A method for predicting the strength of foamed aluminum materials based on multi-source data

Abstract

This invention proposes a method for predicting the strength of aluminum foam based on multi-source data, belonging to the field of data prediction. The invention proposes the H-MSPNet model, applied to the scenario of predicting the strength of aluminum foam, comprising a dynamic multi-scale construction module, a scale interaction module, and a fusion prediction module. Specifically, the dynamic multi-scale construction module, based on a local timescale adjustment mechanism and a frequency-significance driven strategy, can adaptively extract local features of the strength of aluminum foam at different timescales; the scale interaction module achieves deep nonlinear interaction between and within scales through phase similarity modeling, energy transfer mechanisms, and local phase-energy coupling functions; 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. All modules work together to achieve accurate prediction of the strength of aluminum foam.

Description

Technical Field

[0001] This invention belongs to the field of data prediction, specifically relating to a method for predicting the strength of aluminum foam materials based on multi-source data. Background Technology

[0002] Aluminum foam, as a porous metallic material with both lightweight and high energy absorption properties, has wide applications in aerospace, automotive manufacturing, and building vibration reduction. 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), microstructure characteristics (pore size distribution and pore wall thickness), and external load conditions (strain rate and temperature). However, traditional strength prediction methods often rely on a single data source (such as experimental testing or numerical simulation), making it difficult to comprehensively characterize the material behavior under multi-scale and multi-physics field coupling, resulting in insufficient prediction accuracy and low efficiency. On the one hand, its microporous structure is complex and exhibits significant heterogeneity and scale effects, which traditional single-scale prediction methods cannot effectively describe. On the other hand, the actual collected material performance data exhibits significant noise interference, strong non-stationarity, and inter-scale interactive coupling, showing a complex interplay of scale differences, local abrupt changes, and long-term performance variations, which poses challenges to prediction modeling. Therefore, it is urgent to propose a multi-scale analysis and prediction method based on multi-source data to deeply reveal the intrinsic laws governing the strength evolution of aluminum foam, thereby improving the generalization ability and prediction accuracy of the prediction model.

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

[0004] In recent years, the combination of artificial intelligence and multi-source data fusion technology has provided new ideas for predicting material properties. For example, the application of federated learning frameworks in equipment performance prediction shows that distributed data collaborative modeling can improve the generalization ability of models; while the wave finite element method achieves efficient computation by reducing the scale of degrees of freedom, providing a reference for multi-scale modeling. However, existing technologies have not yet achieved full-chain data integration of process-structure-performance in the prediction of aluminum foam strength, and 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] This invention provides a method for predicting the strength of aluminum foam based on multi-source data. Addressing the issues of high 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. This method consists of a dynamic multi-scale construction module, a scale interaction module, and a fusion prediction module. The dynamic multi-scale construction module introduces a three-parameter local timescale adjustment mechanism to construct a dynamic time-distortion sequence under variable scales and extracts representative frequency subsequences based on significance-driven sliding window spectral analysis to achieve multi-scale modeling of the performance response of aluminum foam. The scale interaction module introduces scale phase variables and local phase energy coupling functions, designs an inter-scale phase similarity matrix and energy transfer mechanism, and achieves deep nonlinear interaction and local feature enhancement between different scales. The fusion prediction module, while maintaining scale specificity, integrates the prediction results of each scale through adaptive weights, and combines frequency feature dissimilarity loss and consistency constraints to achieve high-precision prediction of the strength of aluminum foam.

[0006] The technical solution adopted by the present invention to achieve the above objectives specifically includes the following steps:

[0007] S1. Collect strength data of aluminum foam and construct a dataset suitable for predicting the strength of aluminum foam.

[0008] S2. Standardize the strength data of aluminum foam material using the mean normalization method, and divide the data into training set and test set;

[0009] S3. Construct a dynamic multi-scale construction module, build a three-parameter dynamic scale control system, and generate dynamic heterogeneous multi-scale sub-sequences;

[0010] S31. Define the local time scale adjustment factor, and design three sets of parameters: local rate of change, local oscillation rate, and local response amplitude, which together determine the local time scale adjustment factor.

[0011] S32. Accumulate local scale adjustment factors, construct a dynamic time distortion axis, sample on the new time axis, and generate a curved time series;

[0012] S33. Perform multi-frequency-saliency structure-driven multi-scale construction on the curved time series to drive the saliency of multi-frequency features in the time series, thereby realizing the extraction of multi-scale features.

[0013] S4. Construct a scale interaction module, introduce scale phase variables and scale energy conservation and migration mechanism to realize deep nonlinear interaction of information between and within scales;

[0014] S41. Define the phase field for each scale and construct the phase similarity matrix;

[0015] S42. Energy transfer and inter-scale feature update are achieved through similarity matrix;

[0016] S43. Design local enhancement coefficients to enhance features within scale;

[0017] S5. Establish consistency constraints and scale-specific preservation, dynamically integrate all scale predictions through an adaptive coordination function, and input the processed aluminum foam material strength data into the model to obtain the prediction results.

[0018] Preferably, in step S1, to construct a dataset suitable for predicting the strength of aluminum foam materials, strength monitoring equipment, including strain gauges and accelerometers, is installed to ensure coverage of different stress levels, loading rates, and ambient temperature conditions. This is combined with the material's physical parameters, 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, airflow velocity, and the type and concentration of corrosive media, to form three-dimensional strength response data containing time, space, and material properties. All data is stored in a unified format, and failure points are marked, thus completing the construction of the aluminum foam material strength prediction dataset.

[0019] Preferably, the strength data of aluminum foam is preprocessed, including standardizing the original data for predicting the strength of aluminum foam using a mean normalization method. Specifically, the mean of the feature used to characterize the material strength in each sample is subtracted from the mean of the feature in the overall dataset and divided by the standard deviation, thereby eliminating the dimensional differences between different features and improving the model's compatibility and training stability with data at different scales. Furthermore, 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 for verifying the model's generalization ability, so as to improve the adaptability and accuracy of the overall prediction method under different aluminum foam samples.

[0020] Preferably, as a porous lightweight metallic material, the mechanical properties of foamed aluminum material are highly dependent on the synergistic effect of its multi-scale structural characteristics and multi-source physical factors. Its strength is influenced not only by microstructural parameters such as porosity, pore size, and pore size distribution, but also by factors such as pore connectivity, skeleton arrangement direction, and local density at the mesoscale, as well as the overall geometric morphology and loading method at the macroscale. This structural response mode, where multi-dimensional characteristics from the micro to the macro scale jointly determine material properties, indicates that the strength prediction of foamed aluminum material has a significant "multi-scale synergistic driving" characteristic. Based on this characteristic, this invention proposes... The proposed method employs a dynamic multi-scale construction module, a three-parameter dynamic scale control system, and the generation of dynamic heterogeneous multi-scale subsequences. The dynamic multi-scale construction module can flexibly divide the feature domain for the scale non-uniformity of the original data, preserving both 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. The construction of dynamic heterogeneous multi-scale subsequences can reconstruct a sequence structure that better reflects the actual behavior of materials, thereby more efficiently representing the multi-level driving path of structural features in response to intensity.

[0021] Preferably, the local timescale adjustment factor By calculating the distance between the current and previous observations, the local rate of change is obtained to reflect the instantaneous change characteristics of the sequence. Using the weighted difference between the current and two previous observations, the local oscillation rate is calculated to characterize the oscillation intensity of the sequence. Furthermore, based on the local rate of change, a nonlinear adjustment function is introduced to perform nonlinear mapping on the response amplitude. The specific formula is as follows:

[0022] ;

[0023] Where, It is the Sigmoid function, ensuring , , , There are three learnable weight parameters. For bias terms;

[0024] in, The local rate of change is given by the following formula:

[0025] ;

[0026] Where, For the original sequence at time... The observed values, It is the Euclidean norm;

[0027] in, The local oscillation rate is given by the following formula:

[0028] ;

[0029] Where, For the original sequence at time... The observed values, It is the Euclidean norm;

[0030] in, The local response amplitude is given by the following formula:

[0031] ;

[0032] Where, To control the hyperparameters of nonlinear amplitude amplification, It is the hyperbolic tangent function.

[0033] Preferably, by introducing three dynamic features—local rate of change, local oscillation rate, and local response amplitude—a time-varying scale control factor is constructed. This effectively captures local abrupt changes, structural jumps, and nonlinear response characteristics in the strength data of aluminum foam materials. Since aluminum foam materials exhibit significant multi-scale heterogeneity and dynamic fluctuations in pore structure and distribution density, the model's focus on different time scales can be dynamically adjusted according to the local change intensity of the input sequence. This enhances the perception of key structural change regions, thereby improving the sensitivity and robustness of the strength prediction model to abnormal regions and microstructural disturbances, and achieving more adaptive strength estimation and structural response modeling.

[0034] Preferably, the construction of the dynamic time distortion axis is based on the cumulative calculation 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 distortion 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 calculates the value of the new sampling point between adjacent observations of the original time series according to the interpolation weight, thus completing the generation of the warped time series of the original series, and the specific formula is as follows:

[0035] ;

[0036] Where, For a moment The local timescale adjustment factor, For a moment The cumulative local time scale factor;

[0037] Sampling is performed on a new timeline to generate a curved time series. The specific formula is as follows:

[0038] ;

[0039] Where, For the new number of sampling points, On the new timeline The specific calculation formula is as follows: (Number of sampling points)

[0040] ;

[0041] Where, For a moment The cumulative local timescale factor, Rounding up;

[0042] New sampling points are obtained by using linear interpolation to acquire the sampled data. The specific formula is as follows:

[0043] ;

[0044] Where, For the first of the original sequence 1 node The interpolation weights are defined by the following formula:

[0045] ;

[0046] Where, For nodes The cumulative local timescale factor, The time after resampling The cumulative local timescale factor.

[0047] Preferably, by constructing a dynamic time axis based on a local scale control factor and resampling the original sequence on the deformed time axis using linear interpolation, non-uniform sampling processing of the time series is achieved. This effectively addresses the problem of inconsistency between local structural abrupt changes and temporal change rates in the strength data of aluminum foam materials. The mechanical response characteristics of aluminum foam materials under different scale structures may exhibit nonlinear abrupt changes or local oscillations. This strategy dynamically adjusts the time sampling density, making the model sample more densely in areas of drastic structural changes or sensitive responses, and appropriately sparsely in areas of gradual change. This helps to enhance the modeling ability of key structural regions, improve the accuracy and efficiency of strength prediction, suppress redundant information interference, and achieve fine modeling of complex material behavior.

[0048] Preferably, a multi-frequency-saliency structure-driven multi-scale construction is performed, and the specific steps are as follows:

[0049] First, for curved time series Perform sliding window analysis to obtain frequency factors The specific formula is as follows:

[0050] ;

[0051] Where, For The spectrum of the center small window, For frequency domain variables, High-frequency threshold;

[0052] Secondly, calculate the significance factor. The specific formula is as follows:

[0053] ;

[0054] Where, For the Euclidean norm, The new sampling points are obtained through linear interpolation;

[0055] Thirdly, for each scale Define a frequency preference range This indicates the frequency band that the scale focuses on. The specific formula is as follows:

[0056] ;

[0057] Frequency preference range The specific formula is:

[0058] ;

[0059] Where, For scale The corresponding lower frequency bound, scale The corresponding upper frequency bound;

[0060] For each moment ,scale In the window Inner aggregation features, resulting in aggregation features The specific formula is as follows:

[0061] ;

[0062] Where, For activation function, As a significant factor, For scale-focused frequency bands, The width of the window is given by the following formula:

[0063] ;

[0064] Where, Minimum window size, Scaling factor For different scales, ;

[0065] Fourth, dynamic aggregation yields each scale. Aggregate sequence representation The specific formula is as follows:

[0066] ;

[0067] Where, For scale Aggregation features within the window;

[0068] Aggregate each scale Sequence representation To obtain multi-scale sequences The specific formula is as follows:

[0069] ;

[0070] Where, For scale The sequence length, For scale The aggregation representation, For feature dimensions.

[0071] Preferably, a sliding window Fourier transform is used to analyze the fatigue sequence on the dynamic time axis, extract the frequency components and significance indexes at each scale, and generate frequency preference intervals based on the proportion of high-frequency energy and the severity of structural stress, thereby accurately extracting the frequency domain characteristics of the strength data of aluminum foam at different scales.

[0072] Preferably, the strength prediction of aluminum foam materials by the method of the present invention requires characterizing a complex multi-scale mechanism integrating "structure-energy-response". By constructing a scale interaction module and introducing scale phase variables and scale energy conservation and transfer mechanisms, dynamic self-adjustment within the scale and deep nonlinear interaction between scales can be achieved. This can fully explore the cross-scale correlation paths and dominant energy transfer patterns contained in the strength data of aluminum foam, thereby improving the structural sensitivity, prediction accuracy and generalization ability of the model, and providing underlying support for intelligent strength prediction of complex structural materials.

[0073] Preferably, a phase field is defined for each scale. The specific formula is as follows:

[0074] ;

[0075] Where, For sampling nodes, , The phase projection matrix, For paranoia, For sampling nodes lower scale The aggregate sequence representation;

[0076] Construction Scale and scale Phase similarity matrix between The specific formula is as follows:

[0077] ;

[0078] In the formula, For index operations, and All are sampling nodes. , , This is the phase sensitivity hyperparameter.

[0079] Preferably, an independent phase field is defined for each scale and an inter-scale phase similarity matrix is ​​constructed. By measuring the structural consistency between phase modes, phase alignment and coherence modeling between multi-scale fatigue features are achieved, providing a criterion basis for subsequent energy transfer.

[0080] Preferably, the node energy at each scale is calculated. The specific formula is as follows:

[0081] ;

[0082] In the formula, For the first Lower scale of each sampling node The aggregation representation, It is the Euclidean norm;

[0083] Energy transfer is performed using the similarity matrix to obtain the scale... Migration to scale On the node energy The specific formula is as follows:

[0084] ;

[0085] In the formula, For scale At the node The energy of the next node, For scale The sequence length;

[0086] Computational scale The difference between actual energy and received energy The specific formula is as follows:

[0087] ;

[0088] In the formula, For scale At the node The energy of the next node, scale At the node The energy received from the next node;

[0089] Update scale Inter-scale feature representation The specific formula is as follows:

[0090] ;

[0091] In the formula, This is a learnable adjustment coefficient.

[0092] Preferably, an energy transfer mechanism is designed to guide energy transfer between different scales through a phase similarity matrix, dynamically update the feature representations 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.

[0093] Preferably, local enhancement coefficients are designed to perform intra-scale feature enhancement, resulting in a scale-enhanced sequence. The specific formula is as follows:

[0094] ;

[0095] In the formula, For nodes The local neighborhood, For nodes lower scale Updated inter-scale feature representation;

[0096] The Gaussian kernel-normalized weights based on phase difference are formulated as follows:

[0097] ;

[0098] In the formula, For scale phase field, For the Euclidean norm, For nodes The local neighborhood, This refers to the phase sensitivity hyperparameter;

[0099] Design local enhancement coefficient The specific formula is as follows:

[0100] ;

[0101] Where, For the Sigmoid function, It is a fixed constant;

[0102] The local phase energy coupling function is given by the following formula:

[0103] ;

[0104] Where, For scale At the node The energy of the nodes below;

[0105] The local phase difference is given by the following formula:

[0106] ;

[0107] Where, For nodes The local neighborhood, For scale phase field, It is the Euclidean norm.

[0108] Preferably, a local enhancement coefficient and a local phase energy coupling function are introduced to nonlinearly enhance the features within each scale, explicitly characterizing the coupling relationship between local energy changes and phase perturbations, thereby improving the model's sensitivity to identifying sudden fatigue damage.

[0109] Preferably, for each scale Perform individual predictions to obtain each scale Prediction results The specific formula is as follows:

[0110] ;

[0111] Where, For scale-enhanced sequences, MLP stands for Multilayer Perceptron;

[0112] For any scale pair and Establish collaborative constraints and define consistency loss. The specific formula is as follows:

[0113] ;

[0114] Where, For scale The prediction results It is the Euclidean norm;

[0115] The average consistency loss is obtained by averaging the consistency losses of all scale pairs. The specific formula is as follows:

[0116] ;

[0117] Where, For the largest scale;

[0118] Define each scale Local frequency features of the prediction results The specific formula is as follows:

[0119] ;

[0120] Where, For Fast Fourier Transform;

[0121] Define the dissimilarity of frequency features between scales The specific formula is as follows:

[0122] ;

[0123] Where, To normalize the row vectors, for each time step The specific formula is as follows:

[0124] ;

[0125] Where, For scale Local frequency characteristics, For the Euclidean norm, A small constant to prevent division by zero errors;

[0126] The average dissimilarity of frequency features across all scale pairs is obtained by averaging the dissimilarity of these features. The specific formula is as follows:

[0127] ;

[0128] Define the fusion weights for each scale The specific formula is as follows:

[0129] ;

[0130] Where, For scale The prediction results For the Euclidean norm, For index operations;

[0131] The fusion weights are normalized to obtain the normalized fusion weights. The specific formula is as follows:

[0132] ;

[0133] In the formula, the denominator This represents the sum of all scale weights;

[0134] The final prediction result after fusion is The specific formula is as follows:

[0135] ;

[0136] Fusion prediction loss Average consistency loss and frequency characteristic dissimilarity The specific formula is as follows:

[0137] ;

[0138] In the formula, For prediction error, MSE is used. The weight of consistency loss, Weights for frequency characteristic dissimilarity.

[0139] Preferably, a prediction consistency constraint and scale-specificity preservation mechanism are established. By introducing an adaptive coordination function, the prediction results at different scales are dynamically fused. While maintaining the local feature representation ability 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 aluminum foam material, thereby improving the generalization ability and stability of the model.

[0140] In summary, the beneficial effects of this invention due to the adoption of this technical solution are as follows: This invention proposes an H-MSPNet prediction model, applied to the strength prediction scenario of aluminum foam materials, comprising a dynamic multi-scale construction module, a scale interaction module, and a fusion prediction module; specifically, the dynamic multi-scale construction module, based on a local time scale adjustment mechanism and a frequency-significance driven strategy, can adaptively extract local features of fatigue response at different time scales; the scale interaction module achieves deep nonlinear interaction between and within scales through phase similarity modeling, energy transfer 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. All modules work together to achieve accurate prediction of the strength of aluminum foam materials. Attached Figure Description

[0141] Figure 1A flowchart illustrating the steps of a method for predicting the strength of aluminum foam materials.

[0142] Figure 2 This is a diagram of the H-MSPNet prediction model structure.

[0143] Figure 3 A modular structure diagram for dynamic multi-scale construction.

[0144] Figure 4 This is a structural diagram of the scale interaction module.

[0145] Figure 5 The fitting effect diagram of the H-MSPNet prediction model for the strength prediction of aluminum foam material is shown. Detailed Implementation

[0146] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0147] Please see Figures 1-5 This invention provides a technical solution: a method for predicting the strength of aluminum foam materials. The method involves extracting local features at different time scales through a dynamic multi-scale construction module, achieving deep nonlinear interaction between and within scales through a scale interaction module, extracting time-domain information through a time-domain feature extraction module, and dynamically integrating multi-scale prediction results through a fusion prediction module to obtain the predicted strength of the aluminum foam materials. Specific steps are as follows: Figure 1 As shown.

[0148] The H-MSPNet prediction model is constructed as follows: Figure 2 As shown, the specific steps are as follows.

[0149] S1. Collect strength data of aluminum foam materials and construct a dataset suitable for predicting the strength of aluminum foam materials.

[0150] Furthermore, to construct a dataset suitable for predicting the strength of aluminum foam materials, strength monitoring equipment, including strain gauges and accelerometers, was installed to ensure coverage of different stress levels, loading rates, and ambient temperature conditions. This data was then integrated with the material's physical parameters, 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, airflow velocity, and the type and concentration of corrosive media. This resulted in three-dimensional strength response data encompassing time, space, and material properties. All data were stored in a unified format, and failure points or maximum load-bearing strengths were labeled, thus completing the construction of the aluminum foam material strength prediction dataset.

[0151] S2. The preprocessed fatigue life data is standardized using the mean normalization method, and the data is divided into training set and test set, with a ratio of 3:7 between the test set and the training set.

[0152] Furthermore, the strength prediction data for aluminum foam materials were standardized using a mean normalization method, with the specific formula as follows:

[0153] ;

[0154] In the formula, For the original sequence at time... Observed values;

[0155] Original sequence The mean, specifically, is calculated using the following formula:

[0156] ;

[0157] In the formula, The length of the original sequence;

[0158] Original sequence The standard deviation of is given by the following formula:

[0159] ;

[0160] Obtain the normalized sequence The implementation code is:

[0161] # Normalize the mean of the input sequence X

[0162] def normalize_sequence(X):

[0163] mu = np.mean(X)

[0164] sigma = np.std(X)

[0165] x_normalized = (X - mu) / sigma

[0166] return x_normalized, mu, sigma

[0167] # Split the training and test sets, with a default ratio of 7:3.

[0168] def split_train_test(X, train_ratio=0.7):

[0169] split_idx = int(len(X) * train_ratio)

[0170] return X[:split_idx], X[split_idx:].

[0171] S31. Define the local time scale adjustment factor, and design three sets of parameters: local rate of change, local oscillation rate, and local response amplitude, which together determine the local time scale adjustment factor.

[0172] Furthermore, a local timescale adjustment factor is defined in S31. The specific formula is as follows:

[0173] ;

[0174] Where, It is the Sigmoid function, ensuring , , , There are three learnable weight parameters. For bias terms;

[0175] The local rate of change is given by the following formula:

[0176] ;

[0177] Where, For the original sequence at time... The observed values, It is the Euclidean norm;

[0178] The local oscillation rate is given by the following formula:

[0179] ;

[0180] Where, For the original sequence at time... The observed values, It is the Euclidean norm;

[0181] The local response amplitude is given by the following formula:

[0182] ;

[0183] Where, To control the hyperparameters of nonlinear amplitude amplification, The function is the hyperbolic tangent, and its specific formula is:

[0184] ;

[0185] The implementation code is:

[0186] # S31: Local timescale adjustment factor

[0187] def compute_scale_factor(X, w1, w2, w3, b, alpha=2.0):

[0188] # Calculate the local rate of change r

[0189] r = np.linalg.norm(np.diff(X, prepend=X[0])) # Keep the length consistent

[0190] # Calculate local oscillation rate

[0191] o = np.linalg.norm(np.diff(np.diff(X, prepend=X[0]), prepend=0))

[0192] # Calculate the local response amplitude a

[0193] a = alpha * tanh(np.mean(np.abs(X - np.mean(X))))

[0194] # Calculate the scaling adjustment factor s

[0195] s = sigmoid(w1 * r + w2 * o + w3 * a + b)

[0196] return s.

[0197] S32. Accumulate local scale adjustment factors, construct a dynamic time distortion axis, sample on the new time axis, and generate a curved time series.

[0198] Furthermore, the local scale adjustment factor is accumulated in S32 to construct a dynamic time warp axis and generate a new time axis. The specific formula is as follows:

[0199] ;

[0200] Where, For a moment The local timescale adjustment factor, For a moment The cumulative local time scale factor;

[0201] Sampling is performed on a new timeline to generate a curved time series. The specific formula is as follows:

[0202] ;

[0203] In the formula, For the new number of sampling points, On the new timeline The specific calculation formula is as follows: (Number of sampling points)

[0204] ;

[0205] In the formula, For a moment The cumulative local timescale factor, Rounding up;

[0206] New sampling points are obtained by using linear interpolation to acquire the sampled data. The specific formula is as follows:

[0207] ;

[0208] In the formula, For the first part of the original sequence 1 node The interpolation weights are given by the following formula:

[0209] ;

[0210] In the formula, For nodes The cumulative local timescale factor, The time after resampling The cumulative local time scale factor, specifically implemented in the following code:

[0211] # Accumulate local scale adjustment factors to obtain a non-uniform time axis

[0212] def accumulate_scale_factors(scale_factors):

[0213] return np.cumsum(scale_factors)

[0214] # Generate a new timeline for resampling

[0215] def generate_new_time_axis(accumulated, L):

[0216] return np.linspace(0, accumulated[-1], L)

[0217] # Perform linear interpolation on the original signal on the new time axis

[0218] def linear_interpolate(original_signal, original_axis, new_axis):

[0219] return np.interp(new_axis, original_axis, original_signal).

[0220] S33, Multi-scale construction: Multi-frequency-significant structure-driven multi-scale construction on curved time series.

[0221] Furthermore, S33 performs multi-frequency-saliency structure-driven multi-scale construction, specifically through the following steps:

[0222] First, for curved time series Perform sliding window analysis to obtain frequency factors The specific formula is as follows:

[0223] ;

[0224] Where, For The spectrum of the center small window, For frequency domain variables, The high-frequency threshold is set to 0.8;

[0225] Secondly, calculate the significance factor. The specific formula is as follows:

[0226] ;

[0227] Where, For the Euclidean norm, The new sampling points are obtained through linear interpolation;

[0228] Thirdly, for each scale Maximum scale Set to 5 to define a frequency preference range. This indicates the frequency band that the scale focuses on. The specific formula is as follows:

[0229] ;

[0230] Frequency preference range The specific formula is:

[0231] ;

[0232] Where, For scale The corresponding lower frequency bound, scale The corresponding upper frequency bound;

[0233] For each moment ,scale In the window Inner aggregation features, resulting in aggregation features The specific formula is as follows:

[0234] ;

[0235] Where, For activation function, As a significant factor, For scale-focused frequency bands, The width of the window is given by the following formula:

[0236] ;

[0237] Where, Set the minimum window size to 2. Set the scaling factor to 2. For different scales, ;

[0238] Fourth, dynamic aggregation yields each scale. Aggregate sequence representation The specific formula is as follows:

[0239] ;

[0240] Where, For scale Aggregation features within the window;

[0241] Aggregate each scale Sequence representation To obtain multi-scale sequences The specific formula is as follows:

[0242] ;

[0243] Where, For scale The sequence length, For scale The aggregation representation, For the feature dimension, the implementation code is as follows:

[0244] # Calculate the window frequency factor

[0245] def compute_frequency_factor(window_signal, high_freq_threshold=0.8):

[0246] spectrum = np.abs(fft(window_signal))

[0247] energy_total = np.sum(spectrum)

[0248] high_energy = np.sum(spectrum[int(len(spectrum)*high_freq_threshold):])

[0249] return high_energy / energy_total

[0250] # Calculate significance factor

[0251] def compute_salience_factor(window_signal):

[0252] return np.linalg.norm(np.diff(window_signal))

[0253] # Define frequency preference range

[0254] def define_frequency_band(factor, base_band=(0.1, 0.5)):

[0255] band_width = base_band[1]- base_band[0]

[0256] return base_band[0] + factor * band_width, base_band[1] + factor *band_width

[0257] # Multi-scale feature aggregation

[0258] def aggregate_features(signal, window_size):

[0259] features = []

[0260] half = window_size / / 2

[0261] for i in range(half, len(signal) - half):

[0262] window = signal[i - half:i + half + 1]

[0263] salience = compute_salience_factor(window)

[0264] features.append(salience)

[0265] return np.array(features).

[0266] S41. Define the phase field for each scale and construct the phase similarity matrix.

[0267] Furthermore, in S41, a phase field is defined for each scale. The specific formula is as follows:

[0268] ;

[0269] Where, For sampling nodes, , The phase projection matrix, For paranoia, For sampling nodes lower scale The aggregate sequence representation;

[0270] Construction Scale and scale Phase similarity matrix between The specific formula is as follows:

[0271] ;

[0272] Where, For index operations, and All are sampling nodes. , , The phase sensitivity hyperparameter is initially set to 1.5, and the implementation code is as follows:

[0273] # Defining the phase field of the scale

[0274] def compute_phase_field(X, W, b):

[0275] return np.dot(W, X) + b

[0276] # Constructing inter-scale phase similarity matrices

[0277] def compute_phase_similarity(Z_i, Z_j, alpha=1.5):

[0278] T = len(Z_i)

[0279] S = np.zeros((T, T))

[0280] for m in range(T):

[0281] for n in range(T):

[0282] diff = Z_i[m] - Z_j[n]

[0283] S[m, n] = np.exp(-alpha * np.linalg.norm(diff))

[0284] return S.

[0285] S42. Energy transfer is performed through the similarity matrix to achieve inter-scale feature update.

[0286] Furthermore, in S42, the node energy at each scale is calculated. The specific formula is as follows:

[0287] ;

[0288] In the formula, For the first Lower scale of each sampling node The aggregation representation, It is the Euclidean norm;

[0289] Energy transfer is performed using the similarity matrix to obtain the scale... Migration to scale On the node energy The specific formula is as follows:

[0290] ;

[0291] In the formula, For scale At the node The energy of the next node, For scale The sequence length;

[0292] Computational scale The difference between actual energy and received energy The specific formula is as follows:

[0293] ;

[0294] Where, For scale At the node The energy of the next node, scale At the node The energy received from the next node;

[0295] Update scale Inter-scale feature representation The specific formula is as follows:

[0296] ;

[0297] Where, The learnable adjustment coefficient is initially set to 1, and the implementation code is as follows:

[0298] # Calculate the energy (Euclidean norm) of each node at each scale.

[0299] def compute_node_energy(features):

[0300] return np.abs(features)

[0301] # Energy transfer based on phase similarity matrix

[0302] def transfer_energy(E_i, S_ij):

[0303] return np.dot(S_ij.T, E_i)

[0304] # Update scale feature representation

[0305] def update_features(F_j, delta_E, gamma=1.0):

[0306] return F_j + gamma * delta_E.

[0307] S43. Design local enhancement coefficients to enhance features within the scale.

[0308] Furthermore, local enhancement coefficients are designed in S43 to perform intra-scale feature enhancement, resulting in a scale-enhanced sequence. The specific formula is as follows:

[0309] ;

[0310] Where, For nodes The local neighborhood, For nodes lower scale Updated inter-scale feature representation;

[0311] The Gaussian kernel-normalized weights based on phase difference are formulated as follows:

[0312] ;

[0313] Where, For scale phase field, For the Euclidean norm, For nodes The local neighborhood, The phase sensitivity hyperparameter is initially set to 1.5;

[0314] Design local enhancement coefficient The specific formula is as follows:

[0315] ;

[0316] Where, For the Sigmoid function, As a fixed constant, set it to 5;

[0317] The local phase energy coupling function is given by the following formula:

[0318] ;

[0319] Where, For scale At the node The energy of the nodes below;

[0320] The local phase difference is given by the following formula:

[0321] ;

[0322] Where, For nodes The local neighborhood, For scale phase field, For the Euclidean norm, the implementation code is as follows:

[0323] # Calculate the Gaussian weights (normalized kernel) for the phase difference

[0324] def compute_gaussian_weight(Z, i, neighborhood, alpha=1.5):

[0325] weights = []

[0326] for j in neighborhood:

[0327] diff = Z[i] - Z[j]

[0328] w = np.exp(-alpha * np.linalg.norm(diff))

[0329] weights.append(w)

[0330] weights = np.array(weights)

[0331] return weights / np.sum(weights) # Normalization

[0332] # Calculate local phase difference

[0333] def compute_phase_difference(Z, i, neighborhood):

[0334] diffs = [np.linalg.norm(Z[i] - Z[j]) for j in neighborhood]

[0335] return np.mean(diffs)

[0336] # Calculate the local phase energy coupling function

[0337] def compute_PECMF(E, i, pdf):

[0338] return E * pdiff

[0339] # Calculate the enhancement factor

[0340] def compute_enhance_coef(pe, beta=5):

[0341] return 1 / (1 + np. exp(-beta * pe)).

[0342] S5. Establish consistency constraints and scale-specific preservation, dynamically integrate all scale predictions through an adaptive coordination function, and input the processed aluminum foam material strength data into the model to obtain the prediction results.

[0343] Furthermore, in S5 for each scale Perform individual predictions to obtain each scale Prediction results The specific formula is as follows:

[0344] ;

[0345] In the formula, For scale-enhanced sequences, MLP stands for Multilayer Perceptron;

[0346] For any scale pair and Establish collaborative constraints and define consistency loss. The specific formula is as follows:

[0347] ;

[0348] In the formula, For scale The prediction results It is the Euclidean norm;

[0349] The average consistency loss is obtained by averaging the consistency losses of all scale pairs. The specific formula is as follows:

[0350] ;

[0351] In the formula, For the largest scale;

[0352] Define each scale Local frequency features of the prediction results The specific formula is as follows:

[0353] ;

[0354] In the formula, For Fast Fourier Transform;

[0355] Define the dissimilarity of frequency features between scales The specific formula is as follows:

[0356] ;

[0357] In the formula, To normalize the row vectors, for each time step The specific formula is as follows:

[0358] ;

[0359] In the formula, For scale Local frequency characteristics, For the Euclidean norm, To prevent division by zero errors, a small constant is set to... ;

[0360] The average dissimilarity of frequency features across all scale pairs is obtained by averaging the dissimilarity of these features. The specific formula is as follows:

[0361] ;

[0362] Define the fusion weights for each scale The specific formula is as follows:

[0363] ;

[0364] In the formula, For scale The prediction results For the Euclidean norm, For index operations;

[0365] The fusion weights are normalized to obtain the normalized fusion weights. The specific formula is as follows:

[0366] ;

[0367] In the formula, the denominator This represents the sum of all scale weights;

[0368] The final prediction result after fusion is The specific formula is as follows:

[0369] ;

[0370] Fusion prediction loss Average consistency loss and frequency characteristic dissimilarity The specific formula is as follows:

[0371] ;

[0372] Where, For prediction error, MSE is used. The weight for consistency loss is set to 0.5. The weight of frequency characteristic dissimilarity is set to 0.5, and the implementation code is as follows:

[0373] # Multilayer Perceptron Simulation

[0374] def mlp_predict(features, weights, bias):

[0375] return np.dot(features, weights) + bias

[0376] # Consistency Loss

[0377] def consistency_loss(pred_i, pred_j):

[0378] return np.linalg.norm(pred_i - pred_j)

[0379] # Average consistency loss

[0380] def avg_consistency_loss(pred_list):

[0381] n = len(pred_list)

[0382] total = 0

[0383] count = 0

[0384] for i in range(n):

[0385] for j in range(i+1, n):

[0386] total += consistency_loss(pred_list[i], pred_list[j])

[0387] count += 1

[0388] return total / count if count>0 else 0

[0389] # Frequency Domain Feature Extraction

[0390] def compute_local_frequency_feature(x):

[0391] return np.abs(fft(x))

[0392] # Inter-scale frequency feature dissimilarity

[0393] def frequency_divergence(F_list, eps=1e-6):

[0394] norms = [f / (np.linalg.norm(f) + eps) for f in F_list]

[0395] n = len(norms)

[0396] total = 0

[0397] count = 0

[0398] for i in range(n):

[0399] for j in range(i+1, n):

[0400] total += np.linalg.norm(norms[i] - norms[j])

[0401] count += 1

[0402] return total / count if count>0 else 0

[0403] # Fusion prediction

[0404] def fuse_predictions(pred_list):

[0405] norms = np.array([np.linalg.norm(p) for p in pred_list])

[0406] weights = norms / np.sum(norms)

[0407] return np.sum([w * p for w, p in zip(weights, pred_list)], axis=0)。

[0408] Furthermore, the H-MSPNet prediction model was written in Python, and the experiments were run on a Windows operating system. PyTorch was used as the framework in the CUDA 11.27 environment, and training was performed on a GeForce RTX 3090. The optimizer was Adam, the initial learning rate was set to 0.001, the training batch size was set to 64, and the dataset consisted of 140 days of foam aluminum material strength data, which was preprocessed and then input into the H-MSPNet prediction model.

[0409] Furthermore, the H-MSPNet prediction model achieves a good fitting effect for predicting the strength of aluminum foam materials, as shown in the following figure. Figure 5 As shown in the figure, the horizontal axis represents the loading time (days), and the vertical axis represents the degree of strength loss (%). The gray dashed line and dots represent the actual observed values, and the black solid line and squares represent the model's predicted values. The figure shows that the predicted curve generally maintains a high degree of consistency with the actual curve, especially in the early stage of strength change, where the two almost completely overlap, indicating that the model can accurately extract key strength evolution features in the short-term time series. In the middle and later stages, the strength continues to decrease over time, and the model's prediction results can accurately track the strength degradation trend without significant lag or deviation. Comprehensive analysis shows that the model constructed in this invention has good stage fitting ability and trend perception ability, and can effectively support the strength prediction and full-cycle performance evaluation of aluminum foam materials.

Claims

1. A method for predicting the strength of aluminum foam materials based on multi-source data, characterized in that, Includes the following steps: S1. Collect strength data of aluminum foam materials and construct a dataset suitable for predicting the strength of aluminum foam materials. The specific steps are as follows: To address the strength prediction problem of aluminum foam, strength monitoring equipment, including strain gauges and accelerometers, was installed to ensure coverage of different stress levels, loading rates, and ambient temperature conditions. This was combined with the material's physical parameters, 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, airflow velocity, and the type and concentration of corrosive media, to form three-dimensional strength response data encompassing time, space, and material properties. The collected data was normalized and divided into test and training sets for training and evaluating the performance of the aluminum foam strength prediction model. 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 construction module, build a three-parameter dynamic scale control system, and generate dynamic heterogeneous multi-scale sub-sequences; S31. Define the local time scale adjustment factor, and design three sets of parameters: local rate of change, local oscillation rate, and local response amplitude, which together determine the local time scale adjustment factor. S32. Accumulate local scale adjustment factors, construct a dynamic time distortion axis, sample on the new time axis, and generate a curved time series; S33. Perform multi-frequency-saliency structure-driven multi-scale construction on the curved time series to drive the saliency of multi-frequency features in the time series, thereby realizing the extraction of multi-scale features. S4. Construct a scale interaction module, introduce scale phase variables and scale energy conservation and migration mechanism to 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 are achieved through similarity matrix; S43. Design local enhancement coefficients to enhance features within scale; S5. Establish consistency constraints and scale-specific preservation, dynamically integrate all scale predictions through an adaptive coordination function, and input the processed aluminum foam 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, Local time scale adjustment factor in step S31 By calculating the distance between the current and previous observations, the local rate of change is obtained to reflect the instantaneous change characteristics of the sequence. Using the weighted difference between the current and two previous observations, the local oscillation rate is calculated to characterize the oscillation intensity of the sequence. Furthermore, based on the local rate of change, a nonlinear adjustment function is introduced to perform nonlinear mapping on the response amplitude. The specific formula is as follows: ； In the formula, It is the Sigmoid function, ensuring , , , There are three learnable weight parameters. For bias terms; in, The local rate of change is given by the following formula: ； Where, For the original sequence at time... The observed values, It is the Euclidean norm; in, The local oscillation rate is given by the following formula: ； Where, For the original sequence at time... The observed values, It is the Euclidean norm; in, The local response amplitude is given by the following formula: ； In the formula, To control the hyperparameters of nonlinear amplitude amplification, It 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 distortion axis is based on the cumulative calculation 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 distortion 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 calculates the value of the new sampling point between adjacent observations of the original time series according to the interpolation weight, thus completing the generation of the warped time series of the original series. The specific formula is as follows: ； In the formula, For a moment The local timescale adjustment factor, For a moment The cumulative local time scale factor; Sampling is performed on a new timeline to generate a curved time series. The specific formula is as follows: ； Where, For the new number of sampling points, On the new timeline The specific calculation formula is as follows: (Number of sampling points) ； Where, For a moment The cumulative local timescale factor, Rounding up; New sampling points are obtained by using linear interpolation to acquire the sampled data. The specific formula is as follows: ； In the formula, For the first part of the original sequence 1 node The interpolation weights are given by the following formula: ； Where, For nodes The cumulative local timescale factor, The time after resampling The cumulative local timescale factor.

4. The method for predicting the strength of aluminum foam material based on multi-source data according to claim 3, characterized in that, Step S33 involves multi-frequency-saliency structure-driven multi-scale construction, specifically as follows: First, for curved time series Perform sliding window analysis to obtain frequency factors The specific formula is as follows: ； In the formula, For The spectrum of the center small window, For frequency domain variables, High-frequency threshold; Secondly, calculate the significance factor. The specific formula is as follows: ； In the formula, For the Euclidean norm, The new sampling points are obtained through linear interpolation; Thirdly, for each scale Define a frequency preference range This indicates the frequency band that the scale focuses on. The specific formula is as follows: ； Frequency preference range The specific formula is: ； Where, For scale The corresponding lower frequency bound, scale The corresponding upper frequency bound; For each moment ,scale In the window Inner aggregation features, resulting in aggregation features The specific formula is as follows: ； In the formula, For activation function, As a significant factor, For scale-focused frequency bands, The width of the window is given by the following formula: ； Where, Minimum window size, Scaling factor For different scales, ; Fourth, dynamic aggregation yields each scale. Aggregate sequence representation The specific formula is as follows: ； Where, For scale Aggregation features within the window; Aggregate each scale Sequence representation To obtain multi-scale sequences The specific formula is as follows: ； In the formula, For scale The sequence length, For scale The aggregation representation, For feature dimensions.

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, a phase field is defined for each scale. The specific formula is as follows: ； Where, For sampling nodes, , The phase projection matrix, For paranoia, For sampling nodes lower scale The aggregate sequence representation; Construction Scale and scale Phase similarity matrix between The specific formula is as follows: ； In the formula, For index operations, and All are sampling nodes. , , This is the phase sensitivity hyperparameter.

6. The method for predicting the strength of foamed aluminum material based on multi-source data according to claim 5, characterized in that, In step S42, the node energy at each scale is calculated. The specific formula is as follows: ； In the formula, For the first Lower scale of each sampling node The aggregation representation, It is the Euclidean norm; Energy transfer is performed using the similarity matrix to obtain the scale... Migration to scale On the node energy The specific formula is as follows: ； Where, For scale At the node The energy of the next node, For scale The sequence length; Computational scale The difference between actual energy and received energy The specific formula is as follows: ； Where, For scale At the node The energy of the next node, scale At the node The energy received from the next node; Update scale Inter-scale feature representation The specific formula is as follows: ； In the formula, This is a 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, local enhancement coefficients are designed to perform intra-scale feature enhancement, resulting in a scale-enhanced sequence. The specific formula is as follows: ； In the formula, For nodes The local neighborhood, For nodes lower scale Updated inter-scale feature representation; The Gaussian kernel-normalized weights based on phase difference are formulated as follows: ； In the formula, For scale phase field, For the Euclidean norm, For nodes The local neighborhood, This refers to the phase sensitivity hyperparameter; Design local enhancement coefficient The specific formula is as follows: ； Where, For the Sigmoid function, It is a fixed constant; The local phase energy coupling function is given by the following formula: ； Where, For scale At the node The energy of the nodes below; The local phase difference is given by the following formula: ； Where, For nodes The local neighborhood, For scale phase field, It 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, for each scale Perform individual predictions to obtain each scale Prediction results The specific formula is as follows: ； In the formula, For scale-enhanced sequences, MLP stands for Multilayer Perceptron; For any scale pair and Establish collaborative constraints and define consistency loss. The specific formula is as follows: ； In the formula, For scale The prediction results It is the Euclidean norm; The average consistency loss is obtained by averaging the consistency losses of all scale pairs. The specific formula is as follows: ； In the formula, For the largest scale; Define each scale Local frequency features of the prediction results The specific formula is as follows: ； Where, For Fast Fourier Transform; Define the dissimilarity of frequency features between scales The specific formula is as follows: ； Where, To normalize the row vectors, for each time step The specific formula is as follows: ; Where, For scale Local frequency characteristics, For the Euclidean norm, A small constant to prevent division by zero errors; The average dissimilarity of frequency features across all scale pairs is obtained by averaging the dissimilarity of these features. The specific formula is as follows: ； Define the fusion weights for each scale The specific formula is as follows: ； Where, For scale The prediction results For the Euclidean norm, For index operations; The fusion weights are normalized to obtain the normalized fusion weights. The specific formula is as follows: ； In the formula, the denominator This represents the sum of all scale weights; The final prediction result after fusion is The specific formula is as follows: ； Fusion prediction loss Average consistency loss and frequency characteristic dissimilarity The specific formula is as follows: ； In the formula, For prediction error, MSE is used. The weight of consistency loss, Weights for frequency characteristic dissimilarity.

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