Nonlinear structure impact load identification method based on physically guided deep learning

Abstract

The invention discloses a non-linear structure impact load identification method based on physically guided deep learning, and belongs to the technical field of structure health monitoring and intelligent diagnosis. By constructing an enhanced robust neural network, innovatively combining deep learning technologies such as multi-scale convolution, a self-adaptive long-short-term memory network and a multi-head attention mechanism, and integrating knowledge such as physical constraints, high-precision recognition of impact loads of a nonlinear structure system is realized. The core innovation of the method comprises the following steps: designing a self-adaptive preprocessing assembly line, and automatically selecting an optimal processing strategy according to data characteristics; a multi-path nonlinear feature extractor with physical significance is constructed, and nonlinear features of different orders are effectively captured through linear, secondary and tertiary feature path parallel processing; providing a physically guided adaptive loss function, and comprehensively considering a plurality of physical constraints such as time-frequency domain consistency, peak value, energy conservation, gradient continuity and the like; a self-adaptive LSTM block is developed, and the time sequence modeling capability is enhanced through a gating mechanism and residual connection.

Description

Technical Field

[0001] This invention relates to the fields of structural health monitoring, load identification, and intelligent diagnosis, and in particular to a nonlinear structural impact load identification method based on physics-guided deep learning, which can be widely applied to structural safety assessment and health management in aerospace, civil engineering, mechanical engineering, marine engineering and other fields. Background Technology

[0002] Structural load identification is one of the core technologies of structural health monitoring (SHM). In engineering practice, directly measuring external loads acting on a structure is often difficult or infeasible, especially impact loads, which are characterized by short duration, large peak value, and wide bandwidth, making direct measurement even more challenging. Therefore, indirect methods that identify external loads by measuring structural response have significant engineering value and scientific significance.

[0003] Traditional load identification methods mainly fall into two categories: frequency domain methods and time domain methods. Frequency domain methods are based on the frequency response function (FRF) or transfer function, and load identification is achieved through frequency domain inversion. Representative methods include the inverse frequency response function method, modal analysis method, and transfer path analysis. These methods have clear principles and high computational efficiency, but they have the following limitations: (1) they assume the system is linear and cannot handle nonlinear problems; (2) they have low accuracy in identifying transient loads; (3) they suffer from severe ill-conditioning when inverting the frequency response function matrix; and (4) they require complete modal information.

[0004] Time-domain methods directly identify loads in the time domain, mainly including deconvolution methods, state-space methods, Kalman filtering methods, and regularization methods. These methods can obtain the load time history and are suitable for transient load identification, but they also have shortcomings: (1) they are sensitive to measurement noise; (2) they have high computational complexity; (3) they require an accurate system model; and (4) they have significant error accumulation effects.

[0005] In recent years, with the rapid development of artificial intelligence technology, deep learning methods have shown great potential in the field of payload recognition. Convolutional Neural Networks (CNNs) can automatically extract spatial features, Recurrent Neural Networks (RNNs) and Long Short-Term Memory Networks (LSTMs) are adept at processing temporal information, and attention mechanisms can capture long-range dependencies. However, existing deep learning payload recognition methods still have the following problems:

[0006] (1) Pure data-driven black box models lack physical constraints and interpretability, and have poor generalization ability when training data is insufficient or exceeds the training conditions.

[0007] (2) The nonlinear characteristics of the structural system were not fully considered, and there was a lack of targeted design for different types of nonlinearity such as geometric nonlinearity, material nonlinearity, and contact nonlinearity;

[0008] (3) Insufficient feature extraction and failure to effectively utilize multi-scale spatiotemporal features and frequency domain information;

[0009] (4) The loss function design is simple, only considering the prediction error and ignoring the physical consistency constraint;

[0010] (5) Lacking an adaptive processing mechanism, it is unable to automatically adjust the processing strategy according to the characteristics of the data.

[0011] The emergence of Physics-Informed Neural Networks (PINNs) offers a new approach to solving the aforementioned problems. By embedding physical constraints such as governing equations, boundary conditions, and initial conditions into the neural network training process, the accuracy and generalization ability of the model can be significantly improved. However, existing PINN methods are mainly designed for solving forward problems, and their application in inverse problems such as load identification is still immature.

[0012] In conclusion, developing an intelligent load identification method that can effectively handle nonlinearity, has physical consistency, and is robust has significant theoretical and practical value. Summary of the Invention

[0013] To address the shortcomings of existing technologies, the present invention aims to provide a method for identifying impact loads on nonlinear structures based on physics-guided deep learning. This method achieves high-precision identification of impact loads on various nonlinear structural systems by constructing an enhanced robust neural network and combining innovative designs such as adaptive preprocessing, multi-scale feature extraction, and physical constraint loss.

[0014] The technical problems to be solved by this invention include: (1) how to design an adaptive data preprocessing strategy and select the optimal processing method for different data characteristics; (2) how to construct a deep network architecture that can effectively handle various nonlinearities; (3) how to integrate physical constraints and domain knowledge into the deep learning framework; (4) how to improve the robustness of the model in noisy environments; and (5) how to ensure that the computational efficiency of the model meets the real-time monitoring requirements.

[0015] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0016] First, an adaptive preprocessing pipeline is designed. Based on the characteristics of the input data (linear, nonlinear, noise level), the appropriate processing strategy is automatically selected. For linear or slightly nonlinear data, standard filtering and basic feature extraction are used; for strongly nonlinear data, mild filtering is used to preserve nonlinear features and extract additional nonlinear features; for noisy data, robust outlier detection and adaptive filtering are employed.

[0017] Secondly, an Enhanced Robust Neural Network (ERN) is constructed. The network architecture innovatively integrates several specially designed modules: (1) the input projection layer maps the original data to a high-dimensional feature space; (2) the multi-scale convolution module uses parallel convolutions with 5 different kernel sizes to capture multi-scale spatiotemporal features; (3) the nonlinear feature extractor extracts nonlinear features of different orders through three parallel paths (linear, quadratic, and cubic); (4) the peak detection enhancement module specifically identifies and enhances the response of peak regions; (5) the adaptive LSTM block enhances the temporal modeling capability through gating mechanism and residual connection; (6) the multi-head attention mechanism captures long-range dependencies; and (7) the output layer generates the final prediction through a multi-layer fully connected network.

[0018] Third, a physics-guided adaptive loss function is designed. In addition to the basic mean squared error and L1 loss, several physical constraint terms are introduced: peak loss ensures accurate identification of load peaks; correlation loss improves overall waveform matching; gradient loss and acceleration loss guarantee the accuracy of dynamic characteristics; frequency domain loss maintains spectral consistency; and energy loss ensures energy conservation. The weights of the loss function are adaptively adjusted according to the data type, achieving targeted optimization.

[0019] Fourth, advanced training strategies are employed. The AdamW optimizer combined with the OneCycleLR learning rate scheduler is used to achieve efficient and stable training. Overfitting is prevented through techniques such as data augmentation, gradient pruning, and early stopping. Multiple evaluation metrics are monitored during training to select the optimal model.

[0020] Fifth, implement a comprehensive evaluation system. In addition to conventional indicators such as correlation coefficient and mean square error, time-domain indicators (peak error, time offset, rise time, settling time), frequency-domain indicators (spectral correlation, dominant frequency error, total harmonic distortion), and energy indicators (total energy error, energy distribution) are introduced to comprehensively evaluate recognition performance.

[0021] The beneficial effects of this invention are:

[0022] (1) High recognition accuracy: It has excellent performance in geometric nonlinearity, material nonlinearity and combined nonlinearity, with an average correlation coefficient of 0.973, which is significantly better than traditional methods;

[0023] (2) Excellent time-domain accuracy: The average peak error is only 4.0% and the time offset is 3.1ms, which accurately captures the transient characteristics of the load;

[0024] (3) Strong robustness: In a strong noise environment with a signal-to-noise ratio of 10dB, the correlation coefficient still remains above 0.92, demonstrating excellent noise resistance;

[0025] (4) High computational efficiency: The inference time for a single sample is less than 10ms, which meets the requirements of real-time monitoring;

[0026] (5) Good physical consistency: Physical constraints ensure that the prediction results conform to the mechanical principles, with energy error less than 5% and spectral correlation greater than 0.97;

[0027] (6) Strong generalization ability: Through physical guidance and adaptive mechanism, the model can be generalized to working conditions outside the training set;

[0028] (7) Good interpretability: Each module of the network has a clear physical meaning, which is easy to understand and debug. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the overall process of the method of the present invention, which shows the complete process from data acquisition to payload identification.

[0030] Figure 2 This is a detailed schematic diagram of the Enhanced Robust Neural Network (ERN), which shows the input and output dimensions and connections of each module.

[0031] Figure 3 This is a schematic diagram of the internal structure of a nonlinear feature extractor, showing the specific design of three parallel paths.

[0032] Figure 4 This is a schematic diagram of the adaptive LSTM block, including the detailed design of the gating mechanism and residual connections.

[0033] Figure 5 This is a flowchart of the multi-head attention mechanism, showing the parallel computation process of eight attention heads.

[0034] Figure 6 This is a comparison chart of load identification results for planar aerospace composite material plates.

[0035] Figure 7 This is a comparison chart of load identification results for a typical frame structure.

[0036] Figure 8 It is a time-domain history analysis diagram under different nonlinear conditions, including complete time-domain comparison, local magnification, error distribution and cumulative analysis.

[0037] Figure 9This is a comparison chart of recognition performance under different noise levels, demonstrating the robustness of the method. Detailed Implementation

[0038] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0039] Example 1: Impact Load Identification of Geometrically Nonlinear Cantilever Beam Structures

[0040] This embodiment addresses the geometric nonlinearity caused by large deformation, verifying the effectiveness of the method of the present invention.

[0041] Step 1: Experimental System Setup and Data Acquisition

[0042] An aluminum alloy cantilever beam with a length of 500 mm, a width of 50 mm, and a thickness of 5 mm was used as the experimental object. An impact load was applied to the free end of the beam, causing the maximum deflection to reach 15% of the beam length, resulting in a significant geometric nonlinear effect. Three piezoelectric accelerometers were placed on the beam at locations L / 4, L / 2, and 3L / 4, with a sampling frequency of 20 kHz.

[0043] Impact loads of varying amplitudes and pulse widths were applied using a hammer, and 200 sets of load-response data were collected. The peak impact load ranged from 50 to 200 N, and the pulse width ranged from 5 to 20 ms. Each set of data included a 3-channel acceleration response (3×2048 dimensions) and the corresponding impact load time history (1×2048 dimensions).

[0044] Step 2: Data Preprocessing

[0045] First, a data quality check is performed to remove data from faulty sensors or those with abnormal acquisition. Then, the degree of nonlinearity is determined based on the von Mises stress level. When the stress exceeds 80% of the yield strength, it is classified as strong geometric nonlinearity, and an appropriate preprocessing strategy is adopted.

[0046] In the feature extraction stage, a 3-level decomposition is performed using the db6 wavelet basis to extract wavelet coefficients at each level. The Hilbert envelope is calculated to capture transient features. Gradient features are extracted to reflect dynamic changes. For geometric nonlinearities, additional nonlinear features such as square and cube terms are calculated.

[0047] Step 3: Network Construction and Configuration

[0048] An ERN network was constructed with an input dimension of 18 (3 channels × 6 classes of features), a hidden dimension of 256, and an output dimension of 512. The total number of network parameters is approximately 4.8 million.

[0049]

[0050] Step 4: Model Training

[0051] The 200 datasets were divided into a training set (140 datasets), a validation set (30 datasets), and a test set (30 datasets) in a 7:1.5:1.5 ratio. The training configuration is as follows:

[0052] Optimizer: AdamW, learning rate 5e-4, weight decay 1e-5

[0053] Batch size: 32

[0054] Maximum number of rounds: 500

[0055] Early stop strategy: Stop if losses do not decrease after 50 rounds.

[0056] Learning rate scheduling: OneCycleLR, maximum learning rate 5e-4

[0057] During training, the weights of the loss function were set as follows: wmse = 0.5, wpeak = 2.0, wcorr = 2.5, wgrad = 0.8, wfreq = 1.0, emphasizing the accuracy of peak values ​​and correlation.

[0058] Step 5: Results and Analysis

[0059] The model achieved its best performance in round 285, with a correlation coefficient of 0.998 on the validation set. Evaluation results on the test set:

[0060] Correlation coefficient: 0.999 ± 0.001

[0061] R 2 Score: 0.982 ± 0.015

[0062] Peak error: 2.8% ± 0.9%

[0063] Time offset: 1.7 ± 0.6 ms

[0064] Spectral correlation: 0.993 ± 0.004

[0065] Energy error: 1.8% ± 0.7%

[0066] Figure 8 Typical identification results are shown, with the predicted load almost perfectly matching the actual load. The results demonstrate that the method of this invention has extremely high identification accuracy for geometric nonlinearities.

[0067] Example 2: Impact Load Identification of Elastic-Plastic Nonlinear Steel Plates

[0068] This embodiment studies the influence of material nonlinearity on load identification.

[0069] Experimental setup

[0070] The device uses a 300mm×300mm×10mm Q235 steel plate, fixed on all four sides. Plastic deformation is induced by drop hammer impact, with a yield stress of 235MPa. A 5×5 accelerometer array with 25 measuring points is used.

[0071] Data characteristics

[0072] Once the material enters the plastic phase, its stiffness degrades significantly, and the response exhibits strong nonlinearity. 150 sets of data were collected, including 50 sets of elastic response, 50 sets of elastoplastic transition data, and 50 sets of fully plastic response data.

[0073] Preprocessing strategy

[0074] Determining the degree of nonlinearity based on equivalent plastic strain:

[0075] εp < 0.001: Linear processing

[0076] 0.001≤εp<0.01: Slight nonlinear treatment

[0077] εp≥0.01: Strong nonlinear processing

[0078] Training and Results

[0079] The same network configuration as in Example 1 was used, but the weights of the loss function were adjusted to accommodate the nonlinear characteristics of the material. The network converged after 180 training epochs.

[0080] Test results:

[0081] Elastic phase: Correlation coefficient 0.985

[0082] Elastic-plastic transition: Correlation coefficient 0.974

[0083] Perfect plasticity: Correlation coefficient 0.968

[0084] Overall average: Correlation coefficient 0.976

[0085] The results show that this method maintains high recognition accuracy even under strong material nonlinearity conditions.

[0086] Example 3: Contact Nonlinear Load Identification of a Gap-Hinged Structure

[0087] System Description

[0088] In a three-degree-of-freedom chain system, a 0.5mm gap exists at the hinge, resulting in contact nonlinearity. Impact loads cause collisions and separations, leading to a highly nonlinear response.

[0089] Challenges and Solutions

[0090] Contact nonlinearity exhibits strong discontinuities, rendering traditional methods ineffective. This invention addresses this issue through the following strategy:

[0091] 1. Capture collision transients using denser sampling (50kHz)

[0092] 2. Add non-linear feature dimensions

[0093] 3. Strengthen the loss weight of high-frequency components

[0094] Recognition results

[0095] Contact phase: Correlation coefficient 0.912

[0096] Separation phase: Correlation coefficient 0.945

[0097] Overall: Correlation coefficient 0.928

[0098] Although dealing with nonlinearity is the most challenging aspect, this method still achieves good results.

[0099] Example 4: Noise Robustness Test

[0100] Based on the data from Example 1, different levels of Gaussian white noise were added to test robustness.

[0101] Test Results

[0102]

[0103]

[0104] Even under strong noise with an SNR of 10 dB, the correlation coefficient still exceeds 0.92, demonstrating the strong robustness of the method.

[0105] Example 5: Comparison with existing methods

[0106] Comparing multiple methods on the same dataset:

[0107]

[0108] This invention is significantly superior to existing methods in all metrics.

[0109] Example 6: Ablation Experiment

[0110] By gradually removing each module, we can analyze its contribution:

[0111]

[0112] The results show that adaptive preprocessing and physical loss contribute the most, verifying the importance of physical guidance.

[0113] Example 7: Practical Engineering Application

[0114] The method was applied to ground vibration tests on the wings of a certain type of aircraft.

[0115] Application Background: The wing is 8m long and made of composite materials. Vibration tests are conducted at multiple points. Traditional methods, due to the anisotropy and large deformation nonlinearity of composite materials, have an identification accuracy of only 0.65.

[0116] Application results:

[0117] 32 accelerometers were deployed

[0118] Collect 500 sets of excitation data

[0119] Model training for 12 hours

[0120] Relevance coefficient: 0.894

[0121] Peak error: 7.3%

[0122] The reliable load data provided for structural optimization demonstrates the practical value of this invention in engineering applications.

[0123] Summary of technical effects

[0124] Through verification using multiple embodiments, the present invention demonstrates the following technical advantages:

[0125] 1. Wide applicability: Effective for various nonlinearities including geometric, material, and contact nonlinearities;

[0126] 2. High precision: Correlation coefficients generally exceed 0.95, and peak error is less than 5%;

[0127] 3. Strong robustness: It maintains a correlation of over 0.92 even under 10dB noise;

[0128] 4. Fast reasoning: Single recognition is completed within 10ms, meeting real-time requirements;

[0129] 5. Physical consistency: The prediction results conform to the principles of mechanics and are highly interpretable;

[0130] 6. Practical application in engineering: It has been successfully applied in actual engineering projects.

[0131] This invention provides an accurate, robust, and efficient solution for load identification of nonlinear structures, with broad application prospects in structural health monitoring, fault diagnosis, and life prediction. With the continuous development of deep learning technology, this method can be further extended to more complex engineering problems.

[0132] Industrial applicability

[0133] The method of this invention can be widely applied in the following industrial fields:

[0134] Aerospace: Load monitoring of aircraft wings and fuselages; dynamic load identification during rocket launches; micro-vibration analysis of satellites in orbit. Civil Engineering: Vehicle load identification on bridges; wind load monitoring of high-rise buildings; structural response analysis under seismic loads. Mechanical Engineering: Unbalanced load identification of rotating machinery; fault load diagnosis of gearboxes; automotive collision load reconstruction.

[0135] Marine engineering: wave load identification of offshore platforms; ice load monitoring of ships; impact load analysis of subsea pipelines.

[0136] Rail transit: wheel-rail load identification for high-speed trains; dynamic loads caused by track irregularities; impact loads during braking. This invention has applied for relevant software copyrights, and the core algorithm has been packaged into an industrial software module that can be integrated into existing structural health monitoring systems.

Claims

1. A method for identifying impact load of a nonlinear structure based on physically guided deep learning, characterized in that, The method comprises the following steps: Step 1: data collection and organization, for a target structure system, collecting dynamic response data of the structure under impact load through an acceleration sensor, and constructing a load-response data pair, wherein the acceleration response data has a dimension of CxT, C is a sensor channel number, and T is a time series length; Step 2: adaptive data preprocessing, comprising: Step 2.1: outlier detection and processing, using the interquartile range (IQR) method to identify and clip outliers; Step 2.2: selecting a filtering strategy according to the data type, using an 11-point window 3-order Savitzky-Golay filter for linear data, using a 5-point window 2-order filter for nonlinear data, and adaptively adjusting the filter parameters according to the signal-to-noise ratio for noise data; Step 2.3: data standardization, recording the mean and standard deviation for reverse normalization; Step 2.4: feature extraction, including wavelet decomposition, Hilbert envelope, gradient feature and nonlinear feature; Step 3: constructing an enhanced robust neural network model, the network structure comprising: Input projection layer: Xproj = ReLU (BatchNorm (Conv1D (Xinput, Wproj))), wherein Wproj is a learnable convolution kernel; Multi-scale convolution module: using five parallel one-dimensional convolution layers with kernel sizes of {3, 5, 7, 9, 11}; Nonlinear feature extractor: containing three parallel paths to extract linear, quadratic and cubic features respectively; Peak detection enhancement module: identifying and enhancing the peak region through a special convolution layer; Adaptive LSTM block: containing 3 layers of bidirectional LSTM with gating mechanism and residual connection; Multi-head attention mechanism: 8 heads of self-attention layers capture long-range dependencies; Output layer: a multi-layer fully connected network generates load prediction; Step 4: designing a physically guided adaptive loss function: Ltotal = wmse·Lmse + wpeak·Lpeak + wcorr·Lcorr + wgrad·Lgrad + waccel·Laccel + wfreq·Lfreq + wenergy·Lenergy Wherein Lmse is the mean square error loss, Lpeak is the peak error loss, Lcorr is the correlation loss, Lgrad is the first-order gradient loss, Laccel is the second-order gradient loss, Lfreq is the frequency domain loss, Lenergy is the energy loss, and the weight w is adaptively adjusted according to the data type; Step 5: model training and optimization: Using AdamW optimizer, initial learning rate 5x10^-4, weight decay 1x10^-5; Using OneCycleLR learning rate scheduler, cosine annealing strategy; Batch size 32, maximum training rounds 500, early stopping patience value 50; Gradient clipping threshold 1.0 to prevent gradient explosion; Step 6: load identification and post-processing: Input the preprocessed test data into the trained model to obtain the initial prediction result, and perform post-processing through a smoothing filter to finally output the identified impact load time course.

2. The method of claim 1, wherein, The feature extraction in step 2.4 specifically comprises: Wavelet decomposition: linear data is decomposed by db4 wavelet basis with 2 layers, nonlinear data is decomposed by db6 wavelet basis with 3 layers; Hilbert envelope: signal envelope is extracted by Hilbert transform; Gradient feature: first derivative of signal is calculated; Nonlinear feature: for nonlinear data, square term, cubic term, sign function transformed term, and energy, kurtosis, skewness, zero-crossing rate, wave crest factor, etc. statistical features are additionally calculated.

3. The method of claim 1, wherein, The three paths of the nonlinear feature extractor are: Linear path: Xlinear = ReLU(BatchNorm(Conv1D(Xproj))); Quadratic path: Xquad = Tanh(BatchNorm(Conv1D(Xproj))) + 0.1 * Xquad^2; Cubic path: Xcubic = Sigmoid(BatchNorm(Conv1D(Xproj))) + 0.05 * Xcubic^3; The final output is the concatenation of the three paths: Xnonlinear = Concat([Xlinear, Xquad, Xcubic]).

4. The method of claim 1, wherein, The gating mechanism of the adaptive LSTM block is: LSTM output: ht, ct = BiLSTM(xt, ht-1, ct-1); Gating weight: gt = σ(Wg·ht + bg), where σ is the sigmoid activation function; Residual projection: residual = Wr·xt; Final output: ot = gt⊙ht + (1-gt)⊙residual, where ⊙ represents element-wise multiplication.

5. The method of claim 1, wherein, The calculation process of the multi-head attention mechanism is: Query, key, and value projection: Q = XWQ, K = XWK, V = XWV; Attention weight: Attention(Q, K, V) = softmax(QK^T / √dk)V; Concatenate after multi-head parallel calculation: MultiHead = Concat(head1,...,head8)WO; Where dk is the dimension of the key, WQ, WK, WV, WO are learnable parameter matrices.

6. The method of claim 1, wherein, The weights of the loss function are adaptively adjusted according to the data type: nonlinear data: emphasize peak value, correlation and frequency domain features, (wmse, wpeak, wcorr, wfreq) = (0.5, 2.0, 2.5, 1.0); Noise data: balance each index, (wmse, wpeak, wcorr, wfreq) = (0.6, 1.5, 2.0, 0.8); Linear data: focus on basic error, (wmse, wpeak, wcorr, wfreq) = (1.0, 1.0, 1.5, 0.5).

7. The method of claim 1, wherein, The method further includes a data augmentation step, which expands the training data by adding different levels of Gaussian noise, random time shift, amplitude scaling, etc. to enhance the model's generalization ability.

8. The method of claim 1, wherein, The method further includes a model integration step, which trains multiple models with different initializations and obtains the final prediction result through weighted averaging or voting mechanism.

9. The method of claim 1, wherein, The method is suitable for various nonlinear types, including but not limited to: Geometric nonlinearity: stiffness change caused by large deformation; Material nonlinearity: material constitutive relationship such as elastoplasticity, damage, fatigue, etc. Contact nonlinearity: contact behavior such as friction, gap, collision, etc. Combined nonlinearity: coupling of multiple nonlinear mechanisms.

10. The method of claim 1, wherein, The method also includes uncertainty quantification, which evaluates the confidence interval of the prediction result through Monte Carlo Dropout or deep ensemble method.

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