An intelligent optimization method for inverting structural parameters of new materials

Abstract

The present invention provides an intelligent optimization method for inverting the structural parameters of new materials. This method relates to the field of materials science and engineering structural analysis technology. The method comprises: S1, collecting and preprocessing time series data and image data of materials under different loading conditions; S2, constructing a deep diagnostic model, including: constructing a time series feature extractor and an image feature extractor to extract time series features and image topological structure features, respectively; fusing the time series features and image topological structure features via a step-by-step mutual attention mechanism; S3, training a neural network based on the fused feature vector, outputting a final prediction value, and updating the network parameters using a residual-based surrogate hyperplane Kaczmarz optimization method and an oblique projection optimization method; S4, inputting the preprocessed measured data into the trained model, and outputting the inversion results of the material structural parameters. This method achieves rapid inversion of the structural parameters of complex materials, resolving current technical challenges.

Description

Technical Field

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

[0002] In the fields of materials science and engineering structural analysis, accurately obtaining material microstructural parameters (such as elastic modulus, Poisson's ratio, and density) is crucial for structural performance prediction and design optimization. However, traditional parameter inversion methods suffer from low computational efficiency, slow convergence, and susceptibility to local optima when faced with complex nonlinear, multimodal data and high-dimensional parameter spaces. These methods are particularly inadequate for the integrated processing of high-dimensional time series and image data.

[0003] In recent years, the development of artificial intelligence (AI), particularly deep learning and graph neural networks, has provided new technical approaches for material parameter inversion. Furthermore, 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 algorithm, still face bottlenecks in inversion efficiency and accuracy.

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

[0005] This invention aims to address the above-mentioned issues by proposing an intelligent optimization method for inverting the structural parameters of new materials. This method combines the residual surrogate hyperplane Kaczmarz method with oblique projections (RSHKO) and artificial intelligence models (such as neural networks and ensemble learning) to achieve this inversion. This method utilizes AI to extract features and reduce the dimensionality of measured data, combined with RSHKO for efficient and accurate parameter optimization, thereby achieving rapid inversion of complex material structural parameters. This method addresses key technical challenges currently encountered in material parameter inversion.

[0006] To achieve the above objectives, the following technical solutions are adopted:

[0007] An intelligent optimization method for inverting structural parameters of new materials includes the following steps:

[0008] S1. Collect time series data and image data of materials under different loading conditions and perform preprocessing;

[0009] S2. Build a deep diagnostic model, including:

[0010] S2.1. Construct a multimodal feature extractor: including a time series feature extractor and an image feature extractor. 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 an attention mechanism to obtain time series features. The image feature extractor integrates topological data analysis and multi-scale adaptive graph convolution to extract image topological structure features.

[0011] S2.2. Fusing the time series features and the image topology features through a stepwise mutual attention mechanism to obtain a fused feature vector;

[0012] S3. Training a neural network based on the fused feature vector, outputting a final prediction value, and updating network parameters using a residual-based substitute hyperplane Kaczmarz optimization method and an oblique projection optimization method;

[0013] S4. Input the preprocessed measured data into the trained model, output the inversion results of the material structure parameters, and realize real-time online reasoning through the edge-cloud collaborative architecture.

[0014] Furthermore, the time series feature extractor adopts the periodic pyramid Transformer model to process 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, utilizes the attention mechanism to aggregate multi-scale periodic features, and outputs time series features.

[0015] Furthermore, a time series feature extractor using a periodic pyramid Transformer model is constructed, including:

[0016] When performing frequency domain analysis on the input time series, the frequency amplitude sequence of the seasonal part is extracted using fast Fourier transform, and the periodic component is determined by channel dimension averaging and dominant frequency screening;

[0017] Divide the hierarchical periodic components by period length and establish inter-level connection relationships;

[0018] Construct a hierarchical periodic pyramid structure based on the inclusion relationship of periodic components;

[0019] The connection relationship between periodic components is calculated through the attention mechanism, key periodic features are aggregated, and the aggregated time series features are output for multimodal fusion.

[0020] Furthermore, the step of dividing the hierarchical periodic components by period length and establishing a connection relationship between the hierarchical components and constructing a hierarchical periodic pyramid structure according to the inclusion relationship of the periodic components includes:

[0021] By judging whether there is a containment or overlap relationship between periodic components at different levels, the hierarchical containment relationship between periodic components is determined, wherein the upper-level periodic component establishes a containment relationship with the lower-level component through index overlap judgment;

[0022] Construct a hierarchical pyramid structure based on the inclusion relationship between periodic components;

[0023] Different periodic components are mapped to a unified scale through zero padding and linear projection;

[0024] Establish the connection relationship between the current cycle component and the related components in the upper and lower layers;

[0025] By stacking cycle components at different levels, a complete cycle pyramid is constructed.

[0026] Furthermore, the image feature extractor processes image data using a graph convolution model that integrates topological data analysis, constructs a topological evolution process through graph filtering, generates a persistent barcode and embeds it into a topological vector, and extracts image topological structure features through a multi-scale adaptive graph convolution module;

[0027] The construction of the image feature extractor includes:

[0028] Perform graph filtering operations on image data to construct a topological evolution process;

[0029] Eliminate low-importance topological features through node filtering and edge filtering;

[0030] Construct a persistent graph based on persistent homology to record the life cycle of topological features;

[0031] converting the persistent barcode into a topological vector via a learnable embedding function;

[0032] Multi-scale adaptive graph convolution and MixHop convolution strategies are used to extract the deep topological features of image data and obtain the image topological structure features.

[0033] Furthermore, the persistence graph is constructed in the following manner:

[0034] For the simplicial complex S (b) Perform multi-scale filtering and record the appearance time t1 and disappearance time t2 of each topological feature;

[0035] Distinguish topological feature types according to the homology dimension b∈{0,1}, where b=0 corresponds to connected components and b=1 corresponds to ring structures, and construct a persistent barcode;

[0036] Store the life cycle of the topological feature in the form of a tuple (t1, t2) in the set D (b) , forming a persistent graph that describes the evolution of topological features.

[0037] Furthermore, the barcode steering amount embedding is achieved by the following steps:

[0038] For the b-th order persistent barcode in the c-th view Perform parameterized encoding to generate initial topology descriptors;

[0039] By embedding the function Mapping the initial topology descriptor to an N×d-dimensional vector space, where N is the number of graph nodes and d is a preset vector dimension;

[0040] Trainable linear layers or nonlinear activation functions are used to optimize the embedding process so that the topological vector retains the stability information in multi-scale filtering.

[0041] Furthermore, the multi-scale adaptive graph convolution module enhances the graph structure modeling capability through the following operations:

[0042] Perform linear transformation on the input topology vector to generate initial graph features;

[0043] An adaptive adjacency matrix is ​​constructed based on two trainable parameter matrices to capture the dynamic dependencies of the graph structure.

[0044] A multi-order convolutional propagation layer performs power expansion on the adaptive adjacency matrix to capture neighborhood information of each order of the initial graph features;

[0045] Concatenate the results of graph convolution of each order along the feature dimension to obtain the concatenated features;

[0046] A nonlinear activation function is applied to the concatenated features to generate topological structure features of the image.

[0047] Furthermore, in S2.2, the time series features and the image topology features are fused through a stepwise mutual attention mechanism to obtain a fused feature vector, including:

[0048] For each frame feature of the time series, with the time series feature as the main modality and the image topology structure feature as the auxiliary modality, the attention enhancement representation of the image modality to the time series modality is calculated:

[0049] Aggregating the enhanced representations of all frames yields a unified fused feature, i.e., a fused feature vector.

[0050] Furthermore, in step S3, the updating of network parameters using the residual-based substitute hyperplane Kaczmarz optimization method and the oblique projection optimization method includes:

[0051] Calculate the gradient residual vector of the current iteration;

[0052] Constructing an oblique projection direction based on the gradient residual vector;

[0053] The update step size is calculated by the norm of the gradient residual vector and the norm of the oblique projection direction to generate new parameters.

[0054] Compared with the prior art, the present invention achieves the following beneficial effects:

[0055] 1. This invention utilizes joint time-frequency-topology modeling, extracting local patterns through time-frequency analysis (e.g., FFT / wavelet transform) while simultaneously capturing global structure through topological analysis (e.g., persistent homology), achieving multi-scale feature complementarity. A time-driven, image-enhanced, step-by-step mutual attention mechanism achieves deep multimodal fusion. Dynamically adjusting the contribution of time-frequency and topological features through GRU or attention weights avoids information redundancy and addresses the cross-modal semantic gap.

[0056] 2. The present invention constructs a periodic pyramid Transformer model, which constructs a periodic pyramid structure through periodic structure decomposition, hierarchical modeling and attention mechanism, accurately capturing the multi-scale periodic relationship in time series data and improving the model's ability to model the timing of material dynamic response signals.

[0057] 3. The present invention proposes a method that integrates topological data analysis, multi-scale adaptive graph convolution and MixHop convolution: combining the local geometric information and global structural characteristics of material image data, designing a multi-scale information extraction module to adapt to the complex topological characteristics in the material microstructure and enhance the structural recognition ability of the model.

[0058] 4. The present invention performs multimodal fusion through a step-by-step mutual attention mechanism: in the stage of fusion of time series and image data, a cross-modal mutual attention mechanism is designed to capture the correlation features between different modalities in a hierarchical manner, and achieve information alignment and complementarity at the semantic level.

[0059] 5. The present invention optimizes the model based on the residual substitute 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 nonlinear and high-dimensional parameter spaces is solved.

[0060] It should be understood that the contents described in the summary of the invention are not intended to limit the key or important features of the embodiments of the present invention, nor are they intended to limit the scope of the present invention. Other features of the present invention will become readily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] The above and other features, advantages and aspects of the embodiments of the present invention will become more apparent with reference to the following detailed description in conjunction with the accompanying drawings. The accompanying drawings are provided for a better understanding of the present invention and do not constitute a limitation of the present invention. In the accompanying drawings, the same or similar reference numerals represent the same or similar elements, among which:

[0062] Figure 1 1 is a flow chart of an intelligent optimization method for inverting structural parameters of new materials according to an embodiment of the present invention;

[0063] Figure 2 2 is a flow chart of step S2 of an embodiment of the present invention, which is to construct a deep diagnostic model;

[0064] Figure 3 Schematic diagram of the system architecture of an intelligent optimization method for inverting structural parameters of new materials according to an embodiment of the present invention. DETAILED DESCRIPTION

[0065] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0066] In this document, the term "and / or" simply describes a relationship between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. Furthermore, the character " / " in this document generally indicates that the related objects are in an "or" relationship.

[0067] Figure 1 FIG. 1 is a flow chart showing an intelligent optimization method for inverting structural parameters of new materials according to an embodiment of the present invention. Figure 1 As shown, an intelligent optimization method 100 for inverting structural parameters of a new material includes the following steps:

[0068] S1. Collect time series data and image data of materials under different loading conditions and perform preprocessing;

[0069] The main purpose of step S1 is to collect and preprocess multimodal data. It specifically includes the following steps:

[0070] S1.1: Multimodal Data Acquisition

[0071] The present invention first collects the multimodal response data of the material under different loading conditions by combining experimental measurement with numerical simulation. The loading condition refers to the type of external action applied to the material sample and its parameter combination. In the present invention, the loading condition may include 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); multiaxial loading: complex stress state (such as biaxial tension, shear-tension composite 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℃) to high temperature molten state (>1000℃); thermal cycle: rapid heating / cooling (such as 10℃ / s to 100℃ / 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, gamma ray, neutron radiation. (4) Multi-physics field coupling conditions, including: thermal-mechanical coupling: mechanical load and temperature field interact; electro-magnetic-mechanical coupling: electromagnetic field and mechanical stress interact (such as piezoelectric materials, magnetostrictive materials); chemical-mechanical coupling: corrosive medium and stress synergistically act (such as stress corrosion cracking). (5) Special loading modes, including: cyclic loading: sine wave, square wave, random vibration spectrum; pre-damage loading: notched specimen, pre-crack extension; composite loading path: load-unload-reload, variable amplitude cycle.

[0072] Specifically, the multimodal response data of materials under different loading conditions mainly include two categories: time series data and image data.

[0073] In some embodiments, time series data primarily includes continuous signals such as stress-strain curves, acceleration-time responses, acoustic or electromagnetic wave propagation signals, and frequency response functions. This data is collected using devices such as stress testers, laser Doppler vibrometers, ultrasonic sensors, or electromagnetic sensors, reflecting the dynamic response behavior of materials under different external stimuli. Image data includes surface deformation images, strain field distribution maps, thermal infrared images, and microstructure images. This image data can be obtained using imaging devices such as digital image correlation (DIC) systems, high-speed camera systems, infrared thermal imagers, or electron microscopes to capture local deformation, microcrack evolution, or thermal-mechanical coupling characteristics of the material during loading. Furthermore, finite element simulation platforms (such as ABAQUS and ANSYS) can be used to model and simulate the mechanical behavior of the material under different structural parameter assumptions, generating matched time series and image simulation data to enhance data diversity and coverage. Ultimately, a structured multimodal dataset is formed, providing a comprehensive, high-quality input information foundation for subsequent feature extraction, parameter inversion, and intelligent optimization.

[0074] S1.2: Multimodal Data Preprocessing

[0075] For the collected multimodal material response data, the data of different modes need to be preprocessed separately to extract stable and identifiable low-dimensional features to facilitate subsequent inversion modeling.

[0076] For time series data (such as stress-strain curves, acoustic signals, and frequency response data), unified sampling rate resampling, normalization, and filtering noise reduction are performed. For image data (such as deformation images, thermal images, and microstructure images), image enhancement, denoising, resizing, and alignment are performed.

[0077] Figure 2 FIG. 1 is a flow chart of step S2 of an embodiment of the present invention, which is to construct a deep diagnostic model. Figure 2 As shown, S2, build a deep diagnosis model, specifically including:

[0078] S2.1. Construct a multimodal feature extractor: This includes a time series feature extractor and an image feature extractor. The time series feature extractor uses a periodic pyramid Transformer model to capture the multi-scale periodic features of time series through periodic component extraction, hierarchical modeling, and an attention mechanism to obtain time series features. The image feature extractor integrates topological data analysis and multi-scale adaptive graph convolution to extract image topological structure features. This is a dual-engine feature extraction method combining periodic pyramid and persistent coherence.

[0079] S2.1.1: Building a time series feature extractor

[0080] In step S2.1.1, a periodic pyramid Transformer model is proposed to extract key periodic features from collected time series data. Through periodic structure decomposition, hierarchical modeling, and an attention mechanism, this model accurately captures multi-scale periodic relationships in time series, improving the modeling capabilities of temporal features.

[0081] Among them, a time series feature extractor using the periodic pyramid Transformer model is constructed to process time series data. The dominant frequency and corresponding period length are extracted through frequency domain analysis, multi-level period components are divided and hierarchical connections are established, and the multi-scale period features are aggregated using the attention mechanism to output time series features. The specific steps include:

[0082] S2.1.1.1 Periodic component extraction

[0083] When performing frequency domain analysis on the input time series, the frequency amplitude sequence of the seasonal part is extracted by fast Fourier transform, and the periodic component is determined by channel dimension averaging and dominant frequency screening. First, the input normalized time series Perform frequency domain analysis to extract significant periodic components:

[0084]

[0085] 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 channel dimensions; A: frequency amplitude sequence; : The first k dominant frequencies selected from the spectrum; : The period length corresponding to the i-th frequency; i represents the frequency index, which is used to distinguish different frequency components and their corresponding period lengths, which corresponds to discrete frequency points in spectrum analysis (such as frequency bins after Fourier transform); : Round down operation. It represents the kth frequency value with the highest amplitude, corresponding to the kth significant periodic component in the signal.

[0086] This formula obtains the amplitude information of different frequencies by performing Fourier transform on the seasonal part, and selects the period length corresponding to the frequency with larger amplitude, providing a basis for the subsequent division of periodic components.

[0087] S2.1.1.2 Periodic component division

[0088] Furthermore, step S2.1.1.2 divides the hierarchical periodic components according to the period length and establishes the connection relationship between the hierarchical levels; constructs the hierarchical periodic pyramid structure according to the inclusion relationship of the periodic components, including: determining the hierarchical inclusion relationship between the periodic components by judging whether there is an inclusion or overlap relationship between the periodic components at different levels, wherein 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 , divide the time series into multiple levels of periodic components:

[0089]

[0090] :No. l The specific representation of the nth period component (characteristic component) in the layer period pyramid; It is a finite set that contains all independent or associated feature units of the layer, specifically in the first l The collection of all characteristic components in the layer; different layers l Corresponding to different feature abstraction scales (such as low-level details and high-level semantics), the components are connected through the periodic component connection relationship of step S2.1.1.4 Association; the number of layers of feature flow is the total number of components in the kth layer is .

[0091] The inclusion relationship between periodic components at different levels is determined by the following formula to determine whether there is an inclusion or overlap relationship between periodic components at different levels:

[0092]

[0093] in, It is The index of the nth component in the layer; : indicator variable of the relationship between two periodic components; Represents the position index of each data point in the periodic component of this level; when When , it indicates that there is a containment relationship; When , there is 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 time series in the model.

[0094] S2.1.1.3 Periodic component scale mapping

[0095] This step S2.1.1.3 is used to uniformly map periodic components of different period lengths to the same scale by zero-padding and linear projection:

[0096]

[0097] in, : Periodic representation after scale unification; Padding Indicates that the periodic component is zero-filled in the time dimension so that its length is consistent with the original data; Projection Represents a single linear mapping layer, which is used to map the padded periodic components to the appropriate scale.

[0098] This formula ensures the consistency of different periodic components in subsequent calculations.

[0099] S2.1.1.4 Connection relationship of periodic components

[0100] S2.1.1.4 establishes the connection relationship between the current period component and the related components in the upper and lower layers:

[0101]

[0102] Contains The connection relationship with other related components, i.e. components A set of component indices with connection relationships, used to limit the scope of attention calculation (such as considering only local connections or periodic connections); Indicates the parent node of its upper layer; Indicates the child node of its lower layer; j indicates the node with the current component The index of the upper or lower layer components with a connection relationship has the following specific meanings and scopes: In the example, j represents the upper layer (the l- 1st floor) The component index of the connection, ,in It is l- Total number of ingredients in 1 layer; In the example, j represents the lower layer (the l +1 level) with Connected component index ,in It is l +1 layer total number of ingredients; Indicates the l- The jth component of the first layer is l There are connections between the nth components of a layer (and vice versa); Indicates the l The nth component of the layer and the l +1There is a connection between the jth components (and vice versa). and Explicitly model inter-layer dependencies.

[0103] This formula clearly defines how periodic components are connected at different levels, through and , achieving the fusion of upper-level features (such as global trends) and lower-level features (such as local details), thereby realizing cross-level information transfer and providing a foundation for attention calculation. Through this design, the model can adaptively capture periodic patterns in multi-scale structures while avoiding interference from irrelevant components.

[0104] S2.1.1.5 Constructing a complete cycle pyramid

[0105] By stacking different levels of periodic components, a complete periodic pyramid is constructed:

[0106]

[0107] : The final constructed cycle pyramid; Indicates a stacking operation.

[0108] This formula combines the periodic components of each level to form a complete periodic pyramid structure, intuitively demonstrating how the periodic pyramid is constructed.

[0109] S2.1.1.6: Attention Computation

[0110] This step S2.1.1.6 calculates the components based on the periodic component connection relationship of step 2.1.1.4. Attention:

[0111]

[0112] : The weighted output result of the query point ch, by aggregating the key-value pairs related to it Calculated; ch represents the query point index in the attention mechanism, which is used to traverse all query positions that need to calculate attention; 、 and represent query, key, and value vectors respectively; , which means only select the components Key-value pairs with connection relationships participate in the calculation. is the transpose of the mth row in the key matrix K, which corresponds to a key vector representing the feature representation of the mth 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 Sum value vector dimensions are consistent); : Indicates query and key The dot product of The index value after ,measures the correlation between the two (i.e., attention score); : Normalization factor, performing Softmax operation on the attention score.

[0113] In this step, the key matrix K is generated by linear transformation of the input features. For example, it is constructed in the following way: The features are encoded (such as through a fully connected layer or a convolutional layer). The encoded features are mapped to the key space to obtain the key vector (Query vector Sum value vector are also generated in a similar way (shared or independent parameters), e.g. , , ,in , , is the learnable parameter matrix, and For input features. All key vectors Stacked by rows, forming a matrix K. The key matrix K stores the feature information of all components and is used to compare with the query vector Similarity calculation is performed to determine the weight of each component in the attention mechanism.

[0114] This formula captures the complex dependencies in the time series by paying attention to the relevant components, allowing the model to focus on important periodic features.

[0115] S2.1.1.7: Periodic Feature Flow Aggregation

[0116] This step S2.1.1.7 is used to aggregate the key periodic components to form a unified feature representation and output the aggregated time series features for the subsequent step 2.1.3 multimodal feature fusion:

[0117]

[0118] in, is a specific periodic component in the output of Peri-midFormer; Constitute a feature flow; Projection Map each feature stream to the target output length; Ave Perform average pooling operation on the feature stream; is the aggregated time series feature.

[0119] S2.1.2: Build an image feature extractor

[0120] To extract deep structural information from 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 coherence. The image feature extractor uses a graph convolution model integrated with topological data analysis to process image data, constructs a topological evolution process through graph filtering, generates a persistent barcode and embeds it into a topological vector, and extracts image topological structural features through a multi-scale adaptive graph convolution module. The construction of the image feature extractor includes:

[0121] S2.1.2.1: Graph Filtering Operations

[0122] This step S2.1.2.1 is used to perform a graph filtering operation on the image data. By using the graph filtering, a topological evolution process is constructed to analyze the stability of the graph structure at different scales:

[0123]

[0124] : The graph structure under the i'th view (e.g., subgraphs generated by different topological transformations); represents the graph after filtering in step j'; : node collection; : edge set; Represents the i'th view of the graph; j' represents the level number in the graph filtering process (e.g., j'=0 is the initial sparse state, j'=n is the final dense state). j' can reflect the degree of filtering. The closer j' is to 0, the more extensive the filtering.

[0125] This formula represents the i'th transformed graph The process of graph filtering starts from the initial state Gradually filter to the final state . It represents the topological evolution process of a graph from sparse to dense, and is used to characterize the persistence of topological features.

[0126] S2.1.2.2: Node and edge filtering operations

[0127] This step S2.1.2.2 is used to remove low-importance topological features through node filtering and edge filtering. This is done hierarchically based on the importance of nodes or edges, providing a foundation for the subsequent construction of a simplicial complex.

[0128] Node filtering:

[0129]

[0130] This formula is used to determine the j'th step of filtering. Which nodes will be retained. Only when the node go through The result after function processing is less than or equal to the threshold The node will be retained in middle.

[0131] Edge filtering:

[0132]

[0133] This formula is used to determine the j'th step of filtering. Which edges will be retained. Only when the two endpoints of the edge and go through The maximum value of the result after function processing is less than or equal to the threshold This edge will be retained in middle.

[0134] Step S2.1.2.2 implements persistent coherent filtering by Remove noisy topological features while preserving key geometric invariants.

[0135] S2.1.2.3: Constructing a Persistent Graph

[0136] This step S2.1.2.3 constructs a persistent graph based on persistent homology to record the life cycle of topological features, which is used to record the life cycle of different topological features in the graph structure at multiple scales, thereby reflecting its "persistence" and stability.

[0137] Furthermore, the persistence graph is constructed in the following way:

[0138] For the simplicial complex S (b) Perform multi-scale filtering and record the appearance time (birth time) t1 and disappearance time (death time) t2 of each topological feature; distinguish the topological feature type according to the homology dimension b∈{0,1}, where b=0 corresponds to a connected component (such as a discrete point cluster) and b=1 corresponds to a ring structure or tunnel (such as a cyclic pattern), and construct a persistent barcode; store the life cycle of the topological feature in the form of a tuple (t1, t2) in the set D (b) , forming a persistent graph that describes the evolution of topological features.

[0139] Specifically, the persistence graph formula:

[0140]

[0141] S: simplicial complex, for example, S (0) It can represent a 0-dimensional simplex (vertices) generated by the point cloud, S (1) It can represent 1-dimensional simplices connected by edges.

[0142] This formula is used to construct a persistence graph, which records the appearance and disappearance times of simplicial complexes during the graph filtering process in the form of tuples (t1, t2) to form a persistence graph that is used to describe the changes in the topological characteristics of the graph.

[0143] S2.1.2.4: Barcode Turning Quantity Embedding

[0144] In step S2.1.2.4, the persistent barcode is converted into a topological vector using a learnable embedding function. The topological structure is encoded into a learnable vector representation for feature extraction using the multi-scale adaptive graph convolution module in step 2.1.2.5.

[0145] Furthermore, the barcode direction embedding is achieved by the following steps:

[0146] For the b-th order persistent barcode in the c-th view Perform parameterized encoding to generate the initial topology descriptor; by embedding the function The initial topological descriptor is mapped to an N×d-dimensional vector space, where N is the number of graph nodes and d is the preset vector dimension. A trainable linear layer or nonlinear activation function is used to optimize the embedding process so that the topological vector retains stability information during multi-scale filtering. Specifically, the persistent barcode is converted to a topological vector using the following formula:

[0147]

[0148] : represents the b-th order persistent barcode in the c-th view, for example Represents the zero-duration persistent barcode (connected component lifecycle) in the c-th view; : embedding function of barcode into vector space; N: number of nodes in the graph; d: dimension of target vector; c is the number of filter functions and the number of graph views.

[0149] This formula represents the embedding function The process of converting persistent barcodes into topological vectors enables topological features to be expressed in the form of vectors. express.

[0150] S2.1.2.5: Constructing a multi-scale adaptive graph convolution module

[0151] In order to enhance the graph structure modeling capability, 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.

[0152] Furthermore, the multi-scale adaptive graph convolution module enhances the graph structure modeling capability through the following operations:

[0153] Perform a linear transformation on the input topological vector to generate the initial graph features; construct an adaptive adjacency matrix based on two trainable parameter matrices to capture the dynamic dependencies of the graph structure; a multi-order convolutional propagation layer exponentially expands the adaptive adjacency matrix to capture the neighborhood information of each order of the initial graph features; concatenate the results of each order of graph convolution along the feature dimension to obtain the concatenated features; apply a nonlinear activation function to the concatenated features to generate the topological structure features of the image:

[0154]

[0155] : 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 features, which serve as the initial graph features for subsequent graph convolution operations; : These are two trainable parameter matrices used to construct the adaptive adjacency relationship of the graph. Their product is activated by ReLU and SoftMax functions to generate a weight matrix; : Adaptive adjacency matrix, through parameters and Build; : represents the adjacency matrix The g-th power corresponds to the adjacency propagation operation of the g-order graph convolution; : Non-linear activation function, commonly used such as ReLU, ELU or Tanh, is used to increase the expressiveness of the model; : Indicates concatenating graph convolution outputs along different orders g, concatenating the results of graph convolutions of different orders 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 is the image topology structure feature.

[0156] This step S2.1.2.5 is achieved by Limit the scope of attention to focus only on key components, combined with the previous step S2.1.1.4 Dynamically select feature propagation paths, especially for long sequence tasks, to reduce redundant calculations and save computing time.

[0157] S2.2. Fusing the time series features and the image topology features through a stepwise mutual attention mechanism to obtain a fused feature vector;

[0158] This step S2.2 is used to achieve multimodal feature fusion. In order to give full play to the complementarity of multi-source information, the time series features extracted in step S2.1.1 are The image topology features extracted in step S2.1.2 Perform multimodal fusion. A fusion architecture based on a step-by-step mutual attention mechanism is designed. This architecture uses the time series modality as the primary channel and introduces the image modality as an auxiliary cue, performing fine-grained enhancement on each frame along the timeline. This module primarily consists of two stages: mutual multi-head attention calculation and global feature aggregation.

[0159] Furthermore, in S2.2, the time series features and image topology features are fused through a step-by-step 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 topology features as the auxiliary modality, the image modality is calculated to enhance the attention of the time series modality; the enhanced representations of all frames are aggregated to obtain a unified fused feature, i.e., the fused feature vector. Specifically, the following steps are included:

[0160] S2.2.1 Mutual Attention Enhanced Representation Generation (Multi-Head Attention Computation)

[0161] In order to allow the main modality (time series) to integrate the contextual feature information of the auxiliary modality (image), the mutual attention mechanism is introduced. Specifically expressed as:

[0162]

[0163] : An enhanced representation of the primary modality that incorporates information from the auxiliary modality. This fusion is asymmetric and only enhances the primary modality (different from bidirectional cross attention). Indicates the direction of information flow: transferring features from the auxiliary modality F (image) to the main modality Z (time series); : Query representation of the auxiliary modality, represented as the feature matrix of the image modality, used to query the key information in the image; : The key representation of the main mode, expressed as the feature matrix of the time series mode, is used to provide a matching benchmark for the time series; : Value representation of the main mode, which comes from the same source as the Key and carries the original time series features to be corrected; G: 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.

[0164] This formula calculates the importance weight of image features for each frame of the time series features and adjusts the time series representation based on these weights to generate a fused, perceived representation. Time series is dominant, images are auxiliary: Material response signals are the core basis for parameter inversion, while microscopic deformation / thermal maps provide supplementary local details. This conforms to the data value distribution of "time series primary, images auxiliary" in engineering practice. The primary modality Z (time series) preserves the main structure while selectively absorbing only relevant information from the auxiliary modality F (image). A directional enhancement mechanism avoids feature contamination caused by bidirectional fusion (e.g., image noise affecting time series integrity).

[0165] S2.2.2: Overall representation of time series after multimodal fusion (global feature aggregation)

[0166] Aggregate the enhanced features of each frame generated above to obtain the overall expression of the final fused time series. The specific formula is as follows:

[0167]

[0168] : The enhanced representation after the r-th frame time feature is fused with the image feature, which represents the enhanced feature generated by the time modality after the image modality is introduced. 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), represents the generation through the attention mechanism, m' represents the multimodal fusion result; n': the number of frames in the time series, which is determined by the original time series length L and the sampling rate; : Average Pooling function, which performs weighted average of all frame representations and outputs a unified modality representation; : The final time series feature expression after fusion is used for subsequent prediction tasks, which serves as the input vector of the neural network classifier for downstream parameter inversion tasks.

[0169] This formula can be used to aggregate the fusion enhancement features of n' time frames into a single vector through average pooling , as the global representation of the entire time series. This operation is the core output of the step-by-step mutual attention mechanism, which solves the problem of semantic alignment of multimodal data in the temporal dimension.

[0170] In step S2.2, image features are first fused (fine-grained alignment) at each time frame to achieve frame-level enhancement; then, a length-independent fixed-dimensional representation is obtained through pooling to ensure temporal invariance.

[0171] S3. Training a neural network based on the fused feature vector, outputting a final prediction value, and updating network parameters using a residual-based surrogate hyperplane Kaczmarz optimization method and an oblique projection (RSHKO) optimization method;

[0172] Step S3 is used to implement neural network training. After completing the multimodal feature extraction and fusion of step S2, a unified representation of the time series fusion feature vector is obtained. Next, this fused feature will serve as the input to the neural network classifier to achieve accurate prediction or diagnosis of downstream tasks. To further improve training efficiency and convergence stability, this stage introduces a proxy hyperplane residual driving mechanism and an oblique projection direction selection strategy. By guiding the optimization path to adjust the parameter update direction, the model has stronger expressive power and generalization performance in complex multimodal scenarios.

[0173] Furthermore, in step S3, the network parameters are updated 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; and calculating the update step size using the norm of the gradient residual vector and the norm of the oblique projection direction to generate new parameters. Specifically, the following steps are included:

[0174] S3.1 Input feature preparation

[0175] The fused feature vector Input to the neural network model, which usually contains multiple fully connected layers and nonlinear activation functions, and outputs the final predicted value for calculating the loss function with the true label.

[0176] S3.2 Proxy Hyperplane Residual Driven Mechanism

[0177] Traditional neural network training mainly relies on standard back propagation and gradient descent to update weights, but this method is often sensitive to abnormal noise and prone to falling into local optimality. Therefore, in each iterative update of the weights in deep learning back propagation, the optimization step of the residual-based surrogate hyperplane Kaczmarz method and oblique projection (RSHKO) is added. Specifically, in deep learning training, the parameter vector of the neural network is set to , the loss function is , and its residual is defined as:

[0178]

[0179] : parameter vector of the deep learning model at the uth iteration; : The loss function value with the current parameters as input; : The current gradient residual vector (i.e. the gradient of the loss function with respect to the parameters).

[0180] In traditional gradient descent, weight updates are based on the negative gradient direction. This strategy constructs an oblique projection matrix through the residual to obtain the optimal update direction. Using the oblique projection and proxy hyperplane mechanism in the RSHKO idea, the update formula is:

[0181]

[0182] : updated parameter vector; : The square of the second norm of the current residual vector, which measures 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), its expression (i.e. the oblique projection direction in the RSHKO optimization method Generation rules for ):

[0183] 1. When hour:

[0184]

[0185] 2. When When (using optimal oblique projection):

[0186]

[0187] : The constructed feature projection operator matrix can be the identity matrix or a specific construction matrix (such as the feature transformation matrix); : Auxiliary vector of projection direction, gradient projection result of the uth iteration; : No. Auxiliary vector at the iteration; : Vector dot product operation.

[0188] The formula in step S3.2 innovatively transforms the traditional gradient direction update into a residual-guided oblique projection update and constructs a proxy hyperplane using historical gradients, effectively improving training robustness and convergence speed. The RSHKO optimizer achieves a balance between training convergence and accuracy.

[0189] S4. Input the preprocessed measured data into the trained model, output the inversion results of the material structure parameters, and realize real-time online reasoning through the edge-cloud collaborative architecture.

[0190] After completing steps S1 to S3, the present invention enters the system deployment and practical application stage. This stage aims to transform the model capabilities into functional modules that can be used in engineering, and to achieve intelligent inversion and prediction of structural parameters in combination with actual scenarios. Specifically, it includes the following sub-steps:

[0191] Step S4.1 System deployment architecture design

[0192] In order to achieve efficient operation and scalable deployment of the system, the present invention constructs a deployment solution based on edge-cloud collaborative architecture. Figure 3 Figure 2 shows a schematic diagram of the system architecture of an embodiment of the present invention. This system implements: edge computing, which reduces transmission bandwidth requirements and ensures real-time performance; cloud intelligent analysis, which enables efficient computation of complex models; closed-loop verification, which involves inversion results, simulation verification, and model optimization; and industrial compatibility, which integrates existing engineering systems through standard interfaces.

[0193] Specifically, edge devices (such as sensor systems and 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.

[0194] The cloud platform deploys deep learning models and RSHKO optimization algorithm modules, responsible for completing the following key tasks: extracting periodic features and analyzing graph structures of received multimodal 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 topological structural information in images; performing multimodal feature fusion to generate a unified semantic expression; and launching the RSHKO-driven optimization module to complete the rapid inversion solution of structural parameters.

[0195] Through edge-cloud division of labor and collaboration, we can achieve effective distribution of computing load, improve system response speed and enhance real-time data processing capabilities.

[0196] Step S4.2 Model online inference and real-time prediction

[0197] After deployment is complete, the system can perform online inference tasks on newly input measurement data. The specific process is as follows:

[0198] Input data preparation: The user inputs the time series signal and image information of the material under different loading conditions; Feature extraction: The system calls the deployed periodic pyramid Transformer and graph convolutional network to process the data; Fusion prediction: After completing modal fusion through a step-by-step mutual attention mechanism, a high-dimensional embedding representation is generated; Inversion solution: The features are input into a deep neural network, combined with the residual oblique projection optimization module, to quickly output the corresponding material structure parameters.

[0199] This process can achieve millisecond-level response speeds, supporting online monitoring and structural assessment of industrial sites.

[0200] S4.3 Engineering Integration and Interface Opening

[0201] This system supports seamless integration with mainstream materials testing platforms (such as ANSYS and ABAQUS simulation systems) and industrial data acquisition software (such as LabVIEW and MATLAB). By providing standard interfaces (such as RESTful API, WebSocket, and OPC UA protocols), the system enables interactive functionality with existing engineering platforms. These capabilities include: automatically acquiring experimental data and triggering parameter inversion; feeding inversion results back to the simulation platform for performance verification; and providing prediction reports, error analysis, and model interpretability graphs. This open interface significantly enhances the applicability and engineering application potential of this system.

[0202] The present invention can be widely used in the following typical scenarios: new material design and evaluation: in the development of new composite materials and microstructure materials, it can realize the inversion of microstructure parameters and performance prediction; structural health monitoring: in the fields of aerospace and civil engineering, it can track the damage evolution parameters of the structure during service in real time; high-precision experimental inversion: it can assist in solving parameters that cannot be directly observed in complex mechanical experiments, and improve the utilization efficiency of experimental data; intelligent simulation auxiliary system: it can intelligently calibrate the material model parameters before numerical simulation to improve the simulation accuracy.

[0203] In summary, the above embodiments of the present invention have overcome the shortcomings in efficiency, accuracy, and generalization of material parameter inversion in the existing technology through key technologies such as intelligent feature extraction, cross-modal fusion, and optimized inversion, providing technical support for high-end equipment manufacturing, major engineering safety monitoring and other fields.

[0204] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of each step described above can refer to the corresponding process in the aforementioned system embodiment and will not be repeated here.

[0205] It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. 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 methods.

[0206] It should also be noted that, in the embodiments of the present application, relational terms such as first and second, etc. are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprise", "include" or any other variants thereof are intended to cover non-exclusive inclusion, so that the process, method, article or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device comprising the elements.

[0207] The above 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 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 the embodiments shown in the embodiments of the present application, but rather will conform to 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: The following steps are involved: S1. Collect time series data and image data of materials under different loading conditions and perform preprocessing; S2. Build a deep diagnostic model, including: S2.

1. Construct a multimodal feature extractor: including a time series feature extractor and an image feature extractor. 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 an attention mechanism to obtain time series features. The image feature extractor integrates topological data analysis and multi-scale adaptive graph convolution to extract image topological structure features. S2.

2. Fusing the time series features and the image topology features through a stepwise mutual attention mechanism to obtain a fused feature vector; S3. Training a neural network based on the fused feature vector, outputting a final prediction value, and updating network parameters using a residual-based substitute hyperplane Kaczmarz optimization method and an oblique projection optimization method; S4. Input the preprocessed measured data into the trained model, output the inversion results of the material structure parameters, and realize real-time online reasoning through the edge-cloud collaborative architecture.

2. The intelligent optimization method according to claim 1, characterized in that: in, The time series feature extractor adopts the periodic pyramid Transformer model to process time series data, extracts the dominant frequency and corresponding period length through frequency domain analysis, divides the multi-level periodic components and establishes hierarchical connection relationships, and uses the attention mechanism to aggregate multi-scale periodic features to output time series features.

3. The intelligent optimization method according to claim 2, characterized in that: in, Build a time series feature extractor using the periodic pyramid Transformer model, including: When performing frequency domain analysis on the input time series, the frequency amplitude sequence of the seasonal part is extracted using fast Fourier transform, and the periodic component is determined by channel dimension averaging and dominant frequency screening; Divide the hierarchical periodic components by period length and establish inter-level connection relationships; Construct a hierarchical periodic pyramid structure based on the inclusion relationship of periodic components; The connection relationship between periodic components is calculated through the attention mechanism, key periodic features are aggregated, and the aggregated time series features are output for multimodal fusion.

4. The intelligent optimization method according to claim 3, characterized in that: in, The hierarchical periodic components are divided according to the period length, and the connection relationship between the hierarchical levels is established; and the hierarchical periodic pyramid structure is constructed according to the inclusion relationship of the periodic components, including: By judging whether there is a containment or overlap relationship between periodic components at different levels, the hierarchical containment relationship between periodic components is determined, wherein the upper-level periodic component establishes a containment relationship with the lower-level component through index overlap judgment; Construct a hierarchical pyramid structure based on the inclusion relationship between periodic components; Different periodic components are mapped to a unified scale through zero padding and linear projection; Establish the connection relationship between the current cycle component and the related components in the upper and lower layers; By stacking cycle components at different levels, a complete cycle pyramid is constructed.

5. The intelligent optimization method according to claim 4, characterized in that: in, The image feature extractor uses a graph convolution model that integrates topological data analysis to process image data, constructs a topological evolution process through graph filtering, generates a persistent barcode and embeds it into a topological vector, and extracts image topological structure features through a multi-scale adaptive graph convolution module; The construction of the image feature extractor includes: Perform graph filtering operations on 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; converting the persistent barcode into a topological vector via a learnable embedding function; Multi-scale adaptive graph convolution and MixHop convolution strategies are used to extract the deep topological features of image data and obtain the image topological structure features.

6. The intelligent optimization method according to claim 5, characterized in that: in, The persistence graph 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 topological feature types according to the homology dimension b∈{0,1}, where b=0 corresponds to connected components and b=1 corresponds to ring structures, and construct a persistent barcode; Store the life cycle of the topological feature in the form of a tuple (t1, t2) in the set D (b) , forming a persistent graph that describes the evolution of topological features.

7. The intelligent optimization method according to claim 6, characterized in that: The barcode steering amount embedding is achieved by the following steps: For the b-th order persistent barcode in the c-th view Perform parameterized encoding to generate initial topology descriptors; By embedding the function Mapping the initial topology descriptor to an N×d-dimensional vector space, where N is the number of graph nodes and d is a preset vector dimension; Trainable linear layers or nonlinear activation functions are used 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, characterized in that: The multi-scale adaptive graph convolution module enhances the graph structure modeling capability through the following operations: Perform linear transformation on the input topology vector to generate initial graph features; An adaptive adjacency matrix is ​​constructed based on two trainable parameter matrices to capture the dynamic dependencies of the graph structure. A multi-order convolutional propagation layer performs power expansion on the adaptive adjacency matrix to capture neighborhood information of each order of the initial graph features; Concatenate the results of graph convolution of each order along the feature dimension to obtain the concatenated features; A nonlinear activation function is applied to the concatenated features to generate topological structure features of the image.

9. The intelligent optimization method according to claim 8, characterized in that: in, In S2.2, the time series features and the image topology features are fused through a step-by-step mutual attention mechanism to obtain a fused feature vector, including: For each frame feature of the time series, with the time series feature as the main modality and the image topology structure feature as the auxiliary modality, the attention enhancement representation of the image modality to the time series modality is calculated: Aggregating the enhanced representations of all frames yields a unified fused feature, i.e., a fused feature vector.

10. The intelligent optimization method according to claim 8, characterized in that: in, In step S3, the network parameters are updated using the residual-based substitute hyperplane Kaczmarz optimization method and the oblique projection optimization method, including: Calculate the gradient residual vector of the current iteration; Constructing an oblique projection direction based on the gradient residual vector; The update step size is calculated by the norm of the gradient residual vector and the norm of the oblique projection direction to generate new parameters.

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