Technical Papers
Oct 3, 2023

Embedding Prior Knowledge into Data-Driven Structural Performance Prediction to Extrapolate from Training Domains

Publication: Journal of Engineering Mechanics
Volume 149, Issue 12

Abstract

Machine learning (ML)–based data-driven approaches have become increasingly prevalent for predicting structural performance. Because a properly trained ML model can learn hidden patterns in databases of experimental samples, ML model performance sometimes exceeds that of mechanics-based predictive models, especially when the latter either conflates multiple phenomena into a single term or does not represent them at all. Nevertheless, there is almost always an inherent gap between the domain of the collected data—used in developing the predictive models—and the desired prediction domain. For instance, structural testing is often carried out on scaled components with approximated boundary conditions. Although mechanics-based models can usually bridge the said gaps, discrepancies are a perpetual challenge to the extrapolation capabilities of data-driven models. To address this issue, a new data-driven approach, a prior-knowledge embedded data-driven approach (PkeDA), is proposed herein, which integrates valuable prior knowledge embedded in empirical formulas into a data-driven model. A particular realization of this approach, based on artificial neural networks, PkeDA-ANN, is developed. To verify its feasibility and compare it with a model trained through a classic data-driven approach (CDA), a case study for predicting the bending capacities of reinforced concrete beams is carried out. The results indicate that when the model is trained via CDA, it exhibits good interpolation capabilities, as expected, but its extrapolation capabilities are observed to be severely limited. Under identical conditions, the proposed PkeDA was observed to have not only excellent interpolation and extrapolation capabilities but also to dramatically surpass the classic empirical formulas that have been developed for predicting the capacity of concrete beams under bending. As such, PkeDA appears to be a viable approach for developing highly accurate data-driven models when prior knowledge is available.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

The authors greatly appreciate the financial support from National Key R&D Program of China (No. 2021YFB1600300), National Natural Science Foundation of China (No. 52008027), Natural Science Foundation of Jiangsu Province (No. BK20211564), and Fundamental Research Funds for the Central Universities, CHD (No. 300102213209).

References

Abbas, T., I. Kavrakov, G. Morgenthal, and T. Lahmer. 2020. “Prediction of aeroelastic response of bridge decks using artificial neural networks.” Comput. Struct. 231 (Apr): 106198. https://doi.org/10.1016/j.compstruc.2020.106198.
ACI (American Concrete Institute). 2014. Building code requirements for structural concrete. ACI 318. Farmington Hills, MI: ACI.
Agarap, A. F. 2018. “Deep learning using rectified linear units (ReLu).” Preprint, submitted March 22, 2018. http://arxiv.org/abs/1803.08375.
Akiba, T., S. Sano, T. Yanase, T. Ohta, and M. Koyama. 2019. “Optuna: A next-generation hyperparameter optimization framework.” In Proc., 25th ACM SIGKDD Int. Conf. on Knowledge Discovery & Data Mining, 2623–2631. New York: Association for Computing Machinery.
Anowar, F., and S. Sadaoui. 2021. “Incremental learning framework for real-world fraud detection environment.” Comput. Intell. 37 (1): 635–656. https://doi.org/10.1111/coin.12434.
Balestriero, R., J. Pesenti, and Y. LeCun. 2021. “Learning in high dimension always amounts to extrapolation.” Preprint, submitted November 6, 2021. http://arxiv.org/abs/2110.09485.
Bao, Y., and H. Li. 2021. “Machine learning paradigm for structural health monitoring.” Struct. Health Monit. 20 (4): 1353–1372. https://doi.org/10.1177/1475921720972416.
Bažant, Z. P. 1999. “Size effect on structural strength: A review.” Arch. Appl. Mech. 69 (9): 703–725. https://doi.org/10.1007/s004190050252.
Bažant, Z. P. 2001. “Prediction of concrete creep and shrinkage: Past, present and future.” Nucl. Eng. Des. 203 (1): 27–38. https://doi.org/10.1016/S0029-5493(00)00299-5.
Cai, S., Z. Mao, Z. Wang, M. Yin, and G. E. Karniadakis. 2021. “Physics-informed neural networks (PINNs) for fluid mechanics: A review.” Acta Mech. Sin. 37 (12): 1727–1738. https://doi.org/10.1007/s10409-021-01148-1.
Chen, J., Y. Gao, and Y. Liu. 2022a. “Multi-fidelity data aggregation using convolutional neural networks.” Comput. Methods Appl. Mech. Eng. 391 (Mar): 114490. https://doi.org/10.1016/j.cma.2021.114490.
Chen, M., S. Mangalathu, and J.-S. Jeon. 2022b. “Machine learning–based seismic reliability assessment of bridge networks.” J. Struct. Eng. 148 (7): 06022002. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003376.
Chen, S.-Z., and D.-C. Feng. 2022. “Multifidelity approach for data-driven prediction models of structural behaviors with limited data.” Comput.-Aided Civ. Infrastruct. Eng. 37 (12): 1566–1581. https://doi.org/10.1111/mice.12817.
Chen, S.-Z., D.-C. Feng, W.-J. Wang, and E. Taciroglu. 2022c. “Probabilistic machine-learning methods for performance prediction of structure and infrastructures through natural gradient boosting.” J. Struct. Eng. 148 (8): 04022096. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003401.
Chen, S.-Z., G. Wu, T. Xing, and D.-C. Feng. 2017. “Prestressing force monitoring method for a box girder through distributed long-gauge FBG sensors.” Smart Mater. Struct. 27 (1): 015015. https://doi.org/10.1088/1361-665X/aa9bbe.
Chen, T., and C. Guestrin. 2016. “XGBoost: A scalable tree boosting system.” In Proc., 22nd ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, KDD ’16, 785–794. New York: Association for Computing Machinery.
Chen, Y., and D. Zhang. 2022. “Integration of knowledge and data in machine learning.” Preprint, submitted February 15, 2022. http://arxiv.org/abs/2202.10337.
Chen, Z., Y. Liu, and H. Sun. 2021. “Physics-informed learning of governing equations from scarce data.” Nat. Commun. 12 (1): 1–13. https://doi.org/10.1038/s41467-021-26434-1.
CS (Chinese Standard). 2002. Code for design of concrete structures. GB 50010-2010. Beijing: CS.
Erickson, N., J. Mueller, A. Shirkov, H. Zhang, P. Larroy, M. Li, and A. Smola. 2020. “Autogluon-tabular: Robust and accurate automl for structured data.” Preprint, submitted March 13, 2013. http://arxiv.org/abs/1804.08738.
Feng, D.-C., S.-Z. Chen, M. R. Azadi Kakavand, and E. Taciroglu. 2021a. “Probabilistic model based on Bayesian model averaging for predicting the plastic hinge lengths of reinforced concrete columns.” J. Eng. Mech. 147 (10): 04021066. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001976.
Feng, D.-C., Z.-T. Liu, X.-D. Wang, Y. Chen, J.-Q. Chang, D.-F. Wei, and Z.-M. Jiang. 2020. “Machine learning-based compressive strength prediction for concrete: An adaptive boosting approach.” Constr. Build. Mater. 230 (Mar): 117000. https://doi.org/10.1016/j.conbuildmat.2019.117000.
Feng, D.-C., W.-J. Wang, S. Mangalathu, and E. Taciroglu. 2021b. “Interpretable xgboost-shap machine-learning model for shear strength prediction of squat RC walls.” J. Struct. Eng. 147 (11): 04021173. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003115.
Feng, D.-C., and G. Wu. 2022. “Interpretable machine learning-based modeling approach for fundamental properties of concrete structures.” [In Chinese.] J. Build. Struct. 43 (4): 228. https://doi.org/10.14006/j.jzjgxb.2020.0491.
Friedman, J., J. Hastie, and R. Tibshirani. 2009. The elements of statistical learning. New York: Springer.
Fu, B., S.-Z. Chen, X.-R. Liu, and D.-C. Feng. 2022. “A probabilistic bond strength model for corroded reinforced concrete based on weighted averaging of non-fine-tuned machine learning models.” Constr. Build. Mater. 318 (Apr): 125767. https://doi.org/10.1016/j.conbuildmat.2021.125767.
Golinko, E., and X. Zhu. 2018. “Generalized feature embedding for supervised, unsupervised, and online learning tasks.” Inf. Syst. Front. 21 (Feb): 125–142. https://doi.org/10.1007/s10796-018-9850-y.
Gondia, A., M. Ezzeldin, and W. El-Dakhakhni. 2020. “Mechanics-guided genetic programming expression for shear-strength prediction of squat reinforced concrete walls with boundary elements.” J. Struct. Eng. 146 (11): 04020223. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002734.
Gordon, J. E. 2009. Structures: Or why things don’t fall down. Cambridge, MA: Da Capo Press.
Grinsztajn, L., E. Oyallon, and G. Varoquaux. 2022. “Why do tree-based models still outperform deep learning on tabular data?” Preprint, submitted August 26, 2022. http://arxiv.org/abs/2207.08815.
Guo, M., A. Manzoni, M. Amendt, P. Conti, and J. S. Hesthaven. 2022. “Multi-fidelity regression using artificial neural networks: Efficient approximation of parameter-dependent output quantities.” Comput. Methods Appl. Mech. Eng. 389 (Feb): 114378. https://doi.org/10.1016/j.cma.2021.114378.
Haghighat, E., M. Raissi, A. Moure, H. Gomez, and R. Juanes. 2021. “A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics.” Comput. Methods Appl. Mech. Eng. 379 (Jun): 113741. https://doi.org/10.1016/j.cma.2021.113741.
Hjelmstad, K. D. 2005. Fundamentals of structural mechanics. New York: Springer.
Hooker, G. 2004. Diagnostics and extrapolation in machine learning. Stanford, CA: Stanford Univ.
Ikumi, T., E. Galeote, P. Pujadas, A. de la Fuente, and R. López-Carreño. 2021. “Neural network-aided prediction of post-cracking tensile strength of fibre-reinforced concrete.” Comput. Struct. 256 (Mar): 106640. https://doi.org/10.1016/j.compstruc.2021.106640.
Karbassi, A., B. Mohebi, S. Rezaee, and P. Lestuzzi. 2014. “Damage prediction for regular reinforced concrete buildings using the decision tree algorithm.” Comput. Struct. 130 (Jan): 46–56. https://doi.org/10.1016/j.compstruc.2013.10.006.
Karbhari, V. M., and L. Zhao. 2000. “Use of composites for 21st century civil infrastructure.” Comput. Methods Appl. Mech. Eng. 185 (2–4): 433–454. https://doi.org/10.1016/S0045-7825(99)90270-0.
Khaleghi, M., E. Haghighat, M. Vahab, B. Shahbodagh, and N. Khalili. 2022. “Fracture characterization from noisy displacement data using artificial neural networks.” Eng. Fract. Mech. 271 (Aug): 108649. https://doi.org/10.1016/j.engfracmech.2022.108649.
Khalili-Tehrani, P., E. R. Ahlberg, C. Rha, A. Lemnitzer, J. P. Stewart, E. Taciroglu, and J. W. Wallace. 2014. “Nonlinear load-deflection behavior of reinforced concrete drilled piles in stiff clay.” J. Geotech. Geoenviron. Eng. 140 (3): 04013022. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000957.
Kiani, J., C. Camp, and S. Pezeshk. 2019. “On the application of machine learning techniques to derive seismic fragility curves.” Comput. Struct. 218 (Jul): 108–122. https://doi.org/10.1016/j.compstruc.2019.03.004.
Kingma, D. P., and J. Ba. 2014. “Adam: A method for stochastic optimization.” Preprint, submitted March 8, 2023. http://arxiv.org/abs/1412.6980.
Lemnitzer, A., P. Khalili-Tehrani, E. R. Ahlberg, C. Rha, E. Taciroglu, J. W. Wallace, and J. P. Stewart. 2010. “Nonlinear efficiency of bored pile group under lateral loading.” J. Geotech. Geoenviron. Eng. 136 (12): 1673–1685. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000383.
Lu, L., X. Meng, Z. Mao, and G. E. Karniadakis. 2021a. “DeepXDE: A deep learning library for solving differential equations.” SIAM Rev. 63 (1): 208–228. https://doi.org/10.1137/19M1274067.
Lu, X., Y. Xu, Y. Tian, B. Cetiner, and E. Taciroglu. 2021b. “A deep learning approach to rapid regional post-event seismic damage assessment using time-frequency distributions of ground motions.” Earthquake Eng. Struct. Dyn. 50 (6): 1612–1627. https://doi.org/10.1002/eqe.3415.
Luo, H., and S. G. Paal. 2022. “Data-driven seismic response prediction of structural components.” Earthquake Spectra 38 (2): 1382–1416. https://doi.org/10.1177/87552930211053345.
Mangalathu, S., and J.-S. Jeon. 2018. “Classification of failure mode and prediction of shear strength for reinforced concrete beam-column joints using machine learning techniques.” Eng. Struct. 160: 85–94. https://doi.org/10.1016/j.engstruct.2018.01.008.
Martius, G., and C. H. Lampert. 2016. “Extrapolation and learning equations.” Preprint, submitted October 10, 2016. http://arxiv.org/abs/1610.02995.
Park, R., and T. Paulay. 1991. Reinforced concrete structures. New York: Wiley.
Raissi, M., P. Perdikaris, and G. E. Karniadakis. 2017. “Physics informed deep learning (part I): Data-driven solutions of nonlinear partial differential equations.” Preprint, submitted November 28, 2017. http://arxiv.org/abs/1711.10561.
Raissi, M., P. Perdikaris, and G. E. Karniadakis. 2019. “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.” J. Comput. Phys. 378 (Mar): 686–707. https://doi.org/10.1016/j.jcp.2018.10.045.
Ren, P., C. Rao, Y. Liu, J.-X. Wang, and H. Sun. 2022. “PhyCRNet: Physics-informed convolutional-recurrent network for solving spatiotemporal PDEs.” Comput. Methods Appl. Mech. Eng. 389 (Feb): 114399. https://doi.org/10.1016/j.cma.2021.114399.
Shamsabadi, A., A. Dasmeh, A. Nojoumi, K. M. Rollins, and E. Taciroglu. 2020. “Lateral capacity model for backfills reacting against skew-angled abutments under seismic loading.” J. Geotech. Geoenviron. Eng. 146 (2): 04019129. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002183.
Shamsabadi, A., P. Khalili-Tehrani, J. P. Stewart, and E. Taciroglu. 2010. “Validated simulation models for lateral response of bridge abutments with typical backfills.” J. Bridge Eng. 15 (3): 302–311. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000058.
Shin, D., and Y. Y. Kim. 2020. “Data-driven approach for a one-dimensional thin-walled beam analysis.” Comput. Struct. 231: 106207. https://doi.org/10.1016/j.compstruc.2020.106207.
Sobol, I. M. 2001. “Global sensitivity indices for nonlinear mathematical models and their monte Carlo estimates.” Math. Comput. Simul. 55 (1–3): 271–280. https://doi.org/10.1016/S0378-4754(00)00270-6.
Soyoz, S., E. Taciroglu, K. Orakcal, R. Nigbor, D. Skolnik, H. Lus, and E. Safak. 2013. “Ambient and forced vibration testing of a reinforced concrete building before and after its seismic retrofitting.” J. Struct. Eng. 139 (10): 1741–1752. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000568.
Tancik, M., P. Srinivasan, B. Mildenhall, S. Fridovich-Keil, N. Raghavan, U. Singhal, R. Ramamoorthi, J. Barron, and R. Ng. 2020. “Fourier features let networks learn high frequency functions in low dimensional domains.” Adv. Neural Inf. Process. Syst. 33 (Mar): 7537–7547.
Wang, X., R. K. Mazumder, B. Salarieh, A. M. Salman, A. Shafieezadeh, and Y. Li. 2022. “Machine learning for risk and resilience assessment in structural engineering: Progress and future trends.” J. Struct. Eng. 148 (8): 03122003. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003392.
Weng, Y., and S. G. Paal. 2022. “Machine learning-based wind pressure prediction of low-rise non-isolated buildings.” Eng. Struct. 258 (Feb): 114148. https://doi.org/10.1016/j.engstruct.2022.114148.
Wolpert, D. H. 2002. “The supervised learning no-free-lunch theorems.” In Soft computing and industry, 25–42. Berlin: Springer.
Xu, S.-Y., and J. Zhang. 2012. “Axial–shear–flexure interaction hysteretic model for RC columns under combined actions.” Eng. Struct. 34 (Jan): 548–563. https://doi.org/10.1016/j.engstruct.2011.10.023.
Yandex, A. B., and V. Lempitsky. 2015. “Aggregating local deep features for image retrieval.” In Proc., 2015 IEEE Int. Conf. on Computer Vision (ICCV) 1269–1277. New York: IEEE.
Yao, H., Y. Gao, and Y. Liu. 2020. “FEA-Net: A physics-guided data-driven model for efficient mechanical response prediction.” Comput. Methods Appl. Mech. Eng. 363 (May): 112892. https://doi.org/10.1016/j.cma.2020.112892.
Yu, E., J. W. Wallace, and E. Taciroglu. 2007. “Parameter identification of framed structures using an improved finite element model-updating method—Part II: Application to experimental data.” Earthquake Eng. Struct. Dyn. 36 (5): 641–660. https://doi.org/10.1002/eqe.645.
Zhang, K., N. Chen, J. Liu, and M. Beer. 2022. “A GRU-based ensemble learning method for time-variant uncertain structural response analysis.” Comput. Methods Appl. Mech. Eng. 391 (Mar): 114516. https://doi.org/10.1016/j.cma.2021.114516.
Zhang, L., Q. Zhang, L. Zhang, D. Tao, X. Huang, and B. Du. 2015. “Ensemble manifold regularized sparse low-rank approximation for multiview feature embedding.” Pattern Recognit. 48 (10): 3102–3112. https://doi.org/10.1016/j.patcog.2014.12.016.
Zhang, R., Z. Chen, S. Chen, J. Zheng, O. Büyüköztürk, and H. Sun. 2019. “Deep long short-term memory networks for nonlinear structural seismic response prediction.” Comput. Struct. 220 (Aug): 55–68. https://doi.org/10.1016/j.compstruc.2019.05.006.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 149Issue 12December 2023

History

Received: Nov 12, 2022
Accepted: Jul 31, 2023
Published online: Oct 3, 2023
Published in print: Dec 1, 2023
Discussion open until: Mar 3, 2024

Permissions

Request permissions for this article.

ASCE Technical Topics:

Authors

Affiliations

Shi-Zhi Chen, M.ASCE [email protected]
Associate Professor, School of Highways, Chang’an Univ., Xi’an, Shaanxi 710064, China. Email: [email protected]
Shu-Ying Zhang [email protected]
Ph.D. Candidate, School of Highways, Chang’an Univ., Xi’an, Shaanxi 710064, China. Email: [email protected]
Professor, Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education, Southeast Univ., Nanjing 211189, China (corresponding author). ORCID: https://orcid.org/0000-0003-3691-6128. Email: [email protected]
Professor, Dept. of Civil and Environmental Engineering, Univ. of California, Los Angeles, CA 90095. ORCID: https://orcid.org/0000-0001-9618-1210. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share