We advance the state-of-art in predictive simulation of materials, using a multi-scale approach of bridging quantum, atomistic, and continuum scales by means of modern statistical inference and uncertainty quantification techniques.

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The Center for the Exascale Simulation of Materials in Extreme Environments (CESMIX) seeks to advance the state-of-the-art in predictive simulation by connecting quantum and molecular simulations of materials with state-of-the-art programming languages, compiler technologies, and software performance engineering tools, underpinned by rigorous approaches to statistical inference and uncertainty quantification.

Our motivating problem is to predict the degradation of complex (disordered and multi-component) materials under extreme loading, inaccessible to direct experimental observation. This application represents a technology domain of intense current interest, and exemplifies an important class of scientific problems — involving material interfaces in extreme environments.

My primary contribution is in developing components of PotentialLearning.jl, a Julia library for the active learning of machine learning interatomic potentials. In particular, I work on Bayesian inference frameworks for training machine learning interatomic potentials, which allow for uncertainty propagation to observable quantities from molecular dynamics simulation.

More information on the project can be found at cesmix.mit.edu.

We show that a Bayesian filtering technique which probabilistically models unknown inputs of a dynamical system can be used to efficiently estimate critical states of in-situ structures, paving a way for improved structural health monitoring and performance-based design of offshore wind turbines.

References

J. Zou, E. Lourens, A. Cicirello. “Virtual sensing of subsoil strain response in monopile-based offshore wind turbines via Gaussian process latent force models.” Mechanical Systems & Signal Processing. 200 (110488). 2023.  

J. Zou, A. Cicirello, A. Iliopoulos, E. Lourens. “Gaussian process latent force models for virtual sensing in a monopile-based offshore wind turbine.” Proceedings of the European Workshop on Structural Health Monitoring, pp. 290-29. 2022.

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Challenge. Support structures for offshore wind turbines must be designed for efficiency and resiliency in order to meet growing global demand for renewable energy. However, designs must account for the high susceptibility of offshore wind turbines to cyclic (fatigue) damage, due to their widely varying environmental loading conditions over time as well as the potential for resonance effects, which occur when the structure’s natural frequencies coincide with the turbine’s rotor frequencies. Monitoring fatigue-induced strains is generally infeasible, since critical regions of the support structure lie near the mudline in offshore settings where installation and maintenance of sensors often proves unsuccessful.

Solution. Virtual sensing is a promising solution for monitoring the progression of fatigue damage in existing offshore wind farms, many of which are approaching the end of their service life, and informing the performance-based design of new offshore wind farms slated for construction over the next several years. Rather than rely on a physical sensor to measure fatigue-induced strains, virtual sensing extrapolates these strains at inaccessible locations of the structure using a limited and indirect set of vibration measurements from accessible locations. This extrapolation is performed using a hybrid model combining a physics-driven model of the structure with a data-driven model of unknown (latent) quantities.

Methodology. In this work, we propose using a Gaussian process latent force model (GPFLM), a Bayesian filtering technique for joint input-state estimation, to perform the virtual sensing task. In particular, we cast both unknown sources of excitation (the “input”) and unknown strains of the structure (the “state”) into a joint Gaussian process model, redefining the system dynamics to be dictated by a stochastic differential equation. An augmented state space model encodes covariance relationships between the latent quantities and measured accelerations, allowing for the dynamic structural response to be reconstructed by means of Kalman filtering and smoothing.

What’s New? While the input loading is known to dictate the response behavior of structural systems, previous models for virtual sensing would either neglect unknown inputs or treat them as white noise in the dynamics, leading to suboptimal state estimates. The GPLFM is one of the first approaches to provide an explicit time-varying statistical model of the unknown forces and unaccounted noise which is learned from data. Moreover, this statistical model is a non-parametric representation of latent states, such that the problem of learning covariance relationships between states reduces to the inference of parameters of the GP covariance kernel.

Implementation. This work is one of the first studies of the performance of the GPLFM for virtual sensing using in-situ vibration data from an operating structure. We use vibration data collected from an offshore wind turbine in the Westermeerwind Park in the Netherlands, consisting of acceleration data at three points along the height of the turbine tower used for data assimilation and strain data along the profile of the monopile foundation used for validation. We demonstrate that the GPLFM leads to accurate reconstruction of strain time histories of the offshore wind turbine in varying operational states with as few as two sensor channels at accessible locations of the structure. Moreover, we find that when model error is explicitly introduced, the error is accommodated by the use of a probabilistic model of the unknown inputs without sacrificing the performance of strain estimation. Our studies indicate that the use of the GPLFM for virtual sensing leads to greater estimation accuracy, robustness to error, and instrumentation efficiency than comparable non-probabilistic approaches.

We show that a surrogate model for the seismic response of civil infrastructure reduces computational cost of regional-level earthquake simulation while also incorporating additional uncertainty information in seismic risk analysis arising from variability in ground motion loading.

References

J. Zou, D. P. Welch, A. Zsarnoczay, A. Taflanidis, G. Deierlein. “Surrogate Modeling for the Seismic Response Estimation of Residential Wood Frame Structures.” 17th World Conference in Earthquake Engineering. Sendai, Japan. 2020.

Challenge. Seismic risk assessment is a method of evaluating an infrastructure asset’s expected ability to meet service needs under the risk of extreme earthquake events. While this form of risk analysis is traditionally conducted at the level of individual buildings, increasing the scope to a population of buildings is important for quantifying economic risks at the municipality or regional level. However, the state-of-art of estimating seismic response by nonlinear response history analysis (NLRHA) presents a high computational cost which limits the scale and resolution of regional-level earthquake simulations.

Solution. Surrogate modeling provides an efficient computational means for seismic response estimation of structural systems. A probability distribution over the seismic response is approximated from the output of a statistical model at comparable accuracy and a fraction of the cost of performing high fidelity simulation, enabling simulation of the impact of earthquake disasters to civil infrastructure on a regional scale.

Methodology. We demonstrate stochastic kriging as a robust surrogate model which is able to estimate heteroscedastic variance in seismic response resulting from variability in ground motion excitation. Stochastic kriging is a two-tiered statistical model in which one Gaussian process models the relative variability of estimator variance across the parameter space (the “nugget”) and another Gaussian process models the distribution of seismic response incorporating variance information from the first model. The metamodel is constructed using a dataset generated by performing nonlinear response history analysis on a number of building configurations parameterized by structural properties. Replicate simulations are performed for a subset of configurations for learning the GP model of variance. We study the tradeoff in accuracy and cost to determine an appropriate composition of building configurations and replications to query in dataset generation.

What’s New? This work addresses unique challenges with surrogate model development for the case in which seismic hazard is characterized using PEER NGA earthquake ground motion recordings. Recorded ground motions provide a more realistic representation of seismic excitation but introduce a greater amount of aleatory uncertainty in the structural response estimate compared to synthetic ground motion models due to record-to-record variability. This work is a novel application of kriging with a heteroscedastic nugget for quantifying underlying variability in ground motion recordings. Moreover, as a Bayesian technique of surrogate modeling, kriging allows for the propagation of uncertainty in the estimated structural response to decision factors in seismic risk analysis.

We develop the most comprehensive natural hazards simulation software to-date, utilizing machine learning, high performance computing, and uncertainty quantification techniques to evaluate urban infrastructure risk to earthquake and tsunami disasters.

Repository

The NHERI Computational Modeling and Simulation Center (SimCenter) is an NSF-sponsored project developing extensible scientific workflows for quantifying the effect of natural hazards on infrastructure, lifelines, and communities. The software suite enables large-scale simulation of natural hazards, including earthquake, hurricane, and storm surge events, and the resulting impact and damages to physical infrastructure. Monte Carlo realizations of natural hazard events are used to provide a probabilistic estimate of aggregate loss (expressed in quantities such as economic cost, operational downtime, and human casualties) which critically informs risk mitigation strategies in regional-level policy.

In contrast to more general-purpose scientific workflow systems, SimCenter software tools have the added features of 1) access to high-performance computing resources on the cloud through the Texas Advanced Computing Center, to enable parallel workflows for large-scale simulation; 2) uncertainty quantification using Dakota, allowing users to quantify and propagate uncertainties; 3) streamlined interfaces with existing software applications and datasets, such as OpenSees and the PEER Strong Ground Motion Database; and 4) a modular framework allowing developers to incorporate new components to the workflow system.

My contribution was primarily to building the connection between R2D (Regional Resilience Determination) Tool, which provides probabilistic damage and loss estimates for regions subject to natural hazards, and SimCenterBackendApplications, the backend program unifying the workflow components.

More information on the project can be found at simcenter.designsafe-ci.org.