirical mode decomposition, the weighted error data is decomposed into a low-frequency long-term error trend component and a high-frequency transient error component. Perform principal component analysis on the multi-band error characteristic components. By analyzing the correlation between each error characteristic component, the main error characteristics are extracted, and the error contribution rate distribution data is calculated to quantify the influence degree of each characteristic component on the overall error, so as to identify the key factors that dominate the system error under different working conditions. Based on the error contribution rate distribution data, an error characteristic vector is constructed. This vector contains the contribution rates of each error component under different frequency bands, reflecting the multi-dimensional characteristics of the system error. To simplify the complexity of the data, dimensionality reduction processing is performed on the error characteristic vector. During the dimensionality reduction process, by eliminating the characteristic components with less influence on the system error, the high-dimensional error characteristic vector is compressed into a low-dimensional compressed error characteristic vector. Establish an error pattern library containing typical error patterns under different working conditions based on historical detection data. This error pattern library contains typical error patterns under different working conditions, including common error distribution characteristics, error evolution trends, and error response characteristics under specific working conditions. These patterns are obtained through clustering analysis, feature extraction, and statistical modeling of historical data, and can provide a reference basis for the error characteristics under the current working condition. By mapping and matching the error characteristics of each working condition with the typical patterns in the pattern library, a working condition-error mapping relationship table is obtained, showing the possible error patterns of the lead screw module under different working conditions. Combining the compressed error characteristic vector and the working condition-error mapping relationship table, the initial error characteristics are classified and integrated and matrix reconstruction is performed to form a multi-dimensional compressed error matrix. The classification and integration process is to gather the characteristics with similar error patterns together. Through matrix reconstruction, these error characteristics are expressed in matrix form, so that the error characteristics of different dimensions are reflected in a unified mathematical model.The multi-dimensional compression error matrix not only includes the numerical information of error features, but also contains the distribution law and dynamic change trend of these features under different working conditions.

[0029] S4. Input the multi-dimensional compression error matrix into the recursive optimization algorithm for hierarchical parameter iteration to obtain the error compensation parameters;

[0030] Specifically, a global objective function is constructed based on the multi-dimensional compression error matrix to minimize the comprehensive error within the entire motion range of the lead screw module, which is formulated as a problem of minimizing the sum of squared errors or the absolute value of errors. To enhance the convergence and global search ability of the optimization process, the global objective function is input into a recursive optimization algorithm, and an adaptive inertia weight and mutation operation are introduced into the recursive algorithm. The adaptive inertia weight dynamically adjusts the weight coefficient according to the error change during the iteration process, enabling the algorithm to have strong global search ability in the initial stage and gradually enhancing local convergence in the later stage. The mutation operation avoids the algorithm falling into local optimality by introducing random perturbations to maintain the diversity of the population, enabling the algorithm to obtain the global optimal parameter estimation. These global optimal parameters represent the optimal solutions for error compensation within the entire motion range of the lead screw module. The motion range of the lead screw module is partitioned according to its operating characteristics. By dividing the complete stroke of the lead screw module into multiple overlapping intervals, it is ensured that the error characteristics within each interval can be fully considered. At the same time, the design of the overlapping intervals ensures a smooth transition of the error compensation parameters at the interval boundaries. Through this step, the data for the operating interval division is obtained. For each operating interval, a corresponding local objective function is constructed. These local objective functions also aim to minimize the error but only focus on the error characteristics within a specific interval. When constructing the local objective function, the global optimal parameter estimation is used as the initial value, and the recursive least squares method is used to solve it. The recursive least squares method converges quickly to the optimal solution under continuously updated observation data. Through recursive calculation, each interval obtains a set of local optimal parameters, reflecting the error characteristics within a specific interval, and realizing the regional adaptive optimization of error compensation. The local optimal parameters of adjacent intervals are input into a smoothing constraint function for boundary consistency processing. The smoothing constraint function enables the error compensation parameters to achieve a continuous transition at the interval boundaries through interpolation or fitting methods, obtaining smoothed interval parameters. The smoothing process ensures the coherence of the error compensation model and effectively reduces the jitter phenomenon caused by parameter mutations during the motion control process, improving the smoothness and control accuracy of the lead screw module's motion. The smoothed interval parameters are combined with the global optimal parameter estimation to construct a comprehensive error compensation model. The comprehensive error compensation model realizes the combination of global error compensation and local error correction by integrating the global optimization results and local optimization results. After the model is constructed, the error compensation parameters are continuously optimized through multiple recursive iteration calculations. Each iteration adjusts the parameters according to the current error compensation effect, enabling the compensation model to gradually approach the optimal state. Multiple recursive iteration calculations can effectively eliminate the random errors in the system and dynamically adapt to the fluctuations in error characteristics caused by changes in working conditions, thereby ensuring that the lead screw module still maintains high-precision positioning ability under different operating conditions.

[0031] S5. Perform thin plate spline fitting on the error compensation parameters to obtain a spatial error mapping function, calculate the position compensation amount according to the spatial error mapping function, and generate a precise positioning control instruction for the lead screw module.

[0032] Among them, a set of control points is generated within the working space of the lead screw module according to the error compensation parameters. The selection of the control point set is achieved by collecting error compensation data at different positions of the module, and these control points serve as the basic data for thin plate spline fitting. The selection of the control point set covers the entire working space and ensures that these points represent the error characteristic distribution of the lead screw module under various working conditions. Through these control points, the thin plate spline fitting method constructs a multi-dimensional mathematical model to represent the error distribution of the module within the entire working space. Substitute the basic data of thin plate spline fitting into the mathematical model, and determine the coefficients of the thin plate spline by solving a system of linear equations. The thin plate spline model is a mathematical method for describing a surface by fitting a set of control points, which can provide an accurate error compensation surface and ensure the smoothness and continuity of the surface within the entire working space. Through the process of solving the system of linear equations, an initial spatial error mapping function is obtained, which is a key model describing the error distribution and compensation requirements of the lead screw module at each position within its working space. Add a regularization term to the initial spatial error mapping function. The regularization term can control the smoothness of the surface and prevent unreasonable fluctuations. Determine the regularization coefficient through the cross-validation method. This coefficient can effectively balance the fitting accuracy and smoothness. Cross-validation is a method of dividing the data set and repeatedly verifying the model effect, which can avoid overfitting and ensure the robustness and accuracy of the error mapping function in practical applications. After regularization, the obtained regularized spatial error mapping function can reflect the error characteristics of the lead screw module under different working conditions and has better generalization ability. Divide the working space of the lead screw module into multiple overlapping sub-regions. Perform thin plate spline fitting on each sub-region separately to ensure that the error compensation adapts to different local working conditions. To ensure smooth transition of error compensation between adjacent sub-regions, especially in the boundary regions, the fitting results of adjacent sub-regions are merged. In this way, discontinuous error compensation between different regions is avoided, and the error compensation within the entire working space is kept consistent and smooth. The finally obtained piecewise fitting spatial error mapping function accurately reflects the error characteristics of the lead screw module in different sub-regions while maintaining global consistency. Construct a feed-forward compensation unit based on the piecewise fitting spatial error mapping function. The feed-forward compensation unit corrects the target position according to the expected error value of the target position, thereby compensating for the error in advance. In this process, the feed-forward compensation unit calculates the error amount of the target position using the piecewise fitting spatial error mapping function and adjusts the target position according to this error amount to obtain a feed-forward compensation position command. Through feed-forward compensation, the static deviation caused by system errors is effectively reduced, and compensation is performed in advance to achieve more accurate positioning control. The residual error between the actual position and the theoretical position of the lead screw module is monitored in real time, and an additional compensation amount is generated by the PID controller. The PID controller generates an additional compensation amount according to the magnitude and change trend of the real-time error.The PID controller adjusts the system output through proportional, integral and differential control to correct the residual error and improve the accuracy of the system. The feedforward compensation position command is combined with the additional compensation output by the PID controller to form the final compensation. This compensation takes into account both static and dynamic errors to generate accurate screw module positioning control instructions.

[0033] According to the motion range and structural characteristics of the screw module, the workspace is gridded and divided into multiple basic cells to obtain the initial spatial division structure. Each cell represents a relatively independent area, and the error data is processed separately. The error data in the initial spatial division structure is subjected to spatial gradient analysis to identify the error change trend and its distribution law. Spatial gradient analysis can reveal the rate at which the error changes with position. The spatial gradient distribution diagram reflects which areas have more drastic error changes and which areas have smaller error changes, thereby providing a basis for adaptive mesh refinement. Based on this information, the initial spatial division structure is adaptively refined. The process of adaptive refinement is to dynamically adjust the density of the grid, using a denser grid in areas with larger error changes, and keeping a coarser grid in areas with smaller error changes. Through the adaptively optimized spatial grid, a more accurate spatial division structure is obtained, which can better adapt to the error characteristics of the screw module at different positions. The error compensation parameters are allocated according to the new adaptively optimized spatial grid. Through this allocation method, each sub-area has a set of local control point data sets as the input data for subsequent thin plate spline fitting. The control point set of each sub-area represents the error compensation requirements in the area and is used to calculate the local fitting function. For each sub-region, the thin plate spline fitting algorithm will be executed separately and the local coefficient matrix and polynomial coefficient vector will be solved. These coefficients describe the variation law of the error in each sub-region and how to correct it through compensation parameters. Thin plate spline fitting can provide a smooth and continuous compensation surface while ensuring the accuracy of error compensation, so that the error compensation is not only accurate but also smooth, avoiding over-correction or overfitting. After fitting each sub-region separately, the local fitting function obtained can accurately describe the error compensation requirements in each region. A transition weight function is constructed for the overlapping parts of adjacent sub-regions. The function of the transition weight function is to smooth the boundary between the two sub-regions so that the error compensation in the transition region can be smoothly connected. The weight function can perform a weighted combination of multiple local fitting results in the overlapping region, so that the compensation results in the transition region can not only retain the error compensation characteristics in each sub-region, but also achieve a smooth transition between different regions. By weighted combination of the local fitting results of all sub-regions, the block fitting spatial error mapping function is obtained.

[0034] In an example, the motion trajectory and load of the lead screw module are detected to obtain displacement error data and load response data, including:

[0035] Displacement sensors are arranged at both ends, the slider connection point and the middle position of the lead screw module, and the sampling frequency of the displacement sensors is set to collect the original displacement data;

[0036] A strain gauge load sensor is installed at the slider connection point of the lead screw module to monitor the axial force and radial force borne by the lead screw module and obtain load mechanical data;

[0037] An angle encoder is used to record the rotational speed, acceleration and deceleration of the lead screw module to obtain rotational dynamic parameters;

[0038] The lead screw module is subjected to full-stroke reciprocating motion, segmented motion and multiple tests under different speed conditions to obtain a multi-condition operation data set, and a temperature sensor is used to monitor the test environment temperature and the temperature changes of each component of the lead screw module to obtain temperature drift compensation data;

[0039] Time synchronization tags and data fusion are performed on the original displacement data, load mechanical data, rotational dynamic parameters, multi-condition operation data set and temperature drift compensation data to obtain displacement error data and load response data.

[0040] In this example, high-precision displacement sensors are arranged at both ends, the slider connection point and the middle position of the lead screw module. These displacement sensors accurately capture the displacement changes of the lead screw module during movement through optical, magnetic induction or capacitance measurement principles. To ensure the accuracy of data collection, the sampling frequency of the displacement sensors is set to match the movement speed and acceleration of the lead screw module. For example, the sampling frequency needs to be increased during high-speed movement to prevent loss of displacement data due to insufficient sampling. Assume the maximum movement speed of the lead screw module is v max , the sampling frequency should satisfy the Nyquist sampling theorem, that is, the sampling frequency f sIt should be greater than twice the highest signal frequency to ensure the accuracy and integrity of the original displacement data. While acquiring the displacement data, monitor the mechanical state borne by the lead screw module, and install strain gauge load sensors at the slider connection. These sensors measure the changes in axial force and radial force through the tiny deformation of the strain gauges, providing data on the force-bearing state of the system under different working conditions. For example, when the lead screw module bears an additional external load, the strain gauge will undergo a tiny deformation, which is converted into an electrical signal through the change in resistance inside the sensor to obtain accurate load mechanical data. Use an angle encoder to record the rotational speed, acceleration, and deceleration of the lead screw module. The angle encoder obtains the rotational speed data by reading the change speed of the rotation angle, and calculates the acceleration and deceleration parameters through time differentiation. These rotational dynamic parameters can reveal the motion characteristics of the lead screw module during startup, stop, and uniform motion. For example, when the lead screw module accelerates from a stationary state to a set speed, analyze the dynamic response characteristics of the system and the error sources generated during the acceleration process through the acceleration curve. During the data acquisition process, perform full-stroke reciprocating motion, segmented motion, and multiple tests under different speed conditions. For example, conduct multiple round trips within the entire stroke range of the lead screw module to detect the error accumulation during long-distance motion; accurately measure the error distribution at specific positions through segmented motion tests; and tests under different speed conditions can analyze the influence of speed changes on system errors. The accuracy of the lead screw module is also affected by environmental and its own temperature changes. Therefore, during the test process, use temperature sensors to monitor the ambient temperature and the temperature changes of each component of the lead screw module in real time. For example, when the lead screw module runs at high speed for a long time, the temperature rises due to friction, which will cause thermal expansion of the material, thereby affecting the positioning accuracy. Temperature drift compensation data is used to correct the errors caused by temperature changes, thereby improving the stability of the system. After completing the data acquisition of multiple sensors, perform time synchronization marking and data fusion on the original displacement data, load mechanical data, rotational dynamic parameters, multi-condition operation data set, and temperature drift compensation data to ensure that all data sources are aligned under the same time reference to achieve multi-modal fusion of data. Through a high-precision clock or synchronous trigger signal, time-stamp the data collected by different sensors to achieve synchronous fusion of multi-source data. The data fusion process uses methods such as Kalman filtering or weighted averaging to fuse the data from different sensors into a unified error data model, eliminate the noise and errors generated by a single sensor, and improve the reliability and accuracy of the data through the complementarity of multi-source information. To convert the above collected data into specific quantization parameters that can be used for error compensation, convert the fused data into displacement error data and load response data through a mathematical model. For example, calculate the error compensation model through the following formula:

[0041]

[0042] Among them, E(x, y, z) represents the error compensation amount at the position (x, y, z) in the three-dimensional space, and w i is the weight coefficient, representing the contribution rate of different error sources, and f i (x, y, z) is the error source function, used to describe the distribution characteristics of a specific error source in space. N is the total number of error sources, R(T) is the temperature compensation function, and T is the current temperature data. Through the error compensation model, the position, load, dynamic characteristics, and temperature changes are comprehensively considered, and the compensation strategy under different working conditions is dynamically adjusted.

[0043] In an example, a three-dimensional error parameter model is constructed based on the displacement error data and the load response data, and the initial error characteristics are calculated through the three-dimensional error parameter model, including:

[0044] The displacement error data is compared and calculated with the theoretical displacement value of the lead screw module to obtain the displacement error sequence, and the load response data is subjected to spectral analysis to obtain the correlation data between the load change and the displacement error;

[0045] A three-dimensional error parameter model is established based on the displacement error sequence and the correlation data. The three-dimensional error parameter model includes the axial distance error coefficient, the radial offset error coefficient, the vertical displacement error coefficient, the angular rotation error coefficient, the installation spacing error coefficient, the detection aperture error coefficient, and the temperature drift compensation coefficient;

[0046] The three-dimensional error parameter model is calculated by the recursive least squares algorithm to obtain the preliminary values of each error coefficient;

[0047] According to the preliminary values of each error coefficient, a coupling relationship matrix between parameters is constructed, and an error compensation function is created through the coupling relationship matrix between parameters to calculate the initial error characteristics.

[0048] In this example, displacement data is collected at different positions of the lead screw module by high-precision sensors. These sensors continuously monitor the actual position of each point of the lead screw module during movement and compare this position data with the displacement values obtained from theoretical calculations. The theoretical displacement values are ideal values calculated based on parameters such as the geometric dimensions, transmission ratio, and rotational speed of the lead screw module. By subtracting the actual displacement data from the theoretical displacement values, a displacement error sequence is obtained, which reflects the actual error conditions of the lead screw module at different positions. At the same time, the lead screw module is affected by different degrees of load during movement, and the load response data is analyzed. By installing load sensors on the lead screw module, data on load changes are obtained, especially the load changes during the operation of the lead screw module. To analyze the influence of load changes on displacement errors, spectral analysis is performed on the load response data to identify the frequency characteristics and correlations between load changes and displacement errors. For example, when the load changes rapidly, spectral analysis reveals whether this change corresponds to the fluctuations in displacement errors. If there is a strong correlation between the high-frequency components of the load and the high-frequency components of the displacement error, it is speculated that load fluctuations are a major factor causing displacement errors. The correlation data between load changes and displacement errors obtained through spectral analysis provides information for constructing an error model. Based on the displacement error sequence and the correlation data between load and displacement errors, a three-dimensional error parameter model is established. The three-dimensional error parameter model is obtained through multi-dimensional data analysis, taking into account multiple error sources of the lead screw module. The model includes an axial distance error coefficient, a radial offset error coefficient, a vertical displacement error coefficient, an angular rotation error coefficient, an installation spacing error coefficient, a detection aperture error coefficient, and a temperature drift compensation coefficient. These error coefficients respectively represent the error characteristics of the lead screw module in various directions. For example, the axial distance error coefficient represents the displacement error caused by mechanical errors, installation errors, etc. in the axial direction of the lead screw; the radial offset error coefficient represents the offset error that occurs in the radial direction of the lead screw module, caused by the accuracy problem of the lead screw or the deviation of the support structure; the vertical displacement error coefficient represents the error generated in the vertical direction of the lead screw module due to misalignment, etc.; the angular rotation error coefficient reflects the angular error caused by inaccurate assembly during rotational movement; the installation spacing error coefficient refers to the influence of the installation spacing deviation of the lead screw module on the position accuracy; the detection aperture error coefficient is related to the detection aperture of the sensor, and this error coefficient reflects the error introduced by the sensor during measurement; the temperature drift compensation coefficient is used to correct the influence of temperature changes on the accuracy of the lead screw module. By combining these error sources, the error characteristics of the lead screw module are accurately described. The three-dimensional error parameter model is calculated using the recursive least squares algorithm to obtain the initial values of each error coefficient. The recursive least squares algorithm is a parameter estimation method suitable for estimating system parameters in dynamic systems. Through recursive calculation, the estimated values of the error coefficients are continuously optimized and gradually approach the true error coefficients.The recursive least squares algorithm continuously adjusts the values of the error coefficients to minimize the difference between the predicted error and the actual measurement error. For example, in each iteration, the algorithm predicts the displacement error based on the current error coefficients and compares it with the actually measured displacement error to obtain a new estimated error coefficient. Through multiple iterations, a set of optimal error coefficients is finally obtained. Based on the preliminary values of each error coefficient, a coupling relationship matrix between parameters is constructed to reflect the mutual relationship and coupling effect among the error coefficients. During the precision detection process of the lead screw module, various error sources do not exist independently but are coupled with each other. For example, the axial error and the radial error will affect each other, and when performing error compensation, the coupling relationship between these error sources needs to be considered. By constructing the coupling relationship matrix, the mutual influence of these error sources is integrated into a unified compensation function, so that all influencing factors are comprehensively considered during error compensation. Based on the coupling relationship matrix between parameters, an error compensation function is created. The error compensation function accurately compensates the position error of the lead screw module according to the actual working state and error characteristics. For example, assume the compensation function is:

[0049]

[0050] where ΔP represents the error compensation amount, c i represents the error coefficient, and E i represents the influence of the i-th error source. Through the compensation function, according to the real-time error data, the contribution of each error source to the total error is calculated, so as to perform effective error correction. The initial error characteristics are obtained.

[0051] In an example, a working condition adaptive analysis is performed on the initial error characteristics to obtain a multi-dimensional compressed error matrix, including:

[0052] A weight function is constructed based on the speed, load, and temperature parameters of the lead screw module to perform dynamic weight allocation on the displacement error and load error in the initial error characteristics, and the weight allocation error data is obtained;

[0053] Perform multi-scale analysis on the weight allocation error data to obtain multi-band error characteristic components, and perform principal component analysis on the multi-band error characteristic components to obtain error contribution rate distribution data;

[0054] Construct an error characteristic vector based on the error contribution rate distribution data, and perform dimensionality reduction processing on the error characteristic vector to obtain a compressed error characteristic vector;

[0055] Based on historical detection data, an error mode library containing typical error modes under different working conditions is established, and the error characteristics of each working condition are mapped and matched with the mode library to obtain a working condition-error mapping relationship table;

[0056] Based on the compressed error eigenvector and the working condition-error mapping relation table, the initial error features are classified, integrated, and matrix reconstructed to obtain a multi-dimensional compressed error matrix.

[0057] In this example, a weight function is constructed according to the working parameters such as the speed, load, and temperature of the lead screw module to reflect the relative importance of error sources under different working conditions. Speed, load, and temperature are the key factors affecting the accuracy of the lead screw module. For example, under high load, the load error is more significant than the speed error; while in the case of large temperature variations, temperature drift becomes the main source of error. The weight function is dynamically adjusted according to these working conditions. For example, the weight function is defined as:

[0058]

[0059] Among them, w(v, f, T) is the weight function, where v represents the speed, f represents the load, T represents the temperature, α, β, and γ are weight parameters, and Z is the normalization factor. The design of this weight function is adjusted according to experimental data or system characteristics so as to assign different weights to displacement errors and load errors under different working conditions. Dynamic weight allocation is performed on the displacement error and load error in the initial error characteristics. According to the speed, load, and temperature parameters under different working conditions, the weights of the displacement error and load error are dynamically adjusted. By calculating the dynamic weights, the contributions of different error sources to the total error are appropriately adjusted to obtain the weight allocation error data, which reflects the contributions of each error source under different working conditions. Multiscale analysis is performed on the weight allocation error data. Multiscale analysis is a method for analyzing the characteristics of a signal at different frequency scales, which helps to reveal the characteristics of the error data in different frequency bands. For example, the low-frequency components correspond to the long-term stability of the system, while the high-frequency components reflect the instantaneous dynamic changes of the system. By performing multiscale analysis on the error data, multiband error characteristic components are obtained, which represent the characteristic information of the error at different frequencies. Principal component analysis is performed on the multiband error characteristic components to effectively extract the most significant characteristics in the error data. Through principal component analysis, redundant information in the multiband error characteristic components is removed to obtain the main contribution direction and the most important characteristic components of the error, and the error contribution rate of each characteristic component is calculated to obtain the error contribution rate distribution data. According to the error contribution rate distribution data, an error characteristic vector is constructed, which represents the distribution of the error data in each characteristic space. Dimensionality reduction processing is performed on the error characteristic vector to reduce the dimension of the error characteristic vector to a range suitable for actual calculation while retaining as much effective information as possible. Dimensionality reduction processing uses principal component analysis, linear discriminant analysis, or other dimensionality reduction techniques to reduce the computational complexity and improve the efficiency of subsequent analysis. After dimensionality reduction, a compressed error characteristic vector is obtained. An error pattern library containing typical error patterns under different working conditions is established based on historical detection data. The error pattern library is a model based on historical data that corresponds the error characteristics under different working conditions to the actually exhibited error patterns. By analyzing the historical data, the typical error patterns under each working condition are identified and stored in the error pattern library. When the system is in a specific working condition, the most matching error pattern is found through mapping and matching with the error pattern library. This process can effectively predict and compensate for the errors under the current working condition. Based on the compressed error characteristic vector and the working condition-error mapping relationship table, the initial error characteristics are classified, integrated, and matrix reconstructed to obtain a multi-dimensional compressed error matrix. The multi-dimensional compressed error matrix is a comprehensive error description model that integrates the error characteristics under different working conditions and the contributions of each error source, providing a more accurate error compensation scheme. During the matrix reconstruction process, by performing weighted combination on the contributions of different error sources, a more accurate and precise error compensation result is obtained.The multi-dimensional compression error matrix can dynamically adapt to different working environments, achieve real-time error compensation, and improve the positioning accuracy of the lead screw module.

[0060] In one example, the multi-dimensional compression error matrix is input into a recursive optimization algorithm for hierarchical parameter iteration to obtain error compensation parameters, including:

[0061] Construct a global objective function based on the multi-dimensional compression error matrix, input the global objective function into the recursive optimization algorithm, and add an adaptive inertia weight and mutation operation to obtain a global optimal parameter estimate;

[0062] Partition the operating range of the lead screw module according to its operating characteristics, divide the complete stroke of the lead screw module into multiple overlapping intervals, and obtain operating interval division data;

[0063] Construct a local objective function for each interval in the operating interval division data, use the global optimal parameter estimate as the initial value, and solve it by recursive least squares to obtain the local optimal parameters for each interval;

[0064] Input the local optimal parameters of adjacent intervals into a smoothing constraint function for boundary consistency processing to obtain smoothed interval parameters;

[0065] Construct a comprehensive error compensation model based on the smoothed interval parameters and the global optimal parameter estimate, integrate the global optimization result and the local optimization result, and perform multiple recursive iteration calculations to obtain error compensation parameters.

[0066] In this example, a global objective function is constructed based on the multi-dimensional compression error matrix. By comprehensively considering all error sources and the influence of various working parameters, the overall error of the system is estimated. The construction of the global objective function depends on the multi-dimensional compression error matrix, which contains various factors such as displacement error, load error, temperature error, etc. By combining various error sources with weights, a comprehensive objective function reflecting the overall error of the entire system is constructed. The form of the global objective function is expressed as:

[0067]

[0068] where, F g is the global objective function, λ i is the weight of each error source, E i is the error value of the i-th error source, and n is the total number of error sources. By reasonably selecting the weights λ i, so that the global objective function reflects the main contribution of the system error. In practical applications, the global objective function is input into a recursive optimization algorithm for solution. The recursive optimization algorithm minimizes the objective function by continuously iteratively adjusting parameters to obtain the optimal error compensation parameters. During the process of the recursive optimization algorithm, to improve the convergence speed and stability of the algorithm, an adaptive inertia weight and a mutation operation are introduced. The adaptive inertia weight is used to adjust the search strategy of the algorithm in each iteration, enabling it to explore a wider solution space in the initial stage and focus on the local area of the optimal solution in the later stage. The mutation operation introduces a certain degree of randomness to prevent the algorithm from falling into a local optimal solution, thereby enhancing the global search ability of the optimization process. Through this step, the recursive optimization algorithm obtains the global optimal parameter estimation. The operating range of the lead screw module is partitioned according to the operating characteristics of the lead screw module. The complete stroke of the lead screw module is divided into multiple overlapping intervals, and each interval represents a specific working state. A local objective function needs to be constructed separately for each operating interval. The form of the local objective function is similar to that of the global objective function, mainly targeting the error characteristics of a certain interval. When constructing the local objective function, the global optimal parameter estimation is used as the initial value, and then it is optimized and solved by the recursive least squares method. The recursive least squares method continuously adjusts the local parameters by minimizing the sum of squared errors, so that the errors in each interval are optimally compensated. By optimizing each interval separately, the local optimal parameters of each interval are obtained. The boundary consistency of the local optimal parameters of adjacent intervals is processed. A smoothing constraint function is used to smooth the local optimal parameters of adjacent intervals to ensure that the transition between intervals is continuous and there are no abrupt changes. For example, a technique similar to spline interpolation is adopted, so that the change in error compensation at the boundary between adjacent intervals is smooth, thereby avoiding error jumps caused by boundary inconsistency. The smoothing constraint function is expressed as:

[0069] S ij = α·|E i -E j |;

[0070] where S ij represents the smoothness between adjacent intervals i and j, E i and E jThey respectively represent the error compensation parameters for intervals i and j, and α is the smoothing coefficient. Through the smoothing constraint function, the parameter boundaries between different intervals are effectively processed, making the final error compensation model smoother and more coherent. An integrated error compensation model is constructed based on the smoothed interval parameters and the global optimal parameter estimation. Combining the global optimization result and the local optimization result, an integrated error compensation framework is formed. Through multiple recursive iterations, the error compensation parameters are optimized to achieve more precise control and compensation. During each iteration, the recursive optimization algorithm further adjusts the parameters based on the current integrated error compensation model, gradually approaching the optimal error compensation state of the system. After multiple recursive iterations, the algorithm converges to a globally optimal error compensation parameter. This parameter can minimize the errors of the lead screw module under different working conditions and ensure the high-precision operation of the system.

[0071] In one example, thin plate spline fitting is performed on the error compensation parameters to obtain a spatial error mapping function, and the position compensation amount is calculated according to the spatial error mapping function to generate a precise positioning control instruction for the lead screw module, including:

[0072] Generate a control point set within the working space of the lead screw module according to the error compensation parameters to obtain the basic data for thin plate spline fitting;

[0073] Substitute the basic data for thin plate spline fitting into the mathematical model, and determine the thin plate spline coefficients by solving the linear equations to obtain the initial spatial error mapping function;

[0074] Add a regularization term to the initial spatial error mapping function, and determine the regularization coefficient through the cross-validation method to control the surface smoothness, obtaining a regularized spatial error mapping function;

[0075] Divide the working space of the lead screw module into multiple overlapping sub-regions, perform thin plate spline fitting on each sub-region respectively, and merge the results of the boundary regions to obtain a piecewise fitting spatial error mapping function;

[0076] Construct a feedforward compensation unit according to the piecewise fitting spatial error mapping function, calculate the expected error value of the target position, and correct the target position to obtain a feedforward compensation position instruction;

[0077] Monitor the residual error between the actual position and the theoretical position of the lead screw module in real time, generate an additional compensation amount through a PID controller, combine the feedforward compensation position instruction and the additional compensation amount to form a final compensation amount, and output a precise positioning control instruction for the lead screw module.

[0078] In this example, a set of control points is generated within the working space of the lead screw module. These control points are distributed based on error compensation parameters and are selected in combination with the actual working conditions. The set of control points is not only discrete spatial coordinates but also includes the error data measured at these positions. By collecting error data at different positions, an error distribution map covering the entire working space is constructed to obtain the basic data for thin plate spline fitting. Substitute the basic data of thin plate spline fitting into the mathematical model, and determine the coefficients of the thin plate spline by solving the linear equations. The thin plate spline is an efficient method for two-dimensional data interpolation, and its basic model is expressed as:

[0079]

[0080] where E(x, y) is the error compensation amount at the coordinate (x, y); N is the number of control points; α i is the coefficient of the thin plate spline to be determined; P i =(x i , y i ) is the coordinate of the i-th control point; φ(r)=r 2 ln(r) is the radial basis function of the thin plate spline, where r = ∥P i -(x, y)∥ represents the spatial distance; P1(x, y) is a first-order polynomial used to represent the global linear trend. In this model, the solution process of the linear equations involves matrix inversion or the least squares method generated from the control point data to determine the coefficient α i . These coefficients play a key role in the model because they determine the influence of the spline function at each control point and the specific effect of error compensation. A regularization term is introduced into the error mapping function to control the surface smoothness, and the regularization coefficient is determined by the cross-validation method. The goal of regularization is to achieve a balance between the accuracy of error compensation and the smoothness of the model. The spatial error mapping function with the regularization term is expressed as:

[0081]

[0082] where E reg(x, y) is the regularized spatial error mapping function; λ is the regularization coefficient, determined by cross - validation; the integral term represents the curvature of the surface, and surface smoothing control is achieved by minimizing the sum of the squares of the second derivatives. In this process, different regularization coefficients are tested through the cross - validation method, and the parameter value that makes the error mapping function perform best on the test data set is selected, so as to ensure the best balance between the smoothness and fitting accuracy of the model. After the regularization process, in order to improve the accuracy of error compensation, the working space of the lead screw module is divided into multiple overlapping sub - regions. Thin - plate spline fitting is performed separately in different regions, so that the error compensation model can better adapt to local error characteristics. In each sub - region, independent spline fitting is performed through the control point data to obtain the local error mapping function within the region. Since there are overlapping parts between regions, in order to avoid discontinuities in error compensation in these transition regions, a transition weight function is constructed to achieve smooth transition. The calculation of smooth transition is expressed as:

[0083]

[0084] where, E s (x, y) is the spatially error mapping function after smooth transition; M is the number of sub - regions within the overlapping area; w i (x, y) is the transition weight function, satisfying E i (x, y) is the local error mapping function of the i - th sub - region. Through the weighted combination method, the error compensation between adjacent regions is smoothly transitioned at the boundary, eliminating the error mutation phenomenon. According to the spatially error mapping function of piece - wise fitting, a feed - forward compensation unit is constructed. At the target position (x t , y t ), by calculating the expected error value and correcting the target position, the feed - forward compensation position command is obtained:

[0085] P ff (x t , y t )=(x t , y t )+E s (x t , y t );

[0086] This command is used to pre - compensate for the known errors of the system during the movement process. The residual error is monitored in real time through a PID controller, and an additional compensation amount is generated:

[0087]

[0088] where, P pid(t) is the compensation amount output by the PID controller; e(t) is the real-time error, that is, the deviation between the target position and the actual position; K p , K i , K d are the proportional, integral, and differential gain coefficients respectively. Combining the feedforward compensation position command and the PID compensation amount, the final precise positioning control command is obtained:

[0089] P f (t) = P ff (x t , y t ) + P pid (t);

[0090] This formula combines the predictability of feedforward compensation and the dynamic adjustment ability of PID feedback, enabling the lead screw module to maintain high-precision motion control under different working conditions.

[0091] In one example, the working space of the lead screw module is divided into multiple overlapping sub-regions, thin plate spline fitting is performed separately in each sub-region, and the results of the boundary regions are combined to obtain a piecewise fitting spatial error mapping function, including:

[0092] According to the motion range and structural characteristics of the lead screw module, the working space is meshed, and the working space is divided into multiple basic cells to obtain an initial space division structure;

[0093] Perform spatial gradient analysis on the error data in the initial space division structure to obtain a spatial error gradient distribution map;

[0094] Based on the spatial error gradient distribution map, adaptively refine the initial space division structure to obtain an adaptively optimized space grid;

[0095] Allocate the error compensation parameters according to the adaptively optimized space grid, and allocate a local control point set to each sub-region to obtain a sub-region control point data set;

[0096] Perform the thin plate spline fitting algorithm separately on each sub-region control point data set, solve the local coefficient matrix and polynomial coefficient vector, and obtain a sub-region local fitting function;

[0097] Construct a transition weight function for the overlapping parts of all adjacent sub-regions, and perform weighted combination on multiple local fitting results within the overlapping region according to the transition weight function to obtain a piecewise fitting spatial error mapping function.

[0098] In this example, the working space is meshed, and the complex spatially distributed error is divided into multiple controllable basic cells. By dividing the motion range of the lead screw module into a series of regular grids, for example, the X and Y axes in a two-dimensional space are respectively divided according to a specific step size hx and h y Perform discretization to divide the entire workspace into M×N basic cells. Each cell represents the error distribution range of the lead screw module at a specific position, and the size of these cells depends on the resolution of the lead screw module and the required error compensation accuracy. After completing the initial spatial division structure, perform spatial gradient analysis on the error data in these grids to identify the rate of change of the error data at different spatial positions, thereby revealing the changing characteristics of the error distribution. For example, in areas where the error changes more drastically, the spatial gradient value is larger, while in areas where the error changes smoothly, the gradient value is smaller. The spatial error gradient is obtained by calculating the partial derivative of the error in space, and the mathematical expression of the gradient is:

[0099]

[0100] where represents the error gradient at position (x,y), and represent the rates of change of the error in the x and y directions respectively. By calculating the error gradient of the entire space, a spatial error gradient distribution map is obtained, which effectively indicates the areas where the error changes concentratedly, such as error spikes that appear near the boundary or near specific mechanical structure contact points. Based on the spatial error gradient distribution map, perform adaptive refinement on the initial spatial division structure. The process of dynamically adjusting the grid density according to the gradient values in different regions. In areas with a large error gradient, increase the sampling density by reducing the grid cell size, so that the error compensation model can more accurately fit the error characteristics of these complex regions. In areas where the error changes less, maintain a larger grid size to reduce the computational burden. The rules of adaptive refinement are defined by the following formula:

[0101]

[0102] where h ′ (x,y) is the grid size after adaptive refinement; h0 is the initial grid size; k is an adjustment coefficient used to control the refinement degree; is the modulus value of the error gradient, reflecting the intensity of the error change. Through this adaptive refinement formula, the grid will become finer where the error gradient is large, and vice versa, a relatively loose grid division is maintained to obtain an adaptively optimized spatial grid. Allocate the error compensation parameters according to the optimized spatial grid, and allocate the error data in each sub-region to the local control point set. These local control point data sets include not only the position coordinates but also the error values measured at these positions. In each sub-region, independently execute the thin plate spline fitting algorithm to solve the local coefficient matrix and polynomial coefficient vector, and obtain the local fitting function in the sub-region. The thin plate spline fitting function is expressed as:

[0103]

[0104] Among them, E i (x, y) is the local error fitting function of the i-th sub-region; n i is the number of control points in the i-th sub-region; α j is the thin plate spline coefficient, obtained by fitting; φ(r) is the radial basis function, in the form of r 2 ln(r); P i (x, y) is the low-order polynomial term, used to describe the global error trend. Since the fitting functions of different sub-regions are calculated on independent local control point sets, discontinuities or error jumps will occur in the overlapping parts of adjacent regions. A transition weight function is constructed in the overlapping parts of all adjacent sub-regions. By weighted combining multiple local fitting results in the overlapping region, a smooth piecewise fitting spatial error mapping function is obtained. This weighted combination process is achieved through the following formula:

[0105]

[0106] Among them, E s (x, y) is the error mapping function after smooth transition; m is the number of sub-regions in the overlapping region; w i (x, y) is the transition weight function, satisfying the normalization condition. The transition weight function w i (x, y) adopts a weighting method based on spatial distance. For example, in an overlapping region, the closer to the center of a certain sub-region, the larger its weight w i is, making the error mapping in the transition region smoother and avoiding the problem of error mutation at the sub-region boundary. Through the above method, a high-precision piecewise fitting spatial error mapping function is constructed within the working space of the entire lead screw module. This function can reflect the error distribution of the lead screw module at different positions in real time and provide accurate error compensation information.

[0107] Referring to Figure 2 , this embodiment provides a precision detection device for a lead screw module with multi-parameter recursive optimization, including:

[0108] Detection module 1, used to detect the motion trajectory and load of the lead screw module to obtain displacement error data and load response data;

[0109] Construction module 2, used to construct a three-dimensional error parameter model based on the displacement error data and load response data, and calculate the initial error characteristics through the three-dimensional error parameter model;

[0110] An analysis module 3 for performing a working condition adaptive analysis on the initial error characteristics to obtain a multi-dimensional compressed error matrix;

[0111] An iteration module 4 for inputting the multi-dimensional compressed error matrix into a recursive optimization algorithm for hierarchical parameter iteration to obtain error compensation parameters;

[0112] A generation module 5 for performing thin plate spline fitting on the error compensation parameters to obtain a spatial error mapping function, and calculating a position compensation amount according to the spatial error mapping function to generate a precise positioning control instruction for the lead screw module.

[0113] In this embodiment, for the specific implementation of each unit in the above device embodiment, please refer to the description in the above method embodiment and will not be elaborated here.

[0114] It should be noted that in this article, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, device, article or method including a series of elements not only includes those elements but also includes other elements not expressly listed, or further includes elements inherent to such process, device, article or method. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of another identical element in the process, device, article or method including that element.

[0115] The above are only the preferred embodiments of the present invention, and do not limit the patent scope of the present invention accordingly. Any equivalent structural or equivalent process transformation made by using the specification and drawings of the present invention, or directly or indirectly applied to other related technical fields, shall be equally included in the patent protection scope of the present invention.

Claims

1. A precision detection method for a lead screw module with multi-parameter recursive optimization, characterized in that, It includes the following steps: Conduct motion trajectory and load detection on the lead screw module to obtain displacement error data and load response data; Construct a three-dimensional error parameter model based on the displacement error data and the load response data, and calculate the initial error characteristics through the three-dimensional error parameter model; Perform working condition adaptive analysis on the initial error characteristics to obtain a multi-dimensional compressed error matrix; Input the multi-dimensional compressed error matrix into a recursive optimization algorithm for hierarchical parameter iteration to obtain error compensation parameters; Perform thin plate spline fitting on the error compensation parameters to obtain a spatial error mapping function, and calculate the position compensation amount according to the spatial error mapping function to generate a precise positioning control instruction for the lead screw module.

2. The precision detection method for a lead screw module with multi-parameter recursive optimization according to claim 1, characterized in that The conducting motion trajectory and load detection on the lead screw module to obtain displacement error data and load response data includes: Arrange displacement sensors at both ends, the slider connection part and the middle position of the lead screw module, set the sampling frequency of the displacement sensors, and collect the original displacement data; Install a strain gauge load sensor at the slider connection part of the lead screw module to monitor the axial force and radial force borne by the lead screw module to obtain load mechanical data; Use an angle encoder to record the rotation speed, acceleration and deceleration of the lead screw module to obtain rotational dynamic parameters; Perform multiple tests on the lead screw module under full stroke reciprocating motion, segmented motion and different speed conditions to obtain a multi-working condition operation data set, and monitor the test environment temperature and the temperature change of each component of the lead screw module through a temperature sensor to obtain temperature drift compensation data; Perform time synchronization marking and data fusion on the original displacement data, the load mechanical data, the rotational dynamic parameters, the multi-working condition operation data set and the temperature drift compensation data to obtain displacement error data and load response data.

3. The precision detection method of the lead screw module with multi-parameter recursive optimization according to claim 1, characterized in that, The constructing a three-dimensional error parameter model based on the displacement error data and the load response data, and calculating the initial error characteristics through the three-dimensional error parameter model includes: Perform comparison calculation on the displacement error data and the theoretical displacement value of the lead screw module to obtain a displacement error sequence, and perform spectrum analysis on the load response data to obtain the correlation data between load change and displacement error; Establish a three-dimensional error parameter model based on the displacement error sequence and the correlation data. The three-dimensional error parameter model includes an axial distance error coefficient, a radial offset error coefficient, a vertical displacement error coefficient, an angular rotation error coefficient, an installation spacing error coefficient, a detection aperture error coefficient and a temperature drift compensation coefficient; Perform recursive least squares algorithm calculation on the three-dimensional error parameter model to obtain the preliminary values of each error coefficient; Construct a coupling relationship matrix between parameters based on the preliminary values of each error coefficient, create an error compensation function through the coupling relationship matrix between parameters, and calculate the initial error characteristics.

4. The precision detection method for the lead screw module with multi-parameter recursive optimization according to claim 1, characterized in that, The performing working condition adaptive analysis on the initial error characteristics to obtain a multi-dimensional compressed error matrix includes: Construct a weight function based on the speed, load, and temperature parameters of the lead screw module, perform dynamic weight allocation on the displacement error and load error in the initial error characteristics to obtain weight allocation error data; Perform multi-scale analysis on the weight allocation error data to obtain multi-band error characteristic components, and perform principal component analysis on the multi-band error characteristic components to obtain error contribution rate distribution data; Construct an error characteristic vector based on the error contribution rate distribution data, and perform dimensionality reduction processing on the error characteristic vector to obtain a compressed error characteristic vector; Establish an error mode library containing typical error modes under different working conditions based on historical detection data, map and match the error characteristics of each working condition with the mode library to obtain a working condition-error mapping relationship table; According to the compressed error characteristic vector and the working condition-error mapping relationship table, classify and integrate the initial error characteristics and perform matrix reconstruction to obtain a multi-dimensional compressed error matrix.

5. The precision detection method of the lead screw module with multi-parameter recursive optimization according to claim 1, characterized in that, Inputting the multi-dimensional compressed error matrix into a recursive optimization algorithm for hierarchical parameter iteration to obtain error compensation parameters includes: Construct a global objective function based on the multi-dimensional compressed error matrix, input the global objective function into the recursive optimization algorithm, and add an adaptive inertia weight and mutation operation to obtain a global optimal parameter estimate; Perform zoning processing on the operating range of the lead screw module according to the operating characteristics of the lead screw module, divide the complete stroke of the lead screw module into multiple overlapping intervals to obtain operating interval division data; Construct a local objective function for each interval in the operating interval division data, use the global optimal parameter estimate as the initial value, and solve through recursive least squares to obtain the local optimal parameters of each interval; Input the local optimal parameters of adjacent intervals into a smoothing constraint function for boundary consistency processing to obtain smoothed interval parameters; Construct a comprehensive error compensation model based on the smoothed interval parameters and the global optimal parameter estimate, integrate the global optimization result and the local optimization result, and perform multiple recursive iteration calculations to obtain error compensation parameters.

6. The precision detection method of the lead screw module with multi-parameter recursive optimization according to claim 1, wherein Performing thin plate spline fitting on the error compensation parameters to obtain a spatial error mapping function, and calculating a position compensation amount according to the spatial error mapping function to generate a precise positioning control instruction for the lead screw module includes: Generate a control point set within the working space of the lead screw module according to the error compensation parameters to obtain basic data for thin plate spline fitting; Substitute the basic data for thin plate spline fitting into a mathematical model, and determine the thin plate spline coefficients by solving a system of linear equations to obtain an initial spatial error mapping function; Add a regularization term to the initial spatial error mapping function, and determine the regularization coefficient through a cross-validation method to control the surface smoothness to obtain a regularized spatial error mapping function; Divide the working space of the lead screw module into multiple overlapping sub-regions, perform thin plate spline fitting on each sub-region respectively, and merge the results of the boundary regions to obtain a piecewise fitting spatial error mapping function; Construct a feedforward compensation unit according to the piecewise fitting spatial error mapping function, calculate the expected error value of the target position, and correct the target position to obtain a feedforward compensation position instruction; The residual error between the actual position and the theoretical position of the lead screw module is monitored in real time. An additional compensation amount is generated through a PID controller. The feedforward compensation position command and the additional compensation amount are combined to form a final compensation amount, and a precise positioning control command for the lead screw module is output.

7. The precision detection method of the lead screw module with multi-parameter recursive optimization according to claim 6, characterized in that, The method of dividing the working space of the lead screw module into multiple overlapping sub-regions, performing thin plate spline fitting in each sub-region respectively, and combining the results of the boundary regions to obtain a piecewise fitting spatial error mapping function includes: The working space is meshed according to the motion range and structural characteristics of the lead screw module, and the working space is divided into multiple basic cells to obtain an initial spatial division structure; Spatial gradient analysis is performed on the error data in the initial spatial division structure to obtain a spatial error gradient distribution map; Based on the spatial error gradient distribution map, the initial spatial division structure is adaptively refined to obtain an adaptively optimized spatial grid; The error compensation parameters are allocated according to the adaptively optimized spatial grid, and a local control point set is allocated to each sub-region to obtain a sub-region control point data set; The thin plate spline fitting algorithm is separately executed for each sub-region control point data set to solve the local coefficient matrix and the polynomial coefficient vector to obtain a sub-region local fitting function; A transition weight function is constructed for the overlapping parts of all adjacent sub-regions, and multiple local fitting results in the overlapping region are weighted and combined according to the transition weight function to obtain a piecewise fitting spatial error mapping function.

8. A precision detection device for a lead screw module with multi-parameter recursive optimization, characterized in that, For implementing the steps of the method according to any one of claims 1 to 7, the precision detection device for a lead screw module with multi-parameter recursive optimization includes: A detection module for detecting the motion trajectory and load of the lead screw module to obtain displacement error data and load response data; A construction module for constructing a three-dimensional error parameter model according to the displacement error data and the load response data, and calculating initial error characteristics through the three-dimensional error parameter model; An analysis module for performing working condition adaptive analysis on the initial error characteristics to obtain a multi-dimensional compressed error matrix; An iteration module for inputting the multi-dimensional compressed error matrix into a recursive optimization algorithm for hierarchical parameter iteration to obtain error compensation parameters; A generation module for performing thin plate spline fitting on the error compensation parameters to obtain a spatial error mapping function, and calculating a position compensation amount according to the spatial error mapping function to generate a precise positioning control command for the lead screw module.

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