Foamed aluminum material strength prediction method based on multi-source data

Abstract

The invention provides a foamed aluminum material strength prediction method based on multi-source data, and relates to the field of data prediction. The invention provides an H-MSPNet model, which is applied to a foamed aluminum material strength prediction scene and comprises a dynamic multi-scale construction module, a scale interaction module and a fusion prediction module, and specifically, the dynamic multi-scale construction module is based on a local time scale adjustment mechanism and a frequency-significance driving strategy; the local features of the foamed aluminum material strength under different time scales can be adaptively extracted; the scale interaction module realizes depth nonlinear interaction between scales and within the scales through phase similarity modeling, an energy migration mechanism and a local phase energy coupling function; the fusion prediction module dynamically integrates multi-scale prediction results through consistency constraint and a frequency difference adjustment function, the robustness and generalization ability of the model are effectively enhanced, and all the modules work cooperatively to achieve accurate prediction of the strength of the foamed aluminum material.

Description

Technical Field

[0001] The present invention belongs to the field of data prediction, and in particular relates to a method for predicting the strength of foamed aluminum materials based on multi-source data. Background Art

[0002] Aluminum foam, a porous metal material with both lightweight and high energy absorption properties, has been widely used in aerospace, automotive manufacturing, and building shock absorption. Its mechanical properties (such as compressive strength and energy absorption efficiency) are influenced by multiple factors, including preparation process parameters (such as foaming agent type and porosity), microstructural characteristics (pore size distribution and pore wall thickness), and external loading conditions (strain rate and temperature). However, traditional strength prediction methods often rely on a single data source (such as experimental testing or numerical simulation), which makes it difficult to fully characterize the material behavior under multi-scale and multi-physics coupling, resulting in insufficient prediction accuracy and low efficiency. On the one hand, its micropore structure is complex and has significant heterogeneity and scale effects, making traditional single-scale prediction methods difficult to effectively describe this complexity. On the other hand, the actual material performance data collected is characterized by significant noise interference, strong non-stationarity, and cross-coupling between scales. This shows a complex interweaving of scale differences, local mutations, and long-term performance changes, which brings difficulties to predictive modeling. Therefore, it is urgent to propose a multi-scale analysis and prediction method based on multi-source data to deeply reveal the inherent laws of the strength evolution of aluminum foam materials and improve the generalization ability and prediction accuracy of the prediction model.

[0003] In existing research, the collaborative analysis technology of multi-source heterogeneous data (such as process parameters, micromorphology, and mechanical properties) is still immature. For example, patent CN120026550A proposes a damper design based on foamed aluminum, but its strength prediction still relies on traditional mechanical testing and does not introduce data-driven multimodal modeling methods. Similarly, although the earth-rock dam performance evaluation system integrates multi-source heterogeneous data (images, text, sensor data), its technical framework has not been optimized for the field of materials science.

[0004] In recent years, the integration of artificial intelligence and multi-source data fusion technologies has provided new insights into material performance prediction. For example, the application of federated learning frameworks in equipment performance prediction demonstrates that distributed data collaborative modeling can improve model generalization capabilities. The wave finite element method, by reducing the number of degrees of freedom, achieves efficient computation and provides a reference for multi-scale modeling. However, existing technologies have yet to achieve full-chain data integration across the entire process, structure, and performance chain for aluminum foam strength prediction. There is an urgent need to develop hybrid models that combine the advantages of physical mechanisms and data-driven approaches. Summary of the Invention

[0005] The present invention provides a method for predicting the strength of foam aluminum materials based on multi-source data. To address the problems of strong noise, strong non-stationarity and multi-scale feature coupling in performance data, a multi-scale prediction model (Hierarchical Multi-Scale Phase Network, H-MSPNet) based on a hierarchical structure and scale interaction mechanism is proposed. The method consists of a dynamic multi-scale construction module, a scale interaction module and a fusion prediction module. The dynamic multi-scale construction module constructs a dynamic time warp sequence under variable scales by introducing a three-parameter local time scale adjustment mechanism, and extracts representative frequency subsequences based on significance-driven sliding window spectrum analysis to achieve multi-scale modeling of the performance response of foam aluminum materials; the scale interaction module introduces scale phase variables and local phase energy coupling functions, designs an inter-scale phase similarity matrix and an energy migration mechanism, and realizes deep nonlinear interaction and local feature enhancement between different scales; the fusion prediction module integrates the prediction results of each scale through adaptive weights while maintaining scale specificity, and combines frequency feature dissimilarity loss and consistency constraints to achieve high-precision strength prediction of foam aluminum materials.

[0006] The technical solution adopted by the present invention to achieve the above-mentioned purpose specifically includes the following steps: S1. Collect strength data of aluminum foam materials and construct a data set suitable for strength prediction of aluminum foam materials; S2. Standardize the strength data of aluminum foam material using the mean normalization method and divide the data into training set and test set; S3, construct a dynamic multi-scale building module, build a three-parameter dynamic scale control system, and generate dynamic heterogeneous multi-scale subsequences; S31. Define the local time scale adjustment factor, design three sets of parameters: local change rate, local oscillation rate, and local response amplitude, and jointly determine the local time scale adjustment factor; S32, accumulating local scale adjustment factors, constructing a dynamic time warp axis, sampling on the new time axis, and generating a curved time series; S33, performing multi-scale construction driven by a multi-frequency-saliency structure on the curved time series, driving the saliency of multi-frequency features in the time series, and thereby extracting multi-scale features; S4. Construct a scale interaction module, introduce scale phase variables and scale energy conservation migration mechanism, and realize deep nonlinear interaction of information between and within scales; S41, define the phase field for each scale and construct the phase similarity matrix; S42, energy transfer and inter-scale feature update through similarity matrix; S43, designing a local enhancement coefficient to enhance intra-scale features; S5. Establish consistency constraints and scale-specific retention, dynamically integrate all scale predictions through adaptive coordination functions, and input the processed foam aluminum material strength data into the model to obtain the prediction results.

[0007] Preferably, in said S1, for constructing a data set suitable for strength prediction of foam aluminum materials, strength monitoring equipment, including strain gauges and accelerometers, is installed to ensure coverage of different stress levels, loading rates and ambient temperature conditions; and the physical parameters of the material, including foam porosity, unit size, wall thickness distribution, matrix material type and preparation method, and environmental information, including loading mode, test temperature, relative humidity, air flow velocity and type and concentration of corrosive medium are integrated to form three-dimensional strength response data including time, space and material properties. All data are stored in a unified format, and failure points are marked to complete the construction of the foam aluminum material strength prediction data set.

[0008] Preferably, the strength data of the foam aluminum material is preprocessed, including standardizing the original data for the strength prediction of the foam aluminum material using the mean normalization method, specifically subtracting the mean of the feature in the overall data set from the characteristic value used to characterize the material strength in each sample and dividing it by the standard deviation, thereby eliminating the dimensional differences between different features and improving the compatibility and training stability of the model for data of different scales; further, the standardized data is divided into a training set and a test set according to a certain ratio, the training set is used for learning and optimizing the multi-scale model parameters, and the test set is used to verify the generalization ability of the model, so as to improve the adaptability and accuracy of the overall prediction method under different foam aluminum material samples.

[0009] Preferably, as a porous lightweight metal material, the mechanical properties of foam aluminum material are highly dependent on the synergistic effect of the multi-scale structural characteristics of the material and multi-source physical factors; its strength is not only affected by microstructural parameters such as porosity, pore size, and pore size distribution, but also by the comprehensive regulation of factors such as pore connectivity, skeleton arrangement direction, local density at the mesoscale, and overall geometric morphology and loading mode at the macroscale; this structural response mode in which multi-dimensional characteristics from micro to macro jointly determine the material properties determines that the strength prediction of foam aluminum material has obvious "multi-scale synergistic driving" characteristics. Based on this characteristic, the present invention proposes A method is proposed to construct a dynamic multi-scale construction module, a three-parameter dynamic scale control system, and generate dynamic heterogeneous multi-scale sub-sequences. The dynamic multi-scale construction module can flexibly divide the feature domain according to the scale non-uniform characteristics in the original data, retaining microscopic details and macroscopic trends; the three-parameter dynamic scale control system enables the model to dynamically adapt to structural changes at different scales by adjusting the scale window size, time driving factor and scale migration weight; and the construction of dynamic heterogeneous multi-scale sub-sequences can reconstruct a sequence structure that is more in line with the real behavior of the material, thereby more efficiently characterizing the multi-level driving path of the structural characteristics' response to intensity.

[0010] Preferably, the local time scale adjustment factor By calculating the distance between the current moment and the previous moment observation value, the local change rate is obtained to reflect the instantaneous change characteristics of the sequence; using the weighted difference between the current moment and the previous two moments observation value, the local oscillation rate is calculated to characterize the oscillation intensity of the sequence; again, based on the local change rate, a nonlinear adjustment function is introduced to perform nonlinear mapping processing on the response amplitude. The specific formula is: ; Where, Is the Sigmoid function, ensuring , 、 、 are three learnable weight parameters, is the bias term; in, is the local change rate, and the specific formula is: ; Where, For the original sequence at time The observed value of is the Euclidean norm; in, is the local oscillation rate, and the specific formula is: ; Where, For the original sequence at time The observed value of is the Euclidean norm; in, is the local response amplitude, and the specific formula is: ; Where, is a hyperparameter that controls the nonlinear amplitude amplification. is the hyperbolic tangent function.

[0011] Preferably, by introducing three dynamic characteristics of local change rate, local oscillation rate and local response amplitude, a time-varying scale control factor is constructed, which can effectively capture the local mutation, structural jump and nonlinear response characteristics existing in the strength data of foam aluminum materials. Since foam aluminum materials have obvious multi-scale heterogeneity and dynamic volatility in pore structure and distribution density, the model's attention to different time scales can be dynamically adjusted according to the local change intensity of the input sequence, and the perception ability of key structural change areas can be enhanced, thereby improving the sensitivity and robustness of the strength prediction model to abnormal areas and microstructural disturbances, and achieving more adaptive strength estimation and structural response modeling.

[0012] Preferably, the construction of the dynamic time warp axis is based on the cumulative operation of the local time scale adjustment factor at each moment to obtain the cumulative local time scale factor at that moment; based on the dynamic time warp axis, the number of sampling points of the time series is redefined to achieve non-uniform sampling of the time series; the sampling process adopts a linear interpolation method, and the values of the new sampling points are calculated between adjacent observations of the original time series according to the interpolation weight to complete the generation of the curved time series of the original sequence. The specific formula is: ; Where, For the moment The local time scale adjustment factor, For the moment The cumulative local time scale factor of ; Sampling on the new time axis to generate a curved time series , the specific formula is: ; Where, is the new number of sampling points, New timeline Sampling points, the specific calculation formula is: ; Where, For the moment The cumulative local time scale factor, Round up; Use linear interpolation to obtain sampling data to get new sampling points , the specific formula is: ; Where, The first nodes, is the interpolation weight, and the specific formula is: ; Where, For nodes The cumulative local time scale factor, is the time after resampling The cumulative local time scale factor of .

[0013] Preferably, by constructing a dynamic time axis based on the local scale control factor and resampling the original sequence on the deformed time axis by linear interpolation, non-uniform sampling processing of the time series is realized, which can effectively adapt to the problem of inconsistency between local structural mutations and time series change rates in the strength data of foam aluminum materials; the mechanical response characteristics of foam aluminum materials under different scale structures may show nonlinear mutations or local oscillations. This strategy dynamically adjusts the time sampling density to make the model more densely sampled in areas with drastic structural changes or sensitive responses, and appropriately sparse in areas with gentle changes, which helps to strengthen the modeling capabilities of key structural areas, improve the accuracy and efficiency of strength prediction, and suppress redundant information interference, thereby achieving fine modeling of complex material behaviors.

[0014] Preferably, a multi-scale construction driven by multi-frequency-significance structure is performed, and the specific steps are as follows: First, for curved time series Perform sliding window analysis to obtain the frequency factor , the specific formula is: ; Where, For The spectrum of a small window centered on is the frequency domain variable, is the high-frequency threshold; Second, calculate the significance factor , the specific formula is: ; Where, is the Euclidean norm, are new sampling points obtained by linear interpolation; Third, for each scale Define a frequency preference interval , indicating the frequency band that the scale focuses on , the specific formula is: ; Frequency preference interval The specific formula is: ; Where, For scale The corresponding frequency lower bound is, scale The corresponding upper frequency bound; For every moment ,scale In the window Inner aggregation features, get aggregation features , the specific formula is: ; Where, is the activation function, is the significant factor, For the frequency band focused on scale, is the window width, and the specific formula is: ; Where, is the minimum window size, is the scaling factor, For different scales, ; Fourth, dynamic aggregation obtains each scale Aggregate sequence representation of , the specific formula is: ; Where, For scale Aggregate features within a window; Aggregate each scale Sequence representation of , and obtain the multi-scale sequence , the specific formula is: ; Where, For scale The sequence length, For scale The aggregation representation of is the feature dimension.

[0015] Preferably, a sliding window Fourier transform is used to analyze the fatigue sequence on the dynamic time axis, extract the frequency components and significance indicators of each scale, and generate a frequency preference interval based on the proportion of high-frequency energy and the severity of the structure, so as to accurately extract the frequency domain characteristics of the strength data of the foam aluminum material at different scales.

[0016] Preferably, the strength prediction of aluminum foam materials in the method of the present invention requires the characterization of a complex multi-scale mechanism of the trinity of "structure-energy-response". By constructing a scale interaction module, introducing scale phase variables and scale energy conservation migration mechanisms, dynamic self-adjustment within the scale and deep nonlinear interaction between scales can be achieved, which can fully explore the cross-scale correlation paths and dominant energy migration patterns contained in the aluminum foam strength data, thereby improving the structural sensitivity, prediction accuracy and generalization ability of the model, and providing underlying support for the intelligent strength prediction of complex structural materials.

[0017] Preferably, each scale defines a phase field , the specific formula is: ; Where, is the sampling node, , is the phase projection matrix, For paranoid items, For sampling nodes Lower scale The aggregate sequence representation of Construction scale and scale Phase similarity matrix between , the specific formula is: ; Where, For exponential operations, and are sampling nodes, , , is the phase sensitivity hyperparameter.

[0018] Preferably, an independent phase field is defined for each scale and a phase similarity matrix between scales is constructed. By measuring the structural consistency between phase patterns, phase alignment and coherence modeling between multi-scale fatigue features are achieved, providing a criterion basis for subsequent energy migration.

[0019] Preferably, the node energy at each scale is calculated , the specific formula is: ; Where, For the Sampling nodes downscale The aggregation representation of is the Euclidean norm; Energy migration is performed through the similarity matrix, and the scale Migrate to scale Node energy on , the specific formula is: ; Where, For scale At the node The node energy under For scale The length of the sequence; Calculation scale The difference between real energy and received energy , the specific formula is: ; Where, For scale At the node The node energy under scale At the node The node energy received under Update scale Inter-scale feature representation , the specific formula is: ; Where, is the learnable adjustment coefficient.

[0020] Preferably, an energy migration mechanism is designed to guide the energy transfer between different scales through the phase similarity matrix, dynamically update the feature representation of each scale, improve the model's ability to express cross-scale fatigue evolution patterns, and enhance the robustness and accuracy of fatigue life prediction.

[0021] Preferably, the local enhancement coefficient is designed to enhance the features within the scale and obtain the scale enhancement sequence , the specific formula is: ; Where, For nodes The local neighborhood of For nodes Lower scale Updated inter-scale feature representation; is the Gaussian kernel normalization weight based on phase difference, and the specific formula is: ; Where, For scale The phase field, is the Euclidean norm, For nodes The local neighborhood of is the phase sensitivity hyperparameter; Design local enhancement factor , the specific formula is: ; Where, is the Sigmoid function, is a fixed constant; is the local phase energy coupling function, and the specific formula is: ; Where, For scale At the node The node energy under is the local phase difference, and the specific formula is: ; Where, For nodes The local neighborhood of For scale The phase field, is the Euclidean norm.

[0022] Preferably, the local enhancement coefficient and the local phase energy coupling function are introduced to perform nonlinear enhancement on the features within each scale, explicitly characterize the coupling relationship between local energy changes and phase disturbances, and improve the model's recognition sensitivity to sudden fatigue damage.

[0023] Preferably, for each scale Make separate predictions to get each scale The prediction results , the specific formula is: ; Where, is a scale-enhanced sequence, MLP is a multi-layer perceptron; For any scale pair and , establish collaborative constraints and define consistency loss , the specific formula is: ; Where, For scale The prediction results, is the Euclidean norm; The average consistency loss of all scale pairs is averaged to get the average consistency loss , the specific formula is: ; Where, is the maximum scale; Define each scale The local frequency characteristics of the prediction results , the specific formula is: ; Where, is the fast Fourier transform; Define the frequency feature difference between scales , the specific formula is: ; Where, Normalize the row vectors, for each time step , the specific formula is: ; Where, For scale The local frequency characteristics of is the Euclidean norm, A small constant to prevent division by zero errors; The average feature dissimilarity of all scale pairs is taken as the average feature dissimilarity , the specific formula is: ; Define the fusion weights for each scale , the specific formula is: ; Where, For scale The prediction results, is the Euclidean norm, For index operation; Normalize the fusion weight to obtain the normalized fusion weight , the specific formula is: ; In the formula, the denominator represents the sum of all scale weights; The final prediction result after fusion is , the specific formula is: ; Fusion prediction loss , average consistency loss and frequency feature dissimilarity , the specific formula is: ; Where, is the prediction error, using MSE, is the weight of consistency loss, The weight of the frequency feature dissimilarity.

[0024] Preferably, a prediction consistency constraint and a scale-specificity retention mechanism are established, and the prediction results of different scales are dynamically fused by introducing an adaptive coordination function. While maintaining the local feature expression capability of each scale, the consistency and synergy between multi-scale outputs are enhanced; finally, the fused representation is used as the unified output of the model to achieve high-precision prediction of the strength data of the processed foam aluminum material, thereby improving the generalization ability and stability of the model.

[0025] In summary, due to the adoption of the present technical solution, the beneficial effects of the present invention are as follows: the present invention proposes an H-MSPNet prediction model, which is applied to the foam aluminum material strength prediction scenario, and includes a dynamic multi-scale construction module, a scale interaction module and a fusion prediction module; specifically, the dynamic multi-scale construction module is based on the local time scale adjustment mechanism and the frequency-significance driving strategy, and can adaptively extract the local characteristics of fatigue response at different time scales; the scale interaction module realizes deep nonlinear interaction between scales and within scales through phase similarity modeling, energy migration mechanism and local phase energy coupling function; the fusion prediction module dynamically integrates multi-scale prediction results through consistency constraints and frequency difference adjustment functions, effectively enhancing the robustness and generalization ability of the model, and each module works together to achieve accurate prediction of the strength of foam aluminum materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is a step-by-step diagram of the strength prediction method for foam aluminum materials.

[0027] Figure 2 This is the H-MSPNet prediction model structure diagram.

[0028] Figure 3 Schematic diagram of modular structure for dynamic multi-scale construction.

[0029] Figure 4 This is the structural diagram of the scale interaction module.

[0030] Figure 5 The H-MSPNet prediction model realizes the fitting effect diagram of the strength prediction of foam aluminum material. DETAILED DESCRIPTION

[0031] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0032] See also Figure 1-Figure 5 The present invention provides a technical solution: a method for predicting the strength of aluminum foam materials, which extracts local features at different time scales through a dynamic multi-scale construction module, realizes deep nonlinear interaction between scales and within scales through a scale interaction module, and extracts time domain information through a time domain feature extraction module. The fusion prediction module dynamically integrates the multi-scale prediction results to obtain the strength prediction results of aluminum foam materials. The specific steps are as follows: Figure 1 shown.

[0033] Construct the H-MSPNet prediction model, whose structure is as follows Figure 2 The specific steps are as follows.

[0034] S1. Collect strength data of aluminum foam materials and construct a data set suitable for strength prediction of aluminum foam materials.

[0035] Furthermore, in order to construct a data set suitable for strength prediction of foam aluminum materials, strength monitoring equipment, including strain gauges and accelerometers, is installed to ensure coverage of different stress levels, loading rates and ambient temperature conditions; and the physical parameters of the material, including foam porosity, unit size, wall thickness distribution, matrix material type and preparation method, and environmental information, including loading method, test temperature, relative humidity, air flow velocity and type and concentration of corrosive medium are integrated to form three-dimensional strength response data containing time, space and material properties. All data are stored in a unified format and marked with failure points or maximum bearing strength to complete the construction of the foam aluminum material strength prediction data set.

[0036] S2. The preprocessed fatigue life data is standardized using the mean normalization method, and the data is divided into a training set and a test set, with the ratio of the test set to the training set being 3:7.

[0037] Furthermore, the strength prediction data of aluminum foam materials are standardized using the mean normalization method. The specific formula is: ; Where, For the original sequence at time Observed values of The original sequence The specific formula is: ; Where, is the original sequence length; The original sequence The standard deviation of is: ; Get the normalized sequence , the implementation code is: # Perform mean normalization on the input sequence X def normalize_sequence(X): mu = np.mean(X) sigma = np.std(X) x_normalized = (X - mu) / sigma return x_normalized, mu, sigma # Divide the training set and test set, the default ratio is 7:3 def split_train_test(X, train_ratio=0.7): split_idx = int(len(X) * train_ratio) return X[:split_idx], X[split_idx:].

[0038] S31. Define the local time scale adjustment factor and design three sets of parameters: local change rate, local oscillation rate, and local response amplitude, which jointly determine the local time scale adjustment factor.

[0039] Furthermore, the local time scale adjustment factor is defined in S31 , the specific formula is: ; Where, Is the Sigmoid function, ensuring , 、 、 are three learnable weight parameters, is the bias term; is the local change rate, and the specific formula is: ; Where, For the original sequence at time The observed value of is the Euclidean norm; is the local oscillation rate, and the specific formula is: ; Where, For the original sequence at time The observed value of is the Euclidean norm; is the local response amplitude, and the specific formula is: ; Where, is a hyperparameter that controls the nonlinear amplitude amplification. is the hyperbolic tangent function, and the specific formula is: ; The implementation code is: # S31: Local time scale adjustment factor def compute_scale_factor(X, w1, w2, w3, b, alpha=2.0): # Calculate the local rate of change r r = np.linalg.norm(np.diff(X, prepend=X[0])) # Keep the length consistent # Calculate the local oscillation rate o o = np.linalg.norm(np.diff(np.diff(X, prepend=X[0]), prepend=0)) # Calculate the local response amplitude a a = alpha * tanh(np.mean(np.abs(X - np.mean(X)))) # Calculate the scale adjustment factor s s = sigmoid(w1 * r + w2 * o + w3 * a + b) return s.

[0040] S32. Accumulate local scale adjustment factors, construct a dynamic time warp axis, perform sampling on the new time axis, and generate a curved time series.

[0041] Furthermore, in S32, the local scale adjustment factor is accumulated to construct a dynamic time warp axis and generate a new time axis. , the specific formula is: ; Where, For the moment The local time scale adjustment factor, For the moment The cumulative local time scale factor of ; Sampling on the new time axis to generate a curved time series , the specific formula is: ; Where, is the new number of sampling points, New timeline Sampling points, the specific calculation formula is: ; Where, For the moment The cumulative local time scale factor, Round up; Use linear interpolation to obtain sampling data to get new sampling points , the specific formula is: ; Where, The first nodes, is the interpolation weight, and the specific formula is: ; Where, For nodes The cumulative local time scale factor, is the time after resampling The cumulative local time scale factor is: # Accumulate local scale adjustment factors to obtain non-uniform time axis def accumulate_scale_factors(scale_factors): return np.cumsum(scale_factors) # Generate a new resampled timeline def generate_new_time_axis(accumulated, L): return np.linspace(0, accumulated[-1], L) # Linearly interpolate the original signal on the new time axis def linear_interpolate(original_signal, original_axis, new_axis): return np.interp(new_axis, original_axis, original_signal).

[0042] S33. Multi-scale construction, multi-frequency-significance structure-driven multi-scale construction on curved time series.

[0043] Furthermore, in S33, a multi-scale construction driven by multi-frequency-significance structure is performed. The specific steps are as follows: First, for curved time series Perform sliding window analysis to obtain the frequency factor , the specific formula is: ; Where, For The spectrum of a small window centered on is the frequency domain variable, is the high frequency threshold, set to 0.8; Second, calculate the significance factor , the specific formula is: ; Where, is the Euclidean norm, are new sampling points obtained by linear interpolation; Third, for each scale , maximum scale Set to 5 to define a frequency preference interval , indicating the frequency band that the scale focuses on , the specific formula is: ; Frequency preference interval The specific formula is: ; Where, For scale The corresponding frequency lower bound is, scale The corresponding upper frequency bound; For every moment ,scale In the window Inner aggregation features, get aggregation features , the specific formula is: ; Where, is the activation function, is the significant factor, For the frequency band focused on scale, is the window width, and the specific formula is: ; Where, is the minimum window size, set to 2, is the scaling factor, set to 2, For different scales, ; Fourth, dynamic aggregation obtains each scale Aggregate sequence representation of , the specific formula is: ; Where, For scale Aggregate features within the window; Aggregate each scale Sequence representation of , and obtain the multi-scale sequence , the specific formula is: ; Where, For scale The sequence length, For scale The aggregation representation of is the feature dimension, and the implementation code is: # Calculate the window frequency factor def compute_frequency_factor(window_signal, high_freq_threshold=0.8): spectrum = np.abs(fft(window_signal)) energy_total = np.sum(spectrum) high_energy = np.sum(spectrum[int(len(spectrum)*high_freq_threshold):]) return high_energy / energy_total # Calculate significance factor def compute_salience_factor(window_signal): return np.linalg.norm(np.diff(window_signal)) # Define frequency preference interval def define_frequency_band(factor, base_band=(0.1, 0.5)): band_width = base_band[1]- base_band[0] return base_band[0] + factor * band_width, base_band[1] + factor *band_width # Multi-scale feature aggregation def aggregate_features(signal, window_size): features = [] half = window_size / / 2 for i in range(half, len(signal) - half): window = signal[i - half:i + half + 1] salience = compute_salience_factor(window) features.append(salience) return np.array(features).

[0044] S41. Define the phase field for each scale and construct a phase similarity matrix.

[0045] Furthermore, the phase field is defined for each scale in S41 , the specific formula is: ; Where, is the sampling node, , is the phase projection matrix, For paranoid items, For sampling nodes Lower scale The aggregate sequence representation of Construction scale and scale Phase similarity matrix between , the specific formula is: ; Where, For exponential operations, and are all sampling nodes, , , is the phase sensitivity hyperparameter, the initial value is set to 1.5, and the implementation code is: # Define the scale of the phase field def compute_phase_field(X, W, b): return np.dot(W, X) + b # Construct the inter-scale phase similarity matrix def compute_phase_similarity(Z_i, Z_j, alpha=1.5): T = len(Z_i) S = np.zeros((T, T)) for m in range(T): for n in range(T): diff = Z_i[m] - Z_j[n] S[m, n] = np.exp(-alpha * np.linalg.norm(diff)) return S.

[0046] S42. Energy migration is performed through the similarity matrix and inter-scale feature updates are achieved.

[0047] Furthermore, the node energy of each scale is calculated in S42 , the specific formula is: ; Where, For the Sampling nodes downscale The aggregation representation of is the Euclidean norm; Energy migration is performed through the similarity matrix, and the scale Migrate to scale Node energy on , the specific formula is: ; Where, For scale At the node The node energy under For scale The length of the sequence; Calculation scale The difference between real energy and received energy , the specific formula is: ; Where, For scale At the node The node energy under scale At the node The node energy received under Update scale Inter-scale feature representation , the specific formula is: ; Where, is a learnable adjustment coefficient, the initial value is set to 1, and the implementation code is: # Calculate the energy (Euclidean norm) of each scale node def compute_node_energy(features): return np.abs(features) # Energy migration based on phase similarity matrix def transfer_energy(E_i, S_ij): return np.dot(S_ij.T, E_i) # Update scale feature representation def update_features(F_j, delta_E, gamma=1.0): return F_j + gamma * delta_E.

[0048] S43. Design a local enhancement coefficient to enhance the features within the scale.

[0049] Furthermore, in S43, a local enhancement coefficient is designed to enhance the intra-scale features and obtain a scale enhancement sequence , the specific formula is: ; Where, For nodes The local neighborhood of For nodes Lower scale Updated inter-scale feature representation; is the Gaussian kernel normalization weight based on phase difference, and the specific formula is: ; Where, For scale The phase field, is the Euclidean norm, For nodes The local neighborhood of is the phase sensitivity hyperparameter, and its initial value is set to 1.5; Design local enhancement factor , the specific formula is: ; Where, is the Sigmoid function, is a fixed constant, set to 5; is the local phase energy coupling function, and the specific formula is: ; Where, For scale At the node The node energy under is the local phase difference, and the specific formula is: ; Where, For nodes The local neighborhood of For scale The phase field, is the Euclidean norm, and the implementation code is: # Calculate the Gaussian weight of the phase difference (normalized kernel) def compute_gaussian_weight(Z, i, neighborhood, alpha=1.5): weights = [] for j in neighborhood: diff = Z[i] - Z[j] w = np.exp(-alpha * np.linalg.norm(diff)) weights.append(w) weights = np.array(weights) return weights / np.sum(weights) # Normalization # Calculate local phase difference def compute_phase_difference(Z, i, neighborhood): diffs = [np.linalg.norm(Z[i] - Z[j]) for j in neighborhood] return np.mean(diffs) # Calculate the local phase energy coupling function def compute_PECMF(E, i, pdf): return E * pdiff # Calculate the enhancement coefficient def compute_enhance_coef(pe, beta=5): return 1 / (1 + np. exp(-beta * pe)).

[0050] S5. Establish consistency constraints and scale-specific retention, dynamically integrate all scale predictions through adaptive coordination functions, and input the processed foam aluminum material strength data into the model to obtain the prediction results.

[0051] Furthermore, in S5, for each scale Make separate predictions to get each scale The prediction results , the specific formula is: ; Where, is a scale-enhanced sequence, MLP is a multi-layer perceptron; For any scale pair and , establish collaborative constraints and define consistency loss , the specific formula is: ; Where, For scale The prediction results, is the Euclidean norm; The average consistency loss of all scale pairs is averaged to get the average consistency loss , the specific formula is: ; Where, is the maximum scale; Define each scale The local frequency characteristics of the prediction results , the specific formula is: ; Where, is the fast Fourier transform; Define the frequency feature difference between scales , the specific formula is: ; Where, Normalize the row vectors, for each time step , the specific formula is: ; Where, For scale The local frequency characteristics of is the Euclidean norm, To prevent division by zero errors for small constants, set ; The average feature dissimilarity of all scale pairs is taken as the average feature dissimilarity , the specific formula is: ; Define the fusion weights for each scale , the specific formula is: ; Where, For scale The prediction results, is the Euclidean norm, For index operation; Normalize the fusion weight to obtain the normalized fusion weight , the specific formula is: ; In the formula, the denominator represents the sum of all scale weights; The final prediction result after fusion is , the specific formula is: ; Fusion prediction loss , average consistency loss and frequency feature dissimilarity , the specific formula is: ; Where, is the prediction error, using MSE, is the weight of consistency loss, set to 0.5, The weight of the frequency feature dissimilarity is set to 0.5, and the implementation code is: # Multilayer Perceptron Simulation def mlp_predict(features, weights, bias): return np.dot(features, weights) + bias # Consistency loss def consistency_loss(pred_i, pred_j): return np.linalg.norm(pred_i - pred_j) # Average consistency loss def avg_consistency_loss(pred_list): n = len(pred_list) total = 0 count = 0 for i in range(n): for j in range(i+1, n): total += consistency_loss(pred_list[i], pred_list[j]) count += 1 return total / count if count>0 else 0 # Frequency domain feature extraction def compute_local_frequency_feature(x): return np.abs(fft(x)) # Frequency feature dissimilarity between scales def frequency_divergence(F_list, eps=1e-6): norms = [f / (np.linalg.norm(f) + eps) for f in F_list] n = len(norms) total = 0 count = 0 for i in range(n): for j in range(i+1, n): total += np.linalg.norm(norms[i] - norms[j]) count += 1 return total / count if count>0 else 0 # Fusion prediction def fuse_predictions(pred_list): norms = np.array([np.linalg.norm(p) for p in pred_list]) weights = norms / np.sum(norms) return np.sum([w * p for w, p in zip(weights, pred_list)], axis=0).

[0052] Furthermore, the H-MSPNet prediction model was written in Python. The experiment was run on the Windows operating system. Pytorch was selected as the framework in the CUDA11.27 environment and trained on the GeForceRTX3090. Adam was selected as the optimizer, the initial learning rate was set to 0.001, the training batch was set to 64, and the dataset was 140 days of foam aluminum material strength data, which was input into the H-MSPNet prediction model after preprocessing.

[0053] Furthermore, the H-MSPNet prediction model achieves the fitting effect of foam aluminum material strength prediction as follows Figure 5As shown. In the figure, the horizontal axis is the loading time (days), the vertical axis is the degree of strength loss (%), the gray dotted line and the dots represent the actual observation values, and the black solid line and the squares represent the model prediction values. As can be seen from the figure, the predicted curve maintains a high degree of consistency with the true curve as a whole, especially in the early stage of strength change, the two are almost completely overlapped, indicating that the model can accurately extract the key strength evolution characteristics in the short-term time series. In the middle and late stages, the strength continues to decline with time, and the model prediction results can accurately track the strength degradation trend without obvious lag or offset. Comprehensive analysis shows that the model constructed by the present invention has good stage fitting ability and trend perception ability, and can effectively support the strength prediction and full-cycle performance evaluation of foam aluminum materials.

Claims

1. A method for predicting the strength of aluminum foam material based on multi-source data, characterized in that: The following steps are involved: S1. Collect strength data of aluminum foam materials and construct a data set suitable for strength prediction of aluminum foam materials; S2. Standardize the strength data of aluminum foam material using the mean normalization method and divide the data into training set and test set; S3, construct a dynamic multi-scale building module, build a three-parameter dynamic scale control system, and generate dynamic heterogeneous multi-scale subsequences; S31. Define the local time scale adjustment factor, design three sets of parameters: local change rate, local oscillation rate, and local response amplitude, and jointly determine the local time scale adjustment factor; S32, accumulating local scale adjustment factors, constructing a dynamic time warp axis, sampling on the new time axis, and generating a curved time series; S33, performing multi-scale construction driven by a multi-frequency-saliency structure on the curved time series, driving the saliency of multi-frequency features in the time series, and thereby extracting multi-scale features; S4. Construct a scale interaction module, introduce scale phase variables and scale energy conservation migration mechanism, and realize deep nonlinear interaction of information between and within scales; S41, define the phase field for each scale and construct the phase similarity matrix; S42, energy transfer and inter-scale feature update through similarity matrix; S43, designing a local enhancement coefficient to enhance intra-scale features; S5. Establish consistency constraints and scale-specific retention, dynamically integrate all scale predictions through adaptive coordination functions, and input the processed foam aluminum material strength data into the model to obtain the prediction results.

2. The method for predicting the strength of aluminum foam material based on multi-source data according to claim 1, characterized in that: The local time scale adjustment factor in step S31 By calculating the distance between the current moment and the previous moment observation value, the local change rate is obtained to reflect the instantaneous change characteristics of the sequence; using the weighted difference between the current moment and the previous two moments observation value, the local oscillation rate is calculated to characterize the oscillation intensity of the sequence; again, based on the local change rate, a nonlinear adjustment function is introduced to perform nonlinear mapping processing on the response amplitude. The specific formula is: ； Where, Is the Sigmoid function, ensuring , 、 、 are three learnable weight parameters, is the bias term; in, is the local change rate, and the specific formula is: ； Where, For the original sequence at time The observed value of is the Euclidean norm; in, is the local oscillation rate, and the specific formula is: ； Where, For the original sequence at time The observed value of is the Euclidean norm; in, is the local response amplitude, and the specific formula is: ； Where, is a hyperparameter that controls the nonlinear amplitude amplification. is the hyperbolic tangent function.

3. The method for predicting the strength of aluminum foam material based on multi-source data according to claim 2, characterized in that: The construction of the dynamic time warp axis is based on the cumulative operation of the local time scale adjustment factor at each moment to obtain the cumulative local time scale factor at that moment; based on the dynamic time warp axis, the number of sampling points of the time series is redefined to achieve non-uniform sampling of the time series; the sampling process adopts the linear interpolation method, and the value of the new sampling point is calculated between the adjacent observation values of the original time series according to the interpolation weight to complete the generation of the curved time series of the original sequence. The specific formula is: ； Where, For the moment The local time scale adjustment factor, For the moment The cumulative local time scale factor of ; Sampling on the new time axis to generate a curved time series , the specific formula is: ； Where, is the new number of sampling points, New timeline Sampling points, the specific calculation formula is: ； Where, For the moment The cumulative local time scale factor, Round up; Use linear interpolation to obtain sampling data to get new sampling points , the specific formula is: ； Where, The first nodes, is the interpolation weight, and the specific formula is: ； Where, For nodes The cumulative local time scale factor, is the time after resampling The cumulative local time scale factor of .

4. The method for predicting the strength of aluminum foam material based on multi-source data according to claim 3, characterized in that: In step S33, multi-scale construction driven by multi-frequency-significance structure is performed, and the specific steps are as follows: First, for curved time series Perform sliding window analysis to obtain the frequency factor , the specific formula is: ； Where, For The spectrum of a small window centered on is the frequency domain variable, is the high-frequency threshold; Second, calculate the significance factor , the specific formula is: ； Where, is the Euclidean norm, are new sampling points obtained by linear interpolation; Third, for each scale Define a frequency preference interval , indicating the frequency band that the scale focuses on , the specific formula is: ； Frequency preference interval The specific formula is: ； Where, For scale The corresponding frequency lower bound is, scale The corresponding upper frequency bound; For every moment ,scale In the window Inner aggregation features, get aggregation features , the specific formula is: ； Where, is the activation function, is the significant factor, For the frequency band focused on scale, is the window width, and the specific formula is: ； Where, is the minimum window size, is the scaling factor, For different scales, ; Fourth, dynamic aggregation obtains each scale Aggregate sequence representation of , the specific formula is: ； Where, For scale Aggregate features within a window; Aggregate each scale Sequence representation of , and obtain the multi-scale sequence , the specific formula is: ； Where, For scale The sequence length, For scale The aggregation representation of is the feature dimension.

5. The method for predicting the strength of aluminum foam material based on multi-source data according to claim 4, characterized in that: In step S41, each scale defines a phase field , the specific formula is: ； Where, is the sampling node, , is the phase projection matrix, For paranoid items, For sampling nodes Lower scale The aggregate sequence representation of Construction scale and scale Phase similarity matrix between , the specific formula is: ； Where, For exponential operations, and are sampling nodes, , , is the phase sensitivity hyperparameter.

6. The method for predicting the strength of aluminum foam material based on multi-source data according to claim 5, characterized in that: The node energy of each scale is calculated in step S42 , the specific formula is: ； Where, For the Sampling nodes downscale The aggregation representation of is the Euclidean norm; Energy migration is performed through the similarity matrix, and the scale Migrate to scale Node energy on , the specific formula is: ； Where, For scale At the node The node energy under For scale The length of the sequence; Calculation scale The difference between real energy and received energy , the specific formula is: ； Where, For scale At the node The node energy under scale At the node The node energy received under Update scale Inter-scale feature representation , the specific formula is: ； Where, is the learnable adjustment coefficient.

7. The method for predicting the strength of aluminum foam material based on multi-source data according to claim 6, characterized in that: In step S43, a local enhancement coefficient is designed to enhance the feature within the scale to obtain a scale enhancement sequence , the specific formula is: ； Where, For nodes The local neighborhood of For nodes Lower scale Updated inter-scale feature representation; is the Gaussian kernel normalization weight based on phase difference, and the specific formula is: ； Where, For scale The phase field, is the Euclidean norm, For nodes The local neighborhood of is the phase sensitivity hyperparameter; Design local enhancement factor , the specific formula is: ； Where, is the Sigmoid function, is a fixed constant; is the local phase energy coupling function, and the specific formula is: ； Where, For scale At the node The node energy under is the local phase difference, and the specific formula is: ； Where, For nodes The local neighborhood of For scale The phase field, is the Euclidean norm.

8. The method for predicting the strength of aluminum foam material based on multi-source data according to claim 7, characterized in that: In step S5, each scale Make separate predictions to get each scale The prediction results , the specific formula is: ； Where, is a scale-enhanced sequence, MLP is a multi-layer perceptron; For any scale pair and , establish collaborative constraints and define consistency loss , the specific formula is: ； Where, For scale The prediction results, is the Euclidean norm; The average consistency loss of all scale pairs is averaged to get the average consistency loss , the specific formula is: ； Where, is the maximum scale; Define each scale The local frequency characteristics of the prediction results , the specific formula is: ； Where, is the fast Fourier transform; Define the frequency feature difference between scales , the specific formula is: ； Where, Normalize the row vectors, for each time step , the specific formula is: ; Where, For scale The local frequency characteristics of is the Euclidean norm, A small constant to prevent division by zero errors; The average feature dissimilarity of all scale pairs is taken as the average feature dissimilarity , the specific formula is: ； Define the fusion weights for each scale , the specific formula is: ； Where, For scale The prediction results, is the Euclidean norm, For index operation; Normalize the fusion weight to obtain the normalized fusion weight , the specific formula is: ； In the formula, the denominator represents the sum of all scale weights; The final prediction result after fusion is , the specific formula is: ； Fusion prediction loss , average consistency loss and frequency feature dissimilarity , the specific formula is: ； Where, is the prediction error, using MSE, is the weight of consistency loss, The weight of the frequency feature dissimilarity.

9. The method for predicting the strength of aluminum foam material based on multi-source data according to claim 1, characterized in that: To solve the problem of strength prediction of foam aluminum materials, strength monitoring equipment, including strain gauges and accelerometers, was installed to ensure coverage of different stress levels, loading rates and ambient temperature conditions. The physical parameters of the material, including foam porosity, unit size, wall thickness distribution, matrix material type and preparation method, as well as environmental information, including loading method, test temperature, relative humidity, air flow velocity and type and concentration of corrosive media, were integrated to form three-dimensional strength response data including time, space and material properties. The collected data was normalized and divided into test sets and training sets for training and evaluating the performance of the foam aluminum material strength prediction model.

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