Interlaced Characterization and Calibration: In-situ Bayesian optimal experimental design for constitutive model calibration
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The AEOLUS Center is dedicated to developing a unified optimization-under-uncertainty framework for: (1) learning predictive models from data; and (2) optimizing experiments, processes, and designs governed by these models, all driven by complex, uncertain energy systems. AEOLUS addresses the critical need for principled, rigorous, scalable, and structure-exploiting capabilities for exploring parameter and decision spaces of complex forward simulation models. This report summarizes the key highlights of our research during the period of performance.
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Some of the basic concepts are unified that were developed for the problem of finding optimal approximating functions which relate a set of controlled variables to a measurable response. The techniques have the potential for reducing the amount of testing required in experimental investigations. Specifically, two low-order polynomial models are considered as approximations to unknown functionships. For each model, optimal means of designing experimental tests are presented which, for a modest number of measurements, yield prediction equations that minimize the error of an estimated response anywhere inside a selected region of experimentation. Moreover, examples are provided for both models to illustrate their use. Finally, an analysis of a second-order prediction equation is given to illustrate ways of determining maximum or minimum responses inside the experimentation region.
Optimal experimental design is a classic topic in statistics, with many well-studied problems, applications, and solutions. The design problem we study is the placement of sensors to monitor spatiotemporal processes, explicitly accounting for the temporal dimension in our modeling and optimization. We observe that recent advancements in computational sciences often yield large datasets based on physics-based simulations, which are rarely leveraged in experimental design. We introduce a novel model-based sensor placement criterion, along with a highly-efficient optimization algorithm, which integrates physics-based simulations and Bayesian experimental design principles to identify sensor networks that “minimize information loss” from simulated data. Our technique relies on sparse variational inference and (separable) Gauss-Markov priors, and thus may adapt many techniques from Bayesian experimental design. We validate our method through a case study monitoring air temperature in Phoenix, Arizona, using state-of-the-art physics-based simulations. Our results show our framework to be superior to random or quasi-random sampling, particularly with a limited number of sensors. We conclude by discussing practical considerations and implications of our framework, including more complex modeling tools and real-world deployments.
Air-to-refrigerant heat exchangers (HXs) are fundamental components in HVAC&R systems, and considerable research has been dedicated designing continually smaller, lighter, and more efficient HX designs. In recent years, researchers have leveraged advancements in Computational Fluid Dynamics (CFD), Finite Element Analysis (FEA), and optimization algorithms to consider primary tube shape and topology optimization to design highly compact, high performance HXs for a multitude of applications. In this research, we present a computationally efficient, comprehensive, multi-scale, and multi-physics analysis and optimization method for air-to-refrigerant HXs featuring automated CFD and FEA simulations and approximation-assisted optimization. This methodology was utilized to design HXs with shape-optimized, non-round tubes which outperform current state-of-the-art tube-fin HXs without compromising structural integrity. The optimal HXs were shown to deliver similar thermal performance to the baseline HXs while also achieving more than 20% reductions in airside pressure drop and core envelope volume and more than 30% reduction in internal volume. Comprehensive experimental validation of the optimization methodology was conducted through the testing of two prototypes in a standardized wind tunnel facility under multiple operating conditions. For prototype #1 under dry evaporator conditions, the predicted heat load agreed within ± 10% of measured values and the predicted airside pressure drop agreed within ± 30%, while for dehumidifying conditions, the predicted sensible and latent heat loads agreed within ± 10% and ± 20% of the measured values, respectively. For prototype #2, the predicted condenser heat load agreed within ± 3.0% of measured values, and the predicted airside pressure drop agreed within ± 27%. The acceptable agreement between simulation and experimental results for the present application highlights the flexibility of the novel optimization methodology to design next generation HXs with improved performance and reduced volume, weight, and environmental impact.
Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. Estimation of the precision matrix is a fundamental task to infer biological graphical structures like microbial networks. We compare the marginal posterior precision of the precision matrix under four priors: flat, conjugate Normal-Wishart, Normal-MGIG and a general independent. Under the flat and conjugate priors, the Laplace-approximated posterior precision is not a function of the design matrix rendering useless any efforts to find an optimal experimental design to infer the precision matrix. In contrast, the Normal-MGIG and general independent priors do allow for the search of optimal experimental designs, yet there is a sharp upper bound on the information that can be extracted from a given experiment. We confirm our theoretical findings via a simulation study comparing (i) the KL divergence between prior and posterior and (ii) the Stein’s loss difference of MAPs between random and no experiment. Our findings provide practical advice for domain scientists conducting experiments to better infer the precision matrix as a representation of a biological network.
Experiments are indispensable for developing models of complex systems. Carefully designed experiments can provide substantial savings for these expensive data-acquisition opportunities. However, designs based on heuristics are often suboptimal for systems with multiphysics, nonlinear dynamics, and uncertain and noisy environments. Optimal experimental design, while leveraging predictive models, seeks to systematically quantify and maximize the value of experiments. In this project, we focused on the design of multiple experiments, where current approaches are largely suboptimal: batch-design does not adapt to new data acquired during the experiment campaign (no feedback), and greedy/myopic design ignores future dynamics and consequences (no lookahead). We developed the mathematical framework and computational methods for sequential optimal experimental design (sOED) for complex systems. We enabled tractable model-based sOED in a rigorous manner through novel algorithms based on reinforcement learning, and investigated the effects of human experimenters on the design process. Our methods are fully Bayesian, able to quantify and update uncertainty in a principled manner. The traits aimed by our approach—mathematical rigor and optimality, human effects and uncertainty quantification, computational practicality—are crucial for elevating the standards of artificial intelligence (AI) to support decision-making in scientific domains, and contribute toward trust and realistic adoption of AI in experimental design practice.
Accurate material characterization and model calibration are essential for computationally supported high-consequence engineering decisions. Historically, characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data are collected for a specific model of interest, (3) use deterministic methods that provide best-fit parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work brings together several recent advancements into an improved workflow called interlaced characterization and calibration (ICC) that advances the state-of-the-art in constitutive model calibration. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) quantifies parameter uncertainty through Bayesian inference and (4) incorporates these advancements into a quasi real-time feedback loop. The ICC framework is demonstrated here on the calibration of a material model using simulated full-field data for an aluminium cruciform specimen being deformed biaxially. The cruciform is actively driven through the myopically preferred load path using Bayesian optimal experimental design, which selects load steps that yield the maximum expected information gain (EIG). Principal component analysis (PCA) is performed on the model predictions of full-field displacements, and fast surrogate models are built to approximate the input-output relationships of the expensive finite element model. Furthermore, the tools developed and demonstrated here show that high-fidelity constitutive models can be efficiently and reliably calibrated with quantified uncertainty, thus supporting credible decision-making and potentially increasing the agility of solid mechanics modelling by enabling utilization of computational simulations at earlier stages of the design cycle.
Modern advanced manufacturing and advanced materials design often require searches of relatively high-dimensional process control parameter spaces for settings that result in optimal structure, property, and performance parameters. The mapping from the former to the latter must be determined from noisy experiments or from expensive simulations. Here, we abstract this problem to a mathematical framework in which an unknown function from a control space to a design space must be ascertained by means of expensive noisy measurements, which locate control settings generating desired design features within specified tolerances, with quantified uncertainty. We describe targeted adaptive design (TAD), a new algorithm that performs this sampling task efficiently. TAD creates a Gaussian process surrogate model of the unknown mapping at each iterative stage, proposing a new batch of control settings to sample experimentally and optimizing the updated expected log-predictive probability density of the target design. TAD either stops upon locating a solution with uncertainties that fit inside the tolerance box or uses a measure of expected future information to determine that the search space has been exhausted with no solution. TAD thus embodies the exploration-exploitation tension in a manner that recalls, but is essentially different from, Bayesian optimization and optimal experimental design.
The objectives of this paper are to: (1) gain insight into the processing of ceramics and how green processing can affect the properties of ceramics; (2) investigate the technique of slip casting; (3) learn how heat treatment and temperature contribute to density, strength, and effects of under and over firing to ceramic properties; (4) experience some of the problems inherent in testing brittle materials and learn about the statistical nature of the strength of ceramics; (5) investigate orthogonal arrays as tools to examine the effect of many experimental parameters using a minimum number of experiments; (6) recognize appropriate uses for clay based ceramics; and (7) measure several different properties important to ceramic use and optimize them for a given application.
Accurate material characterization and model calibration are pivotal for simulations used for high-consequence engineering decisions. Current characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data is collected for a specific model of interest, (3) provide only mean parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work developed a new paradigm—coined Interlaced Characterization and Calibration (ICC)—which drives forward the state-of-the-art in model calibration by bringing together recent advancements into one improved workflow. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) provides uncertainty metrics on the calibrated model parameters, and (4) incorporates these advances into a quasi real-time feedback loop. The ICC framework was validated synthetically with both low-fidelity and high-fidelity simulations paired with several different elastoplastic material models, and was also demonstrated experimentally with an aluminum 6061 cruciform exemplar specimen. Results showed that the ICC framework—in which Bayesian optimal experimental design actively guided the experiment— resulted in calibrations with similar or better accuracy than predetermined experiments based on subject matter expertise. Moreover, the ICC framework produced a complete model calibration— with quantified uncertainties on model parameters—in 1 week, a 5 - 10× increase in efficiency over traditional approaches. Thus, the ICC paradigm improves both the calibration process and quality, by (1) improving efficiency, which increases agility of solid mechanics modeling and enables utilization of computational simulation (CompSim) at earlier stages of the design cycle and (2) providing quantified, and in some cases reduced, parameter uncertainties, which increases confidence in model predictions and supports credible decision making.
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