An ultra-high precision size calibration method for optical molds

Abstract

The present application relates to a kind of ultra-high precision size calibration method for optical mold, to solve the problems of low efficiency and poor reliability in multi-source coupling error analysis and dynamic compensation in the system. It includes: collecting system optical path, temperature control and mechanical chain physical topology and error characteristics, generating structured error propagation tuples, identifying key error paths through clustering compression, and obtaining lightweight path signatures;Using historical data to establish a mapping library of path signatures and expression templates, and supporting real-time retrieval and injection of low-dimensional physical characteristic variables through hardware compilation, to generate standardized compensation expressions;Compensation actuator, calibrate mold, and close-loop verify model credibility, if verification fails, automatically trigger path re-identification and local template replacement. This method realizes efficient and reliable multi-source error control, improves the calibration accuracy of optical mold and the intelligent level of the system.

Description

Technical Field

[0001] This invention relates to the field of precision dimension calibration and error compensation technology for optical molds, and in particular to an ultra-high precision dimension calibration method for optical molds. Background Technology

[0002] In the current field of high-precision dimensional calibration and dynamic error compensation for optical molds, mainstream technical solutions mostly employ end-to-end numerical fitting methods and complex neural network architectures to optimize compensation parameters. Known technical paths in the industry include graph neural networks for weight learning of the error propagation topology, causal inference models for extracting error coupling relationships, and multi-objective evolutionary algorithms or deep gradient descent frameworks for numerical optimization of compensation parameters. Some patents and published literature have also proposed methods based on federated learning, transfer learning, or particle swarm optimization, combining multimodal data for adaptive compensation strategies. However, these methods generally rely on large network structures and end-to-end black-box modeling, posing significant challenges to system computational resources, model interpretability, and lightweight industrial deployment requirements.

[0003] In practical applications, optical mold measurement systems typically involve complex physical components such as optical transmission chains, temperature control loops, and mechanical positioning chains. The error propagation paths of these systems are highly dynamic and subject to multi-source interference. Traditional compensation algorithms focus on single-objective optimization, making it difficult to achieve a dynamic balance under multiple constraints, including compensation accuracy, computational efficiency, and system stability. Existing methods using end-to-end complex neural networks for error modeling suffer from long model training cycles, exponential parameter scaling, low real-time response capabilities, and poor interpretability. Furthermore, existing technologies have limited adaptability in low-resource environments for industrial scenarios requiring real-time deployment of edge devices.

[0004] Representative technologies such as deep neural networks, graph neural networks, and multi-objective evolutionary algorithms have played a role in the dynamic dimensional calibration and compensation of optical molds. They excel at handling complex coupling relationships in large-scale data and are suitable for batch analysis scenarios in engineering laboratories or high-computing platforms. However, due to the large number of parameters and high computational complexity, these technologies are not suitable for high-frequency online calibration or edge scenarios with strict hardware instruction set compatibility requirements. Furthermore, the interpretability of compensation parameters in black-box models is insufficient, making direct integration with physical control logic difficult in actual production processes. They also exhibit deficiencies in robustness and self-healing capabilities under abnormal operating conditions.

[0005] Existing technologies mainly suffer from the following problems: First, the optimization process of compensation parameters is mostly single-objective or static multi-objective, making it difficult to balance compensation accuracy, real-time performance, and long-term system stability. Second, end-to-end neural network structures cannot clearly demonstrate the physical mechanism of error propagation, resulting in low model transparency and difficulties in debugging and fault diagnosis. Third, model parameter inflation increases deployment difficulty, and the compensation algorithm's response speed is slow when edge device resources are limited, making it difficult to meet the millisecond-level compensation requirements in industrial settings. Fourth, existing methods often use overall model retraining when compensation parameters fail, lacking an efficient self-repair mechanism for local error mismatch, which affects the continuous accuracy output of the system. Fifth, the lack of semantic compression and standardized representation of multi-stage measurement error propagation paths prevents the algorithm from achieving flexible retrieval and template-based compensation.

[0006] In summary, the field of optical mold dimensional calibration and compensation urgently needs a novel compensation parameter generation method that combines high precision, lightweight design, strong interpretability, adaptability to real-time edge deployment, and the ability to achieve dynamic balance across multiple objectives. This technology must not only break free from reliance on end-to-end black-box modeling and deep learning architectures, but also possess semantic transparency mechanisms, symbolic retrieval capabilities, and local self-healing functions for compensation strategies. This will enable long-term stable and high-precision dimensional calibration and error compensation in dynamic, multi-perturbation industrial environments. Summary of the Invention

[0007] This application provides an ultra-high precision dimensional calibration method for optical molds, which aims to solve one of the problems or issues of the prior art mentioned in the background section.

[0008] This application provides an ultra-high precision dimensional calibration method for optical molds, specifically including: S1: Obtain the topological information of the optical path, temperature control and mechanical positioning chain in the optical mold measurement system, extract the type, direction, phase and intensity level of the error source in each link, and generate error propagation semantic tuples.

[0009] S2: Perform clustering compression based on the error propagation semantic tuple, identify the dominant error propagation trunk path and secondary disturbance branches, and generate error propagation path signatures.

[0010] S3: Utilize historical operating data to construct a mapping relationship between path signatures and expression templates, perform numerical stability verification and hardware compilation on candidate templates, and generate a mapping index library.

[0011] S4: The real-time collected temperature gradient, vibration spectrum amplitude, and air refractive index change rate are used as low-dimensional physical feature variables, and the error propagation path signature is input into the mapping index library for matching to obtain the compiled expression template.

[0012] S5: Inject the low-dimensional physical feature variables based on the compiled expression template, and perform symbolic resolution operation to generate a compensation parameter parsing expression.

[0013] S6: Calculate the dynamic compensation amount based on the analytical expression of the compensation parameters, and perform parameter correction control on the actuator of the optical mold calibration system to generate measured residual data.

[0014] S7: Verify the reliability of the measured residual data and the predicted residual, determine whether the positive and negative signs, monotonicity and extreme point positions match, and generate the verification result.

[0015] S8: If the verification result is determined to be a failure three times in a row, the path re-identification is triggered and the template replacement operation is performed to generate an updated error propagation path signature to re-drive the compensation parameter generation process.

[0016] This application provides an ultra-high precision dimensional calibration method for optical molds, which has the following advantages: (1) By shifting the error propagation path modeling in the optical mold measurement system from the traditional numerical fitting paradigm to a semantic encoding mechanism based on physical topology, the interpretability and engineering adaptability of the modeling process are significantly improved. In the prior art, although methods based on graph neural networks or causal reasoning can capture complex relationships between nodes, their black-box characteristics make it difficult to identify key error coupling links, and they are highly dependent on the quality of training data, and are prone to misjudgment and overfitting under dynamic working conditions. This scheme abandons the method of directly learning connection weights, and instead extracts the type label, direction of action, temporal phase and influence intensity level of error sources based on physical structures such as optical path transmission chain, temperature control loop and mechanical positioning chain, constructs structured semantic tuples, and generates error propagation path signatures through hierarchical clustering and redundancy compression. The signature encodes the path topology and dynamic sensitivity features in the form of a fixed-length string, which not only effectively preserves the key information of the dominant propagation backbone path, but also greatly reduces the model storage overhead and computational complexity, and solves the problem of deployment difficulties caused by parameter expansion in traditional methods, which is especially suitable for resource-constrained edge industrial equipment scenarios.

[0017] (2) Regarding the parameter optimization mechanism, a novel symbolic regression-driven "expression retrieval" is adopted to replace the mainstream gradient descent or multi-objective evolutionary algorithms, achieving rapid generation and real-time response of high-precision compensation parameters. Unlike traditional optimization frameworks that rely on iterative search or large-scale computing power, this scheme uses the error propagation path signature as a prompt input to guide the embedded symbolic regression engine to search for the optimal analytical structure that conforms to the semantics of industrial control in a predefined interpretable operator library. The constraint output is a lightweight expression with few variables, shallow nesting, and simple operation, ensuring that the generated result has physical meaning and hardware execution feasibility. Combining the offline-online dual-stage strategy, an offline mapping index library of path signatures and expression templates is constructed, and numerical stability verification and instruction set compilation are completed. In the online stage, only millisecond-level matching of the current signature and injection of real-time collected low-dimensional physical features (such as temperature gradient, vibration spectrum amplitude, and air refractive index change rate) are required to instantly generate compensation parameters, greatly shortening the response delay and meeting the high-frequency dynamic adjustment requirements. This mechanism avoids complex tuning and repeated training processes, significantly improving the robustness and deployment efficiency of the system, and is especially suitable for intelligent manufacturing environments with frequent switching of working conditions.

[0018] (3) A closed-loop credibility feedback mechanism is introduced to further enhance the system's adaptability and operational reliability. By comparing the sign consistency (including positive and negative signs, monotonicity trends, extreme point positions, etc.) between the measured residuals after parameter execution and the expression prediction residuals, the logical level of the compensation effect is verified. When three consecutive verifications fail, the system automatically triggers the path signature re-identification and local expression template replacement process, instead of performing global model retraining or restarting the optimization process, thereby achieving fault isolation and local correction without increasing the computational burden and ensuring long-term operational stability. This mechanism completely avoids the high-cost strategies of federated learning, transfer learning, or incremental updates under the deep learning framework, forming a localized closed-loop optimization system that does not require a large amount of historical data playback and does not rely on cloud collaboration, and has good maintainability and expansion potential.

[0019] In summary, this solution achieves a fundamental reconstruction of the error propagation modeling and parameter generation mechanism through the technical route of "semantic encoding - symbol retrieval - closed-loop verification". While improving the system accuracy, it significantly enhances interpretability, lightweight level and edge adaptability, breaks through the technical bottleneck of traditional data-driven and complex optimization algorithms, and provides a new intelligent compensation architecture that is efficient, reliable and easy to deploy for high-precision optical mold measurement systems. Attached Figure Description

[0020] Figure 1 This is the main flowchart of an ultra-high precision dimensional calibration method for optical molds.

[0021] Figure 2This is a sub-flowchart of an ultra-high precision dimensional calibration method for optical molds.

[0022] Figure 3 This is another sub-flowchart of a method for ultra-high precision dimensional calibration of optical molds. Detailed Implementation

[0023] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0024] The following disclosure provides many different embodiments or examples for implementing different structures of the invention. To simplify the disclosure, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the invention. Furthermore, reference numerals and / or letters may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed.

[0025] like Figure 1 As shown, this application provides an ultra-high precision dimensional calibration method for optical molds, specifically including: S1: Obtain the topological information of the optical path, temperature control and mechanical positioning chain in the optical mold measurement system, extract the type, direction, phase and intensity level of the error source in each link, and generate error propagation semantic tuples.

[0026] S2: Perform clustering compression based on error propagation semantic tuples, identify the dominant error propagation trunk path and secondary perturbation branches, and generate error propagation path signatures.

[0027] S3: Utilize historical operating data to construct a mapping relationship between path signatures and expression templates, perform numerical stability verification and hardware compilation on candidate templates, and generate a mapping index library.

[0028] S4: The real-time collected temperature gradient, vibration spectrum amplitude, and air refractive index change rate are used as low-dimensional physical feature variables, and the error propagation path signature is input into the mapping index library for matching to obtain the compiled expression template.

[0029] S5: Inject low-dimensional physical feature variables based on compiled expression templates, and perform symbolic resolution operations to generate analytical expressions for compensation parameters.

[0030] S6: Calculate the dynamic compensation amount based on the analytical expression of the compensation parameters, and perform parameter correction control on the actuator of the optical mold calibration system to generate measured residual data.

[0031] S7: Verify the reliability of the measured residual data and the predicted residual, determine whether the positive and negative signs, monotonicity and extreme point positions match, and generate the verification result.

[0032] S8: If the verification result fails three times in a row, the path re-identification is triggered and the template replacement operation is performed to generate an updated error propagation path signature to re-drive the compensation parameter generation process.

[0033] Step S1: Obtain the topology information of the optical path, temperature control, and mechanical positioning chain in the optical mold measurement system; extract the type, direction, phase, and intensity level of error sources in each link; and generate error propagation semantic tuples. Specifically, this includes: S1.1: Perform topology analysis on the physical connection relationships of the optical path transmission chain, temperature control loop, and mechanical positioning chain in the optical mold measurement system to obtain system physical topology information including node type and edge connection attributes.

[0034] The input conditions are three types of physical connection paths in the optical mold measurement system: optical path transmission chain, temperature control loop, and mechanical positioning chain. The field acquisition module has already output physical connection data records for each connection link, including the device identification code of the node, structural position coordinates, and the geometric length and media characteristic parameters of the edge connections. For this physical connection data, a node index table is established using a matrix-based topology analysis algorithm, grouping nodes according to device function and labeling them with node type fields. An adjacency matrix is ​​constructed using edge connection parameters, mapping the media type and geometric attributes of each edge to matrix weights to encode the edge connection attributes. A graph traversal function is called to perform a depth-first traversal of the adjacency matrix, accumulating path segment indices by node type during the traversal and recording the physical media characteristics between adjacent nodes, forming a preliminary path segment feature mapping table. The edge connection weights in each path segment feature mapping table are normalized to ensure that the weight data for different links are within a unified numerical range to adapt to the input of the subsequent error modeling module. Connectivity analysis is performed on the normalized adjacency matrix to remove isolated nodes without physical connections, and a complete system physical topology data model is generated. This model outputs system physical topology information containing node types and edge connection attributes, providing the physical constraint basis for subsequent error source identification steps.

[0035] For example, in an optical mold measurement system application comprising an optical path transmission chain, a temperature control loop, and a mechanical positioning chain, the nodes of the optical path transmission chain include three reflectors, one beam splitter, and one receiver. The temperature control loop consists of two sets of heat exchange units and a temperature sensor. The mechanical positioning chain consists of four multi-axis platforms and a positioning encoder. The geometric lengths of the edge connections range from 0.15 meters to 1.2 meters, and the medium characteristics include air, glass, and metal thermal interfaces. Nodes are labeled by function as "optical element," "temperature control module," and "mechanical execution unit." When constructing the adjacency matrix, the weights of air medium edges are assigned a value of 0.2, glass medium edges a value of 0.6, and metal interface edges a value of 0.8. A depth-first traversal is used, starting from the light source node, sequentially visiting the reflectors, beam splitter, and receiver to form an optical path segment feature mapping table. When traversing the temperature control loop, the heat exchange units and sensor nodes are visited sequentially to generate a temperature control segment feature mapping table. The traversal of the mechanical positioning chain generates a mechanical positioning segment feature mapping table. All values ​​are normalized to fall within the 0-1 range, and unconnected backup temperature control module nodes are removed through connectivity analysis. The final generated system physical topology model clarifies the type of each device at the node level and accurately identifies the connection medium and its parameters at the edge connection level. This model serves as structured input information for the error source identification and classification steps, significantly improving the accuracy and robustness of subsequent error analysis.

[0036] S1.2: Based on the system's physical topology information, identify and classify error sources in each link to generate a set of error source type labels for each link, each labeled with a specific error generation mechanism.

[0037] For the system physical topology information from step S1.1, multi-source physical feature cross-retrieval processing is performed on each node of the optical path transmission chain, temperature control loop and mechanical positioning chain to extract the sensor identifiers, material properties, processing records and historical measurement residual distribution data bound to the nodes in order to form a preliminary candidate list of error sources.

[0038] For each type of node in the candidate list, the measurement residual statistical model is called to calculate its error occurrence frequency and amplitude stability index. The error mechanism is inferred by combining physical constants such as the material thermal expansion coefficient, mechanical hysteresis coefficient, and optical transmittance attenuation rate, and error source classification labels with physical interpretation are generated.

[0039] Physical mechanism consistency checks are performed on the above-mentioned set of classification labels. Labels with the same cause but different nodes are merged. The criteria for merging labels of the same type are the similarity threshold matching of the error mechanism description field and the limit constraint of the difference of physical constant.

[0040] For the merged set of error source classification labels, a classification weight vector is constructed using the error occurrence frequency and amplitude stability index. This weight vector is calculated using the following formula: in, This represents the frequency of errors occurring in the node corresponding to this label. The amplitude stability coefficient, This represents the total frequency of all nodes in the link. This represents the sum of amplitude stability. This represents the classification weight of the error source node.

[0041] The aforementioned classification weight vector and physical mechanism description field are encapsulated together into an error source type label set, and the cause, physical attributes, statistical weights and node position index of each label are recorded in a fixed key-value pair format.

[0042] Through the above error source identification and classification processing methods, the system physical topology node information is transformed into a structured set of error source type labels, which serves as the input basis for subsequent error direction and timing phase extraction.

[0043] For example, in an optical mold measurement system, the optical path transmission chain contains 9 nodes, the temperature control loop contains 6 nodes, and the mechanical positioning chain contains 12 nodes. For the optical path node L3, a conventional transmittance value of 0.93 is obtained from the optical transmittance sensor. Combined with the residual statistical model, the error occurrence frequency of this node is found to be 14 times / 100 cycles, and the amplitude stability coefficient is 0.82. For the temperature control node T2, the measured coefficient of thermal expansion of the material is 1.2 × 10⁻⁶. 5 The residual occurrence frequency is 8 times / 100 periods, and the amplitude stability coefficient is 0.76. When performing the formula calculation, for node L3, its weight w = (14 × 0.82) / (total frequency F = 33 + total stability S = 2.34) ≈ 0.325. For node T2, its weight w = (8 × 0.76) / (35.34) ≈ 0.172. Finally, the system generates two main types of labels: "optical transmission attenuation error sources" and "thermal expansion error sources," and annotates the node number, cause, physical constant value, and weight coefficient in the key value. This can be directly used for error direction and temporal phase feature extraction.

[0044] S1.3: Utilize the error source type label set of each stage to perform directional extraction of the error action vector direction and temporal phase characteristics, so as to obtain the error action direction parameters and temporal phase parameters that characterize the spatiotemporal distribution characteristics of the error.

[0045] S1.4: The error impact intensity level is quantitatively evaluated based on the error direction parameter and the time phase parameter to generate an error impact intensity level index that reflects the error propagation amplitude weight.

[0046] S1.5: Integrate the error source type label set, error direction parameters, timing phase parameters, and error impact intensity level indicators of each stage into a structured encapsulation process to generate error propagation semantic tuples for driving subsequent path compression.

[0047] The error source type label set, error direction parameter, timing phase parameter and error influence intensity level index obtained after the previous sub-steps of the optical mold measurement system are converted by a unified data interface protocol to ensure that the field naming, data accuracy and value range of data from different sources are consistent during the encapsulation process.

[0048] The converted error source type label set is indexed and encoded, and the error mechanism characteristics of each node in the physical link are recorded in the form of fixed-length integer indexes and arranged in the topological order of optical path transmission chain, temperature control circuit and mechanical positioning chain.

[0049] The error direction parameter and the temporal phase parameter are combined into a matrix. The three-dimensional spatial direction vector of the error at the node and the corresponding phase timestamp are encapsulated in the same matrix unit to form a spatiotemporal coupling feature matrix.

[0050] Normalization mapping is performed on the error impact intensity level index to convert the intensity values ​​measured by different links into a unified range of quantization levels, and the nodes are matched by time sequence index and node index double key to generate a node-intensity lookup table.

[0051] The error source type label, spatiotemporal coupling feature matrix, and node-intensity lookup table of the index encoding are encapsulated in multiple layers to form an error propagation semantic tuple containing node attributes, edge connection features, and dynamic sensitivity information, providing standardized input for subsequent path compression and clustering analysis.

[0052] Through the above structured encapsulation process, the multi-source error parameters from the previous step are transformed into unified, searchable, and parsable semantic tuple data, thereby achieving standardization and scalability of the data foundation for error propagation modeling.

[0053] For example, in an optical mold measurement system, the identified optical path transmission chain node error source type labels are {"beam deflection":"OPT01", "lens thermal expansion":"THERM01"}, the temperature control loop node label is {"temperature control hysteresis":"THERM02"}, and the mechanical positioning chain node label is {"platform torque fluctuation":"MECH01"}. The error direction parameter is recorded as a unit vector as (0.002, 0.001, ... 0.003), the timing phase parameter is recorded as 0.25s in seconds. The error impact intensity level index is in the range of 0 to 1, with beam deflection at 0.85, lens thermal expansion at 0.65, temperature control hysteresis at 0.40, and platform torque fluctuation at 0.55. After performing data interface protocol conversion, each tag is encoded with an integer index, for example, OPT01 maps to 1, THERM01 to 2, THERM02 to 3, and MECH01 to 4. In the constructed spatiotemporal coupling feature matrix, the first row contains the direction vector and phase of beam deflection (0.25s), the second row contains the direction vector and phase of lens thermal expansion (0.30s), and so on. The normalized intensity level has been matched according to the node index, forming a node-intensity lookup table {1:0.85,2:0.65,3:0.40,4:0.55}. The above encodings, matrices, and lookup tables are encapsulated in topological order to generate error propagation semantic tuples [node index, error mechanism encoding, direction vector, phase, intensity level], where the beam deflection tuple is represented as [1, OPT01, (0.002, 0.001, ...]. [0.003), 0.25, 0.85]. This tuple can be directly used as an input key in subsequent clustering processing, significantly improving the efficiency and accuracy of topology path compression and backbone path identification.

[0054] like Figure 2 As shown, step S2: Perform clustering compression based on the error propagation semantic tuples to identify the dominant error propagation backbone path and secondary perturbation branches, and generate error propagation path signatures. Specifically, this includes: S2.1: Perform vector space mapping on the error action direction parameter and temporal phase parameter in the error propagation semantic tuple to construct an initial error propagation topology graph that represents the spatiotemporal coupling relationship of multi-source errors. This graph contains node error intensity level indicators and edge connection weight attributes, serving as the underlying data structure foundation for subsequent clustering analysis.

[0055] Vector space mapping is performed on the error action direction parameter and temporal phase parameter in the error propagation semantic tuple to establish the underlying topological data structure for cluster analysis.

[0056] The error direction parameter is converted into a direction vector component in a three-dimensional Cartesian coordinate system, and a mapping matrix is ​​defined based on the physical orientation of each link of the optical mold to stably project the direction component onto a unified coordinate base.

[0057] Periodic normalization and phase difference calculation are performed on the timing phase parameters. By constructing periodic basis vectors in the phase difference domain, the phase features are projected onto the orthogonal phase space so that they can form an error spatiotemporal feature vector together with the direction vector.

[0058] The error direction vector and the normalized phase vector are combined to form a set of node feature vectors, and the corresponding error intensity level index is injected as the node weight attribute to establish a node set containing node weights.

[0059] Calculate the cosine similarity of direction vectors and the absolute value of phase difference between adjacent nodes, construct the edge connection weight attribute, and use the following edge weight formula: in, and The direction vectors of adjacent nodes, This represents the phase difference.

[0060] The node weight attributes and edge connection weights are combined to form the data structure of the initial error propagation topology graph. Nodes represent the location of error sources and their intensity levels, while edges represent the error propagation coupling strength and spatiotemporal matching degree.

[0061] By using vector space mapping and weight construction, the semantic tuples from the previous step are transformed into an initial error propagation topology graph containing node error intensity indices and edge connection weight attributes, thus providing a quantitatively analyzable underlying data structure foundation for subsequent hierarchical clustering algorithms.

[0062] For example, in an optical mold measurement system comprising five nodes in the optical path transmission chain, three nodes in the temperature control loop, and four nodes in the mechanical positioning chain, the error direction parameters are defined in a unit spherical coordinate system. The direction for node 1 is (0.8, 0.6, 0.0), and the direction for node 2 is (0.0, 1.0, 0.0), with temporal phase parameters of 0.25π and 0.5π, respectively. After projecting the direction vectors onto a unified Cartesian basis, the cosine similarity of the directions of node 1 and node 2 is calculated, yielding a value of 0.6. Phase difference |Δ |=0.25π. Substituting this into the weight formula, the edge weight between node 1 and node 2 is 0.6×(1-0.25π / π)=0.45. This value is used as the edge connection weight attribute of the topological graph. After construction, the complete topological graph contains 12 nodes, several edges and their weights, providing quantitative and interpretable spatiotemporal coupling information for subsequent adaptive hierarchical clustering, significantly improving the identification accuracy and computational efficiency of error propagation paths.

[0063] S2.2: Based on the edge connection weight attribute in the initial error propagation topology graph, an adaptive hierarchical clustering algorithm is executed to calculate the correlation density coefficient between adjacent error source nodes and generate a hierarchical cluster structure, thereby aggregating discrete single-point error sources into a statistically significant set of error propagation clusters, achieving preliminary merging and dimensionality reduction of error propagation paths.

[0064] S2.3: Utilize the distribution characteristics of the error influence intensity level index within each cluster in the error propagation cluster set to perform principal component contribution rate evaluation processing, so as to quantify the sensitivity weight of each potential propagation path to the overall calibration residual, and then screen out the dominant error propagation backbone path whose cumulative contribution rate exceeds the preset threshold, while marking the secondary disturbance branches below the threshold to be removed.

[0065] Based on the distribution characteristics of error impact intensity level indices within each cluster of the error propagation cluster set, the node intensity value sequence of each cluster is converted into a vector representation with measurable sensitivity, serving as the input data matrix for principal component analysis. Covariance matrix calculation is performed on the data matrix to obtain a quantitative structure measuring the correlation between intensity dimensions. Eigenvalue and eigenvector decomposition is performed on the covariance matrix to extract the principal component loading vectors representing the direction of maximum variance, and the principal component contribution rate index is calculated. The cumulative contribution rate summation formula is then used. in, For cumulative contribution rate, For the first The eigenvalues ​​of the principal components The total number of principal components is used, and the denominator is the sum of all eigenvalues. The calculated contribution rate is compared with a preset sensitivity threshold. Cluster paths with a cumulative contribution rate greater than the threshold are selected and marked as the dominant error propagation backbone paths. Cluster paths with a contribution rate lower than the threshold are marked as secondary perturbation branches for subsequent removal. Through contribution rate evaluation and sensitivity filtering, paths with strong correlation and significant impact on the overall calibration residuals are retained, achieving accuracy and stability in subsequent path skeleton simplification.

[0066] S2.4: Perform topology pruning and redundancy compression on the identified dominant error propagation backbone path and the secondary disturbance branches to be removed, in order to remove secondary disturbance branch nodes with low sensitivity weights and merge the series homogeneous error links, generating a simplified error propagation skeleton diagram that retains only the key error coupling points and core transmission links, which greatly reduces the computational complexity of path representation.

[0067] S2.5: Based on the node type label sequence and the connection relationship of key error coupling points in the simplified error propagation skeleton graph, fixed-length hash encoding is performed to convert the variable-length topology information into an error propagation path signature containing path topology features, dynamic sensitivity identifiers and key node fingerprints.

[0068] The node type label sequence of the simplified error propagation skeleton graph and the connection relationship between the key error coupling points are used as the encoding input set.

[0069] The node type label sequence in the input set is processed by bit weight allocation, which maps different types of nodes to a preset weight coefficient matrix to ensure that the ability to distinguish node categories is preserved during encoding.

[0070] The connection relationships of key error coupling points are serialized and topological path generation is performed to transform the multi-branch structure into a one-dimensional ordered linked list. Dynamic sensitivity flags are marked in the linked list to ensure that subsequent hash calculations can distinguish the structural positions of sensitive nodes and ordinary nodes.

[0071] The above weight coefficient matrix and serialized topological linked list are processed to generate a composite index. The node weight data and the connection sequence are superimposed bit by bit to form a composite index vector, which is used as the original input for fixed-length hash encoding.

[0072] A fixed-length hash encoding algorithm is called to perform hash operations on the composite index vector. A modulo mapping and multi-round XOR stacking strategy are used to uniformly convert topological structure information of different lengths into encoded output of a preset length.

[0073] The encoded output and node sensitivity identifier are fused using a bitmask, and key node fingerprint verification bits are inserted to form an error propagation path signature that includes path topology features, dynamic sensitivity identifiers, and key node fingerprints.

[0074] By combining fixed-length hash encoding with bitmasking, the simplified error propagation skeleton diagram from the previous step is transformed into a standardized retrieval key value, enabling the generation of lightweight path signatures and supporting the rapid execution of subsequent offline index matching and template retrieval.

[0075] For example, in the error propagation skeleton diagram of an optical mold measurement system, the node type label sequence consists of optical path nodes, temperature control nodes, and mechanical positioning nodes, with weight coefficients set to 2, 3, and 5 respectively. The key error coupling point is located between the optical path node and the mechanical positioning node, and the sensitivity flag is set to 1. After serialization, the connection relationship forms a linked list of length 8, containing 5 ordinary node flags and 3 sensitive node flags. The composite index generation process superimposes the weight coefficient matrix onto the linked list bit by bit to obtain a composite index vector of length 8 with elements ranging from 0 to 255. A fixed-length hash encoding algorithm is then called ( ),in It is a composite index vector. For modular mapping table, For XOR operation, As the encoding length is constant, a fixed-length 16-byte encoding result is obtained through multiple rounds of XOR superposition and modulo-digital mapping. Bitmask fusion processing inserts sensitivity flag bits into the 3rd, 7th, and 12th bytes of the encoding result, and adds key node fingerprint verification bits to form the final error propagation path signature. In online matching verification, this path signature significantly improves index retrieval speed and matching accuracy, while maintaining extremely low memory usage, meeting the millisecond-level requirements of real-time dynamic compensation parameter generation for retrieval response.

[0076] like Figure 3 As shown, step S3 involves: constructing a mapping relationship between path signatures and expression templates using historical operating condition data, verifying the numerical stability of candidate templates and compiling them into hardware, and generating a mapping index library. Specifically, this includes: S3.1: Perform correlation analysis on the multi-stage measurement error records and corresponding optical mold calibration residual data in the historical working condition dataset, extract the error propagation path signature corresponding to each group of data as key value identifier, and perform clustering and grouping processing based on the error propagation path signature to generate a set of path signature clusters with statistical significance.

[0077] Multi-source data synchronization processing is performed on the multi-stage measurement error records and corresponding optical mold calibration residual data in the historical working condition dataset. The error records of different measurement stages are aligned by timestamp and abnormal missing values ​​are removed to form a unified data matrix suitable for correlation analysis.

[0078] A bivariate mapping relationship is established between error records and residual data in a unified data matrix. The correlation index between error records and residual data is calculated by calling the Pearson correlation coefficient and mutual information joint evaluation method. Based on the correlation index, data pairs with high correlation are selected according to a preset threshold. The corresponding error propagation path signature is extracted from each data pair as a key value identifier to ensure the consistency between the path signature and the physical error coupling relationship.

[0079] The extracted path signature set is subjected to clustering based on similarity metric. A path signature similarity matrix is ​​formed by a hybrid metric of cosine similarity and weighted Jaccard coefficient. Path signatures with similarity higher than a set threshold are recursively merged through a hierarchical clustering algorithm to generate a set of path signature clusters with statistical significance.

[0080] Calculate the average intra-cluster correlation and inter-cluster separation indices for the formed path signature cluster set, and remove abnormal clusters with low intra-cluster correlation or insufficient inter-cluster separation to ensure that the final cluster set can be used as high-quality template generation input.

[0081] By using multi-source data synchronization, bivariate association analysis, path signature extraction, and clustering, the error propagation path signature from the previous step is transformed into a set of path signature clusters with statistical significance and physical consistency, thereby standardizing the input data for subsequent template generation.

[0082] For example, the historical operating condition dataset contains 150 measurement error records for optical molds under three environments: low temperature, normal temperature, and high temperature, and 150 corresponding calibration residual data records for each environment. The data from each stage are precisely aligned according to the acquisition time to form a unified matrix with a size of 450 rows × 20 columns. When calculating the Pearson correlation coefficient, a threshold of 0.85 and a mutual information threshold of 0.5 are set. The results show that the correlation coefficient between the second-stage error record and the residual data under low temperature conditions is 0.91, and the mutual information is 0.52, meeting the filtering criteria. The corresponding path signature "HASH_0xA1B2C3" is extracted as the key value. In the clustering process, the cosine similarity threshold was set to 0.9 and the weighted Jaccard coefficient threshold was set to 0.75. Finally, five path signature cluster sets were generated. The average correlation of each cluster was greatly improved and the separation between clusters was significantly enhanced. After removing two low-quality cluster sets, the three high-quality cluster sets that were retained could be directly used as input for the generation of the S3.2 template. Performance verification showed that the template generated by this cluster set had a stable compensation effect under extreme temperature gradient conditions, and the real-time performance of the system was significantly improved.

[0083] S3.2: Based on typical sample data in the path signature cluster set, call the linear combination operator, piecewise threshold operator and time delay difference operator in the predefined basic mathematical operator library to perform permutation and combination operations to generate a set of candidate compensation parameter analytical expression templates covering different error coupling modes.

[0084] Based on typical sample data from the path signature cluster set, when performing permutation and combination operations using linear combination operators, piecewise threshold operators, and time-delay differential operators from the predefined basic mathematical operator library, the topological feature sequence of each path signature cluster is used as the operator input index. The coefficient matrix in the linear combination operator is set according to the sensitivity weights corresponding to the main error propagation path, ensuring that the contribution values ​​of each error source are weighted according to their actual impact proportions in the combination operation. When performing piecewise threshold operator combinations, nodes with sensitivity weights higher than the set threshold are used as independent piecewise trigger conditions, forming compensation logic branches with asynchronous triggering characteristics, thereby capturing the critical response behavior of nonlinear error propagation. For time-delay differential operator combinations, node pairs in the path signature with phase delays exceeding a preset delay window are selected, their differential responses are calculated, and delay factor parameters are introduced to simulate the physical hysteresis effects of the temperature control loop and mechanical positioning chain under different operating conditions. When generating analytical expressions for candidate compensation parameters using operator permutations and combinations, the outputs of each operator combination are structurally validated using a unified symbolic resolution framework. Redundant expressions with more than three nested levels are eliminated, and analytical expressions with five or fewer variables and twelve or fewer operators are retained, forming a set of candidate compensation parameter analytical expression templates covering different error coupling modes. Through this processing method, the statistical significance characteristics of the path signature cluster set are transformed into a multi-mode operator combination structure, achieving a technical balance between covering the diversity of error propagation and ensuring real-time performance in the candidate templates.

[0085] For example, in the historical operating data of the optical mold measurement system, the path signature cluster set contains three typical samples, corresponding to the temperature control loop backbone error coupling, the optical path transmission chain backbone coupling, and the mechanical positioning chain hysteresis coupling, respectively. For the temperature control loop cluster, the linear combination operator coefficient matrix is ​​set to 0.8, 0.1, and 0.1, representing the main weight distribution of the temperature control error sources; the trigger threshold of the segmented threshold operator is set to a sensitivity weight of 0.7 to ensure that only high-sensitivity nodes generate compensated segmented responses; the delay factor of the time-delay differential operator is set to 5ms to simulate the actual temperature control hysteresis characteristics. For the optical path transmission chain cluster, the linear combination coefficient matrix is ​​set to 0.5, 0.3, and 0.2, the segmented threshold trigger threshold is adjusted to 0.6, and the time-delay differential delay factor is set to 2ms; for the mechanical positioning chain cluster, the coefficient matrix is ​​set to 0.4, 0.4, and 0.2, the segmented threshold trigger threshold is 0.5, and the delay factor is 10ms. After inputting the above combination into the symbolic parsing framework, the parsing expressions that satisfy nesting level ≤ 3, number of variables ≤ 5, and total number of operators ≤ 12 are retained. In the calculation of linear combination operators, the compensation amount... ,in , , These are the elements of the aforementioned coefficient matrix, where x, y, and z represent the sensitivity weights for different error sources, ensuring that the generated compensation amount is consistent with the actual error effect. Through full-cluster generation, this candidate template set significantly improves real-time performance and coverage. The calculation delay for compensation parameters in online operating condition matching does not exceed 1ms, while also covering three main error coupling modes, thus enhancing compensation accuracy and system stability.

[0086] S3.3: Perform full-condition numerical stability verification on each candidate compensation parameter analytical expression template in the candidate compensation parameter analytical expression template set. Calculate the divergence index by injecting extreme temperature gradients and vibration spectrum amplitude boundary conditions to screen out a subset of stable candidate compensation parameter analytical expression templates that meet the convergence requirements of industrial control.

[0087] Using each template in the candidate compensation parameter analytical expression template set as the verification object, a test dataset covering the entire working condition of the optical mold measurement system is created, which includes boundary condition records of temperature gradient and vibration spectrum amplitude.

[0088] Numerical simulation is performed on each candidate template. The extreme temperature gradient conditions in the test dataset are injected into the template calculation path to capture the output change curve under high temperature rise and rapid cooling conditions, and the peak and valley values ​​of the curve are recorded.

[0089] The boundary conditions of vibration spectrum amplitude in the test dataset are injected into the template calculation path to extract the output change curve under high vibration impact and near-zero vibration conditions, and the fluctuation amplitude of the curve is recorded.

[0090] The divergence index of each candidate template under the above two extreme working conditions is calculated and measured using the mean square error quantization method. The temperature gradient divergence index and the vibration spectrum amplitude divergence index are compared with the industrial control convergence threshold respectively, and any candidate template whose divergence exceeds the threshold is eliminated.

[0091] Perform convergence stabilization time evaluation on the remaining candidate templates, extract the time interval from initial error to stable output under extreme conditions, and remove templates whose stabilization time exceeds the acceptable value of the system.

[0092] Through the above numerical stability verification process, the candidate template set generated in the previous step is transformed into a subset of stable candidate compensation parameter analytical expression templates that meet the convergence requirements of industrial control, thereby achieving precise qualitative analysis of template selection.

[0093] S3.4: Based on the stable candidate compensation parameter parsing expression template subset, perform target hardware compilation operations to convert symbolic logic that conforms to the three-level nesting constraint into binary machine code fragments that can be directly executed by the underlying processor, so as to generate a compiled expression template binary object with millisecond-level response capability.

[0094] S3.5: Use the error propagation path signature as the index key to establish a bidirectional mapping association with the compiled expression template binary object, and write the mapping relationship to a high-speed storage medium for persistent storage, generating a mapping index library.

[0095] A unique association is established between the input error propagation path signature and the compiled expression template binary object, using the hashed path signature as the index key to create a mapping record. A bidirectional index structure is constructed based on this mapping record. The forward mapping table stores the direct association between the path signature and the corresponding binary object, while the reverse mapping table stores the backtracking association between the binary object fingerprint and the path signature, supporting bidirectional retrieval operations. Collision detection is performed on the mapping records. Entries with hash key collisions are sorted and allocated according to the path signature topology feature length and dynamic sensitivity identifier to avoid erroneous associations where different error path signatures point to the same template object. The collision-handled mapping records are then optimized for caching. A block-linked storage structure is used to write the index key and binary object to high-speed storage media with a fixed address offset, while generating a checksum for the storage block to ensure data consistency. The mapping data written to the high-speed storage media is persistently encapsulated, and a partitioned index is generated according to the topology category of the path signature, enabling rapid location and retrieval of the corresponding compiled template by category during online processing. By using bidirectional mapping association and a high-speed persistent storage structure, the compilation results of the previous step are transformed into a real-time searchable mapping index library, achieving the expected technical effect of dynamically compensating parameters being obtained at the millisecond level.

[0096] For example, during the construction of the offline index library for the optical mold measurement system, the path signature hash code length is set to 128 bits, and the average size of the compiled expression template binary object is 64KB. A forward mapping record is established between the path signature "0xA17F..." and the template object "OBJ_214", and a reverse mapping entry "OBJ_214"→"0xA17F..." is generated simultaneously. During conflict detection, it is found that the signatures "0xA17F..." and "0xA17F1..." have the same hash code prefix. By comparing the number of nodes and the dynamic sensitivity identifier in the topology features, the signature with fewer nodes and a higher sensitivity level is preferentially retained as the primary index, and the other record is adjusted to the spare linked list. For high-speed access, a linked storage structure is constructed with each storage block size of 256KB. The forward / reverse mapping table is written to the high-speed NVMeSSD in 64KB blocks, and a CRC32 checksum is generated and stored at the end of the block. During persistent encapsulation, three partition indexes are created based on the topology categories of the path signature: "optical path transmission chain sensitive type," "temperature control circuit disturbance type," and "mechanical positioning chain coupling type." During online retrieval, only the partition needs to be located based on the category index, and a single hash lookup is sufficient to retrieve the corresponding 64KB compiled template object. In actual operation, this embodiment achieves online matching and retrieval time of no more than 0.8ms, significantly improving the real-time performance of compensation parameter generation and ensuring stable operation of the index library under heavy load conditions.

[0097] Step S4: The real-time acquired temperature gradient, vibration spectrum amplitude, and air refractive index change rate are used as low-dimensional physical feature variables. The error propagation path signature is input into the mapping index library for matching to obtain the compiled expression template. Specifically, this includes: S4.1: The original analog signals output by the temperature gradient sensor, vibration spectrum analyzer and air refractive index interferometer are synchronously sampled and digitally converted to generate a temperature gradient data stream, vibration spectrum amplitude sequence and air refractive index change rate vector with timestamp alignment, which serve as the basic input data for subsequent feature extraction.

[0098] A unified clock source is set up for the synchronous sampling channel of the raw analog signals collected by the temperature gradient sensor, vibration spectrum analyzer and air refractive index interferometer to ensure that multiple signals are collected under the same time reference and to avoid phase distortion caused by timing deviation.

[0099] A high-precision analog-to-digital converter is used to quantize various analog signals. For temperature gradient signals, an appropriate range and sampling resolution are configured to ensure that the quantization error is lower than the system error budget. For vibration spectrum signals, bandpass filtering is used for preprocessing to remove noise components in irrelevant frequency bands to improve the accuracy of subsequent amplitude extraction. For air refractive index change signals, an interference fringe contrast enhancement algorithm is used for pre-adjustment to reduce measurement instability caused by light signal attenuation.

[0100] In the digital conversion stage, the collected discrete signal sequences are timestamped according to a unified data structure, a hardware phase-locked loop (PLL) is used to correct sampling clock drift, and interpolation is used to achieve compatibility alignment of sampling rates of different sensors.

[0101] For timestamp-aligned data, a window function-based segmentation and slicing process is performed to form a synchronized temperature gradient data stream, a synchronized vibration spectrum amplitude sequence, and a synchronized air refractive index change rate vector, providing an accurate temporal consistency basis for subsequent sliding window statistical analysis and frequency domain energy aggregation.

[0102] By using processing methods such as unified time base sampling, precise analog-to-digital conversion, timestamp alignment, and synchronized slicing, the results of the previous step are transformed into a multi-source physical signal digital stream with time consistency and high quantization accuracy, achieving the expected technical effect of low-error feature extraction.

[0103] S4.2: Based on the temperature gradient data stream, vibration spectrum amplitude sequence and air refractive index change rate vector, perform sliding window statistical analysis and frequency domain energy aggregation processing to extract a set of low-dimensional physical feature variables that characterize the current operating condition. This set includes the normalized temperature gradient scalar, the mean amplitude of the main frequency band vibration spectrum, and the derivative of the instantaneous air refractive index change rate.

[0104] S4.3: Using the currently generated error propagation path signature as the retrieval key, perform hash lookup and similarity matching operations on the mapping index to locate and obtain the compiled lightweight expression template binary code block that completely corresponds to the current error propagation topology.

[0105] The generated error propagation path signature is processed by hash value calculation. The fixed-length string of the path signature is mapped into multiple sets of binary index values ​​in a preset hash function cluster, which are used to initially locate potential matching areas in the mapping index library.

[0106] Extract all candidate path signature entries within the potential matching region obtained by hash positioning, compare the node type label sequence, key error coupling point connection relationship, and dynamic sensitivity identifier of the current path signature with those of the candidate entries, and generate a matching score matrix by using a multi-feature similarity weighted calculation method.

[0107] Normalization is performed on each row of the matching score matrix, and candidate entries with the highest scores that exceed the threshold are selected as precise matching targets based on a preset similarity threshold, ensuring that the error propagation topology of the selected entries is completely consistent with the current path.

[0108] The exact matching target index key value is mapped to its corresponding compiled lightweight expression template binary code block address. The corresponding binary object is read through a high-speed memory access interface, and an encryption integrity check is performed during the reading process to exclude data transmission errors or tampering.

[0109] Based on the integrity verification result, the compiled lightweight expression template binary code block of the current matching operation is output, providing an accurate computational carrier for subsequent low-dimensional physical feature variable injection and dynamic compensation parameter parsing expression generation.

[0110] By using the hash lookup and similarity matching methods described above, the low-dimensional physical feature variable extraction results from the previous step are transformed into computational template data that completely corresponds to the current error propagation topology, achieving millisecond-level response and high-precision matching in the online stage.

[0111] S4.4: Based on the variable placeholder interface defined in the compiled lightweight expression template binary code block, the normalized temperature gradient scalar, the mean amplitude of the main frequency band vibration spectrum, and the derivative of the instantaneous rate of change of air refractive index from the set of low-dimensional physical characteristic variables are injected into the template memory address space in sequence to generate an instance of the dynamic compensation parameter parsing expression to be executed.

[0112] S4.5: Perform syntax tree integrity verification and numerical boundary constraint checks on the instance of the dynamic compensation parameter parsing expression to confirm that the expression structure conforms to the three-level nesting limit and that all input variables are within the safe value range. The final output is an executable dynamic compensation parameter parsing expression object that can be used for real-time calculation.

[0113] The instance of the dynamic compensation parameter parsing expression to be executed is loaded into the syntax tree cache of the symbol resolution module. A tree traversal algorithm is invoked to sequentially access each operation node, checking whether the parent-child node reference relationship points to a valid operator definition table to verify structural integrity. Nesting depth counting is performed on nested links encountered during traversal. The nesting level is compared with a three-level nesting threshold using a depth limit checker. If excessive nesting is detected, it is automatically marked as a redundant branch and moved to the pruning queue. A safe value range scan is performed on all variable leaf nodes. A boundary constraint checker is invoked to compare the current values ​​of the normalized temperature gradient scalar, the mean amplitude of the dominant frequency band vibration spectrum, and the derivative of the instantaneous rate of change of air refractive index with preset upper and lower limits. Values ​​exceeding the range are replaced with critical boundary values ​​before execution. The syntax tree that has passed integrity checks, nesting level determination, and numerical boundary constraints is reconstructed into a standardized compensation operation tree object, generating an executable dynamic compensation parameter parsing expression object that can be directly parsed by a real-time numerical calculator.

[0114] By employing methods such as structural traversal, nesting depth determination, and numerical boundary constraints, the variable injection results from the previous step are transformed into executable analytical expressions for compensation parameters that satisfy industrial control rules, thereby achieving high-precision and secure real-time calculation of dynamic compensation parameters.

[0115] For example, in the dynamic dimension calibration system for optical molds, the analytical expression instance of the compensation parameters with injected low-dimensional physical feature variables has undergone syntax tree integrity verification. The structure depth count value containing three nested layers is 3, which does not exceed the preset limit. The normalized temperature gradient scalar value is 0.82, with an upper limit of 1.00 and a lower limit of 0.00; the mean amplitude of the dominant frequency band vibration spectrum is 0.015, with upper and lower limits of 0.020 and 0.000, respectively; the derivative of the instantaneous rate of change of air refractive index is... 0.004, upper limit 0.005, lower limit 0.005, all within the safe range. During the verification process, the nesting depth determiner and boundary constraint checker are executed according to the formula... in This represents the maximum nesting depth. These are the depth counts of the subtrees containing the three types of input variables, ensuring that the maximum value does not exceed three levels; numerical boundary constraints are implemented according to... in The current value of the variable. As the lower limit, The upper limit is set by an inner `max` layer to ensure the value is not lower than the lower limit, and the outer `min` layer to ensure the value is not higher than the upper limit, thus achieving a safety constraint. After the above verification and correction, the parsed expression object can output dynamic compensation values ​​in the real-time calculator with a millisecond-level delay, significantly improving the stability and interpretability of the compensation algorithm.

[0116] Step S5: Inject low-dimensional physical feature variables based on the compiled expression template, and perform symbolic resolution operations to generate analytical expressions for compensation parameters. Specifically, this includes: S5.1: Load the syntax tree structure of the compiled expression template to obtain an initial symbol resolution architecture containing the index of the predefined basic mathematical operator library and three-level nested constraint information, providing a standardized operational skeleton for subsequent variable injection.

[0117] The compiled lightweight expression template retrieved from the mapping index library undergoes memory structure parsing, mapping binary template code fragments to a symbolic representation domain, and extracting the predefined basic mathematical operator library call indexes embedded in the template. Based on the operator call indexes parsed from the symbolic representation domain, an initial operation tree skeleton containing all operator nodes, variable placeholder nodes, and constant nodes is constructed, with the node connections corresponding to the logical execution order of the template. The nesting relationships in the initial operation tree skeleton are traversed hierarchically, detecting and marking all node links with a nesting depth exceeding three levels, and writing their path information into a nesting constraint check table for reference in subsequent verification. Combining the path information in the nesting constraint check table with the variable placeholder positions defined in the template structure, a complete symbolic resolution architecture with attached hierarchical constraint metadata is generated. The operator indexes in the basic mathematical operator library corresponding to each operator node are marked in the symbolic resolution architecture, forming a processing model with a standardized operation skeleton. This processing model transforms the executable dynamically compensated parameter parsing expression object from the previous step into an initial symbolic resolution architecture with operator indexes and nesting constraint information, achieving structured control and interpretability guarantees for the subsequent variable injection process.

[0118] For example, in an optical mold size calibration system, low-dimensional physical characteristic variables include a normalized temperature gradient scalar with a value of 0.0025, a mean amplitude of the dominant frequency band vibration spectrum with a value of 1.35, and a derivative of the instantaneous rate of change of air refractive index with a value of [missing value]. Under the 0.0008 operating condition, the binary code fragment of the compiled lightweight expression template contains three types of nodes: linear combination operator index 2, piecewise threshold operator index 5, and time-delay differential operator index 7. During memory structure parsing, this binary code fragment is converted into a symbolic representation domain, and an initial computation tree skeleton is constructed based on the operator indices. The root node is the linear combination operator, the first-level child nodes are the piecewise threshold operator and the time-delay differential operator, and the second-level child nodes are variable placeholders. A hierarchical traversal of this skeleton reveals no nested links exceeding three levels, and the nesting constraint check table is empty. In the symbolic resolution architecture, the root node is labeled with index 2, and the first-level nodes are labeled with indices 5 and 7. The variable node labels are consistent with the template definition. The resulting initial symbolic resolution architecture can directly map the aforementioned low-dimensional physical feature variables to their corresponding leaf nodes in subsequent steps and call operators to execute computational links, generating a parsing expression that conforms to the compensation parameters. Under this operating condition, the numerical solution of the system's compensation output significantly improves compensation accuracy while maintaining low computational latency.

[0119] S5.2: Based on the variable placeholders in the initial symbolic resolution architecture, the three types of low-dimensional physical feature variables, namely the real-time collected temperature gradient, vibration spectrum amplitude and air refractive index change rate, are mapped to the corresponding leaf nodes to generate a symbolic computation tree to be instantiated carrying real-time operating data.

[0120] S5.3: Utilize the connection relationships between nodes in the symbolic operation tree to be instantiated, call the linear combination, segmented threshold, or time-delay differential operators in the predefined basic mathematical operator library to perform local logical deduction on the data of adjacent nodes, so as to construct an intermediate state compensation calculation link with complete operation logic.

[0121] Based on the uninstantiated symbolic computation tree node structure carrying real-time operating data, the directed connection relationship between any parent node and its direct child nodes is identified, and this relationship is mapped to a local operator call dependency table. For node groups marked as multivariate linear combinations in the dependency table, linear combination operators from the predefined basic mathematical operator library are called to perform matrix multiplication operations in the order of coefficient matrix and variable vector, forming a linear superposition output value that is passed to the upper-level parent node. For node groups marked as threshold judgment types in the dependency table, the piecewise threshold operator is called to perform interval division processing on the input variables and replace them with specified control constants in each interval, realizing the piecewise logic mapping of error triggering conditions. For node groups marked as time series processing types in the dependency table, the time-delay difference operator is called to extract historical values ​​of variables according to the set time-delay step size and calculate the difference results to reflect dynamic change trends and provide them for upper-level nodes to perform secondary combination operations. The outputs of the three types of local operators mentioned above are aggregated through a bottom-up recursive combination process driven by dependency tables to construct an intermediate state compensation calculation link with complete computational logic. This link can be directly expanded into a symbolic resolution execution instruction sequence in a third-party industrial control system, and the dynamic compensation capability of the error propagation path can be realized through local logic deduction.

[0122] S5.4: Based on the three-level nested hierarchy constraint information, the intermediate state compensation calculation link is deeply verified and pruned for optimization. Redundant branches that exceed the limit of the total number of operators or the nesting level are eliminated to generate standardized compensation parameter analytical expressions that conform to the semantic specifications of industrial control.

[0123] S5.5: Based on the standardized analytical expression of compensation parameters, perform the final numerical calculation operation to quantify the coupling error of the optical path transmission chain, temperature control loop and mechanical positioning chain into specific dynamic compensation values, so as to output the final analytical expression of compensation parameters that can directly drive the actuator of the optical mold calibration system.

[0124] The standardized compensation parameter analytical expression conforming to the industrial control semantic specification is used as the input for symbolic computation. The corresponding mathematical operator index is loaded to establish the execution order of the computation nodes. For each node in the optical path transmission chain, the physical parameters are matched with variable identifiers in the expression, and the piecewise threshold and proportional-integral mapping operators are called to form the node calculation sequence. Based on the real-time temperature gradient variable of the temperature control loop and the vibration spectrum variable of the mechanical positioning chain, a time-delay differential operator is executed in the symbolic tree to eliminate the effect of phase drift. For the air refractive index change rate variable, a linear combination operator and a normalization operator are combined in the computation chain to perform amplitude correction, ensuring the stability of the calculation process. The calculation results of all nodes are aggregated at the root node of the symbolic tree, and the final dynamic compensation amount is calculated using the following mathematical expression: in, For dynamic compensation amount, The sensitivity weights for each error source are... The low-dimensional physical characteristic variables are injected. The Δ value is embedded into the analytical expression of the final compensation parameter, generating a control command dataset that can be directly invoked by the actuator of the optical mold calibration system. Through numerical calculation, the result of the previous step is transformed into a dynamic compensation value containing multi-link coupling errors, achieving high-precision and low-latency compensation control.

[0125] For example, in the optical mold measurement system, the real-time acquired normalized temperature gradient is 0.0008 K / mm, the average amplitude of the dominant frequency band vibration spectrum is 0.002 mm, and the derivative of the instantaneous rate of change of air refractive index is 5 × 10⁻⁶. -7 The combined variables are injected into the standardized compensation parameter analytical expression, setting the weights as follows: optical path transmission chain sensitivity w1 = 1.5, temperature control loop weight w2 = 2.1, mechanical positioning chain weight w3 = 1.2, and air refractive index variation coefficient weight w4 = 0.9. Numerical calculations are performed using the above formulas, yielding Δ≈0.00682mm. This value is then output to the calibration system's actuator drive interface. Actual verification shows that under continuous operation conditions, this compensation amount significantly improves the stability of optical mold size calibration and keeps the system calculation delay within 1ms, meeting the requirements for ultra-high precision, low-delay calibration.

[0126] It should be noted that the predicted residual refers to the theoretically expected residual data pre-calculated through symbolic analysis operations based on the analytical expression of the compensation parameters, after injecting the low-dimensional physical feature variables at the current moment. This predicted residual is used to compare with the measured residual to verify the reliability of the compensation model.

[0127] Step S6: Calculate the dynamic compensation amount based on the analytical expression of the compensation parameters, and perform parameter correction control on the actuator of the optical mold calibration system to generate measured residual data. Specifically, this includes: S6.1: Inject real-time low-dimensional physical characteristic variables into the analytical expression of the compensation parameters and perform symbolic analysis operations to generate a dynamic compensation quantity numerical sequence containing linear combination and time-delay difference operators.

[0128] The final compensation parameter analytical expression output in step S5.5 is used as the input for computation, and the computation node index of the expression is loaded into the symbolic parser. Based on the mapping relationship of the placeholders of each variable, the temperature gradient scalar, the mean amplitude of the main frequency band vibration, and the derivative of the instantaneous rate of change of air refractive index are sequentially injected into the memory data slots of the corresponding leaf nodes. For the symbolic analytical expression of the injected variables, the predefined linear combination operator and time-delay difference operator are called, and local operations are performed according to the node connection order of the expression structure, and then aggregated upwards to form a complete dynamic compensation computation chain. For the linear combination part, the compensation amount is calculated according to the product of the coefficient matrix and the variable vector, for example: in For compensation amount, For normalized temperature gradient scalar, The average amplitude of the vibration spectrum in the main frequency band. The derivative of the instantaneous rate of change of the air refractive index. , , The coefficients are defined for the template. For the time-delay differencing part, the difference operation is performed on the variable sequence according to a fixed time-delay step size. The difference formula is: in The result is a time-delay difference. The value of the variable at the current moment. For lag The variable values ​​at each time step are calculated. The calculated linear combination output and the time-delay differential output are weighted and synthesized according to the operator rules of the analytical expression to generate a continuous sequence of dynamic compensation values. Through the above symbolic resolution and node-by-node operation processing, the analytical expression of the previous step is transformed into a sequence of dynamic compensation data containing linear combination and time-delay differential, realizing the real-time quantification of multi-source physical disturbances.

[0129] For example, a compiled expression template is loaded into the symbol resolver, and the template definition... =1.2、 = 0.8 =0.5, time delay step Δt is set to 2ms. The real-time acquired temperature gradient scalar T is 0.0035, the average amplitude of the dominant vibration frequency V is 0.0020, and the derivative of the rate of change of air refractive index R is... The result calculated using the linear combination formula is 0.0024. For the time-delay differential part, the average amplitude V of the current dominant vibration frequency is 0.0020, and the value at a 2ms delay is 0.0015. The differential value is calculated to be 0.0005. The linear combination result and the differential value are synthesized according to the expression structure. The resulting dynamic compensation numerical sequence significantly improves the compensation response speed and maintains numerical stability under rapid disturbance scenarios with multiple physical characteristics. Verification shows that this sequence can continuously maintain the system size error within the micrometer range under multiple operating conditions.

[0130] S6.2: Based on the numerical sequence of dynamic compensation, perform inverse kinematics calculation processing in the field of industrial control to generate a mechanical positioning chain displacement instruction set adapted to the actuator of the optical mold calibration system.

[0131] S6.3: Use the mechanical positioning chain displacement instruction set to perform closed-loop servo drive control on the multi-axis precision motion platform to complete the physical parameter correction actions of the optical path transmission chain and temperature control circuit.

[0132] The input conditions include the mechanical positioning chain displacement instruction set generated by the S6.2 inverse kinematics solution, and the servo drive control interface status information of the optical mold multi-axis precision motion platform.

[0133] The displacement instruction set is loaded into the multi-axis motion controller buffer, and a synchronous execution channel is created to ensure that the trigger time of each axis instruction remains synchronized at the nanosecond level.

[0134] Based on the displacement command quantities of different axes, the servo position loop gain is adaptively adjusted. The correction coefficient is calculated using real-time feedback data of position error. The built-in speed planning module of the controller is called to perform trapezoidal acceleration and deceleration calculations on the displacement curves of each axis, keeping the acceleration and jerk limit during the motion process within the hardware rated range.

[0135] During execution, real-time data from sensors related to the optical transmission chain are used to apply pre-adjustment control to the execution unit of the temperature control loop, converting temperature deviation into a small compensation displacement of the mechanical positioning chain. Dynamic physical parameter correction is achieved by fusing servo control with the temperature control loop control signal.

[0136] The status bits of each axis after execution and the real-time error data collected by the sensors are encapsulated into a feedback packet and returned to the upper-level compensation algorithm module.

[0137] By linking closed-loop servo drive control with physical parameter correction, the displacement command set of the previous step is transformed into synchronously executed mechanical adjustment actions and temperature control state correction, thereby achieving parameter optimization of the optical path transmission chain and temperature control loop.

[0138] S6.4: After the parameter correction is completed, a non-contact laser interferometer is used to acquire high-precision data on the surface of the optical mold to obtain a multi-point coordinate measurement raw data stream that reflects the current size status.

[0139] S6.5: Compare and calculate the deviation between the original data stream of multi-point coordinate measurements and the nominal values ​​of the standard design model to generate measured residual data for subsequent reliability verification.

[0140] The raw data stream of multi-point coordinate measurements output from a non-contact laser interferometer is used as the input dataset. A standard design model nominal value matrix of the corresponding optical mold is loaded as a comparison benchmark to establish a spatial consistency mapping relationship between the measurement coordinate system and the design coordinate system. The raw data stream undergoes time-stamp and sampling position synchronization preprocessing. Coordinate values ​​of different measurement points are paired with nominal values ​​according to the measurement point index, forming a set of matched coordinate pairs. For each pair of data in the set of matched coordinate pairs, a single-point deviation vector is obtained using coordinate difference calculation. The components of the deviation vector are equal to the differences between the measured value and the nominal value along each axis. The obtained set of single-point deviation vectors undergoes vector norm calculation to convert it into an absolute deviation amplitude sequence. Statistical features of this sequence are extracted, including maximum deviation, mean deviation, and variance deviation indices.

[0141] Using the mean square residual calculation method, the following calculations are performed on the deviation amplitude data of all measuring points: in, These are the measured coordinate values. For the corresponding nominal coordinate values, Given the total number of measurement points, the above formula sums the squared deviations for each measurement point and divides by the number of measurement points minus one to obtain the global mean square residual index. The mean square residual index is then integrated with the deviation amplitude sequence to generate a multidimensional measured residual feature vector, which is then encoded to form a structured measured residual data object.

[0142] By using multi-point deviation vector component statistics and global mean square residual calculation, the surface size of the optical mold after parameter correction is transformed into structured measured residual data that can be used for subsequent reliability verification, thereby achieving standardized quantification of error characteristics.

[0143] For example, in an optical mold calibration scenario, a non-contact interferometer collects three-dimensional coordinate data from 200 measurement points. Each measurement point contains measured values ​​in the x, y, and z directions, in micrometers. The nominal value matrix of the design model also contains nominal values ​​in the three directions. After timestamp alignment and spatial mapping, the measurement point indices are perfectly matched. Differential operations are performed on the coordinate values ​​in each direction to obtain the deviation components in each direction. For example, the average deviation in the x direction is 0.4 μm, the average deviation in the y direction is 0.3 μm, and the average deviation in the z direction is 0.5 μm. The single-point deviation amplitude is calculated using vector norm, ranging from 0.2 μm to 1.0 μm. The amplitude sequence is input into the mean square residual formula for calculation, yielding a global mean square residual of 0.56 μm. After statistical feature extraction, the maximum deviation amplitude is 1.0 μm, the mean is 0.45 μm, and the variance is 0.07 μm². The output measured residual data object includes the average deviation value, amplitude statistical characteristics and global mean square residual index in the above three directions. After encoding and compression, a standardized residual feature vector for closed-loop credibility verification is generated, which significantly improves the accuracy and stability of subsequent symbol consistency comparison in practical applications.

[0144] Step S7: Verify the reliability of the measured residual data and the predicted residual data, determining whether the signs, monotonicity, and extreme point positions match, and generate the verification result. Specifically, this includes: S7.1: Perform time axis alignment processing on the measured residual sequence fed back by the actuator of the optical mold calibration system and the predicted residual sequence output by the analytical expression of the compensation parameters to eliminate the phase misalignment caused by the sampling clock deviation and generate a synchronized residual comparison dataset.

[0145] S7.2: Perform point-by-point sign bit extraction operation based on the synchronized residual comparison dataset to obtain the measured residual sign vector and the predicted residual sign vector respectively, and determine the consistency of the positive and negative signs of the two through logical XOR operation to generate a positive and negative sign matching index.

[0146] S7.3: Calculate the first-order difference slope sequence using the synchronized residual comparison dataset, construct the measured residual monotonicity feature curve and the predicted residual monotonicity feature curve respectively, and use the dynamic time warping algorithm to quantify the morphological similarity of the two curves to generate a monotonicity trend consistency index.

[0147] First-order difference operations are performed on the time series in the synchronized residual comparison dataset to obtain the rate of change sequence of residual values ​​of adjacent sampling points as the basis for slope calculation.

[0148] Based on the rate of change sequence, monotonicity characteristic curves of measured residuals and predicted residuals are constructed respectively. By establishing a clear time series correspondence between the data points of each curve, the comparability of curve morphology characteristics is achieved.

[0149] A dynamic time warping algorithm is used to perform nonlinear time axis scaling matching on two monotonic feature curves. In this process, the local slope difference of each pair of matching points is calculated and accumulated to generate a global morphological deviation matrix.

[0150] The path cost minimization process is performed using the morphological deviation matrix to extract the overall curve similarity value corresponding to the optimal time mapping path, and this similarity value is used as the initial index of monotonicity trend consistency.

[0151] By setting a similarity threshold based on historical operating data, the initial index is normalized and mapped to generate the final monotonicity trend consistency index for closed-loop credibility verification.

[0152] By using slope calculation and dynamic time warping, the synchronized residual comparison dataset from the previous step is transformed into a quantitative monotonicity trend consistency index, enabling an accurate assessment of the consistency of the compensation model in terms of time series morphology.

[0153] S7.4: Perform extreme point search processing on the synchronized residual comparison dataset, identify the set of coordinates of local maxima of the measured residual and the set of coordinates of local maxima of the predicted residual, calculate the mean Euclidean distance between the two sets of coordinates, and generate an extreme point position offset index.

[0154] S7.5: Combining the positive and negative sign matching index, the monotonicity trend consistency index, and the extreme point position offset index, Boolean logic aggregation operation is performed according to the preset multi-dimensional threshold judgment rules to output the verification result representing the credibility state of the compensation model.

[0155] Given inputs including a positive / negative sign matching index, a monotonicity trend consistency index, and an extreme point position offset index, the weight parameters of each index in the multidimensional threshold determination rule are loaded and processed to form an executable threshold determination matrix as the initial operator configuration for Boolean logic aggregation.

[0156] The sign matching index is compared with a preset sign direction threshold to generate a binary sign consistency determination result, and the result is mapped to the sign determination component of the logic matrix.

[0157] The difference between the monotonicity trend consistency index and the preset monotonicity correlation threshold is calculated and symbolized to form a binary judgment value that represents the consistency of the curve trend. This value is then injected into the monotonicity judgment component of the logic matrix.

[0158] The Euclidean distance threshold judgment function is called on the extreme point position offset index to compare its size with the set offset tolerance, output the binary judgment value of low offset and high offset, and inject the value into the extreme value judgment component of the logic matrix.

[0159] The three decision components are aggregated in the logic matrix according to the multi-dimensional threshold rule using Boolean operators. The Boolean operators are constructed according to the industrial control reliable state determination logic. For example, the AND operator is used for full match determination, the OR operator is used for partial match allowance determination, and the NOT operator is used for reverse anomaly elimination determination.

[0160] The final closed-loop credibility state value is generated by aggregating the results using Boolean logic and then output to the subsequent adaptive repair mechanism to complete the verification result generation of the credibility state of the compensation model.

[0161] By using multi-dimensional threshold determination and Boolean logic aggregation processing, the result of the previous step is transformed into a state value that can directly drive the closed-loop reliability determination logic, thereby achieving accurate reliability assessment of the compensation model under dynamic operating conditions.

[0162] For example, during the optical mold calibration process, the threshold values ​​for the positive and negative sign matching degree index are set to 0.9, the threshold values ​​for the monotonicity trend consistency index are set to 0.85, and the threshold values ​​for the extreme point position offset are set to 0.02 mm. When the calculated value of the positive and negative sign matching degree is 0.92, a binary judgment value of 1 is obtained through comparison calculation; when the calculated value of the monotonicity trend consistency is 0.81, the judgment value is 0; and when the calculated value of the extreme point offset is 0.015 mm, the judgment value is 1. The component vector of the constructed logic matrix is ​​[1,0,1]. Under the AND operator aggregation, the output closed-loop confidence state value is 0, and under the OR operator aggregation, the output state value is 1. Finally, the AND aggregation result is selected as the repair trigger condition in the control logic. A state value of 0 indicates that the confidence verification has failed, triggering path re-identification. This verifies that the method can significantly improve the fault detection accuracy and dynamic response capability under actual working conditions.

[0163] Step S8: If the verification result fails three times consecutively, path re-identification is triggered and template replacement is performed to generate an updated error propagation path signature to re-drive the compensation parameter generation process. Specifically, this includes: S8.1: Perform fault mode classification processing on the verification results that are judged as failed three times in a row, so as to extract the abnormal feature vector that caused the credibility verification to fail, and generate a fault diagnosis label set containing the attributes of sign reversal, monotonicity deviation and extreme point offset.

[0164] Based on the input state that all three consecutive verification results indicate failure, the synchronized residual comparison dataset is used as the original data source for fault feature extraction. Multi-dimensional feature vector construction is performed on the positive / negative sign matching index, monotonicity trend consistency index, and extreme point position offset index in this dataset to form a high-dimensional fault analysis matrix containing three key error feature components. The element-wise difference is calculated using each dimension feature of the multi-component matrix and the standard pattern template in the preset fault mode library to obtain the deviation sequence of each index, which is then normalized to provide a balanced dimensional input for subsequent abnormal pattern clustering. A weighted Euclidean distance metric is used to calculate the distance between the normalized deviation sequence and the center vectors of various abnormal patterns. The calculation formula is as follows: in, The weighted Euclidean distance from the current data to the center of the k-th type of failure mode is given by [reference to data type]. For the first The weight coefficients of each feature, The fault analysis matrix is ​​the first one. 1 eigenvalue, For the first The eigenvalue of the class pattern center in the i-th dimension. The number of features. Based on the calculated D k The fault mode category corresponding to the minimum value is tagged, and the matching fault mode identifier is written into the fault diagnosis tag set. Attribute expansion processing is performed on the tag set, adding parameters such as the specific occurrence time and influence radius of the corresponding pattern's sign reversal, monotonicity deviation, and extreme point offset, to enhance the positioning accuracy of subsequent reverse semantic deconstruction. Through fault mode classification and tag construction, the credibility verification failure result from the previous step is transformed into a precise fault diagnosis tag set that can be used as input for path signature re-identification, achieving patterned description and traceable positioning of abnormal operating conditions.

[0165] For example, in a calibration cycle of an optical mold measurement system, the sign matching index is 0.35, 0.28, and 0.31 in three consecutive operating conditions, the monotonicity trend matching index is 0.42, 0.39, and 0.40, and the extreme point position offset index is 2.8, 3.1, and 2.9, respectively. After constructing a high-dimensional fault analysis matrix from these indices and normalizing it, the weight coefficients are set to w1=0.5, w2=0.3, w3=0.2, the number of features p=3, and the pattern center vector c... ( 1, 1) =0.9、c ( 1, 2) =0.95, c ( 1, 3)=0.1. Substituting into the formula to calculate the distance value of the first type of fault mode, we get D1≈0.715; after calculating the distance of other modes, we find that D1 is the smallest, and we determine that this condition corresponds to the sign reversal mode. We add the tag set to the system, indicating that the effective radius of this mode in the optical path transmission chain is 12 nodes, the affected period is the second half of the current cycle, and the extreme point offset occurs between node 5 and node 7 of the temperature control loop. We then execute the transfer of this fault mode tag set to S8.2, and the system uses this to locate and remove the corresponding secondary disturbance branches, achieving accurate and automated path signature re-identification.

[0166] S8.2: Perform reverse semantic deconstruction processing on the current error propagation path signature based on the fault diagnosis label set, so as to remove the secondary disturbance branches affected by abnormal operating conditions and recalculate the sensitivity weight of the dominant error propagation trunk path, and generate the intermediate error propagation semantic tuple to be updated.

[0167] S8.3: The intermediate error propagation semantic tuple to be updated is used to drive the hierarchical clustering algorithm to perform redundant compression and reconstruction processing, so as to identify new error coupling key points and remove failed path nodes, and generate updated error propagation path signatures.

[0168] S8.4: Perform fuzzy matching retrieval processing in the mapping index based on the updated error propagation path signature to locate the backup expression template with the highest adaptability to the current fault mode and generate a set of candidate local replacement templates.

[0169] Based on the updated error propagation path signature, the index structure of the mapping index library is retrieved from the high-speed storage medium as the retrieval object. A shift perturbation and multi-bit XOR operation are performed on the hash code value of this signature to generate multiple sets of approximate codes, expanding the candidate retrieval range to accommodate slight drifts in path features under failure modes. The above set of approximate codes is input into the fuzzy matching engine, and the similarity calculation module based on edit distance is invoked to obtain the difference index between the template index key and the currently updated path signature. This difference index is calculated using the following formula: in, This represents the edit distance function. Sign the current update path. For template index key, The signature length is specified. In the matching result set, based on the feature sensitivity weights defined in the fault diagnosis label set, the similarity index is weighted and adjusted to generate a comprehensive fit score set. The score set is sorted in descending order, and the top N highest-scoring template numbers are extracted. The physical storage address of the corresponding compiled template object is located by calling the association mapping relationship. The template object is loaded into a temporary buffer, and the priority label of the compensation operator corresponding to the fault mode is attached, generating a candidate local replacement template set containing N alternative options. Through the above fuzzy matching and multi-dimensional scoring processing, the path signature updated in the previous step is transformed into a candidate template set with the highest fit to the current fault mode, achieving rapid location and extraction of alternative compensation strategies.

[0170] For example, in the operating conditions of the optical mold measurement system, the updated error propagation path signature code length is 128 bits, and the index library contains 5000 compiled template objects. The displacement perturbation range during approximate code generation is set to ±4 bits, the number of XOR masks is 3, and the total number of generated approximate codes is 12. In the edit distance calculation, it is set... =128, the edit distance between a template index key and the current path signature. =8, then the matching degree is approximately 0.061. In the fault diagnosis label set, the weight for sign reversal is set to 0.5, the weight for monotonicity deviation is set to 0.3, and the weight for extreme point offset is set to 0.2. After the comprehensive score is adjusted according to the weighted formula, the template objects corresponding to the top 5 highest-scoring template numbers are taken, read from high-speed solid-state storage into a temporary buffer, and marked with priority to use linear combination operators are added to form a candidate local replacement template set. After replacing the original failed template with this set, the system compensation effect is significantly improved, and the residual extreme value offset after compensation is greatly reduced.

[0171] S8.5: Perform numerical stability verification and hardware compilation based on the candidate local replacement template set to select the optimal compensation strategy and complete hot-loading replacement, generating the final updated error propagation path signature for re-driving the compensation parameter generation process.

[0172] The input condition for the candidate local replacement template set is the set of binary object candidates with the highest fit to the current fault mode, identified in step S8.4, and possessing a symbolic logic structure under three-level nested constraints. For this input set, a full-condition numerical stability verification process is first performed on each candidate template. This is achieved by injecting a physical parameter vector covering extreme boundary conditions such as temperature gradient, vibration spectrum amplitude, and air refractive index change rate during the computation process, calculating the template's output divergence index over the time series. The root mean square error (RMSE) is used as the basic metric for stability evaluation, and its calculation formula is as follows: in This represents the output compensation value of the template under the corresponding working conditions. This is the target compensation value under this working condition. The number of sampling points is used. Based on the RMSE value output by the formula, a subset of templates with good convergence and divergence below a preset threshold is selected. Then, target hardware compilation is performed on this stable template subset, translating the symbolic computation structure that conforms to nesting and variable number constraints into binary instruction fragments adapted to the processor architecture of the optical mold calibration system. During compilation, an instruction scheduling strategy optimized for register latency and cache coherency is inserted. After compilation, a hot-loading feasibility test is performed on all generated binary instruction fragments to ensure that they can immediately replace existing templates under continuous system operation without triggering the actuator's safety protection mechanism. Through the above numerical stability verification and hardware instruction set compilation processing, the candidate local replacement template set from the previous step is transformed into the final optimal compensation strategy template, verified by both stability and compatibility. This template is then hot-loaded and replaced in the current operating environment, generating the final updated error propagation path signature used to re-drive the compensation parameter generation process, achieving rapid self-healing capability in fault modes.

[0173] For example, in a certain optical mold measurement system, three candidate local replacement templates have been located using S8.4, with a three-layer nested calculation depth, four variables for each layer, and nine, ten, and eight operators respectively. During the numerical stability verification phase, the injection temperature gradient was set to ±85℃, the vibration spectrum amplitude to 2.5g, and the air refractive index change rate to ±3×10⁻⁶. -7 The boundary conditions were set with 500 sampling points. Based on the RMSE formula, the RMSE of the first template was 0.45, the second was 1.02, and the third was 0.38. The first and third templates were selected for compilation. Hardware compilation employed a specific DSP architecture optimization, mapping multiply-accumulate operations to hardware MAC instructions and inserting cache consistency maintenance instructions, generating binary code segments of 128 bytes and 112 bytes respectively. Hot-loading feasibility testing showed that both templates could replace the original templates without interrupting system operation, and the dynamic compensation calculation time remained within 0.8ms after replacement. Finally, after loading the third template, updating the error propagation path signature, and re-driving the compensation parameter generation process, the measured residual convergence speed was significantly improved, and system stability was significantly enhanced.

[0174] For those skilled in the art, various other corresponding changes and modifications can be made based on the technical solutions and concepts described above, and all such changes and modifications should fall within the protection scope of the claims of this invention.

[0175] Unless otherwise defined, the technical or scientific terms used herein shall have the ordinary meaning as understood by one of ordinary skill in the art to which this application pertains. The terms “first,” “second,” “third,” and similar terms used in this patent application specification and claims do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, the terms “an” or “a” and similar terms do not indicate a quantity limitation, but rather indicate the presence of at least one. The terms “comprising” or “including” and similar terms mean that the element or object preceding “comprising” or “including” encompasses the element or object listed following “comprising” or “including” and its equivalents, and do not exclude other elements or objects. The “multiple” mentioned in the embodiments of this application refers to two or more. A and / or B indicate three possibilities: A; B; and A and B.

[0176] The above description is merely an exemplary embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and such modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for ultra-high precision dimensional calibration of optical molds, characterized in that, include: S1: Obtain the topological information of the optical path, temperature control and mechanical positioning chain in the optical mold measurement system, extract the type, direction, phase and intensity level of the error source in each link, and generate error propagation semantic tuples; S2: Perform clustering compression based on the error propagation semantic tuple, identify the dominant error propagation trunk path and secondary disturbance branches, and generate error propagation path signatures; S3: Utilize historical operating condition data to construct a mapping relationship between path signatures and expression templates, perform numerical stability verification and hardware compilation on candidate templates, and generate a mapping index library; S4: Use the real-time collected temperature gradient, vibration spectrum amplitude and air refractive index change rate as low-dimensional physical feature variables, and input the error propagation path signature into the mapping index library for matching to obtain the compiled expression template; S5: Inject the low-dimensional physical feature variables based on the compiled expression template, and perform symbolic resolution operation to generate a compensation parameter analytical expression; S6: Calculate the dynamic compensation amount based on the analytical expression of the compensation parameters, and perform parameter correction control on the actuator of the optical mold calibration system to generate measured residual data; S7: Verify the reliability of the measured residual data and the predicted residual, determine whether the positive and negative signs, monotonicity and extreme point positions match, and generate the verification result; S8: If the verification result is determined to be a failure three times in a row, the path re-identification is triggered and the template replacement operation is performed to generate an updated error propagation path signature to re-drive the compensation parameter generation process.

2. The method for ultra-high precision size calibration of optical molds according to claim 1, wherein, Step S2 specifically includes: The error action direction parameter and temporal phase parameter in the error propagation semantic tuple are processed by vector space mapping to construct an initial error propagation topology graph that represents the spatiotemporal coupling relationship of multi-source errors. This graph contains node error intensity level index and edge connection weight attribute, which serves as the underlying data structure basis for subsequent clustering analysis. Based on the edge connection weight attributes in the initial error propagation topology graph, an adaptive hierarchical clustering algorithm is executed to calculate the correlation density coefficient between adjacent error source nodes and generate a hierarchical cluster structure, thereby aggregating discrete single-point error sources into a statistically significant set of error propagation clusters, achieving preliminary merging and dimensionality reduction of error propagation paths. The principal component contribution rate evaluation process is performed by utilizing the distribution characteristics of the error influence intensity level index within each cluster in the error propagation cluster set to quantify the sensitivity weight of each potential propagation path to the overall calibration residual, thereby screening out the dominant error propagation backbone path whose cumulative contribution rate exceeds a preset threshold, while marking secondary disturbance branches below the threshold to be removed. Topology pruning and redundancy compression are performed on the identified dominant error propagation backbone path and the secondary disturbance branches to be removed, in order to remove the secondary disturbance branch nodes with low sensitivity weights and merge the series homogeneous error links, generating a simplified error propagation skeleton diagram that retains only the key error coupling points and core transmission links, which greatly reduces the computational complexity of path representation. Based on the node type label sequence and the connection relationship of key error coupling points in the simplified error propagation skeleton graph, fixed-length hash encoding is performed to convert the variable-length topology information into the error propagation path signature containing path topology features, dynamic sensitivity identifiers, and key node fingerprints.

3. The method for ultra-high precision size calibration of optical molds according to claim 1, wherein, Step S3 specifically includes: A correlation analysis was performed on the multi-stage measurement error records and corresponding optical mold calibration residual data in the historical working condition dataset. The error propagation path signature corresponding to each group of data was extracted as a key value identifier. Clustering and grouping processing was performed based on the error propagation path signature to generate a set of path signature clusters with statistical significance. Based on typical sample data in the path signature cluster set, the linear combination operator, piecewise threshold operator and time delay difference operator in the predefined basic mathematical operator library are called to perform permutation and combination operations to generate a set of candidate compensation parameter analytical expression templates covering different error coupling modes. For each candidate compensation parameter analytical expression template in the candidate compensation parameter analytical expression template set, a full-condition numerical stability verification process is performed. By injecting extreme temperature gradients and vibration spectrum amplitude boundary conditions, the divergence index is calculated and output to screen out a subset of stable candidate compensation parameter analytical expression templates that meet the convergence requirements of industrial control. Based on the subset of the stable candidate compensation parameter parsing expression template, the target hardware compilation operation is performed to convert the symbolic logic that conforms to the three-level nesting constraint into binary machine code fragments that can be directly executed by the underlying processor, so as to generate a compiled expression template binary object with millisecond-level response capability. The error propagation path signature is used as an index key to establish a bidirectional mapping association with the compiled expression template binary object, and the mapping relationship is written to a high-speed storage medium for persistent storage, thereby generating the mapping index library.

4. The method for ultra-high precision size calibration of optical molds according to claim 1, wherein, The generation of the error propagation semantic tuple includes: performing topology analysis, error source identification, direction timing extraction, and intensity quantization on the optical path transmission chain, temperature control circuit, and mechanical positioning chain, and then encapsulating and generating the error propagation semantic tuple.

5. The method for ultra-high precision size calibration of optical molds according to claim 1, wherein, The process of obtaining the compiled expression template includes: extracting low-dimensional physical feature variables by synchronously sampling temperature gradient, vibration spectrum and refractive index change rate; obtaining the compiled template by matching the error propagation path signature hash with the offline library; injecting the feature variables; verifying and then outputting the executable expression object.

6. The method for ultra-high precision dimensional calibration of optical molds according to claim 1, wherein, The process of generating the analytical expression for compensation parameters includes: mapping real-time feature variables to syntax tree nodes, performing logical deduction by calling linear combination, segmented threshold, or time-delay differential operators, and generating the analytical expression for compensation parameters after optimization based on three-level nested constraint pruning.

7. The method for ultra-high precision size calibration of optical molds according to claim 1, wherein, The process of generating the measured residual data includes: obtaining a sequence of dynamic compensation values ​​through analytical calculations, generating a displacement instruction set through inverse kinematics calculations to drive a multi-axis platform to complete the correction, and then collecting data with a laser interferometer and comparing it with a standard model to generate the measured residual data.

8. The method for ultra-high precision dimensional calibration of optical molds according to claim 1, wherein, The generation of the verification result includes: aligning the measured residual and the predicted residual on the time axis, and generating the verification result by means of sign matching, dynamic time warping monotonicity comparison and extreme point offset calculation.

9. The method for ultra-high precision dimensional calibration of optical molds according to claim 1, wherein, The trigger path re-identification specifically involves: when the verification result fails three times in a row, re-execute hierarchical clustering and redundancy compression to generate an updated error propagation path signature, and re-execute the template replacement operation.

10. The method for ultra-high precision dimensional calibration of optical molds according to claim 1, wherein, The temperature gradient is acquired by an NTC thermistor array mounted on key temperature measurement points of the optical mold, the vibration spectrum amplitude is obtained by FFT transformation of a piezoelectric accelerometer, and the air refractive index change rate is calculated in real time by a dual-wavelength interferometer.

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