A method for evaluating comprehensive performance of road material with multiple indexes

Abstract

The application relates to a road material multi-index comprehensive performance evaluation method, and belongs to the technical field of data processing. The method comprises the following steps: constructing a road material multi-index data set and performing data labeling; calculating attribute correlation weights and noise robustness factors, dynamically adjusting a normalization scale, and obtaining normalized road material multi-index data; constructing a feature enhancement mapping module, extracting the local structure of the normalized data through a radial basis kernel function, enhancing nonlinear expression capability by using attribute interaction items, extracting high-order nonlinear features, and obtaining final feature enhancement mapping output; constructing a road material multi-index comprehensive performance evaluation model; training the model by using the final feature enhancement mapping output, obtaining a trained model; and inputting new road material data samples into the trained model after the new road material data samples are processed through steps S2 and S3, so that performance grade evaluation results are obtained. The application can improve the accuracy of road material multi-index comprehensive performance evaluation.

Description

Technical Field

[0001] This invention belongs to the field of data processing technology, specifically relating to a method for comprehensive performance evaluation of road materials based on multiple indicators. Background Technology

[0002] With the rapid development of road transportation infrastructure, the performance of road materials directly affects the service life and safety of road projects. Traditional road material evaluation methods often rely on single or a few indicators, such as compressive strength, density, or durability, and are graded through laboratory testing and empirical judgment. This approach has significant limitations: on the one hand, the performance of road materials is determined by a variety of physical, mechanical, chemical, and environmentally sensitive indicators, and a single indicator cannot comprehensively reflect the overall quality of the material; on the other hand, there are often complex nonlinear coupling relationships and physical constraints between different indicators. For example, the product of porosity and water absorption rate has a significant impact on strength, and traditional linear methods cannot effectively capture these deep-seated relationships.

[0003] Existing methods also have shortcomings in data processing. Commonly used normalization methods, such as min-max or z-score, often apply a uniform scaling rule to all attributes, ignoring the correlation and noise differences between attributes. This can easily weaken the contribution of key indicators and amplify noise signals, thus affecting the stability and classification accuracy of the model. Even with the introduction of machine learning or neural network methods, without feature enhancement mechanisms and physical consistency constraints tailored to the characteristics of road materials, the model may still exhibit the problem of "accurate predictions but violating the laws of materials science," such as outputting unreasonable attribute correlation trends. Furthermore, road material data is typically high-dimensional, sparse, and imbalanced. Conventional neural networks are prone to getting stuck in local optima or gradient vanishing during weight initialization and training, leading to blurred classification boundaries and making it difficult to promote in engineering practice.

[0004] The following problems still exist in the existing technology and need to be further solved: Existing min-max or z-score methods scale all attributes indiscriminately, ignoring the correlation and noise differences between attributes, resulting in the weakening of key attributes and the amplification of noise; Principal component analysis, linear projection, or simple polynomial extension can only model shallow linear relationships and cannot effectively capture the nonlinear interactions and coupling effects in material properties; Conventional networks rely on fixed activation functions and are not sensitive to key attributes, which easily leads to gradient vanishing or the averaging of feature contributions; Existing methods only pursue classification accuracy and ignore the physical consistency between material properties, which may output results that violate scientific laws. Summary of the Invention

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] This invention provides a method for evaluating the comprehensive performance of road materials based on multiple indicators, comprising the following steps:

[0007] S1. Construct a multi-index dataset for road materials and label the data;

[0008] S2. Calculate the attribute correlation weight and noise robustness factor for the multi-index data of road materials, and dynamically adjust the normalization scale to obtain normalized multi-index data of road materials.

[0009] S3. Construct a feature enhancement mapping module. This module extracts the local structure of normalized road material multi-index data through radial basis kernel function, and enhances nonlinear expression capability by using attribute interaction term to extract high-order nonlinear features, and obtains the final feature enhancement mapping output.

[0010] S4. Construct a comprehensive performance evaluation model for road materials based on multiple indicators. The model adopts a deep feedforward network design, including an input layer, a hidden layer, and an output layer. The model is trained using the final feature enhancement mapping output to obtain a trained model.

[0011] S5. After processing the new road material data samples in steps S2 and S3, input them into the trained model to obtain the performance level evaluation results.

[0012] Furthermore, road material multi-index data suffers from problems such as high attribute dimensionality, large scale differences, complex correlations between attributes, and significant noise interference. Conventional normalization techniques such as min-max or z-score apply a uniform scaling method to all attributes, ignoring the correlations between attributes and differences in noise distribution. This results in the normalized data failing to effectively retain the weights of key attributes, which can easily amplify the impact of noise and weaken the contribution of highly correlated attributes in subsequent model training.

[0013] This invention dynamically adjusts the normalization scale by calculating attribute correlation weights and noise robustness factors to enhance the contribution of highly correlated attributes and suppress the influence of noise. In step S2, attribute correlation weights are calculated using the Sigmoid function based on the absolute value of the average Pearson correlation coefficient between each attribute and other attributes, thereby strengthening the contribution of highly correlated attributes in normalization and ensuring that important attributes receive higher weights. Based on the absolute deviation of each attribute value from its sample median, a local noise robustness factor is calculated using an exponential decay function to suppress the influence of outliers and reduce the contribution of noisy attributes. Combining the basic scaling of the global mean and standard deviation, attribute correlation weights, and noise robustness factors, normalized multi-index data of road materials are dynamically calculated to ensure that highly correlated attributes are prominent and noise is suppressed.

[0014] Although the normalized data has been scaled, there are complex nonlinear interactions between road material properties. Conventional feature extraction methods such as principal component analysis or linear projection can only capture shallow linear relationships and cannot model high-order nonlinear dependencies. This makes it difficult for subsequent deep networks to distinguish subtle performance differences, such as the classification of high-quality and low-quality materials.

[0015] This invention captures local structure through radial basis kernel functions and enhances nonlinear expressive power by using attribute interaction terms to extract higher-order nonlinear features.

[0016] Furthermore, in step S3, the local structure of the normalized road material multi-index data is captured by the radial basis function: the K-means clustering algorithm is used to perform cluster analysis on the normalized road material multi-index data to generate K cluster centers as the center points of the radial basis function, and the local distribution characteristics of the data are extracted; based on the distance between the sample and the cluster center vector, the similarity between the sample and each cluster center is calculated by the radial basis function, and the local nonlinear characteristics of the data are extracted.

[0017] Furthermore, in step S3, attribute interaction terms are used to enhance the nonlinear expressive power, extract higher-order nonlinear features, and obtain the final feature enhancement mapping output: based on the predefined first attribute pair set, the attribute interaction terms of the corresponding attribute values ​​in the sample are calculated to capture the second-order nonlinear coupling relationship between attributes; the radial basis kernel function value and the attribute interaction terms are concatenated into vectors to form the final feature enhancement mapping output, thereby capturing both local structure and global nonlinear relationship.

[0018] Furthermore, the feature map output exhibits high-dimensional sparsity. Conventional deep neural networks, employing random initialization of weights, are prone to getting trapped in local optima or gradient vanishing problems, especially when the road material data is unevenly distributed, which can easily lead to classification bias. In step S4, the model of this invention calculates initial weights based on the statistical characteristics of the final feature enhancement map output and the intra-class distribution density, ensuring that the initial weight values ​​align with the data distribution, thereby improving training stability: Based on the sample class labels, the feature mean vector for each class is calculated as the representative feature vector for that class; based on the variance and covariance matrix eigenvectors of the feature mean vectors, a distribution divergence correction term is calculated to enhance adaptability to imbalanced data and is used to adjust the initial weight values; the weighted average of the feature mean vectors of each class is added to the distribution divergence correction term to obtain the initial weight matrix for each layer of the neural network, ensuring that the initial weight values ​​align with the data distribution and improving training stability.

[0019] Furthermore, conventional activation functions such as ReLU are insensitive to the local importance of road material properties and cannot dynamically adjust feature contributions, easily leading to key indicators such as compressive strength being overwhelmed by secondary indicators. In step S4, the hidden layer weights feature channels through a gating mechanism and combines attribute importance feedback to dynamically enhance the response of key attributes: based on the absolute value of the input features, the attention score of each dimension of features is calculated through the Softmax function to dynamically identify key attributes and enhance the network's response to important attributes; based on the attention score, a gating vector is generated through the Sigmoid function to control the pass rate of each feature channel and adjust the feature contribution; an adaptive activation function is applied to the linearly transformed features, combining linear and nonlinear transformations to obtain an adaptive activation output vector, enhancing nonlinear expressive power; the gating vector and the adaptive activation output vector are multiplied element-wise to generate the output feature vectors of each layer of the neural network.

[0020] Furthermore, the evaluation of road material performance requires the comprehensive consideration of the nonlinear coupling effect of multiple indicators. Conventional output layers use the standard softmax function to ignore the dynamic interaction and physical constraints between attributes, which can easily lead to a weakening of the contribution of key indicators. In step S4, the output layer dynamically integrates higher-order features and physical priors through attribute attention gating and collaborative calculation with category prototypes to generate predictive outputs that conform to the laws of materials science: Based on the category feature mean vector, correlation weight vector, and feature vector of the neural network output layer, attribute-level attention weights are constructed, and the sensitivity is controlled by the correlation strength coefficient to capture the nonlinear correlation between feature channels and categories, resulting in a correlation vector; Based on the category feature mean vector and the predefined attribute pair interaction term concatenation vector, a gating value is generated by the Sigmoid function, and then combined with the feature mean vector to obtain a physically constrained gating prototype vector; Based on the corresponding product of the correlation vector elements and the gating prototype vector elements, the hyperbolic tangent function and probability scaling factor are applied, and the predictive probability is output through the softmax function, dynamically integrating higher-order features and physical priors.

[0021] Furthermore, the comprehensive performance evaluation model for road materials with multiple indicators integrates classification loss terms and physical consistency loss terms to construct a total loss function.

[0022] Furthermore, the iterative training process of the road material multi-index comprehensive performance evaluation model adopts an optimization algorithm based on gradient descent, with the goal of minimizing the total loss function. Each iteration includes two stages: forward propagation and back propagation. In forward propagation, the input training samples are processed by each layer of the neural network to obtain the predicted output. In back propagation, the gradient of the loss function with respect to the network parameters is calculated, and the weights and bias parameters are updated according to the learning rate.

[0023] Furthermore, the model's stopping iteration condition is based on validation set performance monitoring. Training is stopped early when the validation set loss no longer decreases or begins to increase after 10 consecutive iterations.

[0024] The advantages of this invention are:

[0025] This invention regulates the normalization process by jointly adjusting attribute relevance weights and noise robustness factors, highlighting the contribution of key attributes while suppressing the influence of outliers; it integrates radial basis kernel functions and attribute interaction terms defined by expert priors to capture high-order nonlinear relationships between local and global data; it employs attribute attention, gating mechanisms, and adaptive activation functions to achieve dynamic responses to key indicators and prevent key features from being overwhelmed; and it adds physical relevance constraints in addition to classification loss to force prediction results to conform to the laws of materials science, avoiding the situation of being "accurate but unreasonable". Attached Figure Description

[0026] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0027] Figure 1 This is a flowchart of the steps of the method of the present invention;

[0028] Figure 2 This is a flowchart of the adaptive weighted normalization process of the present invention;

[0029] Figure 3 The impact of the weight sensitivity hyperparameter on classification performance;

[0030] Figure 4 The impact of noise suppression coefficient on classification accuracy;

[0031] Figure 5 A comparison of the performance of different methods in road material evaluation;

[0032] Figure 6 This is a flowchart of the data processing of the feature enhancement mapping module of the present invention;

[0033] Figure 7 This is a typical PCA feature distribution diagram;

[0034] Figure 8 Enhanced distribution of this technical feature;

[0035] Figure 9 This is a flowchart of the neural network modeling process of the present invention;

[0036] Figure 10 A heatmap of the actual physical correlation coefficients;

[0037] Figure 11 Predicting heatmaps without physical constraints;

[0038] Figure 12 The heat map is a prediction of the physical constraints of this technology. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] Example 1

[0041] In this embodiment, as Figure 1 As shown, this invention provides a method for evaluating the comprehensive performance of road materials based on multiple indicators, the specific steps of which include:

[0042] S1. Construct a multi-index dataset for road materials.

[0043] Data acquisition in this invention is primarily conducted through laboratory testing, on-site inspection, and integration of historical databases, specifically including:

[0044] Laboratory testing includes standard experiments on the physical, mechanical, durability and chemical properties of road material samples, such as using a press to measure compressive strength and tensile strength, using a density meter to determine density, using a porosity tester to obtain porosity, and measuring indicators such as water absorption rate and elastic modulus.

[0045] On-site testing involves collecting samples from actual road engineering projects and conducting in-situ tests to obtain material performance data under real-world conditions.

[0046] Historical database integration utilizes accumulated data from existing research or engineering projects to supplement and expand the scale of the dataset;

[0047] In one embodiment, the properties include density (kg / m³), porosity (%), water absorption (%), compressive strength (MPa), tensile strength (MPa), elastic modulus (GPa), Poisson's ratio (dimensionless), abrasion resistance index (dimensionless), water resistance index (dimensionless), temperature sensitivity coefficient (1 / ℃), humidity sensitivity coefficient (1 / %), aging index (dimensionless), fatigue life (cycles), bond strength (MPa), viscosity (Pa·s), softening point (℃), permeability (cm / s), particle size distribution index (dimensionless), compaction degree (%), moisture content (%), pH value (dimensionless), and oxidation degree (%).

[0048] Furthermore, the collected data is labeled. The data labeling process is based on expert knowledge and industry standards and specifications. Each sample is assigned a category label according to its comprehensive performance. The labeling type is classification label. In this embodiment, road materials are divided into three performance levels: high quality, medium quality and low quality.

[0049] S2, Adaptive Weighted Normalization

[0050] Road material multi-index data suffers from high attribute dimensionality, large scale differences, complex correlations between attributes, and significant noise interference. Conventional normalization techniques such as min-max or z-score apply a uniform scaling method to all attributes, ignoring the correlations between attributes and differences in noise distribution. This results in the normalized data failing to effectively retain the weights of key attributes, which can easily amplify the impact of noise and weaken the contribution of highly correlated attributes in subsequent model training.

[0051] This invention dynamically adjusts the normalization scale by calculating attribute correlation weights and noise robustness factors to enhance the contribution of highly correlated attributes and suppress the influence of noise. The adaptive weighted normalization step, such as... Figure 2 As shown:

[0052] 1) Calculate the attribute relevance weights

[0053] Based on the absolute value of the average Pearson correlation coefficient between each attribute and other attributes, the correlation weight is calculated using the Sigmoid function. This strengthens the contribution of highly correlated attributes in the normalization process and ensures that important attributes receive higher weights, as expressed below:

[0054] ,

[0055] In the formula, This represents the relevance weight of the j-th attribute, with a value range of... The larger the value, the more important the attribute. Attributes include density (unit: kg / m³), porosity (unit: %), water absorption rate (unit: %), etc. This represents the weight sensitivity hyperparameter, which controls the steepness of the Sigmoid function. The larger the value, the steeper the function and the higher the weight discrimination. The preferred value is 1.6. Let represent the absolute value of the average Pearson correlation coefficient between the j-th attribute and all other attributes. This value quantifies the global correlation strength of the j-th attribute and is calculated over the entire training set. The calculation method is as follows: Properties include density (in kg / m³), porosity (in %), and water absorption (in %). This represents the total number of attributes, i.e., the dimension of the dataset; j is the index of the first attribute. For the second attribute index; Represents the natural exponential function; Indicates the relationship between the j-th attribute and the j-th attribute. The Pearson correlation coefficient between attributes measures the degree of linear correlation between two attributes. It is calculated using all sample values ​​in the training set. Attributes include density (in kg / m³), porosity (in %), water absorption rate (in %), etc.

[0056] It should be noted that, The term is an application of the Sigmoid function, used to... Mapped to The interval is used as the weight, combined with the weight sensitivity hyperparameter. Control sensitivity, enhance The contribution of highly correlated attributes is weakened. The influence of small, low-correlation attributes is highlighted during the normalization process, making important attributes stand out.

[0057] It should also be noted that attribute relevance weights The absolute value of the mean Pearson correlation coefficient is obtained by using the Sigmoid function. Nonlinear mapping is used to give highly correlated attributes an exponentially enhanced weight. For example, the strong correlation between density and porosity can be given an exponentially enhanced weight, which can significantly amplify the small differences in key physical attributes after normalization, thus solving the problem that conventional linear scaling weakens the contribution of important attributes.

[0058] 2) Calculate the noise robustness factor

[0059] Based on the absolute deviation of each attribute value from its sample median, a local noise robustness factor is calculated using an exponential decay function, thereby suppressing the influence of outliers and reducing the contribution of noise attributes, expressed as:

[0060] ,

[0061] In the formula, This represents the noise robustness factor of the j-th attribute of the i-th sample, and its value ranges from 1 to 2. The smaller the value, the more likely the sample value is to be an outlier. Attributes include density (unit: kg / m³), porosity (unit: %), water absorption rate (unit: %), etc. This represents the noise suppression coefficient, which controls the exponential decay rate. The larger the value, the more sensitive it is to outliers. The preferred value is 2.6. This represents the original data value of the j-th attribute of the i-th sample. Attributes include density (in kg / m³), porosity (in %), water absorption rate (in %), etc. This represents the median of the j-th attribute across all samples, characterizing the central tendency of that attribute. It is not sensitive to outliers. Attributes include density (in kg / m³), porosity (in %), water absorption (in %), etc. It is an exponential function used to calculate the natural exponential value.

[0062] It should be noted that extreme values ​​occasionally appear in road material data, such as extreme values ​​in compressive strength. In such cases, the median value will be used. This serves as a benchmark for suppressing outliers, thereby increasing the noise robustness factor. The normalization result for abnormal samples is close to zero to avoid noise being amplified in subsequent models.

[0063] In one embodiment, such as Figure 3 , Figure 4 As shown, a hyperparameter sensitivity analysis was performed to explore the weight sensitivity hyperparameter. and noise suppression coefficient The experimental results show that the weight sensitivity hyperparameter affects model performance. Peak accuracy and noise suppression coefficient were obtained at a value of approximately 1.6. Peak accuracy is achieved at a value of around 26, and the hyperparameter maintains high accuracy near the optimal value.

[0064] 3) Perform weighted normalization calculation

[0065] By combining the global mean and standard deviation with scaling, attribute correlation weights, and noise robustness factors, the normalized output is dynamically calculated to ensure that highly correlated attributes are highlighted and noise is suppressed, as shown below:

[0066] ,

[0067] In the formula, This represents the j-th attribute of the i-th sample after normalization. Attributes include density (in kg / m³), porosity (in %), water absorption rate (in %), etc. This represents the mean of the j-th attribute across all samples. Attributes include density (in kg / m³), porosity (in %), water absorption (in %), etc. This represents the standard deviation of the j-th attribute across all samples. Attributes include density (in kg / m³), porosity (in %), water absorption (in %), etc.

[0068] It should be noted that, The term is the conventional z-score normalization part, used to scale the data to a mean of 0 and a standard deviation of 1. However, road material data is characterized by complex attribute correlations and significant noise, making it difficult for conventional normalization methods to effectively handle these characteristics. Therefore, it is necessary to combine it with correlation weights. The scaling ratio is adjusted according to the importance of attributes to enhance highly relevant attributes. In addition, it is combined with a noise robustness factor. To suppress the influence of outliers.

[0069] In one embodiment, such as Figure 5 As shown, the classification accuracy of different methods is compared to verify the performance advantage of the proposed method over conventional techniques. The figure compares four road material evaluation methods: a baseline method using standard normalization combined with a linear model, a random forest method based on standard score normalization, a method using principal component analysis combined with support vector machines, and the complete method of adaptive weighted normalization and neural network modeling proposed in this invention. Experimental results show that the proposed method significantly outperforms the other three methods in classification accuracy. Its accuracy histogram is significantly taller than that of conventional methods, and the error bar range is narrower, indicating higher stability. Experimental results show that adaptive weighted normalization enhances the contribution of key attributes (such as the strong correlation between compressive strength and porosity), while conventional methods, due to their uniform normalization strategy and linear feature extraction, cannot handle complex correlations between attributes, leading to blurred classification boundaries.

[0070] S3, Feature Enhancement Mapping

[0071] Although the normalized data has been scaled, there are complex nonlinear interactions between road material properties. Conventional feature extraction methods such as principal component analysis or linear projection can only capture shallow linear relationships and cannot model high-order nonlinear dependencies. This makes it difficult for subsequent deep networks to distinguish subtle performance differences, such as the classification of high-quality and low-quality materials.

[0072] This invention captures local structure through radial basis kernel functions and enhances nonlinear expressive power using attribute interaction terms to extract higher-order nonlinear features, such as... Figure 6 As shown:

[0073] 1) Determine the cluster centers of the radial basis kernel function.

[0074] The K-means clustering algorithm was used to perform cluster analysis on normalized multi-index data of road materials, generating K cluster centers as the center points of the radial basis kernel function, thereby capturing the local distribution characteristics of the data.

[0075] Specifically, the normalized i-th sample is defined as... After clustering all normalized samples using the K-means clustering algorithm, we obtain... Cluster center vectors, This indicates the number of clusters and controls the number of radial basis kernel functions; the preferred value is 5.

[0076] At the same time, in all In the cluster center vectors, the k-th cluster center vector is defined as... The dimension is the same as that of the normalized samples, serving as the center point of the radial basis kernel function, and k is the cluster center index, with a value range of [value missing]. , is a positive integer.

[0077] 2) Calculate the radial basis function value

[0078] Based on the distance between the sample and the cluster center vector, the similarity between the sample and each cluster center is calculated using the radial basis kernel function, capturing the local nonlinear characteristics of the data, as expressed as:

[0079] ,

[0080] In the formula, For radial basis kernel functions, Represents the normalized i-th sample With the k-th cluster center vector The radial basis function values, taking values ​​in the range of A higher value indicates a higher similarity. This represents the kernel width hyperparameter, which controls the decay rate of the radial basis function kernel. The larger the value, the narrower the kernel function. The preferred value is 0.1. The L2 norm is used to calculate the Euclidean distance between vectors. The term represents the normalized i-th sample. With the k-th cluster center vector The Euclidean distance between samples is used to measure the similarity between samples and cluster centers.

[0081] 3) Generate attribute interaction items

[0082] Based on a predefined set of first attribute pairs, calculate the product of the corresponding attribute values ​​in the sample. Capture the second-order nonlinear coupling relationship between attributes;

[0083] in, This represents the m-th attribute of the i-th sample after normalization. Attributes include density (in kg / m³), porosity (in %), water absorption rate (in %), etc. This represents the nth attribute of the i-th sample after normalization. Attributes include density (in kg / m³), porosity (in %), water absorption rate (in %), etc. Index of the third attribute; This is the index of the fourth attribute.

[0084] It should be noted that, The interaction term represents the interaction between the m-th and n-th attributes in the i-th sample. Road material properties exhibit coupling relationships; for example, the product of porosity and water absorption rate jointly affects strength. A purely linear model cannot capture this second-order nonlinear relationship, therefore, the interaction term is used... Used to model nonlinear interaction effects between attributes.

[0085] It should also be noted that interactive items Attributes It should belong to the predefined set of first attribute pairs It contains attribute pairs that need to capture interaction relationships, and the first set of attribute pairs. Based on the principles of materials mechanics and expert experience, it is predefined and includes known pairs of properties with interactive relationships, such as... These properties have a significant physical coupling effect, which is impossible with conventional polynomial expansion because conventional polynomial expansion produces a large number of invalid terms, while the first property pair is a set Expert prior constraints ensure that interaction items focus on key attribute pairs.

[0086] 4) Concatenate and enhance feature vectors

[0087] The radial basis function values ​​and attribute interaction terms are concatenated as vectors to form the final feature enhancement map output, thereby capturing both local structure and global nonlinear relationships, as shown below:

[0088] ,

[0089] In the formula, For feature enhancement mapping function; This indicates a vector concatenation operation.

[0090] It should be noted that, Item representation is composed of all A vector composed of radial basis function values ​​is used to capture the similarity between a sample and each cluster center, and to extract local nonlinear features. A vector representing the values ​​of all predefined attribute pairs in an interaction, used to express non-linear relationships between attributes.

[0091] It should also be noted that, Item identification material subclasses, such as high-porosity asphalt, This method strengthens the coupling of properties within similar materials, such as the relationship between the porosity-water absorption product and freeze-thaw durability. The combination of these two methods can achieve complementary enhancement of local and global nonlinear characteristics, thereby simultaneously distinguishing material types and performance levels. This is something that conventional linear methods such as principal component analysis cannot achieve when faced with complex coupling effects.

[0092] In one embodiment, such as Figure 7 , Figure 8 As shown, the feature space distribution is visualized, with both horizontal and vertical axes representing dimensionless eigenvalues. An experimental comparison of the feature space structures of conventional principal component analysis and the feature enhancement mapping of this invention reveals that in the conventional principal component analysis experimental graph, the scatter points for the three material classes (high-quality / medium-quality / low-quality) severely overlap, demonstrating that linear methods struggle to capture complex relationships between attributes. In contrast, the method of this invention significantly improves class separability, indicating that the radial basis kernel function effectively enhances feature separability through local identification of material subclasses and the modeling of nonlinear coupling by attribute interaction terms.

[0093] S4, such as Figure 9 As shown, the specific process of neural network modeling is as follows:

[0094] S401. Define the neural network structure

[0095] The neural network structure adopts a deep feedforward network design, which includes an input layer, multiple hidden layers, and an output layer.

[0096] The number of neurons in the input layer is the same as the dimension of the output vector of the feature enhancement mapping, and the input layer receives the features after feature enhancement mapping.

[0097] The number of neurons in the hidden layer decreases layer by layer or is adjusted according to the data characteristics. Each layer uses adaptive gating computation and adaptive activation function to dynamically adjust feature contribution and enhance nonlinear expressive power.

[0098] The number of neurons in the output layer is equal to the total number of categories C, and a predicted probability distribution is generated using a class probability prediction mechanism.

[0099] S402, Neural Network Initialization

[0100] Feature mapping outputs have high-dimensional sparsity. Conventional deep neural networks use randomly initialized weights, which can easily lead to local optima or gradient vanishing problems. This is especially true when the distribution of road material data is uneven, which can easily lead to classification bias.

[0101] This invention calculates initial weights based on the statistical properties of the feature map output and the intra-class distribution density, ensuring that the initial weight values ​​closely match the data distribution, thereby improving training stability. This is expressed as:

[0102] 1) Calculate the mean of each category feature

[0103] Based on the sample category labels, the mean feature vector for each category is calculated as the representative feature vector for that category, expressed as:

[0104] ,

[0105] In the formula, The vector represents the feature mean of the y-th category, serving as the prototype representation of that category; y is the index of the first category label. This represents the category label of the i-th sample; It is an indicator function, with a value of 1 when the i-th sample belongs to the y-th category, and 0 otherwise; This represents the set of all samples belonging to the y-th category; This represents the number of samples in the set of all samples belonging to the y-th category; This represents the total number of training samples.

[0106] 2) Calculate the category distribution divergence correction term

[0107] Based on the eigenvectors of the variance and covariance matrices of the eigenvalue mean vector, a distribution divergence correction term is calculated to enhance adaptability to imbalanced data. This term is used to adjust the initial weight values ​​and is expressed as:

[0108] ,

[0109] In the formula, This represents the divergence correction term for the l-th layer of the neural network, used to adjust the initial weight values ​​to fit the data distribution; l is the index of the neural network layer, with a value range of... arrive ; This represents the total number of layers in the neural network, preferably set to 5. This indicates the initial adjustment rate hyperparameter, which controls the magnitude of the correction term; the preferred value is 0.05. Indicates the total number of categories; It is a logarithmic function, with the default base being the natural constant; Let represent the feature variance of the y-th class, used to measure the dispersion of the sample distribution within the class, and calculated as follows: ; The eigenvectors of the covariance matrix of the y-th class reflect the main direction of the class distribution. First, the eigenvectors of the covariance matrix of the y-th class are calculated. The covariance matrix output by the feature mapping of the class samples Then find The principal eigenvector, that is, the eigenvector corresponding to the largest eigenvalue; for transpose; The dimension is A column vector of all 1s; This represents the feature dimension of the l-th layer of the neural network.

[0110] It should be noted that, The weight contribution of high-variance categories is compressed, such as the large performance fluctuations of inferior materials, while the eigenvectors... Adjust the weights along the main direction of the category distribution to make the initialization more closely match the true distribution geometry of the samples.

[0111] 3) Generate initial weights

[0112] The weighted average of the feature mean vectors of each category is added to the distribution divergence correction term to obtain the initial weight matrix of each layer of the neural network. This ensures that the initial weight values ​​closely match the data distribution, improving training stability, and is expressed as follows:

[0113] ,

[0114] In the formula, This represents the initial weight matrix of the l-th layer of the neural network.

[0115] It should be noted that, The term represents the arithmetic mean of the features of each category, providing class-independent basic weights. This ensures that the initial weight values ​​are close to the overall data distribution, avoiding bias towards specific categories and thus improving training stability.

[0116] It should be noted that, The term retains global mean information to avoid the correction term being overly biased towards a specific category, and differs from the distribution divergence correction term. The summation forms a balanced initial state. In the road material scenario, this design makes the initial weights of the neural network sensitive to the scarce class while stabilizing the training of the mainstream class. Even when the samples are severely imbalanced, the neural network can generate meaningful class distinction boundaries in the first round of forward propagation, which significantly alleviates the gradient vanishing problem caused by random initialization.

[0117] S403, Adaptive Gated Calculation

[0118] Conventional activation functions such as ReLU are not sensitive to the local importance of road material properties and cannot dynamically adjust feature contributions, which can easily lead to key indicators such as compressive strength being overwhelmed by secondary indicators.

[0119] This invention uses a gating mechanism to weight feature channels and combines attribute importance feedback to dynamically enhance the response of key attributes, as shown below:

[0120] 1) Calculate attribute attention score

[0121] Based on the absolute value of the input features, the attention score of each feature dimension is calculated using the Softmax function to dynamically identify key attributes and enhance the network's response to important attributes, as shown below:

[0122] ,

[0123] In the formula, This represents the attention score of the r-th dimension feature of the i-th sample in the l-th layer of the neural network, with a value range of... A larger value indicates a more important feature; r is the feature dimension index; This represents the attention temperature coefficient, which controls the sharpness of attention distribution. The larger the value, the sharper the distribution. The preferred value is 1.0. Indicates the neural network's first... Layer The first sample The output feature value of the dimensional neural network, i.e., the dimensional feature value of the dimensional neural network. Layer The first sample The input feature value of dimension, when hour, equal The 3D eigenvalues; Indicates the neural network's first... The feature dimension of a layer, i.e., the number of neurons in that layer, is the same for the input layer. equal Dimensions.

[0124] It should be noted that, The term is a variation of the softmax function, with the input being the absolute value of the eigenvalues ​​multiplied by the attention temperature coefficient. ,pass Adjusting the concentration of attention distribution allows for dynamic identification of key feature channels, enhancing the network's response to important attributes, and improving the model's expressive power.

[0125] It should also be noted that in the evaluation of road materials, The magnitude of an item is directly related to the significance of the attribute. For example, a sudden change in the elastic modulus indicates a material defect, while attention should be paid to the temperature coefficient. It can sharpen the attention distribution, enabling the network to quickly refocus when key metrics show anomalies.

[0126] 2) Calculate the gating vector

[0127] Based on the attention score, a gating vector is generated using the sigmoid function to control the pass rate of each feature channel and adjust the feature contribution, as shown below:

[0128] ,

[0129] In the formula, This represents the gating vector of the i-th sample in the l-th layer of the neural network, with values ​​ranging from 1 to 2. , used to adjust the pass weights of feature channels; This represents the Sigmoid function, which maps the input to... interval; Let $\mathbf{l}$ represent the gating weight matrix of the $l$-th layer of the neural network, which are trainable parameters with dimension $\mathbf{l}$. To ensure The output dimension of the item is ; This represents the attention score vector of the i-th sample in the l-th layer of the neural network, where the r-th element is... .

[0130] 3) Calculate adaptive activation output

[0131] Applying an adaptive activation function to the features after linear transformation, and combining linear and nonlinear transformations, yields an adaptive activation output vector, enhancing the nonlinear expressive power, expressed as:

[0132] ,

[0133] In the formula, This represents the adaptive activation output vector of the i-th sample in the l-th layer of the neural network; This represents the weight matrix of the l-th layer of the neural network, which are trainable parameters initialized to the initial weight matrix of the l-th layer of the neural network. ; Let represent the bias vector of the l-th layer of the neural network, which is a trainable parameter initialized to a vector of all zeros. This represents an adaptive activation function that combines linear and nonlinear transformations. Let its input be... for The calculation method is expressed as follows: ; This indicates the activation gain hyperparameter, which controls the degree of nonlinearity; the preferred value is 0.8. Represents the hyperbolic tangent function; This represents the input to the adaptive activation function, equivalent to .

[0134] It should be noted that the adaptive activation function Combining linear and nonlinear responses, when the input When the value is small, it is approximately linear, preserving the quantitative relationship of physical indicators. Saturation at larger strains suppresses noise amplification and is a specific design for modeling material properties. For example, linear response is required in small strain stages such as elastic deformation, while nonlinear saturation is required in large strain stages such as plastic deformation.

[0135] 4) Weighted output of gating mechanism

[0136] The gating vector is multiplied element-wise with the adaptive activation output vector to generate the output feature vectors of each layer of the neural network, represented as:

[0137] ,

[0138] In the formula, For the neural network Layer The output feature vector of each sample; This indicates element-wise multiplication.

[0139] It should be noted that, The project ultimately achieves dynamic modulation at the feature channel level, enabling the neural network to adapt to the local abrupt changes in material properties. When a certain attribute deviates significantly from the normal state in a specific sample, its attention score increases, and the gating vector... Amplifying the contribution of this channel ensures that key metrics are not overwhelmed; conventional ReLU activation functions cannot achieve this kind of attribute-aware dynamic adjustment.

[0140] S404, Probability Prediction

[0141] The evaluation of road material performance requires a comprehensive consideration of the nonlinear coupling effects of multiple indicators. Conventional output layers use the standard softmax function to ignore the dynamic interaction and physical constraints between attributes, which can easily lead to a weakening of the contribution of key indicators.

[0142] This invention utilizes attribute attention gating and category prototype collaborative computation to dynamically fuse higher-order features and physical priors, generating predictive outputs that conform to the laws of materials science, expressed as:

[0143] 1) Computed Attribute - Category Association Vector

[0144] Based on the category feature mean vector, relevance weight vector, and feature vector of the neural network output layer, attribute-level attention weights are constructed, and the sensitivity is controlled by the association strength coefficient to capture the non-linear association between feature channels and categories, as expressed as:

[0145] ,

[0146] In the formula, Indicates the first The feature channels of the sample and the first The association vector of the category, with dimension 1 ; For the Softmax function; The correlation strength coefficient controls attention sensitivity; the preferred value is 0.7. The feature mean vector of the y-th category serves as the prototype representation of that category. The feature dimension of the Lth layer of the neural network, i.e., the number of neurons in the output layer, is preferably set to be equal to the total number of attributes in the original data. Equal to ensure that each dimension corresponds to a single original attribute; L is the number of hidden layers in the neural network; for transpose; This is the relevance weight vector. ; This represents the relevance weight of the j-th attribute. The relevance weight of the first attribute. The relevance weight of the second attribute. Let be the relevance weight of the D-th attribute; Indicates the transpose operation; For the neural network Layer The output feature vector of each sample.

[0147] 2) Generate gated prototype vectors

[0148] Based on the concatenation vector of the categorical feature mean vector and the predefined attribute pair interaction term, a gating value is generated using the Sigmoid function. Then, combined with the feature mean vector, a physical constraint-enhanced gating prototype vector is obtained, represented as:

[0149] ,

[0150] In the formula, The average of the interaction terms for all samples in the y-th category is expressed as follows: ; Represents the gated prototype vector of the y-th category; Let be the gated weight matrix, which consists of trainable parameters of dimension . ; For the set of first attribute pairs, Indicates the number of elements in the collection according to the first attribute; For the Sigmoid function; Indicates for The vectors are concatenated to obtain a vector of dimension . The vector.

[0151] 3) Calculate the prediction probability

[0152] Based on the corresponding product of the elements of the associated vector and the elements of the gated prototype vector, the hyperbolic tangent function and the probability scaling factor are applied, and the predicted probability is output through the Softmax function. This dynamically fuses higher-order features and physical priors, and is expressed as follows:

[0153] ,

[0154] In the formula, Indicates the neural network for the first... The sample belongs to the first The predicted probability of a class; This is the probability scaling factor, with a preferred value of 1.2; Represents the correlation vector The The element, i.e., the th element The first feature channel and the first Category association weights; Represents the correlation vector The The element, i.e., the th element The first feature channel and the first Category association weights; Indicates the first The feature channels of the sample and the first The association vector of the category; Represents the gated prototype vector The One element; Represents the gated prototype vector The One element; Indicates the first The gated prototype vector of the category; For the second category label index; This indicates the total number of categories.

[0155] It should be noted that, This term combines the association vector and the gate prototype vector, which can generate classification confidence guided by physical laws. If the product of the sample features and the gate prototype is highly consistent in key attributes, a high probability is output, making the prediction results naturally consistent with the principles of materials science.

[0156] In one embodiment, such as Figure 10 , 11 As shown in Figure 12, the physical consistency effect was verified. The effectiveness of the physical constraint loss term was verified using a heatmap. The color scale represents the correlation coefficient (-1 to 1), and the row and column labels are the attribute names. The true physical correlation coefficient graph shows the true correlation coefficients of the six core attributes. Density and porosity are dark blue (strong negative correlation), and compressive strength and elastic modulus are dark red (strong positive correlation), which is consistent with the laws of materials science. The prediction without physical constraints in the prediction graph shows serious deviations. The correlation coefficient of compressive strength and elastic modulus decreases (light red), and the negative correlation of density and porosity weakens (light blue). The prediction results of the physical constraint prediction graph of this technology are highly consistent with the true heatmap. The correlation coefficient error of the key attribute pairs is low, indicating that the physical constraint loss term forces the network to learn the inherent laws such as the porosity necessarily decreasing when density increases and the elastic modulus increasing synchronously when strength increases.

[0157] S405, Loss Function Calculation

[0158] The forward propagation output needs to be classified into road material performance levels. Conventional cross-entropy loss functions ignore the physical constraints between multiple indicators and are sensitive to class imbalance, which can easily lead to blurred classification boundaries and physical inconsistencies.

[0159] This invention integrates classification loss terms and physical consistency loss terms to construct a total loss function. The contribution level is adjusted through the weight coefficients of the physical constraint term, forcing the correlation coefficients between predicted features to be consistent with the true correlation coefficients, thus strengthening the physical consistency of the prediction results. This is expressed as:

[0160] ,

[0161] In the formula, This represents the total loss function, which serves as the optimization objective for network training. This represents the classification loss term, used to ensure classification accuracy. Its calculation method is expressed as follows: ; This represents the weighting coefficient of the physical constraint term, which adjusts the degree of contribution to the physical consistency loss; the preferred value is 0.3. The physical consistency loss term is used to force the correlation coefficient between predicted features to be consistent with the true correlation coefficient. Its calculation method is as follows: ; Indicates the first The true category labels of each sample are encoded using one-hot encoding. Indicates the neural network for the first... The predicted probability distribution of each sample is in vector format. For example, for a total number of categories... When, its dimension is . Indicates the neural network's first... The Pearson correlation coefficient of the layer feature vector with respect to the p-th and q-th features of all training samples; The Pearson correlation coefficient represents the p-th attribute and q-th feature of all training samples in the original training set.

[0162] It should be noted that the preferred settings Therefore, the neural network's first... Layer Output feature vector of each sample The dimensions are consistent with the attribute dimensions of the original training set data;

[0163] This represents a predefined set of second attribute pairs, containing index pairs that need to maintain physical relationships; Index of the fifth attribute; This is the index of the sixth attribute.

[0164] It should be noted that the second attribute applies to the set. The selection is based on prior knowledge in road materials science, including index pairs that need to maintain physical relationships. These attribute pairs have known physical constraints, such as... This attribute has a physical constraint relationship, that is, It is a positive correlation; the modulus usually increases as strength increases. It is a negative correlation; as density increases, porosity decreases.

[0165] It should also be noted that attribute pairs This is used to force the features learned by the network to maintain the same correlation with the real data, ensuring that the prediction results are physically consistent. For example, if compressive strength and elastic modulus are positively correlated in the real data, these two attributes should also be positively correlated in the network's predicted features; otherwise, they will be penalized by loss.

[0166] S406, Iterative Training and Parameter Update

[0167] The iterative training process of the neural network employs a gradient descent-based optimization algorithm, aiming to minimize the total loss function. Each iteration consists of two phases: forward propagation and back propagation.

[0168] In the forward propagation, the input training samples are processed by each layer of the neural network to obtain the predicted output;

[0169] In backpropagation, the gradient of the loss function with respect to the network parameters is calculated, and the weights and bias parameters are updated according to the learning rate.

[0170] During training, batch processing is used to divide the dataset into multiple small batches and update the parameters batch by batch to improve training efficiency and stability.

[0171] The model's stopping iteration condition is based on validation set performance monitoring. When the validation set loss no longer decreases or starts to increase after 10 consecutive iterations, training is stopped early to prevent overfitting.

[0172] At the same time, the maximum number of iterations is set to 1000 as a backup stopping condition.

[0173] S5. Comprehensive Performance Evaluation of Road Materials Based on Multiple Indicators

[0174] After the model training is completed, when evaluating the comprehensive performance of new road material data samples, the same preprocessing steps as in the training phase are first applied. The original attribute data of the new samples are input into the adaptive weighted normalization module to calculate the normalized value.

[0175] Then, the enhanced feature vector is generated through the feature enhancement mapping module;

[0176] Finally, the enhanced features are input into the trained neural network model and forward propagated to obtain the class probability prediction output.

[0177] Based on the predicted probability distribution, the category with the highest probability is selected as the performance level evaluation result of the new sample, such as excellent, medium or poor.

[0178] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for evaluating the comprehensive performance of road materials based on multiple indicators, characterized in that, Includes the following steps: S1. Construct a multi-index dataset for road materials and label the data; S2. Calculate the attribute correlation weight and noise robustness factor for the multi-index data of road materials, and dynamically adjust the normalization scale to obtain normalized multi-index data of road materials. The specific process is as follows: Based on the absolute value of the average Pearson correlation coefficient between each attribute and other attributes, the attribute correlation weight is calculated using the Sigmoid function; based on the absolute deviation of each attribute value from its sample median, the local noise robustness factor is calculated using the exponential decay function. By combining the global mean and standard deviation with scaling, attribute correlation weights and noise robustness factors, normalized multi-index data of road materials are dynamically calculated. S3. Construct a feature enhancement mapping module. This module extracts the local structure of normalized road material multi-index data through the radial basis function kernel function. The specific process is as follows: use the K-means clustering algorithm to perform cluster analysis on the normalized road material multi-index data, generate K cluster centers as the center points of the radial basis function kernel function, and extract the local distribution features of the data; based on the distance between the sample and the cluster center vector, calculate the similarity between the sample and each cluster center through the radial basis function kernel function, and extract the local nonlinear features of the data. Furthermore, attribute interaction terms are used to enhance nonlinear expressive power, extract higher-order nonlinear features, and obtain the final feature enhancement mapping output. The specific process is as follows: Based on a predefined set of first attribute pairs, calculate the attribute interaction terms of the corresponding attribute values ​​in the sample; specifically: based on the predefined set of first attribute pairs, calculate the product terms of the corresponding attribute values ​​in the sample. ,in, This represents the m-th attribute of the i-th sample after normalization. Represents the normalized attribute of the i-th sample and the n-th attribute; interaction term Attributes Belongs to the predefined first attribute pair set It contains attribute pairs that need to capture interaction relationships, and the first set of attribute pairs. Based on the principles of materials mechanics and expert experience, the system predefines and includes known attribute pairs with interactive relationships, which are physically significantly coupled. The radial basis kernel function values ​​and attribute interaction terms are vector-concatenated to form the final feature enhancement mapping output. S4. Construct a comprehensive performance evaluation model for road materials based on multiple indicators. The model adopts a deep feedforward network design, including an input layer, a hidden layer, and an output layer. The model is trained using the final feature enhancement mapping output to obtain a trained model. S5. After processing the new road material data samples in steps S2 and S3, input them into the trained model to obtain the performance level evaluation results.

2. The method for evaluating the comprehensive performance of road materials based on multiple indicators according to claim 1, characterized in that, The model calculates initial weights based on the statistical properties of the final feature enhancement map output and the intra-class distribution density: Based on the sample category labels, calculate the feature mean vector for each category, which serves as the representative feature vector for that category; Based on the eigenvectors of the variance and covariance matrices of the eigenvalue mean vector, the distribution divergence correction term is calculated; expressed as: ， In the formula, This represents the divergence correction term for the l-th layer of the neural network; l is the index of the neural network layer, with a value range of... arrive ; This represents the total number of layers in the neural network. This indicates the initialization of the adjustment rate hyperparameter, which controls the magnitude of the correction term; Indicates the total number of categories; It is a logarithmic function; This represents the feature variance of the y-th category; The eigenvectors represent the covariance matrix of the y-th class; for transpose; The dimension is A column vector of all 1s; This represents the feature dimension of the l-th layer of the neural network; The weighted average of the feature mean vectors of each category is added to the distribution divergence correction term to obtain the initial weight matrix of each layer of the neural network.

3. The method for evaluating the comprehensive performance of road materials based on multiple indicators according to claim 1, characterized in that, The hidden layer uses a gating mechanism to weight feature channels and combines attribute importance feedback to dynamically enhance the response of key attributes: Based on the absolute value of the input features, the attention score of each feature dimension is calculated using the Softmax function; Based on the attention score, a gating vector is generated using the Sigmoid function; an adaptive activation function is applied to the linearly transformed features, and by combining linear and nonlinear transformations, an adaptive activation output vector is obtained; the gating vector and the adaptive activation output vector are multiplied element-wise to generate the output feature vectors of each layer of the neural network.

4. The method for evaluating the comprehensive performance of road materials based on multiple indicators according to claim 1, characterized in that, The output layer dynamically fuses higher-order features and physical priors through attribute attention gating and category prototype collaborative computation to generate predictive outputs that conform to the laws of materials science. Based on the categorical feature mean vector, relevance weight vector, and feature vector of the neural network output layer, attribute-level attention weights are constructed. Sensitivity is controlled by the association strength coefficient, resulting in an association vector; expressed as: ， In the formula, Indicates the first The feature channels of the sample and the first The association vector of the category, with dimension 1 ; For the Softmax function; The correlation strength coefficient; The feature mean vector of the y-th category serves as the prototype representation of that category. Let L be the feature dimension of the Lth layer of the neural network; for transpose; This is the relevance weight vector. ; This represents the relevance weight of the j-th attribute. The relevance weight of the first attribute. The relevance weight of the second attribute. Let be the relevance weight of the D-th attribute; Indicates the transpose operation; For the neural network Layer The output feature vector of each sample; This represents element-wise multiplication. Based on the concatenation vector of the categorical feature mean vector and the interaction term of the predefined attribute pair, a gating value is generated using the Sigmoid function. Then, combined with the feature mean vector, a physical constraint-enhanced gating prototype vector is obtained; represented as: ， In the formula, The average value of the interaction terms for all samples in the y-th category. Represents the gated prototype vector of the y-th category; Let be the gated weight matrix, which consists of trainable parameters of dimension . ; For the set of first attribute pairs; For the Sigmoid function; Indicates for The vectors are concatenated to obtain a vector of dimension . The vector, Indicates the number of elements in the collection according to the first attribute; Based on the corresponding product of the elements of the associated vector and the elements of the gated prototype vector, the hyperbolic tangent function and the probability scaling factor are applied, and the predicted probability is output through the Softmax function.

5. The method for evaluating the comprehensive performance of road materials based on multiple indicators according to claim 1, characterized in that, The comprehensive performance evaluation model for road materials integrates classification loss terms and physical consistency loss terms to construct a total loss function.

6. The method for evaluating the comprehensive performance of road materials based on multiple indicators according to claim 5, characterized in that, The iterative training process of the multi-index comprehensive performance evaluation model for road materials adopts an optimization algorithm based on gradient descent, with the goal of minimizing the total loss function. Each iteration includes two stages: forward propagation and back propagation. In forward propagation, the input training samples are processed by each layer of the neural network to obtain the predicted output. In back propagation, the gradient of the loss function with respect to the network parameters is calculated, and the weights and bias parameters are updated according to the learning rate.

7. The method for evaluating the comprehensive performance of road materials based on multiple indicators according to claim 6, characterized in that, The model's stopping iteration condition is based on validation set performance monitoring. Training is stopped early when the validation set loss no longer decreases or starts to increase after 10 consecutive iterations.

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