Method for establishing LIBS quantitative analysis model based on novel neural network

Abstract

The invention relates to the technical field of establishment methods of quantitative analysis models, in particular to an establishment method of an LIBS quantitative analysis model based on a novel neural network, which comprises the following steps: step 1, establishing a quantitative analysis model based on a KAN network structure; performing standardization processing on the original spectral data; kANLinear transformation is adopted in each layer of a model structure, nonlinear mapping is carried out on input features in a mode of combining a primary function and B spline interpolation, standard linear transformation is carried out on the primary function part, and nonlinear adjustment is carried out through a SiLU activation function; through step-by-step dimensionality reduction of multiple layers of KANLinear, data are sequentially subjected to feature representation of different dimensionalities and are mapped to an output regression layer, and prediction of quantitative indexes is achieved; a mean square error is adopted as a loss function, and an Adam optimization algorithm is used for gradient updating; according to the method, the LIBS quantitative analysis model is constructed on the basis of a Kolmogorov-ArnoldNetwork (KAN) network structure and a Bayesian optimization algorithm, so that the limitation of a traditional LIBS quantitative analysis method is effectively overcome.

Description

Technical Field

[0001] The present invention relates to the technical field of establishing methods for quantitative analysis models, and particularly to a method for establishing a LIBS quantitative analysis model based on a new neural network. Background Art

[0002] Laser-induced breakdown spectroscopy (LIBS) technology, as a rapid and simple elemental analysis method, has been widely used in fields such as aerospace, environmental monitoring, mineral mining, metallurgical analysis, and atmospheric monitoring because it can achieve real-time and on-line detection of solids, liquids, and gases without complex sample pretreatment. The LIBS technology ablates the surface of the sample with a high-energy laser pulse to generate a plasma, and realizes qualitative and quantitative analysis of the sample composition by analyzing the emission spectrum of the plasma. However, despite the many advantages of the LIBS technology, its application in quantitative analysis still faces many challenges.

[0003] In LIBS quantitative analysis, traditional methods mainly include external standard method, internal standard method, and free calibration method, etc. These methods usually rely on the linear or non-linear relationship between the spectral intensity of the standard sample and the element concentration, and realize the quantitative analysis of the unknown sample by constructing a calibration curve. However, these traditional methods have significant limitations in practical applications, mainly reflected in the following four aspects: 1. Limitations of linear assumptions: Traditional quantitative methods usually assume that the spectral intensity and the element concentration are linearly related. However, in practical applications, this relationship may be affected by factors such as sample matrix effects and element self-absorption, resulting in a decrease in quantitative accuracy. This limitation mainly stems from the complexity of the sample matrix and the interaction between elements, making it difficult for the linear assumption to accurately reflect the actual spectral intensity and concentration relationship.

[0004] 2. Challenges in analyzing complex samples: In multi-element analysis, the characteristic spectral lines of different elements may overlap with each other, increasing the difficulty of spectral analysis and thus affecting the accuracy of quantitative analysis. This problem is particularly prominent in the case of coexistence of multiple elements, and traditional methods are difficult to effectively distinguish and analyze overlapping spectral lines.

[0005] 3. Dependence on standard samples: Traditional quantitative methods require a large number of standard samples to construct a calibration curve, which not only increases the experimental cost but also may introduce errors due to the differences between the standard samples and the actual samples. The preparation and selection process of standard samples is complex, and it is difficult to cover all possible sample types and concentration ranges.

[0006] 4. Insufficient model generalization ability: When traditional quantitative methods face samples with different matrices or different concentration ranges, they often need to reconstruct the calibration curve and lack sufficient generalization ability. This limitation restricts the flexibility and adaptability of the LIBS technology in practical applications. Summary of the Invention

[0007] Aiming at the technical problems raised in the background art, the present invention provides a method for establishing a LIBS quantitative analysis model based on a new neural network.

[0008] The technical solution adopted by the present invention is as follows: A method for establishing a LIBS quantitative analysis model based on a new neural network specifically includes the following steps: Step 1, build a quantitative analysis model based on the KAN network structure; Perform standardization processing on the original spectral data; Adopt the KANLinear transformation in each layer of the model structure, and perform non-linear mapping on the input features by combining the basis function and B-spline interpolation. Among them, the basis function part performs standard linear transformation and non-linear adjustment through the SiLU activation function; Through the step-by-step dimensionality reduction of multiple layers of KANLinear, the data sequentially passes through feature representations of different dimensions and is mapped to the output regression layer to realize the prediction of quantitative indicators; Adopt the mean square error as the loss function and use the Adam optimization algorithm for gradient update; Add a regularization loss during model training, including L1 regularization of the activation function output and entropy regularization of the spline weight, to control the model complexity; Step 2, optimize the key hyperparameters of the quantitative analysis model, and use the Bayesian optimization algorithm to tune the model hyperparameters; In one embodiment, Step 2, the specific method for optimizing the key hyperparameters of the quantitative analysis model and using the Bayesian optimization algorithm to tune the model hyperparameters is as follows; Initialization: Randomly select several groups of initial parameters in the hyperparameter space , and calculate their corresponding objective function values ; Construct a probability model: Use Gaussian process regression to model the objective function, and assume that the objective function f(x) follows a Gaussian distribution: ; where, is the mean function, set to a constant or zero mean; is the covariance function, used to describe the correlation between different hyperparameter points; Adopt the radial basis function as the covariance function: ; where is the length scale parameter; Select sampling points: Select the next sampling point based on the acquisition function, and the acquisition function is the expected improvement: ; where is the current optimal objective function value; represents the improvement amount of the new sampling point relative to the current optimal point; The function selects the hyperparameter combination that is most likely to improve performance by balancing exploration and exploitation.

[0009] Evaluate and update: calculate new sampling points The objective function value of , and add it to the historical observation data, then update the Gaussian process model and refit the mean function and covariance function , to reflect new observation information.

[0010] Iterative convergence: Repeat the above steps until the predetermined number of iterations or convergence condition is reached.

[0011] The present invention has the following beneficial effects: Compared with existing technologies, the LIBS quantitative analysis model constructed based on the Kolmogorov-Arnold Network (KAN) structure and the Bayesian optimization algorithm effectively overcomes the limitations of traditional LIBS quantitative analysis methods. In addressing the limitations of linear assumptions, the model leverages the KAN network's powerful nonlinear modeling capabilities to accurately process complex nonlinear relationships in spectral data. Unlike traditional methods that assume a linear relationship between spectral intensity and element concentration, the KAN network fully considers the influence of factors such as sample matrix effects and elemental self-absorption. By parameterizing the activation function using spline functions, it decomposes complex high-dimensional functions into a combination of simple one-dimensional functions, deeply exploring data features and more accurately reflecting the actual relationship between spectral intensity and concentration. This significantly improves the accuracy of quantitative analysis and avoids errors caused by linear assumptions.

[0012] The model's multi-layer feature transformation module and adaptability to multivariate analysis play a key role in addressing the challenge of spectral line overlap in complex sample analysis. The cascade of multiple KANLinear layers combines standard linear transformations with spline interpolation, enhancing nonlinear representation capabilities. Furthermore, the model is able to learn complex patterns in spectral data, effectively addressing spectral line overlap in multi-element analysis, accurately distinguishing and resolving overlapping spectral lines, and improving the accuracy of quantitative analysis of complex samples.

[0013] This model offers significant advantages in reducing reliance on standard samples. Firstly, the KAN network's generalization capabilities are enhanced, allowing it to better adapt to samples of varying matrices and concentration ranges after training. Secondly, the Bayesian optimization algorithm, by constructing a probabilistic model of the objective function, efficiently approaches the global optimal solution within a limited number of iterations, optimizing model hyperparameters and reducing errors introduced by differences between standard samples and actual samples. This not only reduces experimental costs but also addresses the complexities of standard sample preparation and selection, making it difficult to cover all sample types and concentration ranges.

[0014] In addition, the generalization ability of the model is greatly enhanced. The Bayesian optimization algorithm's refined tuning of hyperparameters such as the order of spline basis functions and grid size enables the model to maintain stable and efficient prediction performance when facing samples with different matrices or concentration ranges, without the need to reconstruct the calibration curve. This improves the flexibility and adaptability of LIBS technology in practical applications and promotes its wide application in the fields of high-precision measurement and complex sample analysis. Brief Description of the Drawings

[0015] Figure 1 is a simple principle display diagram of the quantitative analysis model established in the present invention; Figure 2 is the structural diagram of the Bayesian optimization model process in the present invention. Detailed Embodiments

[0016] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by terms such as "front", "upper", "lower", "left", "right", "vertical", "horizontal", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention.

[0017] To solve the problems existing in the background technology, the present application proposes the following technical solution: a method for establishing a LIBS quantitative analysis model based on a new neural network; Scheme Explanation: In the field of LIBS analysis, achieving high-precision and high-reliability quantitative analysis of substances is the core goal, and constructing an analysis model with both high efficiency and strong interpretability is the main challenge currently faced. In response to this challenge, the present invention builds a network model for efficient quantitative detection of LIBS spectroscopy based on the Kolmogorov-Arnold Network (KAN) network structure. At the same time, the Bayesian optimization algorithm is used to automatically tune the key hyperparameters of the built model to further improve the performance and robustness of the model.

[0018] The KAN network architecture is a breakthrough neural network architecture. This network framework stems from the Kolmogorov-Arnold representation theorem, which states that any continuous multivariate function can be decomposed into a combination of a finite number of univariate continuous functions. The core innovation of the KAN network architecture lies in placing learnable activation functions on the connection edges of the network (instead of traditional nodes) and achieving efficient fitting of complex functions through modular design; The quantitative model established by the present invention based on the KAN network architecture mainly consists of the following key components: Input Feature Mapping Module: In the data input stage, this model adopts a method that combines linear transformation with the SiLU activation function to enhance the expressive ability of the input data. This step can effectively adjust the data distribution, making it more suitable for the calculations of subsequent network layers and improving the numerical stability of the model.

[0019] B-Spline Basis Function Calculation Module: Based on the B-spline interpolation theory, this module maps the input data to a higher-dimensional feature space by constructing piecewise polynomial basis functions. By calculating the B-spline basis at multiple nodes, this layer can capture the local structural information of the data, thereby improving the model's ability to depict complex mapping relationships.

[0020] Adaptive Grid Adjustment Module: On the basis of spline calculations, this model introduces an adaptive grid adjustment mechanism, enabling the distribution of grid points to dynamically adapt to the statistical distribution of the input data. This method effectively enhances the expressive ability of the spline function, enabling the model to more accurately fit the data distribution and reduce interpolation errors.

[0021] Layer Feature Transformation Module: This model uses a cascade of multiple KANLinear layers to perform layer-by-layer transformation on the input data. Each layer contains both standard linear transformation and spline interpolation calculations, enabling the network to maintain the advantages of linear calculations while increasing its non-linear expressive ability, thereby improving the fitting effect for complex functions.

[0022] Regularization Control Module: During the model training process, the model introduces regularization losses, mainly including L1 regularization of the activation function output and entropy regularization of the spline weights. This strategy can effectively control the complexity of the model, prevent overfitting, and ensure the generalization ability of the model, enabling it to maintain stable prediction performance when facing new data.

[0023] Based on the above technical solutions, Build a quantitative analysis model based on the KAN network structure, which specifically includes the following steps: Step 1, build a quantitative analysis model based on the KAN network structure; Perform standardization processing on the original spectral data to eliminate scale differences and enhance the training stability of the model.

[0024] Adopt KANLinear transformation in each layer of the model structure, and perform non-linear mapping on the input features by combining basis functions and B-spline interpolation. Among them, the basis function part performs standard linear transformation and non-linear adjustment through the SiLU activation function; The spline interpolation part uses B-spline basis functions to generate local weighted sums, thereby enhancing the feature extraction ability.

[0025] Through the step-by-step dimensionality reduction of multiple layers of KANLinear, the data passes through feature representations of different dimensions such as (1024, 512, 256) in sequence and is mapped to the output regression layer to achieve the prediction of quantitative indicators; The mean squared error is used as the loss function, and the Adam optimization algorithm is used for gradient update; in addition, to prevent the model from overfitting and enhance its generalization ability, we added a regularization mechanism during the training process.

[0026] A regularization loss is added to the model training, including the L1 regularization of the activation function output and the entropy regularization of the spline weights, to control the model complexity, prevent overfitting, and ensure the model generalization ability. This strategy not only restricts the excessive expansion of model parameters but also effectively avoids overfitting, ensuring the stability and reliability of the model on new data. And to further improve the model generalization ability and fitting accuracy, this model dynamically optimizes the positions of B-spline grid points during the training process through an adaptive grid adjustment mechanism to make it more adaptable to the distribution characteristics of the data.

[0027] Step 2: Optimize the key hyperparameters of the quantitative analysis model, and use the Bayesian optimization algorithm to tune the model hyperparameters; In Step 2, the specific method for optimizing the key hyperparameters of the quantitative analysis model and using the Bayesian optimization algorithm to tune the model hyperparameters is as follows; Initialization: Randomly select several groups of initial parameters within the hyperparameter space , and calculate their corresponding objective function values ; Construct a probability model: Use Gaussian process regression to model the objective function, assuming that the objective function f(x) follows a Gaussian distribution: where, is the mean function, set to a constant or zero mean; is the covariance function, used to describe the correlation between different hyperparameter points; Adopt the radial basis function as the covariance function: ; where is the length scale parameter, controlling the smoothness of the function; Select sampling points: Based on the acquisition function, select the next sampling point, and the acquisition function is the expected improvement: ; where is the current optimal objective function value; represents the improvement amount of the new sampling point relative to the current optimal point; The function selects the hyperparameter combination most likely to improve performance by balancing exploration and exploitation.

[0028] Evaluation and update: Calculate the objective function value of the new sampling point , and add it to the historical observation data. Subsequently, update the Gaussian process model and refit the mean function and the covariance function , to reflect the new observation information.

[0029] Iterative convergence: Repeat the above steps until a predetermined number of iterations or convergence conditions are reached.

[0030] The quantitative analysis model based on the KAN network architecture in the present invention is similar to the traditional MLP (Multi-Layer Perceptron) model and has the architecture characteristic of multi-layer stacking.

[0031] However, the model of the present invention realizes higher flexibility and interpretability by placing the learnable activation function on the connection edges of the network instead of the traditional nodes.

[0032] Compared with the MLP, in addition to adjusting parameters such as the basic number of network layers and the number of neurons in each layer, the model of the present invention also introduces a series of additional parameters such as the order of the spline basis function and the grid size, and these parameters have a significant impact on the performance of the model.

[0033] Therefore, in order to fully exploit the potential of the model of the present invention and achieve optimal performance, this study uses the Bayesian optimization algorithm to finely tune the hyperparameters of the model of the present invention.

[0034] Specifically, we first fixed the basic network architecture parameters ([L, 512, 256, 128, Y] architecture, where L is the length of the input spectrum, [512, 256, 128] are the intermediate layers, and Y is the scalar value of the output layer representing the target quantitative variable) to ensure the stability of the basic framework of the model.

[0035] Subsequently, for the parameters unique to the KAN network (such as the order of the spline basis function, the grid size, etc.), we designed a Bayesian optimization process to automatically search for the optimal parameter combination.

[0036] Bayesian optimization constructs a probability model of the mean square error on the validation set of the objective function and efficiently finds the optimal parameter configuration within a limited number of iterations, thereby significantly improving the performance and robustness of the model.

[0037] This optimization process not only reduces the workload of manual parameter tuning but also ensures the efficiency and accuracy of the model in the quantitative analysis task of complex spectral data.

[0038] The optimization ranges of specific parameters are shown in Table 1: Table 1 Optimization ranges of parameters

[0039] Grid Size: This parameter determines the number of grid points for B-spline interpolation, i.e., the number of intervals divided in the input feature space. A larger grid size can provide a finer feature mapping and improve the model's non-linear representation ability, but may lead to overfitting; a smaller grid size reduces the model's flexibility but can improve generalization ability.

[0040] Spline Order: This parameter defines the order of the B-spline basis function, i.e., the smoothness of the interpolation function. A higher spline order can generate a smoother fitting curve and improve the ability to represent complex patterns, but may introduce more computational costs. Common spline orders include 1 (linear spline), 2 (quadratic spline), and 3 (cubic spline, usually used for smooth fitting).

[0041] Spline Scaling Factor: This parameter is used to control the scaling amplitude of the spline interpolation part and determines the contribution of the B-spline to the overall feature transformation. Larger values may enhance the role of spline interpolation, making the model more dependent on non-linear mapping, while smaller values may reduce the impact of non-linear features and make the model tend to linear transformation.

[0042] Activation Function Regularization: This parameter is used to regularize the output of the activation function, usually using L1 regularization to promote sparsity. Stronger regularization can force the activation of some neurons to approach zero, thereby reducing the complexity of the model and improving generalization ability.

[0043] Entropy Regularization: This parameter is used to regularize the distribution of spline weights to ensure that the model does not overly rely on specific B-spline basis functions. By increasing entropy regularization, the weight distribution can be made more uniform, reducing the risk of overfitting and improving the stability of the model.

[0044] To fully verify the performance of the model of the present invention, we conducted a comparative experiment with an MLP model under the same framework. The structure of the MLP was set to the same [L, 512, 256, 128, Y] architecture to ensure the fairness of the control experiment (where L is the length of the input spectrum, [512, 256, 128] are the number of neurons in the intermediate layers, and Y is the scalar value representing the target quantitative variable in the output layer).

[0045] Table 2 Comparison of Experimental Results of All Models

[0046] All models used the same training set and validation set, that is, 180 LIBS spectral data of 6 stainless steel samples collected (each sample has 30 LIBS spectra) were randomly divided into a training set and a test set according to a ratio of 8:2.

[0047] The training parameter settings of the MLP quantitative model used in the present invention and the control are as follows: initial learning rate: 0.0001; optimizer: Adam; batch size: 32. All experimental results are shown in Table 2. The present invention shows significant advantages in the quantitative analysis tasks of 9 elements (Si, Ni, C, Al, W, Ti, V, Mn, Mo) in six stainless steel samples.

[0048] The R² value of the present invention is only slightly lower than that of the MLP model for element C, and the quantitative detection accuracy of other elements is much higher than that of the MLP. At the same time, for the mean value of the quantitative results of these 9 elements, the present invention also far exceeds 0.67 of the MLP with a score of 0.9, further verifying the high prediction accuracy and stability of the present invention.

[0049] The LIBS quantitative analysis model constructed by the present invention based on the Kolmogorov - Arnold Network (KAN) network structure and the Bayesian optimization algorithm effectively overcomes the limitations of traditional LIBS quantitative analysis methods. In solving the limitations of linear assumptions, this model, relying on the powerful non - linear modeling ability of the KAN network, can accurately process the complex non - linear relationships in spectral data. Different from the traditional method that assumes a linear relationship between spectral intensity and element concentration, the KAN network can fully consider the influence of factors such as sample matrix effect and element self - absorption. It decomposes complex high - dimensional functions into combinations of simple one - dimensional functions through spline function - parameterized activation functions, deeply excavates data features, more accurately reflects the actual relationship between spectral intensity and concentration, significantly improves the accuracy of quantitative analysis, and avoids errors caused by linear assumptions.

[0050] For the problem of spectral line overlap in the analysis of complex samples, the multi - layer feature transformation module and multi - variable analysis adaptability of the model play a key role. The cascading of multiple KANLinear layers includes both standard linear transformations and spline interpolation calculations, enhancing the non - linear expression ability. At the same time, the model can learn complex patterns in spectral data, effectively handle the problem of spectral line overlap in multi - element analysis, accurately distinguish and resolve overlapping spectral lines, and improve the accuracy of quantitative analysis of complex samples.

[0051] The present model has obvious advantages in reducing the dependence on standard samples. On the one hand, the generalization ability of the KAN network is improved, and it can better adapt to samples with different matrices and concentration ranges after training; on the other hand, the Bayesian optimization algorithm constructs a probability model of the objective function, efficiently approximates the global optimal solution within a limited number of iterations, optimizes the model hyperparameters, and reduces the error introduced by the difference between standard samples and actual samples. This not only reduces the experimental cost but also solves the problems of complex standard sample preparation and selection processes and difficulty in covering all sample types and concentration ranges.

[0052] In addition, the generalization ability of the model is greatly enhanced. The Bayesian optimization algorithm's refined tuning of hyperparameters such as the order of spline basis functions and grid size enables the model to maintain stable and efficient prediction performance when faced with samples of different matrices or concentration ranges, without the need to reconstruct the calibration curve. This improves the flexibility and adaptability of LIBS technology in practical applications and promotes its wide application in the fields of high-precision measurement and complex sample analysis.

[0053] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for establishing a LIBS quantitative analysis model based on a novel neural network, characterized in that, Specifically, it includes the following steps: Step 1: Build a quantitative analysis model based on the KAN network structure. The specific method is as follows: Perform standardization processing on the original spectral data; At each layer of the model structure, adopt the KANLinear transformation. Through the combination of basis functions and B-spline interpolation, perform non-linear mapping on the input features. Among them, the basis function part performs standard linear transformation and non-linear adjustment through the SiLU activation function; Through the step-by-step dimensionality reduction of multiple layers of KANLinear, the data sequentially passes through feature representations of different dimensions and is mapped to the output regression layer to achieve the prediction of quantitative indicators; Adopt the mean square error as the loss function and use the Adam optimization algorithm for gradient update; Add regularization loss in model training, including L1 regularization of the activation function output and entropy regularization of the spline weights, to control the model complexity; Step 2: Optimize the key hyperparameters of the quantitative analysis model and use the Bayesian optimization algorithm to tune the model hyperparameters.

2. The method for establishing a LIBS quantitative analysis model based on a novel neural network according to claim 1, wherein In step 2, the specific method for optimizing the key hyperparameters of the quantitative analysis model and using the Bayesian optimization algorithm to tune the model hyperparameters is as follows: Initialization: Randomly select several groups of initial parameters within the hyperparameter space and calculate their corresponding objective function values ; Construct a probability model: Use Gaussian process regression to model the objective function, assuming that the objective function f(x) follows a Gaussian distribution: ; where is the mean function, which is set to a constant or a zero mean; is the covariance function, which is used to describe the correlation between different hyperparameter points; The radial basis function is used as the covariance function: ; where is the length scale parameter; Select sampling points: Select the next sampling point based on the acquisition function, and the acquisition function is the expected improvement: ; where is the current optimal objective function value; represents the improvement of the new sampling point relative to the current optimal point; The function selects the hyperparameter combination that is most likely to improve performance by balancing exploration and exploitation; Evaluation and update: Calculate the objective function value of the new sampling point and add it to the historical observation data. Subsequently, update the Gaussian process model and refit the mean function and the covariance function to reflect the new observation information; ​ Iterative convergence: Repeat the above steps until a predetermined number of iterations or convergence conditions are reached.

Images