Intelligent optimization method for inverting new material structure parameters

Abstract

The invention provides an intelligent optimization method for inverting new material structure parameters. The method relates to the technical field of material science and engineering structure analysis, and comprises the following steps: S1, acquiring time sequence data and image data of a material under different loading conditions, and preprocessing; s2, constructing a deep diagnosis model: constructing a time sequence feature extractor and an image feature extractor, and respectively extracting time sequence features and image topological structure features; time sequence features and image topological structure features are fused through a stepped mutual attention mechanism; s3, training a neural network based on the fusion feature vector, outputting a final predicted value, and updating network parameters by adopting a residual error-based alternative hyperplane Kaczmarz optimization method and an oblique projection optimization method; and S4, inputting the preprocessed measured data into the trained model, and outputting a material structure parameter inversion result. In this way, rapid inversion of complex material structure parameters is achieved, and the current technical problem is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of materials science and engineering structure analysis, and particularly to an intelligent optimization method for inverting the structural parameters of new materials. Background Art

[0002] In the field of materials science and engineering structure analysis, accurately obtaining the microstructural parameters of materials (such as elastic modulus, Poisson's ratio, density, etc.) is crucial for structural performance prediction and optimal design. However, traditional parameter inversion methods generally have problems such as low computational efficiency, slow convergence speed, and easy to fall into local optimum when facing complex non-linear, multi-modal data and high-dimensional parameter spaces, especially in the comprehensive processing of high-dimensional time series and image data.

[0003] In recent years, the development of artificial intelligence technologies, especially deep learning and graph neural networks, has provided a new technical path for material parameter inversion. At the same time, classical numerical methods such as the Kaczmarz algorithm have also been widely used in signal processing and image reconstruction. However, traditional Kaczmarz and its variants such as the surrogate hyperplane Kaczmarz still have bottlenecks in inversion efficiency and accuracy.

[0004] Therefore, there is an urgent need for an innovative method that can efficiently fuse multi-modal information, mine multi-scale time series features, and improve the optimization efficiency to solve the key technical problems in current material parameter inversion. Summary of the Invention

[0005] The present invention aims to solve the above problems and proposes an intelligent optimization method for inverting the structural parameters of new materials. The method realizes the inversion of the structural parameters of new materials based on the residual surrogate hyperplane Kaczmarz method and oblique projection (RSHKO) method and artificial intelligence models (such as neural networks, ensemble learning, etc.). This method uses AI to extract features and reduce the dimension of measurement data, and combines RSHKO to perform efficient and accurate parameter optimization and solution, so as to realize the rapid inversion of complex material structure parameters. It solves the key technical problems in current material parameter inversion.

[0006] To achieve the above object, it is realized through the following technical solutions: An intelligent optimization method for inverting the structural parameters of new materials, comprising the following steps: S1. Collect the time series data and image data of the material under different loading conditions and perform preprocessing; S2. Construct a deep diagnosis model, including: S2.1. Construct a multi-modal feature extractor: including a time series feature extractor and an image feature extractor; among them, the time series feature extractor adopts a periodic pyramid Transformer model, captures multi-scale periodic features of the time series through periodic component extraction, hierarchical modeling and attention mechanism, and obtains time series features; the image feature extractor fuses topological data analysis and multi-scale adaptive graph convolution to extract image topological structure features; S2.2. Fuse the time series features and the image topological structure features through a stepped mutual attention mechanism to obtain a fused feature vector; S3. Train a neural network based on the fused feature vector, output the final predicted value, and update the network parameters by using the residual-based surrogate hyperplane Kaczmarz optimization method and the oblique projection optimization method; S4. Input the preprocessed measured data into the trained model, output the inversion result of the material structure parameters, and realize real-time online inference through an edge-cloud collaborative architecture.

[0007] Further, among them, the time series feature extractor uses a periodic pyramid Transformer model to process time series data, extracts the dominant frequency and the corresponding period length through frequency domain analysis, divides multi-level periodic components and establishes hierarchical connection relationships, and uses the attention mechanism to aggregate multi-scale periodic features and output time series features.

[0008] Further, among them, constructing a time series feature extractor using a periodic pyramid Transformer model includes: When performing frequency domain analysis on the input time series, use the fast Fourier transform to extract the frequency amplitude sequence of the seasonal part, and determine the periodic components through channel dimension averaging and dominant frequency screening; Divide the hierarchical periodic components according to the period length and establish the connection relationship between the hierarchies; Construct a hierarchical periodic pyramid structure according to the inclusion relationship of the periodic components; Calculate the connection relationship between the periodic components through the attention mechanism, aggregate the key periodic features, and output the aggregated time series features for multi-modal fusion.

[0009] Further, among them, the hierarchical periodic components are divided according to the period length and the connection relationship between the hierarchies is established; a hierarchical periodic pyramid structure is constructed according to the inclusion relationship of the periodic components, including: By judging whether there is an inclusion or overlap relationship between the periodic components in different layers, determine the hierarchical inclusion relationship between the periodic components, where the upper-layer periodic components establish an inclusion relationship with the lower-layer components through index overlap judgment; Construct a hierarchical pyramid structure based on the inclusion relationship between the periodic components; Map different periodic components to a unified scale through zero-padding and linear projection; Establish the connection relationship between the current periodic component and the relevant components in the upper and lower layers; Construct a complete periodic pyramid by stacking periodic components of different levels.

[0010] Furthermore, the image feature extractor processes image data using a graph convolutional model that fuses topological data analysis, constructs a topological evolution process through graph filtering, generates a persistent barcode and embeds it as a topological vector, and extracts image topological structure features through a multi-scale adaptive graph convolutional module; Among them, the construction of the image feature extractor includes: Perform graph filtering operations on the image data to construct a topological evolution process; Eliminate low-importance topological features through node filtering and edge filtering; Construct a persistent graph based on persistent homology to record the life cycle of topological features; Convert the persistent barcode into a topological vector through a learnable embedding function; Adopt a multi-scale adaptive graph convolution and MixHop convolution strategy to extract the deep topological features of the image data and obtain the image topological structure features.

[0011] Furthermore, the persistent graph is constructed in the following way: Perform multi-scale filtering on the simplicial complex S (b) and record the appearance time t1 and disappearance time t2 of each topological feature; Distinguish the topological feature types according to the homology dimension b ∈ {0, 1}, where b = 0 corresponds to connected components and b = 1 corresponds to loop structures, and construct a persistent barcode; Store the survival period of the topological feature in the form of a tuple (t1, t2) in the set D (b) to form a persistent graph describing the topological feature evolution.

[0012] Furthermore, the barcode-to-vector embedding is realized through the following steps: Perform parametric encoding on the b-th order persistent barcode under the c-th view to generate an initial topological descriptor; Map the initial topological descriptor to an N×d-dimensional vector space through an embedding function , where N is the number of graph nodes and d is the preset vector dimension; Adopt a trainable linear layer or non-linear activation function to optimize the embedding process so that the topological vector retains the stability information in the multi-scale filtering.

[0013] Furthermore, the multi-scale adaptive graph convolution module enhances the graph structure modeling ability through the following operations: Perform a linear transformation on the input topological vector to generate initial graph features; Construct an adaptive adjacency matrix based on two trainable parameter matrices to capture the dynamic dependencies of the graph structure; The multi-order convolutional propagation layer performs power expansion on the adaptive adjacency matrix to capture the neighborhood information of each order of the initial graph features; Concatenate the graph convolution results of each order along the feature dimension to obtain the concatenated features; Apply a non-linear activation function to the concatenated features to generate the topological structure features of the image.

[0014] Furthermore, in the S2.2, the time series features and the image topological structure features are fused through a stepped cross-attention mechanism to obtain a fused feature vector, including: For each frame feature of the time series, taking the time series features as the main modality and the image topological structure features as the auxiliary modality, calculate the attention-enhanced representation of the image modality to the time series modality: Aggregate the enhanced representations of all frames to obtain a unified fused feature, that is, the fused feature vector.

[0015] Furthermore, in step S3, the method of updating network parameters by using the residual-based surrogate hyperplane Kaczmarz optimization method and the oblique projection optimization method includes: Calculate the gradient residual vector of the current iteration; Construct an oblique projection direction based on the gradient residual vector; Calculate the update step size through the norm of the gradient residual vector and the norm of the oblique projection direction to generate new parameters.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. Through time-frequency-topology joint modeling, the present invention extracts local patterns through time-frequency analysis (such as FFT / wavelet transform), and at the same time uses topological analysis (such as persistent homology) to capture the global structure, realizing multi-scale feature complementarity. Based on the stepped cross-attention mechanism dominated by time series and enhanced by images, the depth of multi-modal fusion is realized, and the contribution degrees of time-frequency and topological features are dynamically adjusted through GRU or attention weights, avoiding information redundancy and solving the cross-modal semantic gap problem.

[0017] 2. The present invention constructs a periodic pyramid Transformer model, constructs a periodic pyramid structure through periodic structure decomposition, hierarchical modeling and attention mechanism, accurately captures the multi-scale periodic relationships in time series data, and improves the time series modeling ability of the model for material dynamic response signals.

[0018] 3. The present invention proposes a method that integrates topological data analysis, multi-scale adaptive graph convolution, and MixHop convolution: By combining the local geometric information and global structural features of material image data, a multi-scale information extraction module is designed to adapt to the complex topological characteristics in the microstructure of materials and enhance the structure recognition ability of the model.

[0019] 4. The present invention performs multi-modal fusion through a stepped mutual attention mechanism: In the stage of fusing time series and image data, a cross-modal mutual attention mechanism is designed to hierarchically capture the correlation features between different modalities and achieve semantic-level information alignment and complementarity.

[0020] 5. The present invention optimizes the model based on the residual-based surrogate hyperplane Kaczmarz method and the oblique projection optimization (RSHKO) method. Through the residual update strategy and the efficient Kaczmarz iteration of oblique projection, the solution accuracy and convergence speed in the inversion process are improved, and the computational bottleneck of traditional inversion algorithms in non-linear and high-dimensional parameter spaces is solved.

[0021] It should be understood that the content described in the Summary of the Invention section is not intended to limit the key or important features of the embodiments of the present invention, nor is it used to limit the scope of the present invention. Other features of the present invention will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In combination with the accompanying drawings and with reference to the following detailed description, the above and other features, advantages, and aspects of the embodiments of the present invention will become more apparent. The drawings are used to better understand the solution and do not constitute a limitation to the present invention. In the drawings, the same or similar reference numerals represent the same or similar elements, where: Figure 1 is a schematic flow chart of an intelligent optimization method for inverting the structural parameters of a new material according to an embodiment of the present invention; Figure 2 is a schematic flow chart of step S2, constructing a depth diagnosis model, according to an embodiment of the present invention; Figure 3 is a schematic system architecture diagram of an intelligent optimization method for inverting the structural parameters of a new material according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art without making creative efforts based on the embodiments of the present invention fall within the protection scope of the present invention.

[0024] In addition, the term "and / or" in this text is merely a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " in this text generally indicates that the associated objects before and after are in an "or" relationship.

[0025] Figure 1 shows a schematic flow diagram of an intelligent optimization method for inverse new material structure parameters according to an embodiment of the present invention. As Figure 1 shown, an intelligent optimization method 100 for inverse new material structure parameters includes the following steps: S1. Collect time series data and image data of the material under different loading conditions and perform preprocessing; The main purpose of step S1 is multi-modal data collection and preprocessing. The specific steps are as follows: S1.1: Multi-modal data collection The present invention first collects multi-modal response data of the material under different loading conditions by combining experimental measurement and numerical simulation. Among them, the loading condition refers to the type of external action and its parameter combination applied to the material specimen. In the present invention, the loading condition can include, for example, at least one of the following dimensions: (1) Mechanical loading conditions, static loading: constant stress / strain loading (such as uniaxial tension, compression, bending); dynamic loading: periodic or transient action (such as fatigue load, impact load); multi-axial loading: complex stress state (such as biaxial tension, shear-tension combined loading); loading rate: quasi-static (10 -3 ~10 0 s -1 ) to high rate (10 3 ~10 4 s -1 ). (2) Thermal loading conditions, including: temperature range: for example, from extremely low temperature (-196 °C) to high temperature molten state (>1000 °C); thermal cycle: rapid heating / cooling (such as 10 °C / s to 100 °C / s); thermal gradient: non-uniform temperature field (such as flame impact, laser heating); (3) Environmental medium conditions, including: corrosive environment: acid / alkali / salt solution immersion, gas corrosion (H2S, Cl -); Humidity loading: Relative humidity control (0% - 100% RH); Radiation environment: Ultraviolet rays, γ-rays, neutron radiation. (4) Multi-physical field coupling conditions, including: Thermal-mechanical coupling: The combined action of mechanical load and temperature field; Electro-magnetic-force coupling: The interaction between electromagnetic field and mechanical stress (such as piezoelectric materials, magnetostrictive materials); Chemical-mechanical coupling: The synergistic action of corrosive medium and stress (such as stress corrosion cracking). (5) Special loading modes, including: Cyclic loading: Sine wave, square wave, random vibration spectrum; Pre-damage loading: Notched specimens, prefabricated crack propagation; Composite loading paths: Loading-unloading-reloading, variable amplitude cycling.

[0026] Specifically, the multi-modal response data of the material collected under different loading conditions mainly includes two categories: time series data and image data.

[0027] Among them, in some embodiments, the time series data mainly includes continuous signals such as stress-strain curves, acceleration-time responses, acoustic or electromagnetic wave propagation signals, and frequency response functions. This type of data is collected by devices such as stress testers, laser Doppler vibrometers, ultrasonic sensors, or electromagnetic sensors, reflecting the dynamic response behavior of the material under different external excitations. The image data includes deformation images on the material surface, strain field distribution maps, thermal infrared images, and microscopic tissue structure images, etc. Such image data can be obtained through imaging devices such as digital image correlation (DIC) systems, high-speed camera systems, infrared thermal imagers, or electron microscopes, used to capture local deformations, micro-crack evolutions, or thermal-mechanical coupling characteristics of the material during the loading process. In addition, a finite element simulation platform (such as ABAQUS, ANSYS) can be used to model and simulate the mechanical behavior of the material under different structural parameter assumptions, generating matching time series and image simulation data, thereby enhancing the diversity and coverage of the data. Finally, a structured multi-modal data set is formed, providing a comprehensive and high-quality input information basis for subsequent feature extraction, parameter inversion, and intelligent optimization.

[0028] S1.2: Multi-modal data preprocessing For the collected multi-modal material response data, it is necessary to preprocess the data of different modalities respectively to extract stable and identifiable low-dimensional features for subsequent inversion modeling.

[0029] For time series data (such as stress-strain curves, acoustic signals, frequency response data, etc.), perform unified resampling of the sampling rate, normalization, and filtering and noise reduction processing. For image data (such as deformation images, thermal imaging maps, microscopic tissue maps, etc.), perform image enhancement, denoising, size unification, and alignment processing.

[0030] Figure 2 It is a schematic flow chart of step S2 of the embodiment of the present invention, constructing a deep diagnosis model. As Figure 2As shown in the figure, S2. Build a deep diagnosis model, specifically including: S2.1. Build a multi-modal feature extractor: including a time series feature extractor and an image feature extractor; among them, the time series feature extractor uses a periodic pyramid Transformer model to capture multi-scale periodic features of the time series through periodic component extraction, hierarchical modeling, and attention mechanism, obtaining time series features; the image feature extractor fuses topological data analysis and multi-scale adaptive graph convolution to extract image topological structure features. That is, the periodic pyramid combines persistent homology dual-engine feature extraction.

[0031] S2.1.1: Build a time series feature extractor In this step S2.1.1, a periodic pyramid Transformer model is proposed to extract key periodic features from the collected time series data. This model accurately captures the multi-scale periodic relationships in the time series through periodic structure decomposition, hierarchical modeling, and attention mechanism, improving the modeling ability of time series features.

[0032] Among them, building a time series feature extractor using a periodic pyramid Transformer model processes time series data, extracts the dominant frequency and corresponding period length through frequency domain analysis, divides multi-level periodic components and establishes hierarchical connection relationships, and uses the attention mechanism to aggregate multi-scale periodic features and output time series features. Specifically, it includes the following steps: S2.1.1.1 Periodic component extraction When performing frequency domain analysis on the input time series, the fast Fourier transform is used to extract the frequency amplitude sequence of the seasonal part, and the periodic components are determined through channel dimension averaging and dominant frequency screening. First, the input normalized time series is subjected to frequency domain analysis to extract significant periodic components:

[0033] X: Original input time series data; L: Time step length; C: Number of channels; : Seasonal part of the time series; FFT(·): Fast Fourier transform; Amp(·): Amplitude calculation function; Avg(·): Average over the channel dimension; A: Frequency amplitude sequence; : The top k dominant frequencies selected from the spectrum; : The period length corresponding to the i-th frequency; i represents the index of the frequency, used to distinguish different frequency components and their corresponding period lengths, corresponding to the discrete frequency points in the spectrum analysis (such as the frequency bins after Fourier transform); : Floor operation. represents the frequency value of the k-th highest amplitude, corresponding to the k-th most significant periodic component in the signal.

[0034] By performing a Fourier transform on the seasonal part, this formula obtains the amplitude information at different frequencies and selects the period length corresponding to the frequency with a larger amplitude, providing a basis for subsequent division of periodic components.

[0035] S2.1.1.2 Division of Periodic Components Furthermore, in step S2.1.1.2, hierarchical periodic components are divided according to the period length, and connection relationships between levels are established; a hierarchical periodic pyramid structure is constructed based on the inclusion relationship of periodic components, including: determining the hierarchical inclusion relationship between periodic components by judging whether there is an inclusion or overlap relationship between periodic components in different layers, where the upper-layer periodic components establish an inclusion relationship with the lower-layer components through index overlap judgment. Specifically, according to the frequency obtained in step S2.1.1.1 the time series is divided into periodic components of multiple levels:

[0036] : The specific representation of the nth periodic component (feature component) in the kth layer of the periodic pyramid; l is a finite set containing all independent or associated feature units in this layer, specifically representing the set of all feature components in the kth layer; different layers correspond to different feature abstraction scales (such as low-level details, high-level semantics), and the components are associated through the periodic component connection relationship in step S2.1.1.4 l ; the number of layers of the feature stream is the total number of components in the kth layer is l

[0037] .

[0037] The inclusion relationship between periodic components at different levels is determined by the following formula to judge whether there is an inclusion or overlap relationship between periodic components in different layers:

[0038] where is the index of the nth component in the kth layer; : a relationship indicator variable between two periodic components; represents the position index of each data point in the periodic component at this level; when it indicates an inclusion relationship; when it indicates no overlap. This formula provides a quantitative standard for judging the relationship between periodic components, which helps to accurately capture the multi-period characteristics of the time series in the model.

[0039] S2.1.1.3 Periodic Component Scale Mapping This step S2.1.1.3 is used to uniformly map the periodic components of different cycle lengths to the same scale through zero-padding and linear projection:

[0040] Among them, : Periodic representation after scale normalization; Padding represents zero-padding the periodic components in the time dimension to make their lengths consistent with the original data; Projection represents a single linear mapping layer used to map the padded periodic components to an appropriate scale.

[0041] Through this formula, the consistency of different periodic components in subsequent calculations is ensured.

[0042] S2.1.1.4 Periodic component connection relationship This S2.1.1.4 establishes the connection relationship between the current periodic component and the relevant components in the upper and lower layers:

[0043] includes the connection relationship with other relevant components, that is, the set of indices of the components that have a connection relationship, which is used to limit the scope of attention calculation (such as only considering local connections or periodic connections); represents its upper-layer parent node; represents its lower-layer child node; j represents the index of the upper or lower layer component that has a connection relationship with the current component The specific meaning and range are as follows: In , j represents the index of the component in the upper layer (the l- 1st layer) that is connected to , , where is the total number of components in the l- 1st layer; In, j represents the index of the component in the lower layer (the l +1st layer) that is connected to , where is the total number of components in the l +1st layer; represents that there is a connection between the jth component in the l- 1st layer and the nth component in the l th layer (and vice versa); represents that there is a connection between the nth component in the l th layer and the l ​+1 There is a connection between the j-th components (and vice versa). By and explicitly model the dependencies between layers.

[0044] This formula clearly defines how the periodic components are connected between different levels. By and , it realizes the fusion of upper-layer features (such as global trends) and lower-layer features (such as local details), and then realizes cross-layer information transmission, providing a basis for attention calculation. Through this design, the model can adaptively capture the periodic patterns in the multi-scale structure while avoiding the interference of irrelevant components.

[0045] S2.1.1.5 Construct a complete periodic pyramid By stacking the periodic components of different levels, a complete periodic pyramid is constructed:

[0046] : The finally constructed periodic pyramid; represents the stacking operation.

[0047] This formula combines the periodic components of each level to form a complete periodic pyramid structure, intuitively showing the construction method of the periodic pyramid.

[0048] S2.1.1.6: Attention calculation This step S2.1.1.6 calculates the attention of the component based on the connection relationship of the periodic components in step 2.1.1.4:

[0049] : The weighted output result of the query point ch, calculated by aggregating the relevant key-value pairs ; ch represents the query point index in the attention mechanism, used to traverse all query positions where attention needs to be calculated; , and represent the query, key, and value vectors respectively; , indicating that only the key-value pairs connected to the component are selected to participate in the calculation. is the transpose of the m-th row in the key (Key) matrix K, corresponding to a key vector, representing the feature representation of the m-th component; is a two-dimensional matrix, M represents the total number of components in the input sequence (such as all periodic components or connected components), is the dimension of the key vector (usually the same as the query vector and the value vector has the same dimension); : represents the query and the key dot product divided by the exponential value after : the normalization factor, which performs a Softmax operation on the attention scores.

[0050] In this step, the key matrix K is generated by linear transformation of the input features. For example, it is constructed as follows: encoding the features of the input components (such as through a fully connected layer or a convolutional layer). Mapping the encoded features to the key space to obtain the key vectors (the query vector and the value vector are also generated in a similar way (sharing or independent parameters)), for example, , , , where , , are learnable parameter matrices, and are the input features. Stacking all the key vectors row by row to form the matrix K. The key matrix K stores the feature information of all components and is used to calculate the similarity with the query vector to determine the weight of each component in the attention mechanism.

[0051] This formula captures the complex dependencies in the time series through the attention calculation of relevant components, enabling the model to focus on important periodic features.

[0052] S2.1.1.7: Periodic Feature Stream Aggregation This step S2.1.1.7 is used to aggregate the key periodic components to form a unified feature representation, output the aggregated time series features for the subsequent step 2.1.3 Multimodal Feature Fusion:

[0053] Among them, is a specific periodic component in the output of Peri-midFormer; constitutes a feature stream; Projection maps each feature stream to the target output length; Ave performs an average pooling operation on the feature stream; is the aggregated time series feature.

[0054] S2.1.2: Construct an Image Feature Extractor To extract the deep structural information in the image data, this step S2.1.2 introduces a fusion mechanism of topological data analysis and graph convolution, and captures high-order features in the graph structure through persistent homology. The image feature extractor uses a graph convolution model that integrates topological data analysis to process the image data, constructs a topological evolution process through graph filtering, generates persistent barcodes and embeds them as topological vectors, and extracts the topological structure features of the image through a multi-scale adaptive graph convolution module. Among them, the construction of the image feature extractor includes: S2.1.2.1: Graph Filtering Operation This step S2.1.2.1 is used to perform graph filtering operations on the image data, construct a topological evolution process through graph filtering, and analyze the stability of the graph structure at different scales:

[0055] : The graph structure under the i'-th view (e.g., subgraphs generated by different topological transformations); Represents the graph after the j'-th step of filtering; : Set of nodes; : Set of edges; Represents the i'-th view of the graph; j' represents the layer serial number in the graph filtering process (e.g., j' = 0 is the initial sparse state, j' = n is the final dense state), and j' can reflect the degree of filtering. The closer j' is to 0, the more extensive the filtering is.

[0056] This formula represents the process of graph filtering on the i'-th transformed graph from the initial state gradually filtered to the final state . It represents the topological evolution process of the graph from sparse to dense, and is used to characterize the persistence of topological features.

[0057] S2.1.2.2: Node Filtering and Edge Filtering Operations This step S2.1.2.2 is used to eliminate low-importance topological features through node filtering and edge filtering. Hierarchical elimination is performed according to the importance of nodes or edges, providing a basis for constructing a simplicial complex in the subsequent steps.

[0058] Node Filtering:

[0059] This formula is used to determine which nodes in the graph will be retained during the j'-th step of filtering. Only when the result of the node after being processed by the function is less than or equal to the threshold will the node be retained in In

[0060] Edge filtering:

[0061] This formula is used to determine which edges in the graph will be retained during the filtering at the j'-th step. Only when the maximum value of the results after the two endpoints of the edge and and after passing through the function is less than or equal to the threshold will this edge be retained in In

[0062] Step S2.1.2.2 implements persistent homology filtering, which removes noisy topological features and retains key geometric invariants.

[0063] S2.1.2.3: Construct the persistence diagram This step S2.1.2.3 constructs a persistence diagram based on persistent homology to record the lifespan of topological features, which is used to record the lifespans of different topological features in the graph structure at multiple scales, thereby reflecting their "persistence" and stability.

[0064] Furthermore, among them, the persistence diagram is constructed in the following way: Perform multi-scale filtering on the simplicial complex S (b) and record the emergence time (birth time) t1 and disappearance time (death time) t2 of each topological feature; distinguish the topological feature types according to the homology dimension b ∈ {0, 1}, where b = 0 corresponds to connected components (such as discrete point clusters), and b = 1 corresponds to loop structures or tunnels (such as cyclic patterns), and construct a persistent barcode; store the lifespan of the topological feature in the form of a tuple (t1, t2) into the set D (b) to form a persistence diagram describing the evolution of topological features.

[0065] Specifically, the persistence diagram formula:

[0066] S: Simplicial complex. For example, S (0) can represent the 0-dimensional simplices (vertices) generated by the point cloud, and S (1) can represent the 1-dimensional simplices connected by edges.

[0067] This formula is used to construct a persistence diagram, which records the emergence and disappearance times of the simplicial complex in the graph filtering process in the form of a tuple (t1, t2) to form a persistence diagram for describing the changes in the topological features of the graph.

[0068] S2.1.2.4: Barcode to vector embedding In step S2.1.2.4, the persistent barcode is converted into a topological vector through a learnable embedding function. The topological structure is encoded into a learnable vector representation for feature extraction by the multi-scale adaptive graph convolution module in step 2.1.2.5.

[0069] Furthermore, the barcode-to-vector embedding is achieved through the following steps: Parametrically encode the $b$-th order persistent barcode under the $c$-th view to generate an initial topological descriptor; map the initial topological descriptor to an $N\times d$-dimensional vector space through the embedding function , where $N$ is the number of graph nodes and $d$ is the preset vector dimension; optimize the embedding process using a trainable linear layer or non-linear activation function to make the topological vector retain the stability information in multi-scale filtering. Specifically, the persistent barcode is converted into a topological vector through the following formula:

[0070] : represents the $b$-th order persistent barcode under the $c$-th view, for example represents the 0-th order persistent barcode (connected component life cycle) under the $c$-th view; : the embedding function from barcode to vector space; $N$: the number of nodes in the graph; $d$: the dimension of the target vector; $c$ is the number of filtering functions and the number of views of the graph.

[0071] This formula represents the process of converting the persistent barcode into a topological vector through the embedding function such that the topological features can be represented in the form of a vector .

[0072] S2.1.2.5: Construct a multi-scale adaptive graph convolution module To enhance the graph structure modeling ability, this step S2.1.2.5 adopts multi-scale adaptive graph convolution and MixHop convolution strategies to extract the deep topological features of the image data and obtain the image topological structure features.

[0073] Furthermore, the multi-scale adaptive graph convolution module enhances the graph structure modeling ability through the following operations: Perform a linear transformation on the input topological vector to generate initial graph features; construct an adaptive adjacency matrix based on two trainable parameter matrices to capture the dynamic dependencies of the graph structure; perform power expansion on the adaptive adjacency matrix by a multi-order convolution propagation layer to capture the neighborhood information of each order of the initial graph features; concatenate the graph convolution results of each order along the feature dimension to obtain the concatenated features; apply a non-linear activation function to the concatenated features to generate the topological structure features of the image:

[0074] : The linear transformation matrix at the e-th scale; : The topological vector at the e-th scale obtained in step S2.1.2.4; : Represents the transformed graph feature, which is used as the initial graph feature for subsequent graph convolution operations; : Are two trainable parameter matrices used to construct the adaptive adjacency relationship of the graph. Their product is activated through the ReLU and SoftMax functions to generate the weight matrix; : The adaptive adjacency matrix, which is constructed through the parameters and ; : Represents the g-th power of the adjacency matrix , corresponding to the adjacency propagation operation of the g-th order graph convolution; : The non-linear activation function, commonly such as ReLU, ELU or Tanh, which is used to increase the model's expressive ability; : Represents concatenating the graph convolution outputs along different orders g, that is, concatenating the results of different order graph convolutions along the feature dimension (a common operation in the MixHop structure); : Represents the set of graph convolution orders that need to be aggregated; : The final graph feature output at the e-th scale, that is, the image topological structure feature.

[0075] This step S2.1.2.5 restricts the attention range through , only focuses on the key components, and combines the in the previous step S2.1.1.4 to dynamically select the feature propagation path. Especially for long sequence tasks, it reduces redundant calculations and saves computing time.

[0076] S2.2. Fuse the time series feature and the image topological structure feature through a stepped mutual attention mechanism to obtain a fused feature vector; This step S2.2 is used to achieve multi-modal feature fusion. In order to fully utilize the complementarity of multi-source information, the time series feature extracted in step S2.1.1 and the image topological feature extracted in step S2.1.2 are subjected to multi-modal fusion. A fusion structure based on a stepped mutual attention mechanism is designed, with the time series modality as the main channel and the image modality introduced as an auxiliary hint to perform fine-grained enhancement on each frame along the time axis. This module mainly includes two stages: mutual multi-head attention calculation and global feature aggregation.

[0077] Furthermore, in S2.2, the time series features and the image topological structure features are fused through a stepped mutual attention mechanism to obtain a fused feature vector, including: for each frame feature of the time series, with the time series features as the main modality and the image topological structure features as the auxiliary modality, calculating the attention-enhanced representation of the image modality to the time series modality; aggregating the enhanced representations of all frames to obtain a unified fused feature, that is, the fused feature vector. Specifically, it includes the following steps: S2.2.1 Generation of Mutual Attention Enhanced Representation (Multi-Head Attention Calculation) To enable the main modality (time series) to fuse the context feature information of the auxiliary modality (image), a mutual attention mechanism is introduced. Specifically, it is expressed as:

[0078] : The enhanced representation of the main modality fused with the auxiliary modality information, and this fusion method is asymmetric fusion, only enhancing the main modality (different from bidirectional cross-attention); Indicates the information flow direction: transmitting features from the auxiliary modality F (image) to the main modality Z (time series); : The Query representation of the auxiliary modality, expressed as the feature matrix of the image modality, used to query the key information in the image; : The Key representation of the main modality, expressed as the feature matrix of the time series modality, used to provide the matching benchmark for the time series; : The Value representation of the main modality, with the same source as the Key, carrying the original time series features to be corrected; G: The scaling factor of the feature dimension, used to prevent the attention distribution from being too sharp; : Normalize each row to obtain the attention weight distribution.

[0079] This formula is used to calculate the importance weights of the image features for each frame of the time series features, and based on these weights, adjust the time series representation to generate the fused perception representation. The time series is the dominant, and the image is the auxiliary: The material response signal is the core basis for parameter inversion, and the microscopic deformation / thermal map provides local detail supplement, which conforms to the data value distribution of "time series as the main and image as the auxiliary" in engineering practice. The main modality Z (time series) retains the main structure and only selectively absorbs the relevant information of the auxiliary modality F (image), with a directional enhancement mechanism to avoid feature contamination caused by bidirectional fusion (such as image noise affecting the integrity of the time series).

[0080] S2.2.2: Overall Representation of the Time Series after Multimodal Fusion (Global Feature Aggregation) Aggregate the enhanced features of each frame generated above to obtain the final overall expression of the fused time series. The specific formula is as follows:

[0081] : The enhanced representation after fusing the time features of the r-th frame with the image features, representing the enhanced features generated by the time modality after introducing the image modality. r represents the r-th segment / frame in the time series. Indicates the fusion direction from image features (figure) to time features (time) (auxiliary modality → main modality). Indicates being generated through the attention mechanism (Attention). m’ represents the multimodal (Multimodal) fusion result; n’: the number of frames in the time series, determined by the original time series length L and the sampling rate. : The average pooling function (Average Pooling), which performs weighted averaging on all frame representations and outputs a unified modality representation. : The final time series feature expression after fusion, used for subsequent prediction tasks. It serves as the input vector of the neural network classifier for downstream parameter inversion tasks.

[0082] Through this formula, the fused enhanced features of n’ time frames can be aggregated into a single vector through average pooling. , serving as the global representation of the entire time series. This operation is the core output of the hierarchical mutual attention mechanism, which solves the semantic alignment problem of multimodal data in the time dimension.

[0083] In step S2.2, image features are first fused at each time frame (fine-grained alignment) to achieve frame-level enhancement; then a fixed-dimension representation independent of length is obtained through pooling to ensure temporal invariance.

[0084] S3. Train a neural network based on the fused feature vector, output the final predicted value, and update the network parameters using the residual-based surrogate hyperplane Kaczmarz optimization method and the oblique projection (RSHKO) optimization method. Step S3 is used to implement neural network training. After completing the multimodal feature extraction and fusion in step S2, a temporally fused feature vector with unified representation is obtained. . Next, this fused feature will serve as the input of the neural network classifier to achieve accurate prediction or diagnosis of downstream tasks. To further improve the training efficiency and convergence stability, a surrogate hyperplane residual-driven mechanism and an oblique projection direction selection strategy are introduced in this stage. By guiding the optimization path to adjust the parameter update direction, the model has stronger expression ability and generalization performance in complex multimodal scenarios.

[0085] Further, in step S3, the network parameters are updated by using the residual-based surrogate hyperplane Kaczmarz optimization method and the oblique projection optimization method, including: calculating the gradient residual vector of the current iteration; constructing the oblique projection direction based on the gradient residual vector; calculating the update step size through the norm of the gradient residual vector and the norm of the oblique projection direction, and generating new parameters. Specifically, it includes the following steps: S3.1 Input Feature Preparation The fused feature vector is input into the neural network model, which usually includes multiple fully connected layers and non-linear activation functions, and outputs the final predicted value for calculating the loss function with the true label.

[0086] S3.2 Surrogate Hyperplane Residual Driving Mechanism Traditional neural network training mainly relies on standard backpropagation and gradient descent for weight update, but this method is often sensitive to abnormal noise and prone to falling into local optima. Therefore, in each weight iteration update of deep learning backpropagation, an optimization step based on the residual-based surrogate hyperplane Kaczmarz method and oblique projection (RSHKO) is added. Specifically, in deep learning training, let the parameter vector of the neural network be , and the loss function be , and its residual is defined as:

[0087] : the parameter vector of the deep learning model at the u-th iteration; : the value of the loss function with the current parameters as the input; : the current gradient residual vector (i.e., the gradient of the loss function with respect to the parameters).

[0088] In traditional gradient descent, the weight update is based on the negative gradient direction, while this strategy constructs an oblique projection matrix through the residual to obtain the optimal update direction. Using the oblique projection and surrogate hyperplane mechanism in the RSHKO idea, its update formula is:

[0089] : the updated parameter vector; : the square of the two-norm of the current residual vector, measuring the current error intensity; : the square of the two-norm of the current projection direction vector, used to normalize the step size; : the current oblique projection direction (optimal direction), and its expression (i.e., the generation rule of the oblique projection direction in the RSHKO optimization method): 1. When :

[0090] 2. When (using the optimal oblique projection):

[0091] : The constructed characteristic projection operator matrix can be an identity matrix or a specific constructed matrix (such as a characteristic transformation matrix); : The auxiliary vector of the projection direction, the gradient projection result of the u-th iteration; : At the -th iteration, the auxiliary vector; : The vector dot product operation.

[0092] The essence of the formula in this step S3.2 is to innovatively transform the traditional gradient direction update into an oblique projection update under the guidance of residuals, and construct a surrogate hyperplane through historical gradients, effectively improving the training robustness and convergence speed. The RSHKO optimizer achieves a balance between training convergence and accuracy.

[0093] S4. Input the preprocessed measured data into the trained model, output the inversion result of the material structure parameters, and achieve real-time online inference through the edge-cloud collaborative architecture.

[0094] After the present invention completes steps S1 to S3, it enters the system deployment and actual application stage. This stage aims to transform the model capabilities into engineering-available functional modules and realize the intelligent inversion and prediction of structure parameters in combination with the actual scenario. Specifically, it includes the following sub-steps: Step S4.1 System Deployment Architecture Design To achieve the efficient operation and scalable deployment of the system, the present invention constructs a deployment solution based on the edge-cloud collaborative architecture. As Figure 3 shown, it is the schematic diagram of the system architecture of the embodiment of the present invention. This system realizes: Edge computing: reducing the transmission bandwidth requirement and ensuring real-time performance; Cloud intelligent analysis: efficient calculation of complex models; Closed-loop verification: inversion result → simulation verification → model optimization; Industrial compatibility: integrating existing engineering systems through standard interfaces.

[0095] Specifically, edge devices (such as sensor systems, image acquisition devices) are used to collect material response data in real time, initially complete data preprocessing (such as normalization, noise reduction, image enhancement, etc.), and then upload the preprocessed data to the cloud platform.

[0096] The cloud platform deploys a deep learning model and an RSHKO optimization algorithm module, which is responsible for completing the following key tasks: performing periodic feature extraction and graph structure analysis on the received multi-modal data; using the periodic pyramid Transformer to capture the multi-scale dynamic patterns of time series; applying the multi-scale graph convolution module to extract the topological structure information in the image; performing multi-modal feature fusion to generate a unified semantic representation; and starting the RSHKO-driven optimization module to complete the fast inversion solution of the structural parameters.

[0097] Through the cooperation between the edge and the cloud, the effective allocation of computing load, the improvement of system response speed, and the enhancement of real-time data processing capabilities are achieved.

[0098] Step S4.2 Model Online Inference and Real-Time Prediction After the deployment is completed, the system can perform online inference tasks on the newly input measurement data. The specific process is as follows: Input data preparation: The user inputs the time series signals and image information of the material under different loading conditions; Feature extraction: The system calls the deployed periodic pyramid Transformer and graph convolution network to process the data; Fusion prediction: After completing modal fusion through the stepped mutual attention mechanism, a high-dimensional embedding representation is generated; Inversion solution: The features are input into the deep neural network, combined with the residual oblique projection optimization module, and the corresponding material structure parameters are quickly output.

[0099] This process can achieve a response speed of milliseconds and support online monitoring and structural evaluation in industrial sites.

[0100] S4.3 Engineering Integration and Interface Opening The present invention supports seamless integration with mainstream material testing platforms (such as ANSYS and ABAQUS simulation systems) and industrial acquisition software (such as LabVIEW and MATLAB acquisition systems). The system realizes the interaction function with the existing engineering platform by providing standard interfaces (such as RESTful API, WebSocket interface, OPCUA protocol, etc.), including: automatically obtaining experimental data and triggering parameter inversion; feeding back the inversion results to the simulation platform for performance verification; providing prediction reports, error analysis, and model interpretability maps. The openness of the interface greatly improves the applicability and engineering promotion ability of the present invention.

[0101] The present invention can be widely applied to the following typical scenarios: New material design and evaluation: In the development of new composite materials and microstructural materials, realizing the inversion of microstructural parameters and performance prediction; Structural health monitoring: In the fields of aerospace and civil engineering, tracking in real time the damage evolution parameters of structures during service; High-precision experimental inversion: Assisting in solving parameters that cannot be directly observed in complex mechanical experiments and improving the utilization efficiency of experimental data; Intelligent simulation assistance system: Intelligently calibrating material model parameters before numerical simulation to improve simulation accuracy.

[0102] In summary, the above embodiments of the present invention successively overcome the deficiencies in efficiency, accuracy, and generalization in material parameter inversion in the prior art through key technologies such as intelligent feature extraction, cross-modal fusion, and optimization inversion, providing technical support for fields such as high-end equipment manufacturing and major project safety monitoring.

[0103] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the described steps can refer to the corresponding processes in the foregoing system embodiments and will not be elaborated herein.

[0104] It should be noted that the various embodiments in this specification are described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the various embodiments can be referred to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0105] It should also be noted that in the embodiments of the present application, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "including a..." does not exclude the existence of additional identical elements in the process, method, article or device including the element.

[0106] The foregoing description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined in the embodiments of the present application may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to these embodiments shown in the embodiments of the present application, but rather will be accorded the widest scope consistent with the principles and novel features disclosed in the embodiments of the present application.

Claims

1. An intelligent optimization method for inverting the structural parameters of new materials, characterized in that, It includes the following steps: S1. Collect the time-series data and image data of the material under different loading conditions and perform preprocessing; S2. Construct a deep diagnosis model, including: S2.

1. Construct a multi-modal feature extractor: including a time-series feature extractor and an image feature extractor; among them, the time-series feature extractor uses a periodic pyramid Transformer model to capture the multi-scale periodic features of the time series through periodic component extraction, hierarchical modeling, and attention mechanism, and obtain time-series features; the image feature extractor fuses topological data analysis and multi-scale adaptive graph convolution to extract image topological structure features; S2.

2. Fuse the time-series features and the image topological structure features through a stepped mutual attention mechanism to obtain a fused feature vector; S3. Train a neural network based on the fused feature vector, output the final prediction value, and update the network parameters using the residual-based surrogate hyperplane Kaczmarz optimization method and the oblique projection optimization method; S4. Input the preprocessed measured data into the trained model, output the inversion result of the material structure parameters, and achieve real-time online inference through an edge-cloud collaborative architecture.

2. The intelligent optimization method according to claim 1, wherein Among them, The time-series feature extractor uses a periodic pyramid Transformer model to process time-series data, extracts the dominant frequency and the corresponding period length through frequency-domain analysis, divides multi-level periodic components, establishes hierarchical connection relationships, and aggregates multi-scale periodic features using the attention mechanism to output time-series features.

3. The intelligent optimization method according to claim 2, wherein Among them, Constructing a time-series feature extractor using a periodic pyramid Transformer model includes: When performing frequency-domain analysis on the input time series, use the fast Fourier transform to extract the frequency amplitude sequence of the seasonal part, and determine the periodic components through channel dimension averaging and dominant frequency screening; Divide the hierarchical periodic components according to the period length and establish the connection relationship between levels; Construct a hierarchical periodic pyramid structure according to the inclusion relationship of the periodic components; Calculate the connection relationship between the periodic components through the attention mechanism, aggregate the key periodic features, and output the aggregated time-series features for multi-modal fusion.

4. The intelligent optimization method according to claim 3, wherein Among them, The dividing the hierarchical periodic components according to the period length and establishing the connection relationship between levels; constructing a hierarchical periodic pyramid structure according to the inclusion relationship of the periodic components includes: Determine the hierarchical inclusion relationship between the periodic components by judging whether there is an inclusion or overlap relationship between the periodic components in different layers, where the upper-layer periodic components establish an inclusion relationship with the lower-layer components through index overlap judgment; Construct a hierarchical pyramid structure based on the inclusion relationship between the periodic components; Map different periodic components to a unified scale through zero-padding and linear projection; Establish the connection relationship between the current periodic component and the related components in the upper and lower layers; Construct a complete periodic pyramid by stacking different levels of periodic components.

5. The intelligent optimization method according to claim 4, wherein Among them, The image feature extractor uses a graph convolution model that fuses topological data analysis to process image data, constructs a topological evolution process through graph filtering, generates persistent barcodes and embeds them as topological vectors, and extracts image topological structure features through a multi-scale adaptive graph convolution module; Among them, the construction of the image feature extractor includes: Perform graph filtering operations on the image data to construct a topological evolution process; Eliminate low-importance topological features through node filtering and edge filtering; Construct a persistence diagram based on persistent homology to record the lifespan of topological features; Convert the persistent barcode into a topological vector through a learnable embedding function; Adopt a multi-scale adaptive graph convolution and MixHop convolution strategy to extract deep topological features of the image data and obtain the image topological structure features.

6. The intelligent optimization method according to claim 5, wherein Among them, The persistence diagram is constructed in the following way: For the simplicial complex S (b) perform multi-scale filtering and record the appearance time t1 and disappearance time t2 of each topological feature; Distinguish the topological feature types according to the homology dimension b ∈ {0, 1}, where b = 0 corresponds to connected components and b = 1 corresponds to loop structures, and construct a persistent barcode; Store the lifespan of the topological feature in the form of a tuple (t1, t2) into the set D (b) , forming a persistence diagram that describes the evolution of the topological feature.

7. The intelligent optimization method according to claim 6, wherein The barcode-to-vector embedding is realized through the following steps: Parametrically encode the $b$-th order persistent barcode under the $c$-th view to generate an initial topological descriptor; By an embedding function map the initial topological descriptor to an N×d-dimensional vector space, where N is the number of graph nodes and d is the preset vector dimension; Adopt a trainable linear layer or non-linear activation function to optimize the embedding process so that the topological vector retains the stability information in multi-scale filtering.

8. The intelligent optimization method according to claim 7, wherein The multi-scale adaptive graph convolution module enhances the graph structure modeling ability through the following operations: Perform a linear transformation on the input topological vector to generate initial graph features; Construct an adaptive adjacency matrix based on two trainable parameter matrices to capture the dynamic dependencies of the graph structure; The multi-order convolution propagation layer performs a power expansion on the adaptive adjacency matrix to capture the neighborhood information of all orders of the initial graph features; Concatenate the graph convolution results of all orders along the feature dimension to obtain the concatenated features; Apply a non-linear activation function to the concatenated features to generate the topological structure features of the image.

9. The intelligent optimization method according to claim 8, wherein Among them, In the S2.2, fuse the time series features and the image topological structure features through a stepped mutual attention mechanism to obtain a fused feature vector, including: For each frame feature of the time series, with the time series features as the main modality and the image topological structure features as the auxiliary modality, calculate the attention-enhanced representation of the image modality to the time series modality: Aggregate the enhanced representations of all frames to obtain a unified fused feature, that is, the fused feature vector.

10. The intelligent optimization method according to claim 8, characterized in that Among them, In step S3, the method of using the residual-based surrogate hyperplane Kaczmarz optimization method and the oblique projection optimization method to update the network parameters includes: Calculate the gradient residual vector of the current iteration; Construct an oblique projection direction based on the gradient residual vector; Calculate the update step size through the norm of the gradient residual vector and the norm of the oblique projection direction to generate new parameters.

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