Source-linked AI summary
Physics-guided Convolutional Neural Network (PhyCNN) for Data-driven Seismic Response Modeling
Ruiyang Zhang, Yang Liu, Hao Sun
TL;DR
Structural response prediction from sensing data remains challenging, especially with limited use of advanced deep learning models. The paper proposes PhyCNN, which combines data-driven learning with physics constraints and uses the trained model for seismic response prediction and serviceability analysis. Numerical and experimental examples report accurate predictions and performance improvements over conventional pure data-based neural networks.
Problem
Structural response prediction under future hazards remains challenging, while relatively few studies use advanced deep learning models for this task.
Method
PhyCNN embeds physics knowledge into a CNN trained on seismic input-output datasets and uses K-means clustering to partition limited datasets.
Results
PhyCNN accurately predicts structural responses and outperforms conventional pure data-based neural networks across numerical and experimental examples.
Takeaways & Limitations
The trained PhyCNN functions as a surrogate for seismic response prediction and supports fragility analysis using specified serviceability criteria.
Takeaways & Limitations
Serviceability analysis uses drift angle because inter-story drifts are unavailable from the sensor locations.
Abstract
from arXiv · showhide
Seismic events, among many other natural hazards, reduce due functionality and exacerbate vulnerability of in-service buildings. Accurate modeling and prediction of building's response subjected to earthquakes makes possible to evaluate building performance. To this end, we leverage the recent advances in deep learning and develop a physics-guided convolutional neural network (PhyCNN) framework for data-driven seismic response modeling and serviceability assessment of buildings. The proposed PhyCNN approach is capable of accurately predicting building's seismic response in a data-driven fashion without the need of a physics-based analytical/numerical model. The basic concept is to train a deep PhyCNN model based on available seismic input-output datasets (e.g., from simulation or sensing) and physics constraints. The trained PhyCNN can then used as a surrogate model for structural seismic response prediction. Available physics (e.g., the law of dynamics) can provide constraints to the network outputs, alleviate overfitting issues, reduce the need of big training datasets, and thus improve the robustness of the trained model for more reliable prediction. The trained surrogate model is then utilized for fragility analysis given certain limit state criteria (e.g., the serviceability state). In addition, an unsupervised learning algorithm based on K-means clustering is also proposed to partition the limited number of datasets to training, validation and prediction categories, so as to maximize the use of limited datasets. The performance of the proposed approach is demonstrated through three case studies including both numerical and experimental examples. Convincing results illustrate that the proposed PhyCNN paradigm outperforms conventional pure data-based neural networks.
1. Introduction
Structural response prediction from sensing data remains challenging, particularly with limited use of advanced deep learning models. This paper develops PhyCNN to address data-driven modeling of nonlinear seismic time-history responses.
- Structural response prediction under future hazards remains a challenge despite sensing-based identification, model-updating, and analytical methods.
- Existing studies have reported very limited use of advanced deep learning models, including recurrent and convolutional neural networks, for structural response modeling.
- PhyCNN embeds available physics knowledge into a deep CNN trained on seismic input-output datasets for nonlinear structural seismic time-history prediction.
- The trained PhyCNN serves as a surrogate model for response prediction and can support fragility analysis under specified limit-state criteria.
- Physics constraints are intended to alleviate overfitting, reduce the need for large training datasets, and improve prediction robustness.
2. Physics-guided Convolutional Neural Network (PhyCNN)
PhyCNN combines a one-dimensional CNN, a graph-based tensor differentiator, and physics constraints to model nonlinear dynamic responses from ground-motion time sequences. Its loss combines measurement agreement with physical consistency while preserving temporal output length.
- PhyCNN maps ground acceleration or displacement sequences to state-space outputs containing displacement, velocity, and mass-normalized restoring force.
- The graph-based tensor differentiator computes time derivatives of predicted state variables for constructing the physics loss.
- The total objective combines data loss from measurements with physics loss constraining dependencies among output features.
- Measurements need not cover the complete state because the data loss can use partial state variables or acceleration measurements.
- Convolution Layer: Convolution kernels slide across temporal sequences to capture time dependency, while zero-padding preserves the input sequence length.
- Convolution Layer: The example convolution uses n = 10, k = 5, and s = 1, producing an output length of 10 with shared receptive-field weights.
- Pooling is avoided for time-series regression because temporal down-sampling produces shorter output sequences.
3. Numerical Validation
Numerical examples evaluate PhyCNN for nonlinear structural response prediction, including displacement, velocity, restoring force, and latent displacement prediction from acceleration-only training. Embedding physics constraints improves prediction relative to conventional CNN, including for unknown earthquakes and limited measurements.
- Case 1: Available Measurements: The first numerical example uses a 1DOF nonlinear system with simulated earthquake data and available measurements of displacement, velocity, and restoring force.The system includes linear and nonlinear stiffness terms, with 100 simulated seismic sequences sampled for 1,001 points each.
- Case 1: Available Measurements: PhyCNN substantially improves displacement prediction over CNN across 90 unknown-earthquake datasets.For four examples, PhyCNN correlation coefficients are 0.95, 0.92, 0.87, and 0.61, versus 0.60, 0.72, 0.66, and 0.37 for CNN.
- Case 1: Available Measurements: PhyCNN also predicts velocity and normalized nonlinear restoring force in agreement with the ground truth, including their time histories and hysteresis behavior.The predicted restoring force is evaluated against displacement and velocity through hysteresis plots.
- Case 2: Available Measurements: The second numerical example trains PhyCNN using only acceleration measurements, with 50 datasets for training and 50 unknown datasets for testing.The network differentiates predicted displacement to calculate acceleration and optimizes an acceleration-based objective.
- Case 2: Available Measurements: 0.9: Most predicted accelerations have correlation coefficients above 0.9, while predicted displacements mainly exceed 0.8.Even the worst acceleration example, r = 0.75, reasonably matches the ground truth in magnitude and phase.
- Case 2: Available Measurements: PhyCNN produces accurate displacement predictions from limited acceleration-only training data, demonstrating latent response prediction.This addresses settings where displacement measurements are unavailable for training.
4. Experimental Validation of PhyCNN Performance
Experimental validation applies PhyCNN to limited sensing data from a six-story hotel, using K-means-based dataset partitioning and physics-guided response prediction. The model predicts structural displacements for observed and larger-intensity earthquakes and supports serviceability fragility analysis.
- 4.1. 6-Story Hotel Building in San Bernardino, CA: The six-story San Bernardino hotel uses nine accelerometers, and 23 historical CESMD datasets train PhyCNN for displacement prediction and fragility assessment.Sensors are installed on the 1st, 3rd, and roof floors in both directions, with records spanning 1987–2018.
- 4.2. K-means clustering: K-means clustering partitions limited sensing data into training, validation, and prediction sets using cluster structure, convex-envelope boundary samples, and centroid-near samples.The elbow method selects k = 4; 11 datasets are selected for training, while validation data are sampled across clusters.
- 4.2. K-means clustering: The processed data relate ground acceleration inputs to structural displacement outputs after filtering measured accelerations and deriving displacement time series.A 2-pole Butterworth high-pass filter with a 0.1 Hz cutoff removes low-frequency behavior before displacement estimation.
- 4.3. Predicted displacements using PhyCNN: Prediction errors remain mainly within 5% for the 3rd floor and roof, with confidence intervals of 97% and 93%, respectively.The predictions match historical sensing data for Big Bear Lake 2014 and Loma Linda 2016 earthquakes with different magnitudes and frequency contents.
- 4.3. Predicted displacements using PhyCNN: PhyCNN predicts structural responses for larger Northridge 1994 and Landers 1992 earthquakes outside the boundary of interest, supporting its use in serviceability or fragility assessment.These cases test extrapolation beyond the clustered data region.
- 4.4. Seismic Serviceability Analysis of the Building: The serviceability fragility curve estimates exceedance probabilities of approximately 47%, 78%, and 90% at PGA values of 0.1g, 0.2g, and 0.3g.The curve is generated from PhyCNN-predicted displacements in an incremental dynamic analysis setting using 100 selected PEER ground motions.
5. Conclusions
The paper concludes that PhyCNN provides data-driven surrogate models for seismic response modeling using physics constraints and limited simulation or sensing datasets. Numerical and experimental examples indicate effective, reliable, and computationally efficient modeling, with further use for building serviceability fragility functions.
- 5. Conclusions: PhyCNN combines convolutional and fully connected layers, a graph-based tensor differentiator, and physics constraints to model and predict building seismic response.The physics constraints are intended to alleviate overfitting, reduce reliance on large training datasets, and improve prediction robustness.
- 5. Conclusions: Numerical and experimental examples with limited datasets show that PhyCNN is effective, reliable, and computationally efficient for seismic structural response modeling.The examples use datasets from simulations or field sensing.
- 5. Conclusions: The trained PhyCNN model can serve as a basis for developing fragility functions for building serviceability assessment.The conclusion identifies scalability to other structures as a broader scope of the proposed algorithm.