Gaussian fitting material data analysis method and system based on multi-dimensional evaluation system

Abstract

The application discloses a kind of Gauss fitting material data analysis methods based on multidimensional evaluation system, comprising the following steps: obtaining test data, pre-processing test data, obtaining the standard test data after pre-processing;The quality evaluation driven Gauss fitting image generation model pre-trained is input quality evaluation to the standard test data, and the quality evaluation driven Gauss fitting image generation model is updated by input quality evaluation, and adaptive Gauss fitting material analysis model is obtained;And by adaptive Gauss fitting material analysis model, standard test data is analyzed and output fitting image and analysis result.The application discloses a kind of Gauss fitting material data analysis methods and system based on multidimensional evaluation system, improve the stability and accuracy of fitting image generated in data analysis, reduce the defect of "re-fitting, light evaluation".

Description

Technical Field

[0001] This invention relates to the field of test data analysis technology, specifically to a Gaussian fitting material data analysis method and system based on a multidimensional evaluation system. Background Technology

[0002] In existing technologies, Gaussian functions are widely used in data fitting tasks in scientific and engineering fields due to their excellent data analysis performance (such as symmetry, smoothness, and differentiability). Typical applications include data analysis and processing using Gaussian functions, such as spectral analysis, determination of space target trajectories, and modeling of variable coefficient models.

[0003] For example, in spectral analysis: Gaussian functions are used to fit spectral lines and extract parameters such as full width at half maximum (FWHM) and peak intensity for the identification of substance components and concentration analysis. For example, determining the orbit of a space target: using a Gaussian mixture model to describe the probability distribution of observation uncertainties to achieve optimal estimation of orbital parameters; For example, variable coefficient modeling: In nonlinear systems, radial basis functions (RBF) are used to construct variable coefficient regression models to improve predictive capabilities.

[0004] However, existing spectral analysis methods using Gaussian functions have the following problems: 1. Before data analysis, it is necessary to fit the test data to present a data trend image. However, the fitting process lacks a quality feedback mechanism: most systems only focus on the parameter estimation results and neglect the systematic evaluation of the fitting quality. For example, in cases of low signal-to-noise ratio or sparse data, the traditional least squares method is prone to producing estimates with large biases and wide confidence intervals, but users cannot know the reliability of the results.

[0005] 2. Sensitivity to initial values ​​and prominent optimization divergence issues: Gaussian fitting typically relies on nonlinear optimization (such as gradient descent and Levenberg-Marquardt), and its performance is highly dependent on the choice of initial values. When the initial values ​​deviate significantly from the true values, it is easy to get trapped in local minima or cause the covariance matrix to be non-positive definite, resulting in data analysis divergence problems.

[0006] 3. Insufficient adaptability to complex distributions: Actual observational data often exhibits multimodal, skewed, or heavy-tailed characteristics, which are difficult to accurately characterize with a single Gaussian function. Although Gaussian Mixture Models (GMMs) can improve the flexibility of fitting data trend images in data analysis, their selection of the number of sub-components lacks an automated mechanism, and the training process is susceptible to noise interference.

[0007] 4. Poor interpretability of results and lack of hierarchical decision support: Existing systems mostly output fitting parameters in a "black box" manner, without providing clear quality labels or risk warnings, making it difficult to meet the needs of traceability and decision support in industrial applications.

[0008] 5. Weak interactivity and engineering integration capabilities: Most research remains at the algorithm level, lacking a user-friendly human-computer interaction interface and batch processing capabilities, which limits its deployment in actual production environments.

[0009] In summary, there is an urgent need for a Gaussian function spectral analysis method and system that can integrate quality evaluation, adaptive optimization, and engineering integration to address the shortcomings of existing technologies, such as low analytical accuracy and poor analytical stability caused by "emphasizing fitting over evaluation" and "emphasizing results over process". Summary of the Invention

[0010] This invention overcomes the shortcomings of the prior art and provides a Gaussian fitting material data analysis method and system based on a multidimensional evaluation system, which improves the stability and accuracy of generating fitted images in data analysis and reduces the defect of "emphasizing fitting and neglecting evaluation".

[0011] To achieve the above objectives, the technical solution adopted by this invention is: a Gaussian fitting material data analysis method based on a multidimensional evaluation system, comprising the following steps: Obtain test data; The test data is preprocessed to obtain preprocessed standard test data; The standard test data is evaluated for input quality using a pre-trained quality assessment-driven Gaussian fitting image generation model. An adaptive Gaussian-fitted material analysis model is obtained by updating the quality assessment-driven Gaussian-fitted image generation model through input quality assessment. An adaptive Gaussian fitting material analysis model is used to fit images to standard test data, and the fitted images and analysis results of the test data are output.

[0012] In a preferred embodiment of the present invention, the preprocessing includes the following steps: Data cleaning is performed on the test data to obtain cleaned data. Data cleaning includes: removing invalid values ​​based on the 3σ criterion or median absolute deviation; filling missing points using linear interpolation or spline interpolation; and using wavelet denoising with a soft thresholding function. The cleaned data is smoothed using a smoothing algorithm.

[0013] In a preferred embodiment of the present invention, the soft threshold function includes: σ is the noise standard deviation, and N is the number of data points; The smoothing algorithm includes: performing p-order polynomial fitting on the data within the window, with the following formula: , Let be the fitted value of the i-th point within the window, m be the half-length of the window, and the window contains 2m+1 data points. The coefficient 'a' is solved using the least squares method. k The smoothed value is reconstructed by minimizing the sum of squared residuals between the actual and fitted values ​​within the window. The formula includes: , Let j be the original observation value at the j-th position within the window. Here, p represents the polynomial fit value at the corresponding position, and p is the polynomial order. Within a sliding window centered at i, a p-degree polynomial is used to approximate the 2m+1 original data points within the window, and the polynomial coefficients are solved using the least squares method. and the value of the center point Achieve smoothness.

[0014] In a preferred embodiment of the present invention, the input quality assessment (DQS) includes: employing a multi-dimensional assessment; the multi-dimensional assessment includes: Signal-to-noise ratio (SNR): ;in, The mean of the signal represents the average strength of the effective signal. The total noise standard deviation reflects the overall fluctuation level of noise in the data; dB is the decibel, the unit of signal-to-noise ratio. Percentage of valid data points: ;in, : Number of valid data points, i.e., the number of usable data points retained after cleaning; : Total number of raw data points, including all collected data points (including invalid or missing points); Anomaly score is calculated based on the sample path length h(x) from the isolated forest: ; Where x is the sample point to be evaluated; N is the total number of samples; h(x) is the path length of sample x in each tree in the isolated forest; E|h(x)| is the expected value (average) of the path length of sample x in all trees; c(N) is the normalization factor of the average path length of the binary search tree when the number of samples is N, used to standardize the path length; S(x,N) is the anomaly score of sample x, with a value range of (0,1], and the closer the score is to 1, the more likely it is to be an anomaly. Based on IQR = Q3 - Q1, the outlier range Q1 is the first quartile, Q3 is the third quartile; IQR is the interquartile range; 1.5IQR is the outlier threshold. Uniformity of distribution: , The supremum; Let be the empirical cumulative distribution function, and be the cumulative distribution calculated based on n sample data. ; The cumulative distribution function is the theoretically uniform distribution. The DQS comprehensive calculation formula includes: ; in, The signal-to-noise ratio (SNR) is normalized to [0,1], linearly mapping the original SNR to accommodate different measurement ranges; Completeness represents the percentage of valid data points. The value range is [0,1]; Snorm is the normalized value of the anomaly score of the isolated forest, S(x,N)∈(0,1]. The higher the score, the more anomaly it is. 1-Snorm is used as the quality contribution; D KS The KS statistic (Kolmogorov-Smirnov statistic) is a nonparametric statistic with a value range of [0,1]. A smaller value indicates a more uniform distribution. A 1-D statistic is used. KS As a contribution to quality, w1, w2, w3, and w4 are the weights corresponding to each dimension, satisfying... However, this is not the only factor; specific values ​​can be determined based on expert experience or optimization algorithms according to the actual application scenario (for example, the default value is 0.25).

[0015] In a preferred embodiment of the present invention, the establishment of a quality assessment-driven Gaussian fitting image generation model includes: The data is modeled using a Gaussian mixture model: ; in, Let the weight of the k-th Gaussian component satisfy the following condition: ; A single Gaussian distribution is: ; Where K is the number of sub-components of the Gaussian component; x is a random variable representing the data point to be fitted. The mean of the k-th Gaussian component determines the center position of that component; Let be the variance of the k-th Gaussian component; The standard deviation and the two together determine the width and dispersion of the detected component; To be at a given mean and variance Under the condition that x appears, the probability density of x; The optimal K value is determined using the Bayesian Information Criterion (BIC). ; Where L(K) is the maximum value of the model likelihood function; p(K) = 3K-1 is the number of model parameters, i.e., each of the K Gaussian components has three parameters μ, σ, and ω, and the weight constraint reduces one degree of freedom; N is the number of data points; selection strategy: traversal. Choose the K value that minimizes BIC.

[0016] In a preferred embodiment of the present invention, a robust parameter optimization quality assessment-driven Gaussian fitting image generation model is employed, comprising: introducing SR-UKF for iterative parameter updates, the steps of which include: Define the state vector as , The dimension is 3K; SR-UKF is a square root unscented Kalman filter; The SR-UKF algorithm includes: ; in, The initial covariance matrix is ​​given by `chol()`, which represents the Cholesky decomposition; 2n+1 Sigma points are generated. and corresponding weights ; The mean, The weights are set; their diagonal elements are preset with reasonable uncertainties (e.g., mean) based on the physical range of each parameter. The initial standard deviation is taken as 10% of the data range, and the weights are... The initial standard deviation is taken as 0.1). Convergence criterion: When the parameter changes The iteration will terminate when the maximum number of iterations is reached. Optimal parameter estimation: , Let be the parameter vector for the t-th iteration (i.e., when convergence). Parameter uncertainty estimation: , The covariance matrix of the parameters, The sensitivity matrix at convergence; For matrix The transpose of .

[0017] In a preferred embodiment of the present invention, the process quality monitoring and visualization module calculates and displays the parameter quality indices of the adaptive Gaussian fitting material analysis model; the parameter quality indices include: adjusted coefficient of determination, root mean square of residuals, and local fit confidence. The adjusted coefficient of determination is: ;in, Adjust the coefficient of determination to evaluate the goodness of fit of the model and penalize the number of parameters; R 2The coefficient of determination reflects the proportion of the total variation in the data explained by the model; N is the total number of samples, i.e., the number of data points involved in the fitting; p is the number of model parameters, and for a Gaussian mixture model, p = 3K-1. The root mean square (RMS) of the residuals is: ; The confidence level for local fitting is calculated based on Mahalanobis distance.

[0018] In a preferred embodiment of the present invention, a Gaussian fitting material analysis system based on a multidimensional evaluation system includes: Memory, used to store computer programs / instructions; A processor is used to execute the computer program / instructions to implement the steps of a Gaussian fitting material data analysis method based on a multidimensional evaluation system.

[0019] This invention addresses the deficiencies in the technical background, and the beneficial technical effects of this invention are: A Gaussian fitting material data analysis method and system based on a multidimensional evaluation system improves the stability and accuracy of generating fitted images in material test data analysis and reduces the defect of "emphasizing fitting and neglecting evaluation". Attached Figure Description

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] Figure 1 The system overall architecture and data flow diagram of a preferred embodiment of the present invention; Figure 2 This is a flowchart illustrating the quality evaluation system of a preferred embodiment of the present invention. Figure 3 This is a schematic diagram of the interactive fitting main interface of a preferred embodiment of the present invention; Figure 4 This is a schematic diagram of the interactive fitting main interface for sampling data group 1 according to a preferred embodiment of the present invention; Figure 5 This is a schematic table illustrating the output results of sampling data group 1 according to a preferred embodiment of the present invention; Figure 6 This is a schematic diagram of the interactive fitting main interface for sampling data group 2 according to a preferred embodiment of the present invention; Figure 7 This is a schematic table illustrating the output results of sampling data group 2 according to a preferred embodiment of the present invention; Figure 8 This is a schematic diagram of the interactive fitting main interface for sampling data group 3 according to a preferred embodiment of the present invention; Figure 9 This is a schematic table illustrating the output results of sampling data group 3 according to a preferred embodiment of the present invention; Figure 10 This is a schematic diagram of the interactive fitting main interface for sampling data group 4 according to a preferred embodiment of the present invention; Figure 11 This is a schematic table illustrating the output results of sampling data group 4 in a preferred embodiment of the present invention; Figure 12 This is a schematic diagram of the interactive fitting main interface for the sampling data group 5 in a preferred embodiment of the present invention; Figure 13 This is a schematic table illustrating the output results of sampling data group 5 in a preferred embodiment of the present invention; Figure 14 This is a schematic diagram of the interactive fitting main interface for the sampling data group 6 in a preferred embodiment of the present invention; Figure 15 This is a schematic table illustrating the output results of sampling data group 6 in a preferred embodiment of the present invention. Detailed Implementation

[0022] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. These drawings are simplified schematic diagrams, which are only used to illustrate the basic structure of the present invention and therefore only show the components relevant to the present invention.

[0023] It should be noted that if directional indicators (such as up, down, bottom, top, etc.) are involved in the embodiments of the present invention, these directional indicators are only used to explain the relative positional relationship and movement of the components in a specific posture. If the specific posture changes, the directional indicators will also change accordingly. The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, features defined with "first" and "second" may explicitly or implicitly include one or more of that feature. Unless otherwise explicitly specified and limited, the terms "set," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal connection of two components. For those skilled in the art, the specific meaning of the above terms in the present invention can be understood according to the specific circumstances.

[0024] Example 1, as Figures 1-3 As shown, a Gaussian fitting material data analysis method based on a multidimensional evaluation system includes the following steps: Step 1: Obtain test data. Step two: preprocess the test data to obtain preprocessed standard test data.

[0025] The preprocessing includes the following steps: performing data cleaning on the test data to obtain cleaned data. Data cleaning includes: removing invalid values ​​based on the 3σ criterion or median absolute deviation, filling missing points using linear interpolation or spline interpolation; performing wavelet denoising using a soft threshold function; and smoothing the cleaned data using a smoothing algorithm.

[0026] Specifically, the soft threshold function includes: σ is the noise standard deviation, and N is the number of data points; σ is obtained by: using wavelet decomposition to obtain the high-frequency subband coefficients, taking the median absolute value of the first-level high-frequency coefficients (such as detail coefficients) and dividing it by a constant 0.6745, i.e.: ;in, These are the high-frequency coefficients of the first-level wavelet decomposition; is a robust noise estimation method commonly used in wavelet denoising, suitable for practical signal processing scenarios with unknown noise levels.

[0027] Specifically, the 3σ criterion includes: assuming the data follows a normal distribution, calculating the mean μ and standard deviation σ; if the absolute value of the difference between a data point and the mean is greater than 3σ, it is considered an outlier and removed. This criterion is applicable to scenarios where the data distribution is symmetrical and there is no severe skewness.

[0028] Specifically, the median absolute deviation (MAD) is defined as the median of the absolute values ​​of the differences between a data point and the median, i.e., MAD = median(|x_i - median(X)|). If a data point satisfies |x_i - median(X)| > 3 × MAD, it is considered an outlier and removed. This method is more robust to skewed distributions or data containing outliers.

[0029] Specifically, linear interpolation assumes that the changes between two adjacent valid data points are linearly related, and estimates the value of the missing point in the middle through a linear equation. It is suitable for situations where the data changes gradually and the missing interval is small.

[0030] Specifically, spline interpolation: A cubic spline function is used to fit the data points piecewise, ensuring a smooth connection between each segment of the interpolation curve. This method is suitable for situations with complex data variations or many missing points, and can more realistically reproduce data trends.

[0031] Specifically, the smoothing algorithm includes: performing p-order polynomial fitting on the data within the window, with the following formula: , Let be the fitted value of the i-th point within the window, m be the half-length of the window, and the window contains 2m+1 data points. The coefficient 'a' is solved using the least squares method. k The smoothed value is reconstructed by minimizing the sum of squared residuals between the actual and fitted values ​​within the window. The formula includes: , Let j be the original observation value at the j-th position within the window. Here, p represents the polynomial fit value at the corresponding position, and p is the polynomial order. Within a sliding window centered at i, a p-degree polynomial is used to approximate the 2m+1 original data points within the window, and the polynomial coefficients are solved using the least squares method. and the value of the center point Achieve smoothness.

[0032] Step 3: The standard test data is subjected to input quality assessment using a pre-trained quality assessment-driven Gaussian fitting image generation model. The input quality assessment is then used to update the quality assessment-driven Gaussian fitting image generation model to obtain an adaptive Gaussian fitting material analysis model. Finally, the standard test data is fitted using the adaptive Gaussian fitting material analysis model, and the fitted image and the analysis results of the test data are output.

[0033] Working principle: A Gaussian fitting material data analysis method and system based on a multidimensional evaluation system improves the stability and accuracy of the fitted images generated by data analysis and reduces the defect of "emphasizing fitting and neglecting evaluation".

[0034] Example 2, based on Example 1, the input quality assessment DQS includes: employing multi-dimensional assessment; the multi-dimensional aspects include: Signal-to-noise ratio (SNR): ;in, The mean of the signal represents the average strength of the effective signal. The total noise standard deviation reflects the overall fluctuation level of noise in the data; dB is the decibel, the unit of signal-to-noise ratio. Percentage of valid data points: ;in, : Number of valid data points, i.e., the number of usable data points retained after cleaning; : Total number of raw data points, including all collected data points (including invalid or missing points); Anomaly score is calculated based on the sample path length h(x) from the isolated forest: Where x is the sample point to be evaluated; N is the total number of samples; H(x) is the path length of sample x in each tree in the isolated forest; E|h(x)| is the expected value (average) of the path length of sample x in all trees; c(N) is the normalization factor of the average path length of the binary search tree when the number of samples is N, used to standardize the path length as S(x,N): the anomaly score of sample x, with a value range of (0,1], the closer the score is to 1, the more likely it is to be an anomaly. Based on IQR = Q3 - Q1, the outlier range Uniformity of distribution: ; Furthermore, the DQS comprehensive calculation formula includes: ; in, The signal-to-noise ratio (SNR) is a normalized value, linearly mapping the original SNR (in dB) to [0,1] to accommodate different measurement ranges; Completeness is the percentage of valid data points, i.e. The value range is [0,1]; Snorm is the normalized value of the anomaly score in the isolated forest, usually S(x,N)∈(0,1], the higher the score, the more anomaly it is, therefore 1-Snorm is used as the quality contribution; D KS This is the Kolmogorov-Smirnov (KS) statistic, with values ​​ranging from [0,1]. Smaller values ​​indicate a more uniform distribution; therefore, 1-D is used. KS As a quality contribution; w1, w2, w3, w4 are the weights of each dimension, satisfying... The specific value can be determined based on the actual application scenario through expert experience or optimization algorithms (the default value in this embodiment is 0.25).

[0035] Specifically, the establishment of a quality assessment-driven Gaussian fitting image generation model includes: The data is modeled using a Gaussian mixture model: ;in, Let the weight of the k-th Gaussian component satisfy the following condition: ; The mean, is the standard deviation; K is the number of sub-components of the Gaussian; A single Gaussian distribution is: Where x is a random variable, representing the data point to be fitted (such as spectral intensity, wavenumber, etc.). The mean of the k-th Gaussian component determines the center position (e.g., peak position) of that component. Let be the variance of the k-th Gaussian component; The standard deviation and the two together determine the width (e.g., half-width at half-maximum) and dispersion of the component; To be at a given mean and variance Under the condition that x appears, the probability density of x; The optimal K value is determined using the Bayesian Information Criterion (BIC). Where L(K) is the maximum value of the model likelihood function; p(K) = 3K-1 is the number of model parameters, i.e., each of the K Gaussian components has three parameters: μ, σ, and ω, with the weight constraint reducing one degree of freedom; N is the number of data points; selection strategy: traversal. Choose the K value that minimizes BIC.

[0036] Specifically, a robust parameter optimization quality assessment-driven Gaussian fitting image generation model is adopted, including: introducing SR-UKF for parameter iterative updates, the steps of which include: Define the state vector as , ; Dimension n=3K; SR-UKF is a square root unscented Kalman filter; The SR-UKF algorithm includes: ; in The initial covariance matrix is ​​given by `chol()`, which represents the Cholesky decomposition; 2n+1 Sigma points are generated. and corresponding weights Its diagonal elements are preset with reasonable uncertainties based on the physical range of each parameter (e.g., mean). The initial standard deviation is taken as 10% of the data range, and the weights are... The initial standard deviation is set to 0.1), and `chol()` represents the Cholesky decomposition; it generates 2n+1 Sigma points. and corresponding weights ; Convergence criterion: When the parameter changes The iteration will terminate when the maximum number of iterations is reached. Optimal parameter estimation: , Let be the parameter vector for the t-th iteration (i.e., when convergence). Parameter uncertainty estimation: , The covariance matrix of the parameters, The sensitivity matrix at convergence; For matrix The transpose of .

[0037] Specifically, after determining the optimal number of components KK of the Gaussian mixture model (using the BIC criterion), the model parameters are iteratively optimized using the square root unscented Kalman filter (SR-UKF); the optimization object of the square root unscented Kalman filter is the parameter vector of all Gaussian components. The optimal parameter estimate is obtained by minimizing the error between the observed data and the model prediction. Compared with the traditional gradient descent method, SR-UKF does not require the calculation of the Jacobian matrix and has stronger numerical stability in nonlinear systems.

[0038] The process quality monitoring and visualization module calculates and displays the parameter quality indices of the adaptive Gaussian fitting material analysis model. These indices include: adjusted coefficient of determination, root mean square residuals, and local fit confidence. Specifically, the module calculates and dynamically displays the quality indices of the adaptive Gaussian fitting material analysis model in real time during the SR-UKF parameter iteration optimization process, achieving closed-loop monitoring of the fitting process. The monitoring mechanism employed includes: calculating the quality indices and refreshing the interface display after each SR-UKF iteration parameter update; issuing warnings when indices fall below preset thresholds or show divergence trends; and immediately recalculating the quality indices and updating the visualization results after the user adjusts the peak position or width via mouse drag-and-drop interaction, forming a real-time quality closed loop of "adjustment-feedback."

[0039] The adjusted coefficient of determination is: ;in, Adjust the coefficient of determination to evaluate the goodness of fit of the model and penalize the number of parameters; R 2 The coefficient of determination reflects the proportion of the total variation in the data explained by the model; N is the total number of samples, i.e., the number of data points involved in the fitting; p is the number of model parameters. For a Gaussian mixture model, p = 3K-1, where K is the number of Gaussian components. The root mean square (RMS) of the residuals is: ; The local fit confidence score is calculated based on the Mahalanobis distance. Specifically, for each data point i, the residual is calculated. ; Let i be the residual vector of the i-th pair of standard test data and i samples of the standard test data; calculate the local covariance matrix of the residuals within a local window centered at point i. ; Calculate the distance of Mahalanobis to standard test data , Let be the Mahalanobis distance between the i-th pair of standard test data and the i-th sample of the standard test data; convert the Mahalanobis distance between the standard test data and the standard test data into a confidence score in the interval [0,1] through the cumulative distribution function of the chi-square distribution or a linear mapping. The closer the score is to 1, the more reliable the fit at that point.

[0040] The working principle is as follows: A Gaussian fitting material data analysis method and system based on a multidimensional evaluation system improves the stability and accuracy of the fitted images generated by data analysis and reduces the defect of "emphasizing fitting and neglecting evaluation".

[0041] The system first enters the data quality assessment phase, calculating a comprehensive data quality score (DQS). This is followed by the model fitting and process monitoring phase, which not only performs adaptive GMM modeling and SR-UKF optimization but also calculates and adjusts process quality indicators such as R² and residual RMS in real time. In the results comprehensive rating phase, the system automatically grades the fitting results according to preset rules (combining DQS and key goodness-of-fit indicators) (A / B / C levels, representing three levels, with specific dividing lines adjusted according to actual testing needs), and outputs a structured report with quality labels, forming a complete quality closed loop from input to output.

[0042] Example 3, based on Example 1 or Example 2, adjusts the interactive parameters to: support adjusting peak position and width by dragging control points with the mouse; and recalculate and update quality indicators in real time. Specifically, a drawing area is constructed using a Qt or WPF graphical interface framework, interactive control points are drawn at the top of each Gaussian peak of the fitted curve, and mouse events are bound to the control points; when the mouse drags a control point, the system determines whether the control point has been hit by Euclidean distance, maps the screen coordinate displacement to the data coordinate displacement, and updates the peak position of the corresponding Gaussian component in real time. or width Parameters; after the parameters are updated, an incremental recalculation mechanism is triggered to perform finite-step iterative SR-UKF optimization to quickly update the fitted curve, and the quality evaluation module is called to calculate and adjust the coefficient of determination, root mean square of residuals, local fit confidence and other quality indicators in real time; double buffering plotting technology is used to refresh the fitted curve display, and the UI controls automatically update the quality indicator values; The batch processing functionality includes: support for cascading folder imports and automatic traversal of all files to be processed; parallel execution of fitting tasks based on OpenMP multithreading; and the ability to set output formats (TXT, JSON, Excel) and paths. Specifically, it supports traversing specified folders and their subfolders using a recursive algorithm, filtering files in target formats, and building a thread-safe file queue; based on the OpenMP parallel framework, it uses the `pragma omp parallel for` directive to evenly distribute fitting tasks across multiple threads for parallel execution, using atomic variables and mutexes to ensure progress synchronization and safe log output; it provides output format selection (TXT, JSON, Excel), calls the corresponding serialization library to complete structured output, and supports user-defined output paths.

[0043] Example 4: A Gaussian fitting material analysis system based on a multidimensional evaluation system, comprising: Memory, used to store computer programs / instructions; A processor is used to execute the computer program / instructions to implement the steps of the Gaussian fitting material data analysis method based on a multidimensional evaluation system as described in any of the embodiments 1 to 3.

[0044] Example 5, based on any one of Examples 1 to 3, such as Figure 3 The image shows an example of a graphical user interface (GUI).

[0045] The graphical user interface (GUI) is the specific implementation carrier of the technical solution of this system, and forms a close functional correspondence with the core modules in the aforementioned method claims: 1. The data loading and preprocessing module is implemented through the file import button and the data preview area. The preprocessing results are presented in the form of a scatter plot. 2. The Data Quality Assessment (DQS) module provides real-time feedback on data quality through the DQS numerical display area and quality level indicators (A / B / C, representing the three levels, with the specific dividing lines adjusted according to actual testing requirements); 3. The adaptive fitting and parameter optimization module visualizes the fitting results and adjustable parameters of the Gaussian mixture model through the fitting curve (solid line) and control points (dots); 4. The process quality monitoring module dynamically presents the fitting quality through R², DQS values, and local fitting confidence heatmaps; 5. The interactive parameter adjustment function triggers background parameter updates and quality index recalculation by dragging control points with the mouse, forming an "adjustment-feedback" closed loop; 6. Batch processing function supports users in efficiently processing large-scale data through interface elements such as folder import, output format selection, and parallel progress bar.

[0046] This GUI not only encapsulates the steps of the aforementioned method claims, but also lowers the barrier to entry for advanced fitting algorithms through intuitive interaction, reflecting the technical characteristics of this system: "emphasis on evaluation, emphasis on interaction, and emphasis on engineering integration".

[0047] The main area of ​​the interface displays a scatter plot of the original data (points) and a Gaussian fitted curve (solid line) and a half-width at half-maximum (WHM) indicator line (dashed line) superimposed on it. Interactive control points are prominently displayed, such as dots for adjusting peak position and dots for adjusting peak width. A parameter panel on one side of the interface displays fitting parameters such as peak position (xc), width (w), and amplitude (A) in real time, as well as a quality index display area that dynamically updates values ​​such as R² and DQS. This figure illustrates the intuitive and user-friendly interactive features of this invention.

[0048] Example 6: Based on any of Examples 1 to 3, in the automatic multi-peak analysis and quality assessment of Raman spectral data.

[0049] The application scenario is as follows: in material testing, Raman spectroscopy is used to analyze the characteristic peaks (such as D peak and G peak) of carbon materials to determine their structural characteristics.

[0050] The implementation steps include: Step S1, Data Input: Load records containing wavenumbers (cm) -1 ) and intensity information in CSV format spectral data files.

[0051] Step S2, Preprocessing and Initial Quality Assessment: The system automatically performs baseline correction and smoothing. The DQS of the spectral data is calculated, and considering its signal-to-noise ratio (SNR=32dB) and data integrity, the DQS is found to be 0.91. The system indicates "Excellent data quality".

[0052] Step S3, Adaptive Fitting: Within the preset wavenumber interval, the adaptive modeling unit identifies two distinct overlapping peaks. Using the BIC criterion, K=1, 2, and 3 are compared, and the optimal K=2 is determined. Subsequently, the SR-UKF optimization unit iteratively optimizes the parameters of these two Gaussian peaks, converging after 18 iterations.

[0053] Step S4, Result Output and Decision: The system outputs the precise location of the two Gaussian peaks (1350.2 cm). -1 1580.5cm -1 The system calculates the half-width at half-maximum (FWHM) and intensity ratio. The overall fit R² is 0.997. Combining DQS = 0.91 and R² = 0.997, the system automatically rates the result as Grade A (reliable). Based on the detection neighborhood, and using a preset odd-number threshold, the analysis results are evaluated. The report simultaneously provides a fitting curve and a quality heatmap, showing that the fitting confidence in the overlapping area is slightly lower but overall reliable. Specific rating classifications are set based on the actual detection field, combining the DQS and R² parameter ranges to achieve the analysis and evaluation of the tested items.

[0054] In this specific example, such as Figure 4 , Figure 6 , Figure 8 , Figure 10 , Figure 12 , Figure 14 As shown, curve fitting is performed based on sampled data to facilitate understanding of the data situation; for example... Figure 5 , Figure 7 , Figure 9 , Figure 11 , Figure 13 , Figure 15 As shown, the extraction of fitted image data has completed multi-peak decomposition and parameter extraction, without the need for manual pre-setting of the number of peaks; the provided A-level quality label allows researchers to confidently use the data directly for subsequent graphitization degree calculations.

[0055] Working principle: like Figures 1-15As shown, by introducing the SR-UKF optimization algorithm, nonlinearity and uncertainty are effectively handled. Experimental data show that when the angular observation accuracy reaches 0.1 arcseconds, the target distance estimation error using the method of this invention can be stably controlled within ±1 kilometer, which is an order of magnitude higher than the accuracy of traditional least squares or extended Kalman filtering methods.

[0056] Enhanced stability: By maintaining the square root of the covariance matrix, the SR-UKF algorithm fundamentally avoids the numerical divergence problem caused by non-positive definite matrices during iteration. Under the same test conditions, the failure (divergence) rate of the fitting process is significantly reduced from approximately 8% for traditional methods at lower observation precision (5 arcseconds) to 0.2% for high-precision (0.1 arcseconds) observations, resulting in a qualitative leap in system robustness.

[0057] Enhance the ability to adaptively model complex data and improve the level of automation. By automatically selecting the optimal number of components K of the Gaussian mixture model through the BIC criterion, the system is completely free from the dependence on the user's prior experience, enabling the system to adaptively fit complex data distributions such as multimodal and skewed distributions.

[0058] The entire process is more robust to low signal-to-noise ratio, sparse data, and data containing outliers, reduces noise interference, and broadens the applicable scenarios of the method.

[0059] The multi-threaded parallel batch processing architecture, which significantly improves processing efficiency and engineering integration capabilities, delivers a revolutionary efficiency boost. Examples show that processing a batch orbit determination task containing 150 independent orbits reduces the total time from approximately 100 hours using traditional serial methods to approximately 6 minutes.

[0060] Standardized input / output interfaces, modular design, and batch processing capabilities enable this system to be seamlessly integrated into automated testing lines or large-scale scientific data processing platforms, demonstrating significant engineering application value.

[0061] The graphical user interface (such as supporting dragging control points to adjust parameters, real-time visual feedback, and undo / redo operations) optimizes user experience and operational flexibility, making parameter tuning intuitive and efficient, breaking down the technical barriers to the use of advanced fitting algorithms.

[0062] Innovative visualization tools, such as quality heatmaps, provide users with intuitive insights into quality distribution, helping to quickly locate poorly fitted areas and improving the depth and efficiency of analysis.

[0063] The above specific embodiments are specific support for the concept proposed in this invention, and should not be used to limit the scope of protection of this invention. Any equivalent changes or modifications made on the basis of this technical solution in accordance with the technical concept proposed in this invention shall still fall within the scope of protection of this invention.

Claims

1. A Gaussian fitting material data analysis method based on a multidimensional evaluation system, characterized in that: Includes the following steps: Obtain test data. The test data is preprocessed to obtain preprocessed standard test data; The standard test data is evaluated for input quality using a pre-trained quality assessment-driven Gaussian fitting image generation model. An adaptive Gaussian-fitted material analysis model is obtained by updating the quality assessment-driven Gaussian-fitted image generation model through input quality assessment. An adaptive Gaussian fitting material analysis model is used to fit images to standard test data, and the fitted images and analysis results of the test data are output.

2. The Gaussian fitting material data analysis method based on a multidimensional evaluation system according to claim 1, characterized in that: The preprocessing includes the following steps: Data cleaning is performed on the test data to obtain cleaned data. Data cleaning includes: removing invalid values ​​based on the 3σ criterion or median absolute deviation; filling missing points using linear interpolation or spline interpolation; and using wavelet denoising with a soft thresholding function. The cleaned data is smoothed using a smoothing algorithm.

3. The Gaussian fitting material data analysis method based on a multidimensional evaluation system according to claim 2, characterized in that: Soft threshold functions include: σ is the noise standard deviation, and N is the number of data points; The smoothing algorithm includes: performing p-order polynomial fitting on the data within the window, with the following formula: , Let be the fitted value of the i-th point within the window, m be the half-length of the window, and the window contains 2m+1 data points. The coefficient 'a' is solved using the least squares method. k The smoothed value is reconstructed by minimizing the sum of squared residuals between the actual and fitted values ​​within the window. The formula includes: , Let j be the original observation value at the j-th position within the window. is the polynomial fit value at the corresponding position, where p is the polynomial order.

4. The Gaussian fitting material data analysis method based on a multidimensional evaluation system according to claim 3, characterized in that: Input Quality Assessment (DQS) includes: employing a multi-dimensional assessment; the multi-dimensional assessment includes: Signal-to-noise ratio (SNR): ;in, The mean of the signal represents the average strength of the effective signal. The total noise standard deviation reflects the overall fluctuation level of noise in the data; dB is the decibel, the unit of signal-to-noise ratio. Percentage of valid data points: ;in, : Number of valid data points, i.e., the number of usable data points retained after cleaning; : Total number of raw data points, including all collected data points; Anomaly score is calculated based on the sample path length h(x) from the isolated forest: ; Where x is the sample point to be evaluated; N is the total number of samples; h(x) is the path length of sample x in each tree in the isolated forest; E|h(x)| is the expected value of the path length of sample x in all trees; c(N) is the normalization factor of the average path length of the binary search tree when the number of samples is N, used to standardize the path length; S(x,N) is the anomaly score of sample x, with a value range of (0,1], and the closer the score is to 1, the more likely it is to be an anomaly. Based on IQR = Q3 - Q1, the outlier range Q1 is the first quartile, Q3 is the third quartile; IQR is the interquartile range; 1.5IQR is the outlier threshold. Uniformity of distribution: , The supremum; Let be the empirical cumulative distribution function, and be the cumulative distribution calculated based on n sample data. ; The cumulative distribution function is the theoretically uniform distribution. The DQS comprehensive calculation formula includes: ； in, The signal-to-noise ratio (SNR) is normalized to [0,1], linearly mapping the original SNR to accommodate different measurement ranges; Completeness represents the percentage of valid data points. The value range is [0,1]; Snorm is the normalized value of the anomaly score of the isolated forest, S(x,N)∈(0,1]. The higher the score, the more anomaly it is. 1-Snorm is used as the quality contribution; D KS This is the KS statistic, a nonparametric statistic, with values ​​ranging from [0,1]. Smaller values ​​indicate a more uniform distribution. A 1-D statistic is used. KS As a quality contribution; w1, w2, w3, w4 are the weights corresponding to each dimension, satisfying... .

5. The Gaussian fitting material data analysis method based on a multidimensional evaluation system according to claim 4, characterized in that: The establishment of a quality assessment-driven Gaussian fitting image generation model includes: The data is modeled using a Gaussian mixture model: ; in, Let the weight of the k-th Gaussian component satisfy the following condition: ; Where K is the number of sub-components of the Gaussian component; x is a random variable representing the data point to be fitted. The mean of the k-th Gaussian component determines the center position of that component; Let be the variance of the k-th Gaussian component; The standard deviation and the two together determine the width and dispersion of the detected component; To be at a given mean and variance Under the condition that x occurs, the probability density of x.

6. The Gaussian fitting material data analysis method based on a multidimensional evaluation system according to claim 5, characterized in that: A single Gaussian distribution is: ； The optimal K value is determined using the Bayesian Information Criterion (BIC). ； Where L(K) is the maximum value of the model likelihood function; p(K) = 3K-1 is the number of model parameters, i.e., each of the K Gaussian components has three parameters μ, σ, and ω, and the weight constraint reduces one degree of freedom; N is the number of data points; selection strategy: traversal. Choose the K value that minimizes BIC.

7. The Gaussian fitting material data analysis method based on a multidimensional evaluation system according to claim 6, characterized in that: A robust parameter optimization-driven Gaussian fitting image generation model is adopted, including: introducing SR-UKF for iterative parameter updates, the steps of which include: Define the state vector as , The dimension is 3K; SR-UKF is a square root unscented Kalman filter; The formulas for SR-UKF include: ; in, The initial covariance matrix is ​​given by `chol()`, which represents the Cholesky decomposition; it generates 2n+1 points. and corresponding weights ; The mean, For weights.

8. The Gaussian fitting material data analysis method based on a multidimensional evaluation system according to claim 7, characterized in that: The convergence criterion for Gaussian fitting image generation models includes: when the parameter changes... The iteration will terminate when the maximum number of iterations is reached. Optimal parameter estimation: , Let be the parameter vector for the t-th iteration; Parameter uncertainty estimation: , The covariance matrix of the parameters, The sensitivity matrix at convergence; For matrix The transpose of .

9. The Gaussian fitting material data analysis method based on a multidimensional evaluation system according to claim 8, characterized in that: The process quality monitoring and visualization module calculates and displays the parameter quality indices of the adaptive Gaussian fitting material analysis model. The parameter quality indices include: adjusted coefficient of determination, root mean square of residuals, and local fit confidence. The adjusted coefficient of determination is: ;in, Adjust the coefficient of determination to evaluate the goodness of fit of the model and penalize the number of parameters; R 2 The coefficient of determination reflects the proportion of the total variation in the data explained by the model; N is the total number of samples, i.e., the number of data points involved in the fitting; p is the number of model parameters, and for a Gaussian mixture model, p = 3K-1. The root mean square (RMS) of the residuals is: ; The confidence level for local fitting is calculated based on Mahalanobis distance.

10. A Gaussian fitting material analysis system based on a multidimensional evaluation system, characterized in that: include: Memory, used to store computer programs / instructions; A processor for executing the computer program / instructions to implement the steps of the Gaussian fitting material data analysis method based on a multidimensional evaluation system as described in any one of claims 1-9.

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