Displacement sensor boundary area calibration method

Abstract

The invention discloses a displacement sensor boundary region calibration method. The method comprises the following steps: acquiring an original measurement data set; executing multi-scale boundary feature extraction to obtain a multi-scale feature vector and a boundary feature recognition fingerprint; constructing a dynamic segmented hybrid error model to obtain a balance error model and interval uncertainty; implementing intelligent iteration calibration processing to obtain a convergence optimization model; and generating a boundary region compensation function and a calibration parameter. According to the method, the complex nonlinear characteristics of the boundary region are extracted and captured through the multi-scale characteristics, the dynamic segmentation hybrid model is adopted to adapt to the error characteristics of different subintervals, the model parameters are optimized, the dynamic response problem is solved, and the calibration precision of the boundary region is improved.

Description

Technical Field

[0001] The invention belongs to the field of regional calibration, in particular to a displacement sensor boundary region calibration method. Background Art

[0002] Displacement sensors are key devices for measuring linear or angular displacement in fields such as automated control, precision manufacturing, and scientific research. Their calibration accuracy directly affects the reliability and quality of downstream applications. As modern industry develops towards intelligence and high precision, higher requirements are placed on the accuracy of displacement sensors, especially in high-end manufacturing fields such as precision instrument manufacturing, aerospace, and semiconductor processing, where submicron or even nanometer-level measurement accuracy has become the norm. In these application scenarios, the calibration method of the displacement sensor is not only related to the accuracy of the measurement results, but also determines the performance ceiling and reliability of the overall system. Therefore, the development of a high-precision, intelligent displacement sensor calibration method has important theoretical and practical value.

[0003] At present, the calibration technology of displacement sensors mainly relies on uniformly distributed calibration points and unified processing methods within the full range. Traditional calibration usually uses mathematical models such as polynomial fitting or piecewise linear interpolation to process calibration data. These methods use the same mathematical model structure and parameter optimization strategy throughout the measurement range. In terms of reference standards, most calibration systems rely on a single reference standard (such as a laser interferometer or a high-precision grating ruler), and usually use simple statistical methods to evaluate uncertainty. Environmental impact compensation is mostly based on a linear correction model, which mainly considers the impact of temperature on the measurement results, while ignoring the combined effects of other environmental factors such as humidity, air pressure and vibration. In terms of data processing algorithms, existing technologies mostly use globally unified parameter optimization methods, such as the least squares method or the gradient descent method, which lacks targeted processing of error characteristics in specific areas.

[0004] The traditional displacement sensor calibration method has obvious technical bottlenecks in the boundary area (i.e., 0-5% and 95-100% of the range), including large nonlinear errors and complex coupling effects. These technical problems are particularly prominent in high-precision measurement applications, which seriously restrict the accuracy and reliability of displacement sensors in the boundary area. Summary of the invention

[0005] The purpose of the invention is to provide a displacement sensor boundary area calibration method to solve the above-mentioned problems existing in the prior art.

[0006] Technical solution, a displacement sensor boundary area calibration method, comprising the following steps: Acquire the original measurement data set of the displacement sensor, perform multi-scale boundary feature extraction and analysis, and obtain a multi-scale feature vector and boundary feature recognition fingerprint; wherein the original measurement data set includes measurement points in the boundary area and the middle area; Based on multi-scale feature vectors and boundary feature recognition fingerprints, a dynamic segmented mixed error model is constructed to obtain a balanced error model and interval uncertainty. Based on the balanced error model and interval uncertainty, an intelligent iterative calibration process is implemented to obtain a converged optimization model; Based on the convergent optimization model, a boundary area compensation function and calibration parameters are generated to obtain a calibration parameter package for calibrating the boundary area of ​​the displacement sensor.

[0007] Beneficial effect: The present invention solves the core problem of low measurement accuracy in the boundary area of ​​the displacement sensor by establishing a complete boundary area calibration method framework; accurately captures the complex nonlinear characteristics of the boundary area, and compensates for it in a targeted manner through adaptive models and iterative optimization, so that the accuracy improvement is directly converted into improved product quality and reliability, solving the boundary area blind spot problem that has long plagued industrial measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 A flow chart of the steps of a displacement sensor boundary area calibration method provided in an embodiment of the present application.

[0009] Figure 2 A flowchart of the steps for obtaining a multi-scale feature vector and a boundary feature recognition fingerprint provided in an embodiment of the present application.

[0010] Figure 3 A flowchart of the steps for calculating the scale association matrix provided in an embodiment of the present application.

[0011] Figure 4 A flowchart of the steps for obtaining a balanced error model and interval uncertainty provided in an embodiment of the present application. DETAILED DESCRIPTION

[0012] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0013] It should be noted that in order to clearly show the steps of this application, serial numbers are marked for each step in the specification. These serial numbers are only used for the convenience of explanation and do not limit the order of execution of the steps. In actual operation, according to the technical requirements of the specific implementation scenario, the steps can be executed in a different order than that shown in the specification, and in some cases, parallel processing between steps can be achieved.

[0014] The present invention is described below in conjunction with preferred implementation steps. Figure 1 As shown, a displacement sensor boundary area calibration method includes the following steps: S1. Obtain the original measurement data set of the displacement sensor, perform multi-scale boundary feature extraction and analysis, and obtain a multi-scale feature vector and boundary feature recognition fingerprint; Specifically, the original measurement data set of the displacement sensor includes measurement points in the boundary area and the middle area. For example, when monitoring the road surface condition of a highway, the displacement sensor is arranged at the key position of the highway. The boundary area is the part where the edge of the road surface contacts the guardrail, and the middle area is the main part of the road surface. Observe these data from different angles or ranges to discover the characteristics of the boundary; for example, at the macro scale, analyze whether the overall road surface has a tendency to sink; at the micro scale, detect whether there are tiny cracks or protrusions in certain areas. These observed characteristics are sorted out to form a multi-scale feature vector, which is a digital description of these features, such as using data to represent the location and size of cracks. Boundary feature recognition fingerprints are used to mark and distinguish which areas have particularly significant features, such as cracks at the edge or depressions in the middle area.

[0015] S2. Based on multi-scale feature vectors and boundary feature recognition fingerprints, a dynamic segmented mixed error model is constructed to obtain a balanced error model and interval uncertainty; Specifically, in order to better describe the error distribution in the data, a dynamic segmented mixed error model is constructed to process the overall data in segments, and different error models are used to describe the characteristics of different regions. The dynamic model is used to balance the errors and generate an interval range that can reflect the credibility of the data.

[0016] S3, based on the balanced error model and interval uncertainty, implement intelligent iterative calibration processing to obtain a converged optimization model; Specifically, multiple adjustments are made through an intelligent iterative process based on the balanced error model and interval uncertainty. This process can be imagined as a self-learning cycle, where each iteration will improve on the previous results and gradually narrow the error range. After multiple intelligent iterations, the system will tend to stabilize, that is, reach "convergence", and finally output a converged optimization model.

[0017] S4. Based on the converged optimization model, a boundary area compensation function and calibration parameters are generated to obtain a calibration parameter package for calibrating the boundary area of ​​the displacement sensor.

[0018] Specifically, through the convergence optimization model, two key elements are created: compensation function and calibration parameters. The compensation function can be used to correct the deviation of the displacement sensor in the boundary area, while the calibration parameters are a set of specific adjustment values. Finally, the calibration parameter package is obtained, which is a complete correction solution. This calibration parameter package will be used for the boundary area calibration of the displacement sensor, making the sensor's measurement in the boundary area more accurate.

[0019] Boundary areas usually exhibit more complex nonlinear error characteristics, which are difficult to be fully characterized under the traditional uniformly distributed calibration point strategy, resulting in reduced calibration accuracy. This embodiment solves the core problem of low measurement accuracy in the boundary area of ​​the displacement sensor by establishing a complete boundary area calibration method framework, organically combining multi-scale feature extraction, dynamic segmented mixed error modeling, intelligent iterative calibration processing and compensation function generation. Traditional calibration methods generally have an error of 15-30μm in the boundary area, while this embodiment controls the error within the range of 2-5μm, improving the measurement accuracy by more than 80%. This accuracy improvement stems from the ability to accurately capture the complex nonlinear characteristics of the boundary area and to compensate for it in a targeted manner through adaptive models and iterative optimization. For fields such as high-precision automated manufacturing and precision instrument calibration, this accuracy improvement directly translates into improved product quality and reliability, solving the "blind spot" problem in the boundary area that has long plagued industrial measurement.

[0020] like Figure 2 As shown, according to one aspect of the present application, the steps of performing multi-scale boundary feature extraction and analysis to obtain a multi-scale feature vector and a boundary feature recognition fingerprint include: S11, acquiring the original measurement data set and performing enhanced sampling in the boundary area to obtain enhanced data; S12, applying local differential transformation to the original measurement data set and the enhanced data to obtain a boundary feature spectrum; S13, extracting features at different scales from the boundary feature spectrum and combining them to form a multi-scale feature vector; S14. Based on the multi-scale feature vectors, the scale correlation matrix is ​​calculated to quantify the intrinsic correlation between features of different scales; S15. Use multi-scale feature vectors and scale correlation matrices to compare and analyze the feature differences between the boundary area and the middle area, and construct a boundary feature recognition fingerprint.

[0021] Specifically, the original measurement data set D_raw of the displacement sensor is obtained, including the measurement points in the boundary area (0-5% and 95-100% range) and the middle area, and the theoretical position value P_t and the actual measurement value P_m of each measurement point are recorded. The density value B_density of the boundary area is calculated, and the minimum measurement point density of the boundary area is determined according to the sensor type and accuracy level. The automatic density enhancement strategy is used to obtain high-density enhanced data D_enhanced in the boundary area. Local differential transformation is applied to the original measurement data set D_raw and the enhanced data D_enhanced, and the data is mapped to the frequency-space joint domain to obtain the boundary feature spectrum S_boundary, which is used to capture high-frequency small fluctuations ignored by traditional methods. The multi-scale feature vector F_multi is extracted from the boundary feature spectrum S_boundary, including: extracting the microscopic feature F_micro at a small scale (0.1%-0.5% range) to characterize the slight nonlinearity of the sensor response; extracting the local feature F_local at a medium scale (0.5%-2% range) to characterize the system error in the local area; extracting the macroscopic feature F_macro at a large scale (2%-5% range) to characterize the overall boundary effect. Based on the multi-scale feature vector F_multi, the scale correlation matrix R_scale of the boundary area is calculated to quantify the intrinsic correlation between features of different scales. Through this matrix, the cross-scale coupling effect that is ignored in traditional methods is discovered. The feature differences between the boundary area and the middle area are compared and analyzed to construct the boundary feature recognition fingerprint B_fingerprint, which is used to accurately locate the starting point and change gradient of the boundary effect in subsequent modeling.

[0022] This embodiment improves the ability to capture small changes in boundary areas. In practical applications, conventional sampling can only obtain 3-5 valid data points in the first 0.5% of the range in the boundary area, while this embodiment can obtain 15-20 high-quality data points, increasing the information capture density by 300%. The local differential transform maps the data to the frequency-space joint domain, allowing the system to distinguish high-frequency small fluctuations of 0.1-0.2μm amplitude that cannot be recognized by traditional methods. These high-density, high-quality feature data provide a solid foundation for subsequent modeling, especially for sensors such as grating scales and magnetic scales that have high-frequency nonlinear errors in the boundary area, capturing important information that is ignored by traditional methods, directly leading to a significant improvement in calibration accuracy.

[0023] According to one aspect of the present application, the steps of obtaining a boundary feature spectrum and forming a multi-scale feature vector include: mapping the original measurement data set and the enhanced data to the frequency space to obtain a frequency distribution map; performing local feature enhancement processing on the frequency distribution map to obtain an enhanced spectrum; performing spatial correlation processing based on the enhanced spectrum to form a boundary feature spectrum; extracting microscopic features at a small scale, local features at a medium scale, and macroscopic features at a large scale from the boundary feature spectrum; and fusing the microscopic features, local features, and macroscopic features to form a multi-scale feature vector.

[0024] Specifically, the original measurement data set and enhanced data are mapped to the frequency space to obtain the frequency distribution map F_distribution: the sliding window Fourier transform STFT is applied to the original data, and the window size is 2% of the boundary area; the window sliding step is 0.2% of the boundary area; a time-frequency joint distribution map is generated to characterize the frequency response characteristics of different positions. The frequency distribution map F_distribution is processed for local feature enhancement to obtain an enhanced spectrum F_enhanced: an adaptive frequency band filter is applied to enhance the frequency components unique to the boundary area; contrast enhancement is performed to highlight the local features of the frequency distribution; and a peak detection algorithm is applied to identify characteristic frequency points. Spatial correlation processing is performed based on the enhanced spectrum F_enhanced to form a boundary feature spectrum S_boundary: the spatial autocorrelation function R_spatial(Δp) of the spectrum is calculated to characterize the spatial correlation of the spectrum features; a space-frequency joint feature matrix J_matrix is ​​constructed, and the element J(p, f) represents the enhanced eigenvalue of the frequency f at position p; principal component analysis is applied to reduce the dimension to extract the main space-frequency mode; and the boundary feature spectrum S_boundary is reconstructed to retain the main space-frequency coupling features. Extract microscopic features at small scale, local features at medium scale and macroscopic features at large scale from the boundary feature spectrum S_boundary. Fuse microscopic features, local features and macroscopic features to form a multi-scale feature vector.

[0025] This embodiment realizes full spectrum analysis of the complex characteristics of the boundary area through boundary feature spectrum construction and multi-scale feature vector formation technology. Experiments have shown that this embodiment can simultaneously capture the characteristics of three frequency bands: low-frequency system error (≤1Hz), medium-frequency interference (1-10Hz) and high-frequency noise (>10Hz), forming a complete "error fingerprint" of the boundary area. Traditional methods often only focus on a specific frequency band, resulting in incomplete calibration. For example, in the tested linear displacement sensor, the traditional method missed the fluctuation interference with an amplitude of 1.2μm in the range of 2-5Hz, while this embodiment successfully identified and subsequently compensated, reducing the standard deviation of the boundary area error by 42%. This embodiment can deal with errors of different sources and characteristics in a targeted manner, solving the calibration blind spot problem caused by traditional single frequency band analysis.

[0026] The error characteristics of the boundary area often show a multi-scale structure, including error components at the micro, local and macro levels. There is a complex coupling relationship between these error components at different scales. Traditional single-scale analysis methods are difficult to capture this cross-scale coupling effect. Figure 3 As shown, according to one aspect of the present application, the step of calculating the scale association matrix includes: S141, decomposing the multi-scale feature vector into three sub-vectors of microscopic, local and macroscopic features; S142, constructing a feature mapping space, projecting the three sub-vectors into the same reference coordinate system, and obtaining standardized microscopic features, standardized local features, and standardized macroscopic features; S143, using a sliding window technique to calculate the cross-correlation function between the standardized micro-features, the standardized local features, and the standardized macro-features, to obtain a cross-correlation vector set; S144. Based on the cross-correlation vector set, a cross-correlation tensor representing the correlation between different scales and positions is constructed and singular value decomposition is performed to extract cross-scale patterns; S145. Based on the cross-scale pattern, a scale correlation matrix is ​​constructed to quantify the overall correlation strength between features of different scales; the eigenvalues ​​and eigenvectors of the scale correlation matrix are calculated to obtain the correlation eigenvectors used to characterize the dominant pattern of cross-scale coupling in the boundary area.

[0027] Specifically, receive the multi-scale feature vector F_multi and decompose it into three sub-vectors: micro feature F_micro, local feature F_local and macro feature F_macro. Construct the feature mapping space M_space and project the feature vectors of the three scales into the same reference coordinate system: apply the scale magnification transformation to the micro feature F_micro to obtain the standardized micro feature F_micro_std; apply the scale reduction transformation to the macro feature F_macro to obtain the standardized macro feature F_macro_std; perform centralization on the local feature F_local to obtain the standardized local feature F_local_std. Calculate the cross-correlation function C_cross between the three scale features. Different from the traditional method of only calculating the simple correlation coefficient, the sliding window technology is used here: set the window width to 1% of the boundary area; slide the window in the boundary area with a step size of 0.1%; calculate the cross-correlation value of the three scale features at each window position; and obtain the position-related cross-correlation vector set C_vectors. Based on the cross-correlation vector set C_vectors, the cross-correlation tensor T_correlation is constructed. This is a three-dimensional data structure, where each element T(i, j, k) represents the correlation coefficient between scale i and scale j at position k. The cross-correlation tensor T_correlation is subjected to singular value decomposition to extract the main cross-scale modes P_modes, which reveal the structured correlation patterns between errors of different scales. Based on the cross-scale modes P_modes, the scale correlation matrix R_scale is constructed. Each element R(i, j) in the matrix quantifies the overall correlation strength between scale i and scale j while retaining the position correlation information. Unlike traditional correlation analysis that only focuses on the same-scale features or uses the global average correlation value, this matrix captures the complete correlation structure of cross-scale and position correlation. The eigenvalues ​​and eigenvectors of the scale correlation matrix R_scale are calculated to obtain the correlation eigenvector E_relation, which is used to characterize the dominant mode of cross-scale coupling in the boundary region.

[0028] This embodiment breaks through the limitation of traditional methods that treat errors of different scales as independent components and quantifies the cross-scale coupling relationship. Experimental data show that in the boundary area of ​​the tested optical ruler sensor, there is a correlation coefficient of up to 0.72 between the microscale and macroscale features, indicating that they are not independent but influence each other. By extracting the associated eigenvectors, the system can identify and describe this cross-scale coupling mode, such as the synchronization of microscopic displacement pulses and macroscopic nonlinear drifts, which cannot be discovered by traditional methods. In actual calibration, after considering the cross-scale coupling effect, the peak error in the first 1% range of the boundary area was reduced by 62%, and the root mean square error was reduced by 47%. This embodiment provides key information for accurate modeling and solves the problem of model distortion caused by ignoring cross-scale coupling in traditional methods.

[0029] According to another aspect of the present application, the method further includes step S16, calculating the scale correlation transformation index T_transform based on the multi-scale feature vector F_multi and the scale correlation matrix R_scale. Specifically, S161, calculating the eigenvalue decomposition of the scale correlation matrix R_scale, obtaining the main eigenvalue λ_main and the corresponding eigenvector v_main; S162, construct a transformation mapping function M_transform: M_transform(p) = Σ[λ_i * v_i(p)], where p is a position point and i is a eigenvalue index; S163, applying the transformation mapping function M_transform to perform a projection transformation on the multi-scale feature vector F_multi to obtain an enhanced feature vector F_enhanced; S164, calculating a feature gradient vector G_feature based on the enhanced feature vector F_enhanced and the boundary feature recognition fingerprint B_fingerprint; S165. Set an adaptive threshold T_adaptive =α* mean(|G_feature|)+β* std(G_feature) for subsequent key turning point identification.

[0030] The existing unified mathematical model cannot adapt to both the high-frequency small fluctuations in the boundary area and the stable characteristics in the middle area. Especially when polynomial fitting is used, the fitting accuracy of the boundary area has to be sacrificed to avoid the influence of the Runge phenomenon on the middle area. Figure 4 As shown, according to one aspect of the present application, the steps of constructing a dynamic segmented hybrid error model and obtaining a balanced error model and interval uncertainty include: S21, identifying a set of key turning points in the boundary area based on the multi-scale feature vector and the boundary feature recognition fingerprint, and dividing the boundary area into a predetermined number of sub-intervals accordingly; S22, constructing a specific basis function for each subinterval to obtain an adaptive basis function library; S23, according to the key turning point set, decomposing the error response characteristics of the boundary region into multi-modal components, including reference component, system component, random component and coupling component; S24. Based on the adaptive basis function library and the multimodal component, a dynamic segmented mixed error model is constructed; a model complexity penalty factor is introduced into the dynamic segmented mixed error model to obtain a balanced error model; S25. Calculate the interval uncertainty of the balanced error model and assign an uncertainty assessment value to each sub-interval of the model.

[0031] Specifically, based on the multi-scale feature vector F_multi and the boundary feature recognition fingerprint B_fingerprint, the key turning point set T_points in the boundary area is identified. These points divide the boundary area into multiple sub-intervals, each of which has relatively consistent error characteristics. A specific basis function set is designed for each sub-interval, and an adaptive basis function library B_functions is constructed: for the high-frequency micro-fluctuation interval, a wavelet basis function B_wavelet is constructed; for the medium-frequency transition interval, a fractional polynomial basis function B_fractional is constructed; for the low-frequency system error interval, an exponential decay basis function B_exponential is constructed. According to the key turning point set T_points, the error response characteristics of the boundary area are decomposed into multimodal components C_components, including: the base component C_base: reflects the basic linear response of the measurement system; the system component C_system: reflects the inherent system deviation of the sensor; the random component C_random: reflects the random fluctuations in the measurement process; the coupling component C_coupling: reflects the mutual interference between different error sources. Based on the adaptive basis function library B_functions and multimodal components C_components, a dynamic segmented mixed error model M_error is constructed. The model can automatically select the optimal basis function combination in different sub-intervals to achieve an accurate description of the error characteristics. The model complexity penalty factor P_complexity is introduced to automatically balance the fitting accuracy and complexity of the model to avoid overfitting problems and obtain the optimized balanced error model M_balanced. The interval uncertainty U_interval of the balanced error model M_balanced is calculated, and an uncertainty evaluation value is assigned to each sub-interval of the model for precision control of subsequent iterative calibration.

[0032] This embodiment solves the problem that a unified model is difficult to adapt to the complex characteristics of boundary areas by identifying key turning points and decomposing multimodal components. Traditional calibration usually uses a global high-order polynomial model, which is prone to the "Runge phenomenon" in the boundary area, resulting in the coexistence of overfitting and underfitting. The key turning points identified in this embodiment can accurately capture the changes in error characteristics. For example, in the tested sensor, characteristic mutation points at positions such as 2.5mm and 7.5mm are automatically identified. These points are usually caused by sensor design and manufacturing characteristics. After interval division based on these turning points, the modeling fitting residuals are reduced by an average of 78%, avoiding the problem of drastic fluctuations of the global model in the boundary area. At the same time, the interval uncertainty assessment provides an accurate confidence level indicator for subsequent optimization, so that calibration resources can be more effectively allocated to high uncertainty areas, improving overall calibration efficiency.

[0033] According to one aspect of the present application, the step of constructing a specific basis function for each subinterval to obtain an adaptive basis function library includes: The characteristics of the boundary area sub-intervals are analyzed according to the key turning point set, and the interval characteristics classification is obtained, including high-frequency micro-fluctuation interval, medium-frequency transition interval and low-frequency system error interval; For the high-frequency micro-fluctuation interval, the wavelet basis function is constructed; for the medium-frequency transition interval, the fractional polynomial basis function is constructed; for the low-frequency system error interval, the exponential decay basis function is constructed; The parameters of wavelet basis functions, fractional polynomial basis functions and exponential decay basis functions are optimized to make them best suit the error characteristics of the corresponding interval, and the optimized basis function set is obtained; the optimized basis function set is integrated into an adaptive basis function library.

[0034] This embodiment designs specific basis functions for sub-intervals with different characteristics, solving the problem that a single basis function cannot adapt to different error characteristics at the same time. In the experiment, after the wavelet basis function was used in the high-frequency micro-fluctuation interval (0-2.5mm), the fitting residual was reduced by 65%; after the fractional polynomial basis function was used in the medium-frequency transition interval (7.5-15mm), the fitting residual was reduced by 57%; after the exponential decay basis function was used in the low-frequency system error interval (26-42mm), the fitting residual was reduced by 42%. This "tailor-made" basis function design method enables the model to accurately match the error characteristics of different intervals and improves the expressive power of the model. Compared with the traditional unified polynomial model, the adaptive basis function library improves the fitting accuracy by an average of 53% with the same number of parameters, while avoiding the instability of the high-order polynomial model, solving the model adaptability problem that has long plagued the calibration of displacement sensors.

[0035] According to one aspect of the present application, the step of decomposing the error response characteristics of the boundary region into multi-modal components comprises: The error response analysis of the boundary area is performed according to the set of key turning points to obtain the error response characteristics; the reference component reflecting the basic linear response of the measurement system is extracted from the error response characteristics; the system component reflecting the inherent system deviation of the sensor is extracted by combining the error response characteristics and the reference component; the random component reflecting the random fluctuations in the measurement process is extracted based on the error response characteristics, the reference component and the system component; the interaction between the reference component, the system component and the random component is analyzed to extract the coupling component reflecting the mutual interference of different error sources; the reference component, the system component, the random component and the coupling component are integrated into a multimodal component.

[0036] This embodiment decomposes the boundary area error into reference component, system component, random component and coupling component, and realizes accurate identification and separation of error sources. Traditional calibration methods usually regard errors as a single source, resulting in incomplete compensation. This embodiment successfully separated the system component with an average amplitude of 0.012mm, the random component with a standard deviation of 0.003mm and the coupling component with a maximum amplitude of 0.005mm in the test sensor. This embodiment can adopt different compensation strategies for different error sources: deterministic compensation for system components, statistical noise reduction for random components, and cross-influence compensation for coupling components. Experiments have shown that after multi-modal decomposition, the stability of the calibration effect is improved by 65% ​​within the temperature change range of ±10°C, and the anti-interference ability is improved by 47%. This embodiment provides a basis for high-robustness calibration and solves the problem of unstable calibration effect of traditional methods in complex environments.

[0037] According to another aspect of the present application, step S21 may also be: based on the enhanced feature vector F_enhanced, the feature gradient vector G_feature and the adaptive threshold T_adaptive, identify a set of key turning points T_points within the boundary area. Specifically: S211, calculating the local extreme point set P_extrema of the feature gradient vector G_feature; S212, screening effective extreme value points based on the adaptive threshold T_adaptive to form a candidate turning point set P_candidates; S213, combining the boundary feature to identify the spatial distribution characteristics of the fingerprint B_fingerprint, and evaluating the significance score S_significance of each candidate point; S214, select points whose significance scores exceed the threshold, and ensure that the minimum distance between points meets the resolution requirement, and finally obtain the key turning point set T_points.

[0038] According to one aspect of the present application, the steps of implementing intelligent iterative calibration processing to obtain a converged optimization model include: S31. Based on the balanced error model and interval uncertainty, an iterative optimization objective function considering global accuracy and local peak error is constructed; S32, assigning differentiated learning rate parameters according to the error characteristics of different sub-intervals in the boundary area to form an adaptive learning rate matrix; so that a more radical optimization strategy can be obtained for the high uncertainty interval; S33, using a region-sensitive gradient descent algorithm, dynamically adjusting the optimization step size according to the iterative optimization objective function and the adaptive learning rate matrix, and calculating the optimization gradient vector of the model parameters; S34, updating the parameters of the balanced error model based on the optimized gradient vector, obtaining an iterative optimization model, and calculating the residual vector of the model; S35, introduce the residual resampling mechanism, and automatically generate a new set of calibration sampling points according to the distribution characteristics of the residual vector; these points are concentrated in the area with large residuals to achieve accurate allocation of calibration resources; S36. Use the calibration sampling point set to obtain new measurement data, and perform iterative optimization until a preset accuracy threshold or an upper limit of the number of iterations is reached to obtain a converged optimization model.

[0039] Specifically, the calibration sampling point set P_calibration is used to obtain new measurement data, and the original measurement data set D_raw and the enhanced data D_enhanced are updated. The above steps are repeated until the preset accuracy threshold or the upper limit of the number of iterations is reached, and finally the converged optimization model M_converged is obtained.

[0040] This embodiment achieves a dual improvement in calibration accuracy and efficiency by constructing an optimization objective function that takes into account both global accuracy and local peak error, as well as iterative optimization based on region-sensitive gradient descent and residual resampling. Traditional calibration usually adopts fixed sampling points and a global unified optimization strategy, which leads to slow iterative convergence and easy to fall into local optimality. In the test, this embodiment allocates differentiated learning rates to different sub-intervals through an adaptive learning rate matrix, allocates a learning rate of 0.068 to the high-frequency micro-fluctuation interval (0-2.5mm), and allocates a learning rate of 0.025 to the low-frequency system error interval (42-50mm), so that high-difficulty areas obtain more aggressive optimization strategies. At the same time, the residual resampling mechanism concentrates sampling resources on areas with large residuals. For example, after the first iteration, 8 sampling points are allocated in the 0-5mm range, while only 5 points are allocated in the 15-50mm range. This embodiment increases the calibration convergence speed by 3.2 times, compresses the traditional method from 12-15 rounds of iteration to 4 rounds to achieve the same accuracy, and reduces the calibration cost and time.

[0041] According to one aspect of the present application, the step of forming an adaptive learning rate matrix includes: Based on the balanced error model and interval uncertainty, the error gradient of each subinterval in the boundary area is calculated to represent the rate at which the error changes with position. Combining the error gradient and interval uncertainty, the optimization difficulty index of each subinterval is calculated to quantify the optimization difficulty and risk of the subinterval. Based on the optimization difficulty index, the initial learning rate distribution is constructed, and a higher initial learning rate is assigned to the high-difficulty area; the optimization interference coefficient between sub-intervals is calculated, and an interference matrix that characterizes the cross-effect of parameter changes is constructed; based on the initial learning rate distribution and the interference matrix, an adaptive learning rate matrix is ​​constructed, including direct learning rate and cross-learning rate; A dynamic balancing algorithm is applied to adjust the adaptive learning rate matrix to ensure the stability of the overall optimization process.

[0042] Specifically, the balanced error model M_balanced and interval uncertainty U_interval are received as input data. The error gradient G_error of each subinterval in the boundary area is calculated, which represents the rate at which the error changes with position. Unlike traditional methods, the global average gradient is not used here, but the complete local gradient information is retained. Combining the error gradient G_error and the interval uncertainty U_interval, the optimization difficulty index D_difficulty of each subinterval is calculated: high gradient areas have higher optimization difficulty; high uncertainty areas have higher optimization risks; these two factors are fused through a nonlinear combination function: D_difficulty=α·|G_error|·(1+β·U_interval 2 ), where α and β are weight coefficients, which are adaptively adjusted according to the sensor type. Based on the optimization difficulty index D_difficulty, the initial learning rate distribution L_initial is constructed. This is a position-dependent vector, rather than the scalar learning rate used in traditional gradient descent: for high-difficulty areas, a higher initial learning rate is assigned to accelerate convergence; for low-difficulty areas, a lower initial learning rate is assigned to improve stability; the learning rate is nonlinearly related to the difficulty index: L_initial(p) = L_base · [D_difficulty(p)] γ; Where L_base is the basic learning rate and γ is the adjustment index. Calculate the optimization interference coefficient I_interference between subintervals to characterize the degree of influence of parameter changes in one interval on other intervals, which is a factor that is often ignored in traditional optimization methods: For each pair of adjacent subintervals (i, j), calculate the cross-effect of parameter changes; Construct the interference matrix I_matrix, where the element I(i, j) represents the degree of influence of interval i on interval j. Based on the interference matrix I_matrix and the initial learning rate distribution L_initial, construct a complete adaptive learning rate matrix L_rate: The diagonal elements L(i, i) of the matrix are the direct learning rates of interval i, based on the initial learning rate distribution L_initial; The non-diagonal elements L(i, j) represent the effective learning rate of the parameter optimization of interval i on interval j after considering interference; Calculation formula: L(i, j) = L(i, i)·I(i, j)·α_decay; Where α_decay is the distance decay factor. Apply the dynamic balancing algorithm to adjust the adaptive learning rate matrix L_rate to ensure the stability of the overall optimization process: check the distribution balance of the learning rate in each interval; identify potential unstable areas; apply constraints to ensure that the condition number of the learning rate matrix is ​​within a controllable range; output the balanced adaptive learning rate matrix L_rate.

[0043] This embodiment solves the problem of inefficiency of traditional fixed learning rate in complex error scenarios by calculating the optimization difficulty index and the optimization interference coefficient between subintervals. In the test, the system automatically identified the high difficulty characteristics of high gradient areas (G_error=0.015) and high uncertainty areas (U_interval=±0.006mm), and assigned higher learning rates to these areas to accelerate convergence. At the same time, the interference matrix captures the cross-influence coefficient of 0.3-0.5 between adjacent subintervals, indicating that parameter optimization is not independent but interrelated. This embodiment makes model parameter optimization more efficient and stable, especially in complex nonlinear error scenarios in boundary areas, avoiding the oscillation and divergence problems that are prone to traditional methods. Experiments show that the adaptive learning rate matrix increases the convergence speed of parameter optimization in boundary areas by 2.8 times, while reducing the parameter oscillation amplitude by 65%, providing a more stable and reliable optimization path for the calibration process.

[0044] In another embodiment of the present application, based on the optimization difficulty index, the initial learning rate distribution can also be constructed as follows: the global basic learning rate L_base is determined based on the sensor type and the current iteration round iter_current: L_base = L_0 *(1 - Δ * iter_current / iter_max), where L_0 is the initial basic learning rate, Δ is the attenuation factor, and iter_max is the maximum iteration round. For each subinterval i, the adaptive value of the adjustment index γ is determined: γ(i) = γ_base *(1 + α * log(iter_max / iter_current)) * (1 - β * convergence_rate(i)), where convergence_rate(i) represents the convergence rate of interval i, which is determined by the reduction in the error of the interval in recent rounds of iterations; γ_base is the original adjustment index. Calculate the position-related learning rate distribution: L_initial(p) = L_base * [D_difficulty(p)] γ(i) , p is within interval i. Apply boundary constraints to ensure that the learning rate is within a reasonable range: L_initial(p) = min(max(L_initial(p), L_min), L_max). Where L_max is the maximum learning rate and L_min is the minimum learning rate.

[0045] According to one aspect of the present application, a region-sensitive gradient descent algorithm is used to dynamically adjust the optimization step size according to the iterative optimization objective function and the adaptive learning rate matrix, and the step of calculating the optimization gradient vector of the model parameters includes: According to the adaptive learning rate matrix and the iterative optimization objective function, the local gradient is calculated for each subinterval of the boundary area to form a partitioned gradient set; Based on the adaptive learning rate matrix, different optimization steps are assigned to each subinterval to form a variable step vector. According to the partitioned gradient set and the variable step vector, the overall optimization gradient vector is aggregated. The stability of the optimization gradient vector is tested to prevent the gradient explosion or disappearance problem, and the corrected gradient vector is obtained. Based on the corrected gradient vector, the optimization path is predicted to ensure the consistency of the convergence direction and obtain the final optimization gradient vector.

[0046] Specifically, calculate the local gradient for each sub-interval i in the boundary region: G_local(i) = ΨF_objective / Ψθ(i), where θ(i) is the model parameter vector of sub-interval i; Ψ is the partial derivative; F_objective is the iterative optimization objective function. Allocate different optimization step sizes for each sub-interval based on the adaptive learning rate matrix L_rate: S_variable(i) = min(max(||G_local(i)|| * L_rate(i, i), S_min), S_max), where S_min = 0.001 and S_max = 0.1 are the lower and upper limits of the step size. According to the partition gradient set and the variable step size vector, aggregate to form the overall optimization gradient vector G_opt: G_opt(i) = G_local(i) * S_variable(i) + Σ[G_local(j) * L_rate(i, j) * S_variable(j)], where the summation range is for all sub-intervals where j ≠ i. Conduct a stability test on the optimization gradient vector: calculate the L2 norm of the gradient: ||G_opt||2; if ||G_opt||2 > G_threshold (set to 5.0), then apply gradient clipping: G_opt_clipped = G_opt * (G_threshold / ||G_opt||2); if ||G_opt||2 < G_min (set to 0.001), then apply gradient enhancement: G_opt_enhanced = G_opt * (G_min / ||G_opt||2); obtain the corrected gradient vector G_corrected. Predict the optimization path based on the corrected gradient vector: calculate the expected parameter after updating the current parameter θ_current: θ_predicted = θ_current - G_corrected; verify whether the expected parameter results in a decrease in F_objective; if F_objective does not decrease, then reduce the step size and recalculate; ensure the consistency of the convergence direction to obtain the final optimization gradient vector G_final.

[0047] This embodiment solves the problem of poor performance of traditional gradient descent in non-uniform error distribution scenarios. In the test sensor, the optimization complexity of different areas varies significantly. For example, the gradient modulus in the 0-2.5mm range is 0.032, which is much higher than 0.008 in the 42-50mm range. Traditional fixed-step gradient descent can cause low-gradient areas to converge too slowly or high-gradient areas to be unstable. This embodiment allocates adaptive step sizes in the range of 0.001-0.1 to different areas through variable step vectors, and prevents gradient explosion and disappearance problems through stability tests. Experiments have shown that this embodiment reduces the model parameter optimization residual of traditional gradient descent by 38%, and reduces the number of iterations required for convergence by 56%. Especially for the high-complexity intervals in the 0-5% range of the boundary area, the optimization efficiency is most significantly improved, providing an efficient and reliable parameter optimization method for the calibration system.

[0048] According to one aspect of the present application, the steps of implementing intelligent iterative calibration processing to obtain a converged optimization model may also be: Based on the balanced error model and interval uncertainty, an iterative optimization model is constructed and the difference between its predicted value and the actual measured value is analyzed to obtain the residual vector; a density estimation analysis is performed on the residual vector to construct a residual probability distribution that reflects the distribution of the residual in the position domain; based on the residual probability distribution, the position-related uncertainty entropy value is calculated to quantify the prediction uncertainty of each position; a sampling importance function is constructed by combining the uncertainty entropy value, interval uncertainty and residual vector; a non-uniform sampling strategy is constructed based on the sampling importance function to generate a set of candidate sampling points; information gain evaluation is applied to the candidate sampling point set to eliminate points with redundant information and obtain a set of calibration sampling points; based on the calibration sampling point set, a sampling execution instruction containing precise position information and measurement parameter configuration is generated; based on the sampling execution instruction, iterative optimization is performed until the preset accuracy threshold or the upper limit of the number of iterations is reached to obtain a converged optimization model.

[0049] Specifically, the iterative optimization model M_iterated and the residual vector R_residual are received as input data, where the residual vector R_residual contains the difference between the model prediction value and the actual measurement value. The residual vector R_residual is subjected to density estimation analysis. Unlike the traditional method that directly uses the absolute value of the residual, a complete residual probability distribution P_residual is constructed here: the distribution of the residual in the position domain is calculated using the kernel density estimation method; multiple local peaks and valleys of the residual distribution are identified; the spatial structural characteristics of the residual are captured, rather than just focusing on the numerical value. Based on the residual probability distribution P_residual, the position-related uncertainty entropy value H_entropy is calculated to quantify the prediction uncertainty of each position: for areas with a wider residual distribution, a higher entropy value is assigned; for areas where the residual distribution is concentrated but deviates from the zero point, a higher entropy value is also assigned; the entropy value calculation considers two factors: the amplitude of the residual and the local rate of change. Construct the sampling importance function I_importance, combining the uncertainty entropy value H_entropy and the interval uncertainty U_interval: I_importance(p)=w1·H_entropy(p)+w2·U_interval(p)+ w3·|R_residual(p)|, where w1, w2, and w3 are adaptive weights that are dynamically adjusted according to the iteration stage. Construct a non-uniform sampling strategy, which is different from the traditional uniform encryption or simple sampling by residual size: calculate the cumulative importance function C_importance; use the inverse function method to generate new sampling points from the cumulative importance function C_importance; add small random perturbations to avoid excessive concentration of sampling points; generate the initial candidate sampling point set P_candidates. Apply information gain evaluation to the candidate sampling point set P_candidates, which is a missing step in the traditional sampling method: calculate the expected information gain provided by each candidate point; eliminate points with redundant information and retain the point set with the largest information gain; output the optimized calibration sampling point set P_calibration. Based on the calibration sampling point set P_calibration, a sampling execution instruction E_sampling is generated, which contains precise position information and measurement parameter configuration to guide the next round of calibration measurement.

[0050] This embodiment solves the problem of inefficiency of traditional uniform sampling under limited resources through density estimation analysis and information gain evaluation. In the test, the boundary area accuracy of traditional uniform sampling under 20 calibration points is ±0.008mm, while this embodiment improves the accuracy to ±0.0022mm with the same number of points, an increase of 73%. This is due to the system's ability to automatically identify the key features of the residual distribution and accurately allocate limited sampling resources to the position with the highest information value. For example, after the first round of iterations, the system found that the root mean square value of the residual in the 0-5mm range was 0.0042mm, which is much higher than 0.0009mm in the 15-50mm range, so more sampling points are allocated to the former in the next round of iterations. The sampling importance function is adjusted through dynamic weights, focusing more on entropy value (w1=0.55) in early iterations and more on residual (w3=0.35) in later iterations, so that the sampling strategy is adaptively adjusted with the optimization process. This embodiment improves the calibration efficiency, and can reduce the number of sampling points by 30-50% while maintaining the same accuracy, reducing the calibration cost and time.

[0051] In another embodiment of the present application, the sampling importance function can also be constructed by combining the uncertainty entropy value, the interval uncertainty and the residual vector: Calculate the global convergence characteristic index of the current iteration: convergence_rate = 1 -(mean(|R_residual_current|) / mean(|R_residual_initial|)); stability_index =std(|R_residual_current|) / mean(|R_residual_current|). Dynamically adjust the weight based on the iteration characteristics: w1(iter) = w1_base * (1 - convergence_rate) 2, early attention is paid to entropy; w2(iter) = w2_base* (1 - stability_index), when unstable, attention is paid to interval uncertainty; w3(iter) = w3_base *(remaining_iterations / total_iterations), later attention is paid to residual. Calculate the comprehensive sampling importance function: I_importance(p) = w1(iter) * H_entropy(p) + w2(iter) * U_interval(p) + w3(iter) * |R_residual(p)|. Apply normalization to ensure that the importance function value range is in the range of [0, 1]: I_importance_norm(p) = I_importance(p) / max(I_importance). Among them, R_residual_current is the residual vector of the current iteration; R_residual_initial is the initial residual vector; stability_index is the stability index; w1_base is the basic value of the entropy weight; w2_base is the basic value of the interval uncertainty weight; w3_base is the basic value of the residual weight; remaining_iterations is the current remaining number of iterations; total_iterations is the total number of iterations.

[0052] The existing calibration system does not pay enough attention to the dynamic response characteristics of the sensor, and only focuses on static error compensation while ignoring the sensitivity changes that may exist in the boundary area of ​​the sensor, resulting in additional errors in actual dynamic measurement applications. Therefore, according to one aspect of the present application, the step of generating a boundary area compensation function and calibration parameters to obtain a calibration parameter package includes: S41. Based on the convergence optimization model, the error compensation coefficient set of each sub-interval in the boundary area is extracted. These coefficients directly describe the system error characteristics of the sensor at different positions. A piecewise continuous compensation function is constructed. The function connects the error compensation of each sub-interval through the spline interpolation method to ensure that the compensation function has a smooth transition within the entire range and avoids the introduction of new discontinuities artificially. S42, calculating the derivative of the piecewise continuous compensation function to obtain a sensitivity compensation function, which is used to correct the sensitivity change of the sensor in the boundary area and solve the dynamic response problem ignored by the traditional calibration method; S43, combining the piecewise continuous compensation function and the sensitivity compensation function to generate a complete calibration parameter package, including static compensation parameters and dynamic response parameters, covering the calibration requirements of the sensor under different working conditions; S44, performing data compression processing on the calibration parameter package, using wavelet transform and principal component analysis methods to extract key features of the parameter package, generate compressed calibration parameters, reduce storage space requirements and improve calibration calculation efficiency.

[0053] This embodiment solves the problem of discontinuity of the traditional compensation function at the interval boundary by constructing a piecewise continuous compensation function and connecting it with spline interpolation. In the sensor test, the traditional piecewise compensation method has a jump of up to 0.003mm at the sub-interval boundary (such as the 7.5mm position), resulting in an uneven sensor output. The smooth transition function of this embodiment reduces these jumps to less than 0.0001mm, ensuring the continuity of the compensation function within the entire range. At the same time, the data compression process compresses the original calibration parameters (3.2KB) to 0.48KB, with a compression rate of 85%, while keeping the accuracy loss after decompression less than 1%. It can be easily stored in the sensor's internal EEPROM, supporting plug-and-play field calibration capabilities and avoiding the need for additional storage devices. In addition, the real-time solution delay of the compressed parameters is less than 0.2ms, which meets the requirements of high-frequency control systems for real-time calibration and provides a practical and efficient calibration parameter solution for the industrial application of displacement sensors.

[0054] According to one aspect of the present application, the step of calculating the derivative of the piecewise continuous compensation function to obtain the sensitivity compensation function includes: Calculate the position derivative of the piecewise continuous compensation function to obtain a sensitivity change curve that characterizes the spatial change of sensor sensitivity; identify the sensitivity mutation points in the sensitivity change curve, record the positions and change amplitudes of these points, and form a sensitivity mutation point list; divide the range into predetermined sensitivity intervals based on the sensitivity mutation point list, and construct a sensitivity interval segmentation model; The response differences of the displacement sensor at different measurement rates are analyzed, and the mapping relationship between rate and sensitivity change is established to form a rate-dependent model. The sensitivity interval segmentation model and the rate-dependent model are integrated to generate a comprehensive sensitivity compensation function. A sensitivity smooth transition mechanism is constructed to eliminate the discontinuity of the comprehensive sensitivity compensation function at the derivative level to obtain the final sensitivity compensation function.

[0055] Specifically, a piecewise continuous compensation function F_compensation is received as input, which describes the static error compensation value of the sensor at each position. The position derivative of the piecewise continuous compensation function F_compensation is calculated to obtain the initial sensitivity change curve S_initial: the numerical derivative is calculated using the central difference method; a low-pass filter is applied to the derivative result to remove high-frequency noise; and a curve representing the spatial change of sensor sensitivity is obtained. The sensitivity mutation points S_jumps in the sensitivity change curve S_initial are identified. These points represent the locations where the sensor response characteristics change significantly: a threshold is set to detect the location where the sensitivity change rate exceeds a preset value; the location and change amplitude of these mutation points are recorded; and a sensitivity mutation point list L_jumps is output. A sensitivity interval segmented model M_sensitivity is constructed. Unlike the traditional method that only considers the average sensitivity, an independent sensitivity characterization is established for each interval here: the range is divided into multiple sensitivity intervals based on the sensitivity mutation point list L_jumps; a local sensitivity model is fitted for each interval; and a segmented sensitivity model is formed comprehensively. Develop dynamic response characteristic analysis, which is a completely missing link in traditional static calibration: analyze the response difference of the sensor at different rates; establish a mapping relationship between rate and sensitivity change; construct a rate-dependent model M_rate to describe the change characteristics of sensor sensitivity with measurement rate. Fusion sensitivity interval segmentation model M_sensitivity and rate-dependent model M_rate to generate a comprehensive sensitivity compensation function F_sensitivity: F_sensitivity(p, v) = M_sensitivity(p)·[1 + α(p)·v + β(p)·v 2 ], where p is the position, v is the measurement rate, and α(p) and β(p) are the position-related rate dependence coefficients. A sensitivity smooth transition mechanism is designed to ensure the continuity of sensitivity compensation at the interval boundary: a weight fusion function is applied near the interval boundary; discontinuity of the compensation function at the derivative level is eliminated; and the final continuous sensitivity compensation function F_sensitivity is output.

[0056] This embodiment solves the problem of traditional methods ignoring dynamic response characteristics by fusing position derivative calculation and rate-dependent model. In the test sensor, the sensitivity change rate in the boundary area (0-5% range) reaches ±12%, and the error of traditional static calibration increases in dynamic measurement. This embodiment successfully identifies the sensitivity mutation point in the boundary area (such as 2.5mm) by calculating the derivative of the compensation function, and constructs a sensitivity interval segmentation model. Experiments have shown that under static measurement conditions, the sensitivity change is reduced from ±12% to ±1.5%; more importantly, under 10mm / s dynamic measurement conditions, the sensitivity deviation is reduced from ±18% to ±2.8%, which improves the dynamic measurement accuracy. The rate-dependent model M_rate establishes a mapping relationship between the measurement rate and the sensitivity change (α=-0.0012s / mm, β=0.00005s 2 / mm 2 ), so that the system can adjust the calibration parameters in real time according to the current measurement rate. This allows the sensor to maintain high accuracy in variable speed measurement environments, providing a reliable displacement measurement solution for dynamic application scenarios such as robot control and CNC machining.

[0057] According to another aspect of the present application, the method further includes step S45, applying the compression calibration parameter C_compressed to perform real-time calibration. Specifically, S451, designing a compression parameter decompression algorithm A_decompress, for quickly restoring key calibration parameters from compressed calibration parameters C_compressed; S452. Develop an efficient real-time computing engine E_realtime, integrating decompression algorithm and compensation function calculation; S453, implement the real-time calibration process of the sensor boundary area: receive the original measurement value R_measure of the sensor; determine whether the measurement value is located in the boundary area; if it is in the boundary area, use the efficient real-time calculation engine E_realtime and the compression calibration parameter C_compressed to calculate the compensation value C_adjust; output the calibrated measurement value O_calibrated = R_measure + C_adjust; S454, construct a calibration performance monitoring module M_monitor to evaluate the calibration effect in real time and trigger adaptive optimization when necessary.

[0058] In a specific embodiment of the present application, a boundary area calibration method for an optical ruler displacement sensor is provided. In view of the nonlinear error and sensitivity change problems existing in the 0-5% and 95-100% range of the optical ruler, a comprehensive solution is provided for multi-scale feature extraction and analysis, dynamic segmented mixed error modeling, intelligent iterative calibration processing, and boundary area compensation function generation.

[0059] The experimental equipment and conditions include: test equipment: JSW-5000 high-precision optical scale displacement sensor; standard instrument: Renishaw XL-80 laser interferometer (accuracy ±0.5ppm); measurement range: 0-1000mm; environmental conditions: temperature 23±0.5℃, humidity 45±5%RH; processing platform: Intel i7 processor, 16GB memory, Python 3.8 programming environment. The specific process is: Step 1: Extract and analyze multi-scale boundary features. Get the measurement data: set the measurement range of the optical ruler to 0-1000mm; collect measurement data at 50mm intervals in the middle area (50-950mm) to obtain 19 measurement points; set a non-uniform sampling strategy in the boundary area (0-50mm and 950-1000mm): 0-10mm and 990-1000mm area: 1mm interval, a total of 20 points; 10-20mm and 980-990mm area: 2mm interval, a total of 10 points; 20-50mm and 950-980mm area: 5mm interval, a total of 12 points; repeat the measurement 5 times for each measurement point, and take the average value as the actual measurement value P_m of the point; calculate the error E_raw = P_m - P_t between the theoretical value P_t and the actual measurement value P_m of each measurement point; the obtained original measurement data set D_raw contains 61 measurement points, including 42 points in the boundary area and 19 points in the middle area.

[0060] Enhanced sampling of the boundary area. Based on the initial measurement, enhanced sampling is performed on the boundary area: the density value B_density = 2.5 points / mm (determined based on the sensor accuracy level) of the boundary area is calculated; high-density sampling with an interval of 0.5mm is applied in the 0-5mm and 995-1000mm areas to obtain 20 additional measurement points; step-by-step interval sampling is applied in the 5-50mm and 950-995mm areas: 5-10mm and 990-995mm: 0.5mm interval, a total of 20 points; 10-30mm and 970-990mm: 1mm interval, a total of 40 points; 30-50mm and 950-970mm: 2mm interval, a total of 20 points; repeat the measurement 3 times for each enhanced sampling point, and take the average value as the actual measurement value of the point; calculate the error between the theoretical value and the actual measurement value of the enhanced sampling point; the enhanced sampling obtains the D_enhanced data set, which contains 100 additional measurement points, mainly distributed in the boundary area.

[0061] Apply local differential transformation. Apply local differential transformation to the original measurement data set D_raw and the enhanced data D_enhanced: merge the original measurement data set D_raw and the enhanced data D_enhanced to form a comprehensive data set D_combined. Apply sliding window Fourier transform (STFT) to the comprehensive data set D_combined: set the Hanning window, the window width is 2% (10mm) of the boundary area; the window sliding step is 0.2% (1mm) of the boundary area; calculate the spectrum for each window position to form a joint time-frequency distribution F_distribution. The dimension of the frequency distribution graph F_distribution is [number of position points, number of frequency points], which characterizes the frequency response characteristics of different positions.

[0062] Perform local feature enhancement and generate boundary feature spectrogram. Perform feature enhancement based on frequency distribution map F_distribution: Design adaptive frequency band enhancement filter H_filter: H_filter(f) = 1 + α * exp(-(f-f_c) 2 / (2σ 2 )), where f_c is the center frequency, determined by the peak value of the spectrum in the boundary area, α=2.5, σ=0.15*f_c; apply the adaptive band enhancement filter H_filter to the frequency distribution map F_distribution to obtain the enhanced spectrum F_enhanced. Perform contrast stretching on the enhanced spectrum F_enhanced to highlight local features: F_contrast(p, f) = (F_enhanced(p, f)- min(F_enhanced)) / (max(F_enhanced) - min(F_enhanced)). Calculate the spatial autocorrelation function to characterize the spatial correlation of the spectral features: R_spatial(Δp) = Σ[F_contrast(p, f) * F_contrast(p+Δp, f)] / Σ[F_contrast(p, f) 2 ], where Δp is the spatial displacement variable, and the summation range covers all frequencies f. Construct the space-frequency joint feature matrix J_matrix: J_matrix(p, f) = F_contrast(p, f) * (1 + β * R_spatial(p)), where β=1.5 is the spatial correlation enhancement coefficient. Apply singular value decomposition (SVD) to the space-frequency joint feature matrix J_matrix: J_matrix = U * Σ * V T; Select the first k principal components (k=10) to reconstruct and obtain the boundary feature spectrum S_boundary: S_boundary = U_k * Σ_k * V_k T , where U_k, Σ_k, V_k are the sub-matrices of the left singular vector matrix U, the diagonal matrix Σ, and the right singular vector matrix V corresponding to the first k principal components respectively.

[0063] Perform multi-scale feature extraction. Extract multi-scale features from the boundary feature spectrum S_boundary: Extract small-scale microscopic features F_micro: Apply a high-pass filter (cutoff frequency 10Hz) to extract the high-frequency components in the boundary feature spectrum S_boundary; calculate the root mean square value, peak value and waveform factor of the high-frequency components within the range of 0.1%-0.5% (1-5mm); form a microscopic feature vector F_micro with a dimension of [number of positions, 3]. Extract mid-scale local features F_local: Apply a bandpass filter (1-10Hz) to extract the mid-frequency components in the boundary feature spectrum S_boundary; calculate the mean, standard deviation and skewness of the mid-frequency components within the range of 0.5%-2% (5-20mm); form a local feature vector F_local with a dimension of [number of positions, 3]. Extract large-scale macro features F_macro: Apply a low-pass filter (cutoff frequency 1Hz) to extract the low-frequency components in the boundary feature spectrum S_boundary; calculate the trend slope, curvature and nonlinearity of the low-frequency components in the 2%-5% range (20-50mm) to form a macro feature vector F_macro with a dimension of [number of positions, 3]. Fuse the three scale features to form a multi-scale feature vector F_multi: F_multi = [F_micro, F_local, F_macro] with a dimension of [number of positions, 9].

[0064] Calculate the scale correlation matrix based on the multi-scale feature vector F_multi: Decompose the multi-scale feature vector F_multi into three sub-vectors F_micro, F_local and F_macro. Construct the feature mapping space M_space and project the three scale features into the same reference coordinate system: Apply a scale magnification transformation to the micro feature F_micro: F_micro_std = F_micro *W_micro, where W_micro is the micro feature magnification weight matrix, so that the amplitude range of the micro feature F_micro is close to that of the local feature F_local; Apply a scale reduction transformation to the macro feature F_macro: F_macro_std = F_macro * W_macro, where W_macro is the macro feature reduction weight matrix; Centralize the local feature F_local: F_local_std = F_local - mean(F_local); Set the sliding window width to 1% (5mm) of the boundary area and the step size to 0.1% (0.5mm); Calculate the cross-correlation value at each window position p: C_micro_local(p)=correlation(F_micro_std(pw / 2:p+w / 2), F_local_std(pw / 2:p+w / 2)); C_local_macro(p)=correlation(F_local_std(pw / 2:p+w / 2), F_macro_std(pw / 2:p+w / 2)); C_micro_macro(p)=correlation(F_micro_std(pw / 2:p+w / 2), F_macro_std(pw / 2:p+w / 2)); where w is the window width and correlation() is the Pearson correlation coefficient calculation function. Integrate the cross-correlation values ​​of all window positions to form a cross-correlation vector set C_vectors. Construct a three-dimensional cross-correlation tensor T_correlation with dimension [3, 3, number of position points]: T_correlation[0, 1, p] = T_correlation[1, 0, p] = C_micro_local(p); T_correlation[1, 2, p] = T_correlation[2, 1, p] = C_local_macro(p); T_correlation[0, 2, p] = T_correlation[2, 0, p] = C_micro_macro(p); T_correlation[i, i, p] = 1.0 (autocorrelation is 1).The third dimension (position dimension) of the three-dimensional cross-correlation tensor T_correlation is averaged to obtain the scale correlation matrix R_scale: R_scale = mean(T_correlation, axis=2), with dimension [3, 3], which represents the overall correlation strength between the three scales. Calculate the eigenvalue decomposition of the scale correlation matrix R_scale: R_scale = Q * Λ * Q. T , we get the eigenvalue vector λ and the eigenvector matrix Q; where Λ is a diagonal matrix. We extract the principal eigenvector (the eigenvector corresponding to the maximum eigenvalue) as the associated eigenvector E_relation.

[0065] Compare and analyze the feature differences between the boundary area and the middle area, and construct the boundary feature recognition fingerprint: divide the measurement range into the boundary area (0-5% and 95-100% range) and the middle area (5-95% range), and calculate the mean of the multi-scale feature vectors of the boundary area and the middle area respectively: F_multi_boundary = mean(F_multi[boundary area index]); F_multi_middle = mean(F_multi[middle area index]); calculate the feature difference vector: F_diff = F_multi_boundary - F_multi_middle; calculate the significance index of the feature difference, and obtain the p value through the t-test: P_values= t_test(F_multi[boundary area index], F_multi[middle area index]); construct the boundary feature recognition fingerprint B_fingerprint: B_fingerprint = F_diff * (1 - P_values), where element multiplication is the multiplication of corresponding elements, and 1-P_values ​​represents the statistical significance of the feature difference. The boundary feature recognition fingerprint B_fingerprint is normalized: B_fingerprint_norm = (B_fingerprint - min(B_fingerprint)) / (max(B_fingerprint) - min(B_fingerprint)). In this embodiment, the normalized boundary feature recognition fingerprint B_fingerprint_norm finally obtained is a 9-dimensional vector: [0.92, 0.78, 0.85, 0.64, 0.53, 0.42, 0.31, 0.25, 0.18], and each element corresponds to the significant weighted difference value of the three indicators of microscopic features, local features and macroscopic features.

[0066] Step 2: Construct a dynamic segmented mixed error model. Based on the multi-scale feature vector and boundary feature recognition fingerprint, identify the key turning points in the boundary area: Based on the multi-scale feature vector F_multi and the scale correlation matrix R_scale, calculate the enhanced feature vector F_enhanced: F_enhanced = F_multi * R_scale * F_multi T ,in TFor transpose; calculate the feature gradient vector G_feature: G_feature(p) =(F_enhanced(p+Δp) - F_enhanced(p-Δp)) / (2*Δp), where Δp is the position increment and is taken as 0.5mm; set the adaptive threshold T_adaptive: T_adaptive = 0.8 * mean(|G_feature|) + 1.5 * std(G_feature), and in this embodiment, T_adaptive = 0.023. Calculate the set of local extreme points of G_feature: if G_feature(p-Δp)<G_feature(p)>G_feature(p+Δp), then p is a local maximum point; if G_feature(p-Δp)>G_feature(p)<G_feature(p+Δp), then p is a local minimum point; combine all local extreme points to form the set of local extreme points P_extrema. Screen valid extreme points based on the adaptive threshold T_adaptive: P_candidates = {p ∈ P_extrema | |G_feature(p)|>T_adaptive}; calculate the significance score of each candidate point: S_significance(p)=|G_feature(p)|* B_fingerprint_norm[closest_feature_index(p)], where closest_feature_index(p) is the most significant feature index at position p. Select points whose significance score exceeds the threshold: T_points_prelim = {p ∈ P_candidates | S_significance(p)>0.015}; apply the minimum distance constraint to ensure that the distance between points is not less than 1mm: sort T_points_prelim in descending order of significance score; select the first point to add to T_points; sequentially examine the remaining points, and if the minimum distance from the selected points is greater than 1mm, then add it to T_points. In this example, the set of key turning points T_points identified is: lower boundary region: 2.5mm, 7.5mm, 15mm, 26mm, 42mm; upper boundary region: 958mm, 974mm, 985mm, 992.5mm, 997.5mm.

[0067] Design specific basis functions for each sub-interval and build an adaptive basis function library: analyze the characteristics of the boundary area sub-intervals according to the key turning point set T_points: calculate the error mean, standard deviation, frequency characteristics, etc. of each sub-interval; classify them into high-frequency micro-fluctuation interval, medium-frequency transition interval and low-frequency system error interval based on the characteristics. The classification results of the sub-intervals in the lower boundary area are as follows: 0-2.5mm: high-frequency micro-fluctuation interval; 2.5-7.5mm: high-frequency micro-fluctuation interval; 7.5-15mm: medium-frequency transition interval; 15-26mm: medium-frequency transition interval; 26-42mm: low-frequency system error interval; 42-50mm: low-frequency system error interval. The classification results of the upper boundary area sub-intervals are as follows: 950-958mm: low-frequency system error interval; 958-974mm: low-frequency system error interval; 974-985mm: medium-frequency transition interval; 985-992.5mm: medium-frequency transition interval; 992.5-997.5mm: high-frequency micro-fluctuation interval; 997.5-1000mm: high-frequency micro-fluctuation interval. For the high-frequency micro-fluctuation interval, the wavelet basis function B_wavelet is designed: B_wavelet(p; a, b, s) = a * (1 / sqrt(s)) * ψ((pb) / s), where ψ is the Morlet wavelet function, a is the amplitude parameter, b is the position parameter, and s is the scale parameter. For the medium-frequency transition interval, the fractional polynomial basis function B_fractional is designed: B_fractional(p; a, b, c, α) = a / (1 + (|pb| / c) α ), where a is the amplitude parameter, b is the center position parameter, c is the width parameter, and α is the shape parameter. For the low-frequency system error interval, an exponential decay basis function B_exponential is designed: B_exponential(p; a, b, λ) = a * exp(-λ * |pb|), where a is the amplitude parameter, b is the reference position parameter, and λ is the attenuation rate parameter. Parameters of various basis functions are optimized to make them most suitable for the error characteristics of the corresponding interval: nonlinear least squares fitting is performed on the error data of each sub-interval; the optimal parameter value is determined to minimize the fitting residual; and an optimized basis function set is formed. Various optimized basis functions are integrated to form an adaptive basis function library B_functions. In this example, the optimized wavelet basis function parameters for the 0-2.5mm high-frequency micro-fluctuation interval are: a= 0.023, b= 1.2mm, s= 0.8.

[0068] Decompose the error response characteristics of the boundary area into multimodal components: obtain the error response characteristics E_response of the boundary area, that is, the error value of the boundary area in the original measurement data; extract the reference component C_base: apply linear regression to the error response characteristics E_response: E(p) = k*p + b, obtain the slope k and intercept b, and calculate the reference component: C_base(p) =k*p + b. Calculate the initial residual: R_initial = E_response - C_base; extract the system component C_system: apply low-pass filtering (cutoff frequency 0.5Hz) to the initial residual R_initial to obtain the system component C_system; calculate the secondary residual: R_secondary = R_initial - C_system; extract the random component C_random: apply autocorrelation analysis to the secondary residual R_secondary to determine the random noise level; design a Wiener filter to reduce random noise; the difference between the original residual and the filtered residual is the random component C_random. Calculate the cubic residual: R_tertiary = R_secondary -C_random; extract the coupling component C_coupling: R_tertiary is the coupling component C_coupling; verify the cross-correlation between the coupling component C_coupling and the reference component C_base and the system component C_system to ensure that the cross-modal coupling effect is captured. Integrate the reference component C_base, the system component C_system, the random component C_random and the coupling component C_coupling into multimodal components C_components. In this example, the multimodal component decomposition results in the 0-2.5mm range are: C_base: 0.0015*p - 0.0002; C_system: average amplitude 0.012mm, showing nonlinear characteristics; C_random: standard deviation 0.003mm; C_coupling: maximum amplitude 0.005mm, mainly distributed in the 1-1.5mm area.

[0069] Based on the adaptive basis function library and multimodal components, a dynamic segmented mixed error model is constructed: for each subinterval i, the most suitable basis function type is selected: high-frequency micro-fluctuation interval: select the wavelet basis function B_wavelet; medium-frequency transition interval: select the fractional polynomial basis function B_fractional; low-frequency system error interval: select the exponential decay basis function B_exponential. Construct the subinterval error model M_local(i): M_local(i)(p) = C_base(p) + w_sys *B_selected(p; θ_sys) + w_rand * noise(p) + w_coup * B_coupling(p;θ_coup), where C_base(p) is the reference component; B_selected is the selected basis function; θ_sys is the system component parameter; noise(p) is the random noise model; B_coupling is the coupling component model function; θ_coup is the coupling component parameter; w_sys, w_rand, w_coup are the weights of each component. Design a smooth transition function S_transition at the subinterval boundary: S_transition(p; p1, p2) = 0.5 + 0.5 * tanh((p-0.5*(p1+p2)) / (0.1*(p2-p1))), where p1 and p2 are the boundary points of adjacent subintervals. Integrate all subinterval models to form a dynamic segmented mixed error model M_error: M_error(p) =Σ[M_local(i)(p) * S_i(p)], where S_i(p) is the weight of position p in subinterval i, calculated by the smooth transition function S_transition.

[0070] Introduce the model complexity penalty factor in the dynamic segmented mixed error model to obtain the balanced error model: Define the model complexity measure C_complexity: C_complexity = Σ[w_i * n_i], where w_i is the complexity weight of subinterval i, and n_i is the number of model parameters in subinterval i. Define the optimization objective function J_objective with penalty term: J_objective = MSE + λ * C_complexity, where MSE is the mean square error and λ is the complexity penalty coefficient. Optimize the model parameters of each subinterval and minimize J_objective to obtain the balanced error model M_balanced. Calculate the interval uncertainty U_interval of the balanced error model M_balanced: For each subinterval, calculate the residual between the model prediction value and the actual measurement value; calculate the standard deviation of the residual and multiply it by the coverage factor k=2; obtain the expanded uncertainty at the 95% confidence level; distribute it to each subinterval to form the interval uncertainty U_interval. In this example, the uncertainty assessment values ​​of each sub-interval in the lower boundary area are: 0-2.5mm: ±0.006mm; 2.5-7.5mm: ±0.005mm; 7.5-15mm: ±0.004mm; 15-26mm: ±0.003mm; 26-42mm: ±0.002mm; 42-50mm: ±0.001mm.

[0071] Step 3: Perform intelligent iterative calibration. Based on the balanced error model and interval uncertainty, construct the iterative optimization objective function: Design the global accuracy term G_accuracy: G_accuracy = 1 / N * Σ[(M_balanced(p_i) -E_actual(p_i)) 2 ], where N is the number of measurement points, p_i is the position of the measurement point, E_actual is the actual measurement error, and M_balanced is the balanced error model. Design the local peak error term L_peak: L_peak = max(|M_balanced(p) -E_actual(p)|), which represents the maximum local error. Construct the comprehensive optimization objective function F_objective: F_objective =(1-α) * G_accuracy + α * L_peak, where α is the trade-off coefficient, which is 0.3 in this example.

[0072] According to the error characteristics of different subintervals in the boundary area, an adaptive learning rate matrix is ​​designed: the error gradient G_error of each subinterval in the boundary area is calculated: G_error(i) = Σ[|dE_actual(p) / dp|] / length(interval i), which represents the average rate at which the error changes with position in interval i; the optimization difficulty index D_difficulty of each subinterval is calculated: D_difficulty(i) = 1.2 * |G_error(i)| * (1 + 1.5 * U_interval(i) 2 ), where U_interval(i) is the uncertainty of interval i; determine the global base learning rate L_base: L_base = 0.05 *(1 - 0.2 * iter_current / iter_max), where iter_current is the current iteration round, iter_max is the maximum iteration round (set to 10). Calculate the adjustment index γ for each subinterval: γ(i) = 0.5 * (1 + 0.8 * log(iter_max / iter_current)) * (1 - 0.6 * convergence_rate(i)), where convergence_rate(i) represents the convergence rate of interval i, and the initial value is 0. Calculate the position-dependent initial learning rate distribution L_initial: L_initial(i) = L_base * [D_difficulty(i)] γ(i) ; Calculate the optimized interference coefficient between subintervals and construct the interference matrix I_matrix: I(i, j) = exp(-0.5 * (d(i, j) / σ) 2 ), where d(i, j) is the distance between the center positions of intervals i and j, and σ is the characteristic length (set to 10mm). Construct an adaptive learning rate matrix L_rate: L(i, i) = L_initial(i), the diagonal elements are direct learning rates; L(i, j) = L(i, i) * I(i, j) * 0.2, and the non-diagonal elements are cross-learning rates. Apply a dynamic balance algorithm to ensure the stability of L_rate: check whether the condition number of L_rate is less than the threshold (set to 20). If the condition number is too large, regularize it. In the first round of iterations, the initial learning rate of each sub-interval is: 0-2.5mm: 0.068; 2.5-7.5mm: 0.063; 7.5-15mm: 0.052; 15-26mm: 0.041; 26-42mm: 0.032; 42-50mm: 0.025.

[0073] Based on the adaptive learning rate matrix, the region-sensitive gradient descent algorithm is implemented: in this embodiment, the optimized gradient vector of the high-frequency micro-fluctuation range (0-2.5 mm) of the first round of iteration is [-0.032, 0.021, -0.015], corresponding to the update direction of the wavelet basis function parameters [a, b, s].

[0074] Update the parameters of the balanced error model based on the optimized gradient vector: Update the model parameters of each sub-interval: θ_new(i) = θ_current(i) - G_final(i); where G_final(i) is the final gradient vector; Use the updated parameters to rebuild the model and obtain the iterative optimization model M_iterated. Calculate the difference between the predicted value of M_iterated and the actual measured value to obtain the residual vector R_residual: R_residual(p) = M_iterated(p) - E_actual(p). Statistical residual analysis: Calculate the residual mean: mean(R_residual); Calculate the residual standard deviation: std(R_residual); Calculate the maximum residual: max(|R_residual|); Calculate the residual root mean square: RMS(R_residual). After the first round of iterations, the statistical characteristics of the residuals in the boundary area are: mean: 0.0002mm; standard deviation: 0.0018mm; maximum residual: 0.0045mm; root mean square: 0.0018mm.

[0075] Based on the distribution characteristics of the residual vector, the residual resampling mechanism is implemented: the residual vector R_residual is subjected to density estimation analysis: the residual distribution is estimated by applying the kernel density estimation method (bandwidth h=2mm) to obtain the residual probability distribution function P_residual(p). The position-related uncertainty entropy value H_entropy is calculated: for each position p, the standard deviation σ_local(p) of the residual is calculated within its neighborhood (±2mm); the local entropy value is calculated: H_entropy(p) = log(σ_local(p) * sqrt(2πe)). Combining the uncertainty entropy value, interval uncertainty and residual vector, the sampling importance function I_importance is constructed: the dynamic weight is determined: w1= 0.6 * (1 - convergence_rate) 2, convergence_rate is the overall convergence rate of the model; w2= 0.3 * (1 - stability_index), stability_index is the residual distribution stability index; w3= 0.1 * (remaining_iterations / total_iterations); calculate I_importance(p) =w1* H_entropy(p) + w2* U_interval(p) + w3* |R_residual(p)|; normalization: I_importance_norm(p) = I_importance(p) / max(I_importance). Design a non-uniform sampling strategy: Calculate the cumulative importance function: C_importance(p) = ∫[0, p] I_importance_norm(t) dt; Generate 30 random numbers {r_i} uniformly in the interval [0, 1]; For each r_i, solve p_i so that C_importance(p_i) = r_i; Add a random perturbation of ±0.2mm to obtain the candidate sampling point set P_candidates. Apply information gain evaluation to the candidate sampling point set: Define the information gain function IG(p) = H(model) - H(model|measure at p); Calculate the expected information gain E[IG(p)] for each candidate point; Sort the candidate points from high to low according to the information gain; Select points in turn, and if the minimum distance to the selected point is greater than 0.5mm, add them to the final sampling point set; Finally, select 20 points to form the calibration sampling point set P_calibration. According to this embodiment, the distribution of the generated calibration sampling point set in the lower boundary area (0-50mm) is: high-density area (0-5mm): 8 points; medium-density area (5-15mm): 7 points; low-density area (15-50mm): 5 points; the point distribution of the upper boundary area (950-1000mm) is similar.

[0076] Use the calibration sampling point set to obtain new measurement data and perform iterative optimization: use the calibration sampling point set P_calibration to obtain new measurement data; update the original measurement data set D_raw and the enhanced data D_enhanced; repeat the multi-scale feature extraction, dynamic segmentation model construction and parameter optimization steps; calculate the performance indicators of the updated model: residual root mean square RMSE; maximum absolute error MAE; uncertainty U. Check the termination condition: if RMSE<0.001mm or the improvement of RMSE in two consecutive rounds is less than 5% or the maximum number of iterations (10 rounds) is reached, stop the iteration and output the converged optimization model M_converged. In this embodiment, after 4 rounds of iterations, the model performance indicators reach: RMSE: 0.0009mm; MAE: 0.0022mm; uncertainty U: ±0.0018mm (k=2); meet the termination conditions, and obtain the converged optimization model M_converged.

[0077] Step 4. Construct the boundary area compensation function and generate calibration parameters. Based on the converged optimization model M_converged, extract the error compensation coefficient set of each sub-interval in the boundary area: decompose the converged optimization model M_converged into the local model component M_local(i) of each sub-interval. For each sub-interval i in the lower boundary area (0-50mm): extract the basis function coefficient C_base(i) from the local model M_local(i), including: wavelet basis function interval: extract [a, b, s] parameters; fractional polynomial interval: extract [a, b, c, α] parameters; exponential decay interval: extract [a, b, λ] parameters. Perform the same operation on the upper boundary area (950-1000mm). Map the basis function coefficients to the standardized error compensation domain: design the mapping function f_map(i) for each sub-interval i; calculate the standardized compensation coefficient: C_norm(i) = f_map(i)(C_base(i)). Apply the denormalization transformation and convert it into the error compensation coefficient of the actual physical quantity: define the denormalization function g(i); calculate the error compensation coefficient: E_coefficients(i) = g(i)(C_norm(i)). Verify the continuity at the sub-interval boundary: for adjacent sub-intervals i and j, check |E_coefficients(i)(p_border) - E_coefficients(j)(p_border)|<ε. If it is not satisfied, apply the smooth transition function to adjust, where p_border is the boundary position of the adjacent sub-intervals i and j; ε is the continuity tolerance between the allowed error compensation coefficients. Integrate the error compensation coefficients of each sub-interval to form a complete error compensation coefficient set E_coefficients. In this embodiment, the final error compensation coefficient of the 0-2.5mm sub-interval in the lower boundary area is the wavelet basis function parameter [0.021, 1.35, 0.75].

[0078] Construct a piecewise continuous compensation function to ensure smooth transition over the entire measuring range: Based on the error compensation coefficient set E_coefficients, calculate the compensation value of each sub-interval: For position p in sub-interval i: Comp_i(p) = Calculate the compensation value based on E_coefficients(i). Design a smooth transition function S_smooth for the sub-interval boundary: S_smooth(p; p1, p2, w) = 0.5 - 0.5 * cos(π * (p-p1) / (p2-p1)); if p1 ≤ p ≤ p2, otherwise 0 or 1; where p1, p2 are the transition interval boundaries, and w is the transition width. Construct a piecewise continuous compensation function F_compensation: F_compensation(p) = Σ[Comp_i(p) * (1 - S_smooth(p; p_i, p_i+1, w_i)) + Comp_i+1(p) * S_smooth(p; p_i, p_i+1, w_i)], where p_i, p_i+1 are the boundaries of subintervals i and i+1, and w_i is the transition width. Verify the continuity of the piecewise continuous compensation function F_compensation: Calculate the left and right limits of the compensation function at the boundaries of each subinterval; ensure that the difference is less than the accuracy requirement (0.0001mm).

[0079] Calculate the derivative of the compensation function to obtain the sensitivity compensation function: Calculate the position derivative of the compensation function F_compensation: S_initial(p) = dF_compensation(p) / dp; Use the central difference method: S_initial(p) = (F_compensation(p+h) - F_compensation(ph)) / (2h), where h=0.01mm. Apply a low-pass filter (cutoff frequency 10Hz) to the position derivative S_initial to remove high-frequency noise and obtain a smooth sensitivity change curve S_smooth. Identify the sensitivity mutation point in the sensitivity change curve S_smooth: Set the threshold T_jump = 3 * std(dS_smooth / dp). If |dS_smooth(p) / dp|>T_jump, then p is the sensitivity mutation point; Record the mutation point position and change amplitude to form a sensitivity mutation point list L_jumps. Based on L_jumps, the measuring range is divided into multiple sensitivity intervals, and the sensitivity interval segmentation model M_sensitivity is constructed: a local sensitivity model is fitted for each sensitivity interval; the lower boundary area is divided into 4 sensitivity intervals: 0-3mm, 3-10mm, 10-30mm, 30-50mm; a polynomial model is fitted for each interval: S_poly(p) = a0 + a1*p + a2*p 2 + a3*p 3 , where a0 is the constant term; a1 is the coefficient of the linear term; a2 is the coefficient of the quadratic term; and a3 is the coefficient of the cubic term. Analyze the response differences of the sensor at different measurement rates: measure the standard displacement at 3 different rates (1mm / s, 5mm / s, 10mm / s); analyze the effect of rate on sensitivity; establish a mapping relationship between rate and sensitivity change; and construct a rate-dependent model M_rate: M_rate(v) = 1 + α*v + β*v 2 , where v is the measurement rate, α=-0.0012s / mm, β=0.00005s 2 / mm 2 . The sensitivity interval segmentation model M_sensitivity and the rate-dependent model M_rate are integrated to generate the comprehensive sensitivity compensation function F_sensitivity: F_sensitivity(p, v) = M_sensitivity(p) * M_rate(v), where p is the position and v is the measurement rate. Design a sensitivity smooth transition mechanism: apply cubic spline interpolation at the boundary of the sensitivity interval; ensure the continuity of the compensation function at the derivative level; and output the final continuous sensitivity compensation function F_sensitivity.

[0080] Combine the compensation function and the sensitivity compensation function to generate a complete calibration parameter package: integrate the compensation function F_compensation and the sensitivity compensation function F_sensitivity to form the initial calibration parameters: P_initial = {F_compensation, F_sensitivity}. Sample the compensation function evenly to generate the position-compensation value lookup table LUT_compensation: use 0.1mm interval sampling in the boundary area; generate the position point set p_i and the corresponding compensation value c_i; form the lookup table: LUT_compensation = {(p_i, c_i)}. Sample the sensitivity compensation function to generate the position-rate-sensitivity lookup table LUT_sensitivity: use 0.5mm intervals in the position dimension; use 1mm / s intervals in the rate dimension, ranging from 0-10mm / s; generate a three-dimensional lookup table: LUT_sensitivity = {(p_i, v_j, s_ij)}, where v_j is the rate and s_ij is the sensitivity. Construct a static compensation parameter set P_static: P_static = {LUT_compensation, compensation function coefficient}; construct a dynamic response parameter set P_dynamic: P_dynamic = {LUT_sensitivity, rate dependence coefficient, sensitivity interval boundary}. Generate a complete calibration parameter package C_parameters: C_parameters = {P_static, P_dynamic, metadata}, where the metadata includes calibration date, sensor information, calibration accuracy, etc.

[0081] The calibration parameter package is compressed and real-time calibration is realized: the lookup table is compressed using wavelet transform: discrete wavelet transform (DWT) is applied to the lookup table LUT_compensation to retain wavelet coefficients with energy accounting for more than 99.5%; the wavelet coefficients are quantized and encoded. The sensitivity parameters are compressed using principal component analysis: a matrix is ​​constructed for the three-dimensional lookup table LUT_sensitivity; PCA is applied for dimensionality reduction to retain principal components with explained variance exceeding 99%; the principal components and their coefficients are stored. The compressed calibration parameters C_compressed are generated: C_compressed = {compressed static parameters, compressed dynamic parameters, decompression instructions, metadata}. In this example, the parameter compression rate reaches 85%, and the original parameters of 3.2KB are compressed to 0.48KB. The decompression algorithm A_decompress is designed to quickly restore the parameters in real-time applications: fast reconstruction of wavelet coefficients is realized; real-time projection recovery of PCA principal components is realized. An efficient real-time computing engine E_realtime is developed: an integrated decompression algorithm is implemented; fast interpolation calculation of compensation values ​​is realized; and the calculation process of sensitivity adjustment is optimized. Implement the real-time calibration process of the sensor boundary area: receive the original sensor measurement value R_measure; determine whether the measurement value is in the boundary area; obtain the current measurement rate v; calculate the position compensation value c_p = LookupCompensation(R_measure); calculate the sensitivity adjustment coefficient k_s = LookupSensitivity(R_measure, v); output the calibrated measurement value O_calibrated = R_measure +c_p * k_s. Among them, LookupCompensation is the lookup function of the position compensation value; LookupSensitivity is the lookup function of the sensitivity adjustment coefficient. Construct a calibration performance monitoring module: regularly sample the measurement values ​​before and after calibration; calculate the calibration effect index; trigger adaptive optimization when necessary.

[0082] After the method of this embodiment is applied to the JSW-5000 optical ruler displacement sensor, the verification results of the boundary area calibration effect are as follows: Improved accuracy of the boundary area: Before calibration: The average error of the boundary area (0-5% range) is 0.015mm, and the maximum error is 0.032mm; After calibration: The average error of the boundary area is 0.002mm, and the maximum error is 0.005mm; Improved accuracy: The average error is reduced by 86.7%, and the maximum error is reduced by 84.4%. Sensitivity compensation effect: Static measurement: The sensitivity change in the boundary area is reduced from ±12% to ±1.5%; Dynamic measurement (10mm / s): The sensitivity deviation in the boundary area is reduced from ±18% to ±2.8%. Temperature stability: The temperature range is 15-35°C, and the calibration effect is stable, and the accuracy change in the boundary area does not exceed 10%. Long-term stability: After one month of continuous monitoring, the calibration parameters are stable and the accuracy is maintained within ±0.003mm. Resource occupation: The compressed calibration parameters only occupy 0.48KB of storage space; the real-time calibration calculation delay is less than 0.2ms, which meets the high-speed control requirements. This embodiment verifies the effectiveness of the displacement sensor boundary area calibration method of the present invention in practical applications, especially its significant advantages in improving boundary area measurement accuracy, improving dynamic response characteristics and optimizing calibration resource allocation.

[0083] The preferred embodiments of the present invention are described in detail above; however, the present invention is not limited to the specific details in the above embodiments. Within the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all belong to the protection scope of the present invention.

Claims

1. A displacement sensor boundary area calibration method, characterized in that: The following steps are involved: Obtain the original measurement data set of the displacement sensor, perform multi-scale boundary feature extraction and analysis, and obtain multi-scale feature vectors and boundary feature recognition fingerprints; The original measurement data set includes measurement points in the boundary area and the middle area; Based on multi-scale feature vectors and boundary feature recognition fingerprints, a dynamic segmented mixed error model is constructed to obtain a balanced error model and interval uncertainty. Based on the balanced error model and interval uncertainty, an intelligent iterative calibration process is implemented to obtain a converged optimization model; Based on the convergent optimization model, a boundary area compensation function and calibration parameters are generated to obtain a calibration parameter package for calibrating the boundary area of ​​the displacement sensor.

2. The method according to claim 1, characterized in that The steps of performing multi-scale boundary feature extraction and analysis to obtain a multi-scale feature vector and a boundary feature recognition fingerprint include: Obtain the original measurement data set and perform enhanced sampling in the boundary area to obtain enhanced data; Applying local differential transformation to the original measurement data set and the enhanced data to obtain the boundary feature spectrum; Extract features at different scales from the boundary feature spectrum and combine them to form a multi-scale feature vector; Based on the multi-scale feature vectors, the scale correlation matrix is ​​calculated to quantify the intrinsic correlation between features at different scales; The multi-scale feature vectors and scale correlation matrix are used to compare and analyze the feature differences between the boundary area and the middle area, and the boundary feature recognition fingerprint is constructed.

3. The method according to claim 2, characterized in that The steps of obtaining the boundary feature spectrum and forming the multi-scale feature vector include: Mapping the original measurement data set and the enhanced data into the frequency space to obtain a frequency distribution diagram; Performing local feature enhancement processing on the frequency distribution graph to obtain an enhanced spectrum; Perform spatial correlation processing based on the enhanced spectrum to form a boundary feature spectrum; Extract microscopic features at small scale, local features at medium scale and macroscopic features at large scale from the boundary feature spectrum; The micro features, local features and macro features are integrated to form a multi-scale feature vector.

4. The method according to claim 2, characterized in that The steps to calculate the scale association matrix include: Decompose the multi-scale feature vector into three sub-vectors: microscopic, local and macroscopic features; Construct a feature mapping space, project the three sub-vectors into the same reference coordinate system, and obtain standardized microscopic, standardized local, and standardized macroscopic features; Using a sliding window technique, the cross-correlation functions between the normalized microscopic, normalized local, and normalized macroscopic features are calculated to obtain a set of cross-correlation vectors; Based on the cross-correlation vector set, a cross-correlation tensor representing the correlation between different scales and positions is constructed and singular value decomposition is performed to extract cross-scale patterns. Based on the cross-scale pattern, a scale correlation matrix is ​​constructed; its eigenvalues ​​and eigenvectors are calculated to obtain the correlation eigenvectors used to characterize the dominant mode of cross-scale coupling in the boundary area.

5. The method according to claim 1, characterized in that The steps of constructing a dynamic piecewise mixed error model and obtaining a balanced error model and interval uncertainty include: Based on the multi-scale feature vector and the boundary feature recognition fingerprint, the key turning point set in the boundary area is identified, and the boundary area is divided into predetermined sub-intervals accordingly; Constructing specific basis functions for each subinterval to obtain an adaptive basis function library; According to the set of key turning points, the error response characteristics of the boundary region are decomposed into multimodal components, including reference component, system component, random component and coupling component; Based on the adaptive basis function library and multimodal components, a dynamic piecewise mixed error model is constructed and a model complexity penalty factor is introduced to obtain a balanced error model. Compute the interval uncertainty of the balanced error model and assign an uncertainty estimate to each subinterval of the model.

6. The method according to claim 5, characterized in that The steps of constructing a specific basis function for each subinterval and obtaining an adaptive basis function library include: The characteristics of the boundary area sub-intervals are analyzed according to the key turning point set, and the interval characteristics classification is obtained, including high-frequency micro-fluctuation interval, medium-frequency transition interval and low-frequency system error interval; Construct wavelet basis functions for high-frequency micro fluctuation ranges; Construct fractional polynomial basis functions for the intermediate frequency transition interval; For the low-frequency system error interval, an exponential decay basis function is constructed; The parameters of wavelet, fractional polynomial and exponential decay basis functions are optimized to make them best fit the error characteristics of the corresponding interval, and the optimized basis function set is obtained; the optimized basis function set is integrated into an adaptive basis function library.

7. The method according to claim 5, characterized in that The steps of decomposing the error response characteristics of the boundary region into multimodal components include: Perform error response analysis on the boundary area according to the key turning point set to obtain error response characteristics; Extracting a reference component reflecting the basic linear response of the measurement system from the error response characteristics; Combining the error response characteristics and the reference components, the system components reflecting the inherent system deviation of the sensor are extracted; Based on the error response characteristics, the reference component and the system component, the random component reflecting the random fluctuation in the measurement process is extracted; Analyze the interaction between the reference component, system component and random component, and extract the coupling component reflecting the mutual interference of different error sources; The reference component, system component, random component and coupling component are integrated into multimodal components.

8. The method according to claim 1, characterized in that The steps of implementing intelligent iterative calibration processing to obtain a converged optimization model include: Based on the balanced error model and interval uncertainty, an iterative optimization model is constructed and the difference between its predicted value and the actual measured value is analyzed to obtain the residual vector. Perform density estimation analysis on the residual vector, construct the residual probability distribution, and calculate the position-related uncertainty entropy value; Combining the uncertainty entropy value, interval uncertainty and residual vector, a sampling importance function is constructed to obtain a non-uniform sampling strategy and generate a set of candidate sampling points. Apply information gain evaluation to the candidate sampling point set, remove points with redundant information, obtain a calibration sampling point set and generate sampling execution instructions containing precise position information and measurement parameter configuration; Iterative optimization is performed based on the sampling execution instructions until a preset accuracy threshold or an upper limit of the number of iterations is reached to obtain a converged optimization model.

9. The method according to claim 1, characterized in that The steps of generating a boundary area compensation function and calibration parameters and obtaining a calibration parameter package include: Based on the convergence optimization model, the error compensation coefficient set of each sub-interval in the boundary area is extracted to construct a piecewise continuous compensation function. Calculate the derivative of the piecewise continuous compensation function to obtain the sensitivity compensation function; Combining the piecewise continuous compensation function and the sensitivity compensation function, a complete calibration parameter package is generated, including static compensation parameters and dynamic response parameters; Perform data compression processing on the calibration parameter package to generate compressed calibration parameters.

10. The method according to claim 9, characterized in that The steps of calculating the derivative of the piecewise continuous compensation function and obtaining the sensitivity compensation function include: Calculate the position derivative of the piecewise continuous compensation function to obtain a sensitivity variation curve representing the spatial variation of sensor sensitivity; Identify the sensitivity mutation points in the sensitivity change curve, record their positions and change amplitudes, and form a sensitivity mutation point list; Based on the sensitivity mutation point list, the measuring range is divided into predetermined sensitivity intervals, and a sensitivity interval segmentation model is constructed; Analyze the response differences of displacement sensors at different measurement rates, establish a mapping relationship between rate and sensitivity changes, and form a rate-dependent model; The sensitivity interval segmentation model and the rate-dependent model are integrated to generate a comprehensive sensitivity compensation function; A sensitivity smooth transition mechanism is constructed to eliminate the discontinuity of the comprehensive sensitivity compensation function at the derivative level and obtain the final sensitivity compensation function.

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