Laser interference measurement data processing method based on PEKF-DGRNN neural network

Abstract

The invention provides a laser interference measurement data processing method based on a PEKF-DGRNN neural network, and belongs to the technical field of laser interference measurement data processing. The technical problem to be solved is to provide a laser interference measurement data processing method based on a PEKF-DGRNN neural network. According to the technical scheme, the method comprises the steps that original data measured by a laser interferometer are collected, the collected data are preprocessed, and missing data, abnormal values and noise are processed; performing data normalization or standardization operation, and periodically traversing implementation of the extended Kalman filter; constructing a PEKF-DGRNN network model, determining the number of neurons of an input layer, a mode layer, a summing layer and an output layer of a DGRNN network structure, setting smoothing parameters for the DGRNN model, and controlling the generalization ability of a learning process through the smoothing parameters; the method is applied to laser interference measurement.

Description

Technical Field

[0001] The invention provides a laser interferometry data processing method based on a PEKF-DGRNN neural network, belonging to the technical field of laser interferometry data processing. Background Art

[0002] As an efficient and high-precision measurement method, laser interferometry precision measurement technology is widely used in scientific research and industrial manufacturing, such as the processing of large machinery, precise positioning of satellite positions, installation and commissioning of large instruments, etc. This measurement method can provide millimeter or even nanometer measurement accuracy, and can play an important role in precision engineering and scientific research.

[0003] In the measurement process of laser interferometry, angle measurement is a key step, which requires measuring the angle difference between the two wavefronts formed by laser interference to achieve the purpose of high-precision measurement. However, in practical applications, the measurement signal will be affected by various factors, such as environmental noise, system errors, temperature changes, etc. These factors will affect the accuracy and stability of the angle measurement data, resulting in the accuracy of laser interferometry measurement failing to meet actual application requirements.

[0004] In addition, in the field of precision measurement technology, although the existing precision measurement data prediction and correction methods provide certain solutions, there are still some significant deficiencies, which limit their effectiveness and reliability in high-demand application scenarios, mainly including:

[0005] Limited ability to handle nonlinear problems: Many traditional forecasting models, especially those based on linear assumptions, have difficulty accurately handling nonlinear data, resulting in insufficient forecast accuracy in complex or highly variable environments;

[0006] High sensitivity to noisy data: Existing technologies are often overly sensitive to noise and outliers, which can affect the stability and accuracy of the final prediction results. This defect is particularly prominent in practical application environments with more noise;

[0007] Insufficient real-time data processing capabilities: When processing streaming data, especially when rapid response is required, existing systems often fail to achieve efficient real-time data analysis and correction, thus affecting the response speed and efficiency of the entire system.

[0008] Limited adaptability and scalability: Many existing methods lack sufficient flexibility in their design and have difficulty adapting to new data types or sudden changes in environmental conditions. In addition, the scalability of these systems is often limited, making it difficult to adapt to the needs of increased scale or increased task complexity.

[0009] Based on the above defects, it can be seen that a new laser interferometry solution needs to be proposed to process precise measurement data in complex, dynamic and high-noise environments. Summary of the invention

[0010] In order to overcome the deficiencies in the prior art, the present invention aims to solve the following technical problem: to provide a laser interferometry data processing method based on a PEKF-DGRNN neural network.

[0011] In order to solve the above technical problems, the technical solution adopted by the present invention is: a laser interferometry data processing method based on PEKF-DGRNN neural network, comprising the following data processing steps:

[0012] Step S1: Data preparation and preprocessing:

[0013] Step S11: collecting raw data measured by the laser interferometer, including angle measurement data, ambient temperature, humidity, and equipment stability data;

[0014] Step S12: preprocessing the collected data to handle missing data, outliers and noise;

[0015] Step S13: performing data normalization or standardization operations, and performing feature extraction and selection;

[0016] Step S2: Implementation of the cyclic traversal extended Kalman filter:

[0017] Step S21: Determine the system period T and initialize state estimation Covariance matrix P0;

[0018] Step S22: At each time step k, based on the current state estimate and the process model, predict the state at the next moment;

[0019] Step S23: combining the observation model and the actual observation value to update and correct the predicted state;

[0020] Step S24: Adjust the cycle ergodicity and at the end of each cycle, calculate the state estimate and the covariance matrix P k Adjust to the form of the cycle starting state;

[0021] Step S25: periodically executing the prediction and update steps until the required time step or number of cycles is reached;

[0022] Step S3: Construct the PEKF-DGRNN network model. The specific method is as follows:

[0023] Step S31: Preparation of input data with input variable x iand the corresponding output variable y i The training data set is

[0024] Step S32: constructing a model by calculating radial basis functions, local responses, and output weights;

[0025] Step S33: performing parameter selection, weight calculation, and model training respectively during the training process;

[0026] Step S34: For new input x, use the trained model to obtain the predicted output through radial basis function and weight calculation

[0027] Step S4: Determine the number of neurons in the input layer, pattern layer, summation layer, and output layer of the DGRNN network structure, set smoothing parameters for the DGRNN model, and control the generalization ability of the learning process through the smoothing parameters;

[0028] Step S5: training and testing the PEKF-DGRNN network model, dividing the preprocessed data set into a training data set and a test data set, using the training data set to train the PEKF-DGRNN model, and using the test data set to evaluate the performance of the model to determine the prediction accuracy of the model;

[0029] Step S6: using the trained PEKF-DGRNN model to predict and correct the angle measurement data of laser interferometry;

[0030] Step S7: deploying the trained and corrected model to the laser interferometry data processing system for operation;

[0031] Step S8: After the system integration is completed, an operation is performed to process the laser interferometry measurement data.

[0032] The specific method of step S22 is:

[0033] Step S221: Perform state prediction, and the calculation formula used for processing data is:

[0034]

[0035] Step S222: Calculate the Jacobian matrix F of the state transfer matrix k-1 , the calculation formula is:

[0036]

[0037] Step S223: predict the covariance matrix, the matrix expression is:

[0038]

[0039] The specific method of step S23 is:

[0040] Step S231: Calculate the Jacobian matrix H of the observation matrix k , the calculation formula is:

[0041]

[0042] Step S232: Calculate the Kalman gain P k , the calculation formula is:

[0043]

[0044] Step S233: Update the predicted state estimate, and the calculation formula is:

[0045]

[0046] Step S234: Update the covariance matrix. The matrix expression is:

[0047] P k =(1-K k H k ) k|k-1 .

[0048] The specific method of step S24 is:

[0049] Step S241: Set the cycle traversal start state to satisfy:

[0050]

[0051] Step S242: Set the periodic traversal starting covariance matrix to satisfy:

[0052] P k+T =P k .

[0053] The specific method of step S32 is:

[0054] Step S321: construct radial basis function: GRNN performs nonlinear mapping based on radial basis function, and the expression is:

[0055]

[0056] Among them, x i is the i-th input sample in the training data, σ is the parameter that controls the width of the radial basis function;

[0057] Step S322: Local response weight: For each training sample i, calculate its weight in the model, usually using a Gaussian kernel function, and the calculation formula is:

[0058]

[0059] For further optimization calculation, the DGRNN calculation formula used is:

[0060]

[0061] In the formula, n is the sample size, p is the dimension of variable x, and σ is the bandwidth coefficient of the kernel function;

[0062] Step S323: Output weights: Normalize the weights of all data in the training set, and perform regression or classification prediction based on these weights. The calculation formula used is:

[0063]

[0064] Among them, y i is the output of the i-th sample in the training set;

[0065] From this we get, is the weighted sum of all dependent variables, with weights of:

[0066] For further optimization calculation, the DGRNN calculation formula used is:

[0067]

[0068] The specific method of step S6 is:

[0069] Step S61: input the angle measurement data collected during the actual measurement into the trained PEKF-DGRNN model to obtain the predicted value of the angle measurement data;

[0070] Step S62: comparing the difference between the predicted value and the actual measured value, and correcting the system error according to the difference;

[0071] Step S63: Analyze the accuracy of the corrected data, evaluate the effectiveness of the entire prediction correction process, and readjust the parameters or training process of the PEKF-DGRNN model based on the result feedback.

[0072] The specific method of step S7 is:

[0073] Step S71: Integrate the trained model into the laser interferometry system to realize the automatic angle measurement data prediction and correction function;

[0074] Step S72: optimizing the system performance according to the actual application situation;

[0075] Step S73: Develop a user interface capable of viewing data in real time, adjusting parameters, and receiving system warnings, and provide functions for real-time monitoring and adjusting prediction parameters.

[0076] The beneficial effects of the present invention compared with the prior art are as follows: the present invention provides a combination of a periodic ergodic extended Kalman filter and a dual-factor generalized regression neural network, and based on the model, efficient, accurate and resource-optimized prediction and correction are achieved in the laser interferometry process, overcoming the defects of nonlinear problems, noise sensitivity, real-time data processing capability, adaptive capability and resource consumption; the measurement scheme provided by the present invention can effectively process complex nonlinear data, improve the prediction accuracy of the system in a changing environment, and effectively filter noise and outliers by using the periodic ergodic extended Kalman filter. At the same time, the powerful nonlinear fitting ability of the DGRNN ensures that the core features of the data are accurately captured, thereby improving the robustness of the system to noise, and by optimizing the data processing process and algorithm, supports efficient real-time data analysis and correction, and meets the application requirements in a high-speed data flow environment. In addition, the PEKF-DGRNN model provided by the present invention can dynamically adjust its parameters to adapt to new data types and mutation environments, and has good scalability, can adapt to application scenarios of different scales and complexities, significantly improves the prediction accuracy of angle measurement data and performs high-precision correction, improves the accuracy and precision of laser interferometry, and adapts to a wider range of application requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] The present invention will be further described below in conjunction with the accompanying drawings:

[0078] Figure 1 Schematic diagram of the framework structure of the PEKF-DGRNN neural network of the present invention;

[0079] Figure 2 This is a flow chart of the steps of using the PEKF-DGRNN neural network to perform laser interferometry measurement in the present invention;

[0080] Figure 3 A scatter diagram of actual values ​​and predicted values ​​of laser interferometry angle measurement data in an embodiment of the present invention;

[0081] Figure 4 The present invention is a flowchart of the steps of predicting and correcting laser interferometry data. DETAILED DESCRIPTION

[0082] like Figures 1 to 4As shown, the present invention provides a laser interferometry data processing method based on a PEKF-DGRNN neural network, and specifically relates to a solution for predicting and highly accurate correction of laser interferometry data. To implement the solution, the present invention proposes a novel neural network model based on a periodic extended Kalman filter (PEKF) combined with a double-factor generalized regression neural network (DGRNN), referred to as a PEKF-DGRNN model. The model aims to improve the accuracy and efficiency of data processing by integrating the advantages of PEKF and DGRNN. The periodic extended Kalman filter is an effective linear dynamic system estimation technology, which takes into account the extended Kalman's filtering ability for data and utilizes the periodic characteristics of the system to optimize state estimation and improve filtering performance. GRNN is a nonlinear regression method based on kernel technology, which has strong nonlinear mapping ability and fault tolerance. Compared with traditional regression analysis methods, the PEKF-DGRNN used in the present invention can more effectively handle nonlinear problems and has good robustness to data noise.

[0083] The above-mentioned periodic ergodic extended Kalman filter (PEKF) is an improved extended Kalman filter (EKF) algorithm, which is mainly used to improve the accuracy of state estimation in nonlinear systems; EKF processes nonlinear state and observation equations by linearizing nonlinear systems, and PEKF is further optimized on this basis to reduce the error introduced by linearization; the dual-factor generalized regression neural network (DGRNN) is an improved algorithm based on the generalized regression neural network (GRNN). Since the selection of smoothing factors will have a great impact on the performance of the entire neural network, and the generalized regression neural network with a single smoothing factor can only have a good effect on static data, the generalized regression neural network with a double smoothing factor is used to enhance its dynamic performance and enhance the calculation speed of the neural network.

[0084] The advantages of the PEKF-DGRNN model used in the present invention include:

[0085] (1) Data fusion and optimization processing: The cyclic extended Kalman filter is used to perform preliminary filtering and noise reduction on the input data, providing DGRNN with clearer and more accurate input data;

[0086] (2) Dynamic learning and real-time adjustment: The DGRNN part uses its ability to quickly adapt to changes to dynamically learn and adjust the data output by the PEKF in real time, further improving the accuracy of the prediction model;

[0087] (3) Error tolerance and self-correction: Combining the estimation error correction capability of PEKF and the generalization capability of DGRNN, the system can effectively cope with sudden variables and input errors, maintaining high stability and high accuracy;

[0088] (4) Improvements are made to the extended Kalman filter (EKF) algorithm and the generalized regression neural network (GRNN) algorithm to improve the algorithm performance and its operation speed, making it more universal and capable of processing more extensive data.

[0089] The present invention predicts and corrects laser interferometry angle measurement data through the PEKF-DGRNN neural network. It can accurately predict new measurement data by learning the rules and characteristics in historical measurement data, and then perform high-precision correction on the measurement data according to the prediction results. This method can significantly improve the accuracy and reliability of measurement data and provide strong support for precision measurement. The present invention also enhances the system's ability to adapt to environmental changes and potential errors, and while solving many limitations in traditional prediction models, provides a new solution for various high-precision measurement applications.

[0090] The present invention provides a solution for predicting and correcting data of laser interferometric precision measurement, which is specifically based on the PEKF-DGRNN neural network to predict data in precision measurement and perform high-precision correction, including a two-stage data processing flow: first, the original measurement data is preliminarily estimated and corrected by a cyclic extended Kalman filter, which includes the prediction and update of the dynamic system state, effectively reducing the error caused by measurement noise and system uncertainty; second, the output of the periodic extended Kalman filter is further analyzed and corrected by a double-factor generalized regression neural network, and the DGRNN optimizes the prediction accuracy of the data through its powerful nonlinear mapping ability; the above-mentioned solution mainly includes:

[0091] The goal of the program is to use the data prediction characteristics of the constructed PEKF-DGRNN neural network to predict and accurately correct the angle measurement data in laser interferometry. The specific contents include:

[0092] Collect the raw data measured by the laser interferometer, including angle measurement data and various environmental parameters that may affect the measurement accuracy (such as temperature, humidity, etc.). It is necessary to ensure that the amount of data collected is large enough to train the deep learning model and cover various possible environmental conditions;

[0093] First, the collected precision measurement data is preprocessed, including filtering out noise and outlier processing; the key features that affect the laser interferometry angle measurement data are selected, including but not limited to temperature, humidity, measurement time, equipment status, etc.;

[0094] The feature data is then standardized or normalized to eliminate the dimension effect and speed up the model training process to facilitate the training and prediction of the neural network.

[0095] Design a deep DGRNN model:

[0096] The advantage of DGRNN lies in its powerful nonlinear mapping ability and the ability to learn the intrinsic patterns of data. Based on the core idea of ​​DGRNN, a neural network structure is designed, which specifically includes an input layer, a pattern layer, a summation layer and an output layer. A deep network structure can be constructed by stacking multiple DGRNN layers to improve the model's adaptive learning ability to changes in temperature and humidity. The output layer should be designed to be able to predict the compensation value of the impact of environmental factors on the accuracy of laser interferometry measurement. The bandwidth (smoothing parameter) of the radial basis function in the pattern layer is optimized to obtain the best prediction performance; then the integration of the periodic ergodic extended Kalman filter and the dual-factor generalized regression neural network (PEKF-DGRNN) is used. On the basis of the prediction and correction provided by the periodic ergodic extended Kalman filter, a generalized regression neural network is used to further analyze and predict the data pattern. DGRNN can handle nonlinear problems and optimize the model to adapt to complex patterns and structural changes in the data.

[0097] The collected data are divided into training set, validation set and test set. The training set data is used to train the PEKF-DGRNN model. The network weights are optimized through the back propagation algorithm to minimize the error between the predicted compensation value and the actual compensation value. The model performance is tested on the validation set. The network structure and parameters are adjusted according to the actual results. Techniques such as dropout and regularization are used to prevent overfitting.

[0098] Finally, the trained DGRNN model is integrated into the laser interferometry system, and the prediction performance of the model is verified with a test data set, and necessary calibration is performed. The angle measurement data is received in real time, and the compensation value is predicted and output. The system performance is evaluated in the actual use environment, including compensation accuracy, real-time performance, etc. The model is continuously optimized based on new data collected in actual applications to cope with possible environmental changes. The present invention also requires an adaptive adjustment and optimization mechanism, which dynamically adjusts the parameters of PEKF and DGRNN according to feedback and environmental changes in actual operations to ensure that the system maintains high performance when facing new or changing measurement conditions.

[0099] Furthermore, the precision measurement data prediction and high-precision correction scheme based on the periodic extended Kalman filter (PEKF) and the dual-factor generalized regression neural network (DGRNN) provided by the present invention specifically includes the following implementation steps:

[0100] Step S1: Data preparation and preprocessing:

[0101] Step S11: First, it is necessary to collect a sufficient amount of raw data measured by the laser interferometer, which should include actual angle measurement data and other factors that may affect the measurement results, such as ambient temperature, humidity, equipment stability, etc.;

[0102] Step S12: pre-process the collected data to handle missing data, outliers and noise to ensure data quality;

[0103] Step S13: Perform data normalization or standardization operations, as well as possible feature extraction and selection. The purpose of the processing is to improve the data quality and make it more suitable for neural network training and prediction.

[0104] Step S2: Implementation of the Periodic Extended Kalman Filter (PEKF):

[0105] Step S21: Initialization: Determine the system period T; Initialize state estimation and covariance matrix P0;

[0106] Step S22: Prediction step: At each time step k, the state at the next moment is predicted based on the current state estimation and the process model. The specific method is:

[0107] Step S221: Perform state prediction, and the calculation formula used for processing data is:

[0108]

[0109] Step S222: Calculate the Jacobian matrix F of the state transfer matrix k-1 , the calculation formula is:

[0110]

[0111] Step S223: predict the covariance matrix, the matrix expression is:

[0112]

[0113] Step S23: combining the observation model and the actual observation value, updating and correcting the predicted state, the specific method is:

[0114] Step S231: Calculate the Jacobian matrix H of the observation matrix k , the calculation formula is:

[0115]

[0116] Step S232: Calculate the Kalman gain P k , the calculation formula is:

[0117]

[0118] Step S233: Update the predicted state estimate, and the calculation formula is:

[0119]

[0120] Step S234: Update the covariance matrix. The matrix expression is:

[0121] P k =(1-K k H k ) k|k-1 ;

[0122] Step S24: Adjust the cycle ergodicity, that is, at the end of each cycle, the state estimate and the covariance matrix P k Adjust to the starting state of the cycle so that it can be continued in the next cycle. The specific method is:

[0123] Step S241: Set the cycle traversal start state to satisfy:

[0124]

[0125] Step S242: Set the periodic traversal starting covariance matrix to satisfy:

[0126] P k+T =P k ;

[0127] Step S25: Cycle traversal: Cycle the prediction and update steps until the required time step or number of cycles is reached.

[0128] Step S3: Construct the PEKF-DGRNN network model. The specific method is as follows:

[0129] Step S31: Data preparation: Preparation of input data with input variables x i and the corresponding output variable y i The training data set is

[0130] Step S32: constructing a model: including radial basis function, local response, and output weight calculation. The specific method is as follows:

[0131] Step S321: construct radial basis function: GRNN performs nonlinear mapping based on radial basis function, and the expression is:

[0132]

[0133] Among them, x iis the i-th input sample in the training data, σ is the parameter that controls the width of the radial basis function;

[0134] Step S322: Local response weight: For each training sample i, calculate its weight in the model, usually using a Gaussian kernel function, and the calculation formula is:

[0135]

[0136] For further optimization calculation, the DGRNN calculation formula used is:

[0137]

[0138] In the formula, n is the sample size, p is the dimension of variable x, and σ is the bandwidth coefficient of the kernel function;

[0139] Step S323: Output weights: Normalize the weights of all data in the training set, and perform regression or classification prediction based on these weights. The calculation formula used is:

[0140]

[0141] Among them, y i is the output of the i-th sample in the training set;

[0142] From this we get, is the weighted sum of all dependent variables, with weights of:

[0143] For further optimization calculation, the DGRNN calculation formula used is:

[0144]

[0145] Step S33: During the training process, parameter selection, weight calculation, and model training are performed respectively, wherein:

[0146] Parameter selection is used to select the appropriate width σ and other hyperparameters of the radial basis function;

[0147] The weight calculation is used to calculate the radial basis function value and local response weight of each training sample;

[0148] Model training is used to calculate and optimize the output weights of the model based on the training data set;

[0149] Step S34: Finally, apply the trained model:

[0150] For new input x, the trained model is used to obtain the predicted output through radial basis function and weight calculation.

[0151] Step S4: Adjust the constructed PEKF-DGRNN network model. The specific method is as follows:

[0152] Step S41: The network structure of DGRNN generally includes an input layer, a pattern layer, a summation layer, and an output layer. Determine the number of neurons in each layer, especially the number of neurons in the input layer should be consistent with the number of data features (measurement parameters);

[0153] Step S42: Set an appropriate smoothing parameter (sigma) for the DGRNN model. This parameter controls the generalization ability of the learning process. Usually, the determination of the smoothing parameter needs to be optimized through methods such as cross-validation.

[0154] Step S5: Use Python to train and test the PEKF-DGRNN network model:

[0155] Step S51: Divide the data into a training set, a validation set and a test set;

[0156] Step S52: Divide the preprocessed data set into a training set and a test set. Usually, 70%-80% of the data set is used for training, and the rest is used for testing;

[0157] Step S53: Use the training data set to train the PEKF-DGRNN model. Since PEKF-DGRNN is an instance-based learning algorithm, it can directly build the model based on the training data set;

[0158] Step S54: Use the test set to evaluate the performance of the model and determine the prediction accuracy of the model. If necessary, the model can be fine-tuned and optimized by adjusting smoothing parameters.

[0159] Step S6: Use the trained PEKF-DGRNN model to predict and correct the angle measurement data of laser interferometry. The specific method is as follows:

[0160] Step S61: input the angle measurement data collected during the actual measurement into the trained PEKF-DGRNN model to obtain the predicted value of the angle measurement data;

[0161] Step S62: Compare the difference between the predicted value and the actual measured value, and correct the system error according to the difference. The correction method can be a simple linear correction or a complex nonlinear correction, depending on the nature of the error;

[0162] Step S63: Analyze the accuracy of the corrected data and evaluate the effectiveness of the entire prediction and correction process. If necessary, readjust the parameters or training process of the PEKF-DGRNN model based on the result feedback to further improve the accuracy of prediction and correction.

[0163] Step S7: deploy the trained and corrected model to the laser interferometry system for use. The specific method is as follows:

[0164] Step S71: Integrate the trained model into the laser interferometry system to realize the automatic angle measurement data prediction and correction function;

[0165] Step S72: optimizing the performance of the system according to the actual application situation, and improving the speed and stability while ensuring the accuracy;

[0166] Step S73: Develop a user-friendly interface that allows users to view data, adjust parameters, and receive system warnings in real time, and provides the functions of real-time monitoring and adjustment of prediction parameters.

[0167] Step S8: Integration and operation, the specific method is:

[0168] Step S81: Integrate all hardware and software components into a complete measurement system;

[0169] Step S82: monitor system performance in real time, and adjust PEKF and DGRNN parameters based on feedback to adapt to changing environment and data characteristics;

[0170] Step S83: According to different working environments and equipment conditions, independently train or fine-tune the model to provide targeted prediction adjustment strategies;

[0171] Step S84: Finally, according to specific application requirements, such as angle measurement data, adjust the model hyperparameters, or even add specific data processing procedures to achieve customized services.

[0172] The present invention specifically improves the extended Kalman filter (EKF) algorithm and the generalized regression neural network (GRNN) algorithm, and improves them into a periodic extended Kalman filter (PEKF) and a dual-factor generalized regression neural network (DGRNN) with superior performance and algorithm, and integrates the periodic extended Kalman filter (PEKF) and the dual-factor generalized regression neural network (DGRNN) to form a dual data processing flow, performs preliminary data correction through PEKF, and then performs in-depth analysis and further precise correction through DGRNN, which can effectively improve the prediction accuracy and correction effect of laser interferometry data; the present invention adopts the real-time prediction capability of DGRNN to perform real-time prediction and high-precision correction of angle measurement data in laser interferometry, effectively improves the accuracy and reliability of measurement data, uses the difference between the prediction result and the actual measurement value to perform detailed error analysis, and adopts a special correction mechanism to efficiently correct systematic errors.

[0173] The present invention can realize dynamic learning and real-time adjustment. The DGRNN part utilizes its characteristic of quickly adapting to changes to dynamically learn and adjust the data output by the PEKF in real time, so as to further improve the accuracy of the prediction model. By applying GRNN to process the output of the PEKF, it can effectively identify and process nonlinear and complex data patterns, especially when processing data with high variability and nonlinear characteristics. By optimizing the smoothing parameter (sigma) of the DGRNN, it is ensured that the prediction model can capture the complex relationship in the data and avoid overfitting, thereby ensuring the generalization ability of the model. In addition, the present invention also has a wide range of applications and a powerful ability to solve complex problems. The method can not only be used for the prediction and correction of angle measurement data in laser interferometry, but can also be extended to other precision measurement fields, such as length measurement, temperature measurement, etc. It has broad application prospects, can handle data prediction problems with nonlinearity and high complexity, and provides an effective solution for measurement data that is difficult to accurately predict and correct by traditional methods.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A laser interferometry data processing method based on PEKF-DGRNN neural network, characterized in that: The data processing steps include the following: Step S1: Data preparation and preprocessing: Step S11: collecting raw data measured by the laser interferometer, including angle measurement data, ambient temperature, humidity, and equipment stability data; Step S12: preprocessing the collected data to handle missing data, outliers and noise; Step S13: performing data normalization or standardization operations, and performing feature extraction and selection; Step S2: Implementation of the cyclic traversal extended Kalman filter: Step S21: Determine the system period T and initialize state estimation Covariance matrix P0; Step S22: At each time step k, based on the current state estimate and the process model, predict the state at the next moment; Step S23: combining the observation model and the actual observation value to update and correct the predicted state; Step S24: Adjust the cycle ergodicity and at the end of each cycle, calculate the state estimate and the covariance matrix P k Adjust to the form of the cycle starting state; Step S25: periodically executing the prediction and update steps until the required time step or number of cycles is reached; Step S3: Construct the PEKF-DGRNN network model. The specific method is as follows: Step S31: Preparation of input data with input variable x i and the corresponding output variable y i The training data set is Step S32: constructing a model by calculating radial basis functions, local responses, and output weights; Step S33: performing parameter selection, weight calculation, and model training respectively during the training process; Step S34: For new input x, use the trained model to obtain the predicted output through radial basis function and weight calculation Step S4: Determine the number of neurons in the input layer, pattern layer, summation layer, and output layer of the DGRNN network structure, set smoothing parameters for the DGRNN model, and control the generalization ability of the learning process through the smoothing parameters; Step S5: training and testing the PEKF-DGRNN network model, dividing the preprocessed data set into a training data set and a test data set, using the training data set to train the PEKF-DGRNN model, and using the test data set to evaluate the performance of the model to determine the prediction accuracy of the model; Step S6: using the trained PEKF-DGRNN model to predict and correct the angle measurement data of laser interferometry; Step S7: deploying the trained and corrected model to the laser interferometry data processing system for operation; Step S8: After the system integration is completed, an operation is performed to process the laser interferometry measurement data.

2. The laser interferometry data processing method based on the PEKF-DGRNN neural network according to claim 1 is characterized in that: The specific method of step S22 is: Step S221: Perform state prediction, and the calculation formula used for processing data is: Step S222: Calculate the Jacobian matrix F of the state transfer matrix k-1 , the calculation formula is: Step S223: predict the covariance matrix, the matrix expression is:

3. The laser interferometry data processing method based on the PEKF-DGRNN neural network according to claim 1 is characterized in that: The specific method of step S23 is: Step S231: Calculate the Jacobian matrix H of the observation matrix k , the calculation formula is: Step S232: Calculate the Kalman gain P k , the calculation formula is: Step S233: Update the predicted state estimate, and the calculation formula is: Step S234: Update the covariance matrix. The matrix expression is: B=(1-KH)P 对-1 。 4. The laser interferometry data processing method based on the PEKF-DGRNN neural network according to claim 1 is characterized in that: The specific method of step S24 is: Step S241: Set the cycle traversal start state to satisfy: Step S242: Set the periodic traversal starting covariance matrix to satisfy: P k+T =P k 。 5. The laser interferometry data processing method based on PEKF-DGRNN neural network according to claim 1 is characterized in that: The specific method of step S32 is: Step S321: construct radial basis function: GRNN performs nonlinear mapping based on radial basis function, and the expression is: Among them, x i is the i-th input sample in the training data, σ is the parameter that controls the width of the radial basis function; Step S322: Local response weight: For each training sample i, calculate its weight in the model, usually using a Gaussian kernel function, and the calculation formula is: For further optimization calculation, the DGRNN calculation formula used is: In the formula, n is the sample size, p is the dimension of variable x, and σ is the bandwidth coefficient of the kernel function; Step S323: Output weights: Normalize the weights of all data in the training set, and perform regression or classification prediction based on these weights. The calculation formula used is: Among them, y i is the output of the i-th sample in the training set; From this we get, is the weighted sum of all dependent variables, with weights of: For further optimization calculation, the DGRNN calculation formula used is:

6. The laser interferometry data processing method based on PEKF-DGRNN neural network according to claim 1, characterized in that: The specific method of step S6 is: Step S61: input the angle measurement data collected during the actual measurement into the trained PEKF-DGRNN model to obtain the predicted value of the angle measurement data; Step S62: comparing the difference between the predicted value and the actual measured value, and correcting the system error according to the difference; Step S63: Analyze the accuracy of the corrected data, evaluate the effectiveness of the entire prediction correction process, and readjust the parameters or training process of the PEKF-DGRNN model based on the result feedback.

7. The laser interferometry data processing method based on PEKF-DGRNN neural network according to claim 1 is characterized in that: The specific method of step S7 is: Step S71: Integrate the trained model into the laser interferometry system to realize the automatic angle measurement data prediction and correction function; Step S72: optimizing the system performance according to the actual application situation; Step S73: Develop a user interface capable of viewing data in real time, adjusting parameters, and receiving system warnings, and provide functions for real-time monitoring and adjusting prediction parameters.

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