Polynomial Chaos Based Design of Robust Input Shapers

A probabilistic approach, which exploits the domain and distribution of the uncertain model parameters, has been developed for the design of robust input shapers. Polynomial chaos expansions are used to approximate uncertain system states and cost functions in the stochastic space. Residual energy of the system is used as the cost function to design robust input shapers for precise rest-to-rest maneuvers. An optimization problem, which minimizes any moment or combination of moments of the distribution function of the residual energy is formulated. Numerical examples are used to illustrate the benefit of using the polynomial chaos based probabilistic approach for the determination of robust input shapers for uncertain linear systems. The solution of polynomial chaos based approach is compared with the minimax optimization based robust input shaper design approach, which emulates a Monte Carlo process.

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Uncertainty Propagation Analysis of Computational Models in Laser Powder Bed Fusion Additive Manufacturing Using Polynomial Chaos Expansions

Journal of Manufacturing Science and Engineering ◽

10.1115/1.4041179 ◽

2018 ◽

Vol 140 (12) ◽

Cited By ~ 16

Author(s):

Gustavo Tapia ◽

Wayne King ◽

Luke Johnson ◽

Raymundo Arroyave ◽

Ibrahim Karaman ◽

...

Keyword(s):

Additive Manufacturing ◽

Computational Models ◽

Polynomial Chaos ◽

Uncertainty Propagation ◽

Model Parameters ◽

Powder Bed Fusion ◽

Multiple Sources ◽

Powder Bed ◽

Model Code ◽

Polynomial Chaos Expansions

Computational models for simulating physical phenomena during laser-based powder bed fusion additive manufacturing (L-PBF AM) processes are essential for enhancing our understanding of these phenomena, enable process optimization, and accelerate qualification and certification of AM materials and parts. It is a well-known fact that such models typically involve multiple sources of uncertainty that originate from different sources such as model parameters uncertainty, or model/code inadequacy, among many others. Uncertainty quantification (UQ) is a broad field that focuses on characterizing such uncertainties in order to maximize the benefit of these models. Although UQ has been a center theme in computational models associated with diverse fields such as computational fluid dynamics and macro-economics, it has not yet been fully exploited with computational models for advanced manufacturing. The current study presents one among the first efforts to conduct uncertainty propagation (UP) analysis in the context of L-PBF AM. More specifically, we present a generalized polynomial chaos expansions (gPCE) framework to assess the distributions of melt pool dimensions due to uncertainty in input model parameters. We develop the methodology and then employ it to validate model predictions, both through benchmarking them against Monte Carlo (MC) methods and against experimental data acquired from an experimental testbed.

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Drag Parameter Estimation Using Gradients and Hessian from a Polynomial Chaos Model Surrogate

Monthly Weather Review ◽

10.1175/mwr-d-13-00087.1 ◽

2014 ◽

Vol 142 (2) ◽

pp. 933-941 ◽

Cited By ~ 13

Author(s):

Ihab Sraj ◽

Mohamed Iskandarani ◽

W. Carlisle Thacker ◽

Ashwanth Srinivasan ◽

Omar M. Knio

Keyword(s):

Inverse Problem ◽

Posterior Distribution ◽

Polynomial Chaos ◽

Monte Carlo Sampling ◽

Chaos Expansion ◽

Optimal Parameters ◽

Computational Burden ◽

Similarities And Differences ◽

Polynomial Chaos Expansions ◽

The Cost

Abstract A variational inverse problem is solved using polynomial chaos expansions to infer several critical variables in the Hybrid Coordinate Ocean Model’s (HYCOM’s) wind drag parameterization. This alternative to the Bayesian inference approach in Sraj et al. avoids the complications of constructing the full posterior with Markov chain Monte Carlo sampling. It focuses instead on identifying the center and spread of the posterior distribution. The present approach leverages the polynomial chaos series to estimate, at very little extra cost, the gradients and Hessian of the cost function during minimization. The Hessian’s inverse yields an estimate of the uncertainty in the solution when the latter’s probability density is approximately Gaussian. The main computational burden is an ensemble of realizations to build the polynomial chaos expansion; no adjoint code or additional forward model runs are needed once the series is available. The ensuing optimal parameters are compared to those obtained in Sraj et al. where the full posterior distribution was constructed. The similarities and differences between the new methodology and a traditional adjoint-based calculation are discussed.

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Efficient Bayesian calibration of aerodynamic wind turbine models using surrogate modeling

10.5194/wes-2021-58 ◽

2021 ◽

Author(s):

Benjamin Sanderse ◽

Vinit V. Dighe ◽

Koen Boorsma ◽

Gerard Schepers

Keyword(s):

New Mexico ◽

Wind Turbine ◽

Polynomial Chaos ◽

Global Sensitivity Analysis ◽

Measurement Data ◽

Model Parameters ◽

Test Cases ◽

Parameter Calibration ◽

Bayesian Calibration ◽

Polynomial Chaos Expansions

Abstract. This paper presents an efficient strategy for the Bayesian calibration of parameters of aerodynamic wind turbine models. The strategy relies on constructing a surrogate model (based on adaptive polynomial chaos expansions), which is used to perform both parameter selection using global sensitivity analysis and parameter calibration with Bayesian inference. The effectiveness of this approach is shown in two test cases: calibration of airfoil polars based on the measurements from the DanAero MW experiments, and calibration of five yaw model parameters based on measurements on the New MEXICO turbine in yawed conditions. In both cases, the calibrated models yield results much closer to the measurement data, and in addition they are equipped with an estimate of the uncertainty in the predictions.

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SURROGATE MODELING FOR STOCHASTIC DYNAMICAL SYSTEMS BY COMBINING NONLINEAR AUTOREGRESSIVE WITH EXOGENOUS INPUT MODELS AND POLYNOMIAL CHAOS EXPANSIONS

International Journal for Uncertainty Quantification ◽

10.1615/int.j.uncertaintyquantification.2016016603 ◽

2016 ◽

Vol 6 (4) ◽

pp. 313-339 ◽

Cited By ~ 20

Author(s):

Chu V. Mai ◽

Minas D. Spiridonakos ◽

Eleni N. Chatzi ◽

Bruno Sudret

Keyword(s):

Dynamical Systems ◽

Polynomial Chaos ◽

Surrogate Modeling ◽

Stochastic Dynamical Systems ◽

Polynomial Chaos Expansions ◽

Nonlinear Autoregressive

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Accommodating Taste and Scale Heterogeneity for Front-Seat Passenger’ Choice of Seat Belt Usage

Mathematics ◽

10.3390/math9050460 ◽

2021 ◽

Vol 9 (5) ◽

pp. 460 ◽

Cited By ~ 2

Author(s):

Mahdi Rezapour ◽

Khaled Ksaibati

Keyword(s):

Mixed Model ◽

Seat Belt ◽

Model Fit ◽

Model Parameters ◽

Extended Model ◽

Random Parameters ◽

Front Seat ◽

Scale Heterogeneity ◽

Error Terms ◽

The Cost

There is growing interest in implementation of the mixed model to account for heterogeneity across population observations. However, it has been argued that the assumption of independent and identically distributed (i.i.d) error terms might not be realistic, and for some observations the scale of the error is greater than others. Consequently, that might result in the error terms’ scale to be varied across those observations. As the standard mixed model could not account for the aforementioned attribute of the observations, extended model, allowing for scale heterogeneity, has been proposed to relax the equal error terms across observations. Thus, in this study we extended the mixed model to the model with heterogeneity in scale, or generalized multinomial logit model (GMNL), to see if accounting for the scale heterogeneity, by adding more flexibility to the distribution, would result in an improvement in the model fit. The study used the choice data related to wearing seat belt across front-seat passengers in Wyoming, with all attributes being individual-specific. The results highlighted that although the effect of the scale parameter was significant, the scale effect was trivial, and accounting for the effect at the cost of added parameters would result in a loss of model fit compared with the standard mixed model. Besides considering the standard mixed and the GMNL, the models with correlated random parameters were considered. The results highlighted that despite having significant correlation across the majority of the random parameters, the goodness of fits favors more parsimonious models with no correlation. The results of this study are specific to the dataset used in this study, and due to the possible fact that the heterogeneity in observations related to the front-seat passengers seat belt use might not be extreme, and do not require extra layer to account for the scale heterogeneity, or accounting for the scale heterogeneity at the cost of added parameters might not be required. Extensive discussion has been made in the content of this paper about the model parameters’ estimations and the mathematical formulation of the methods.

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Extending bluff-and-fix estimates for polynomial chaos expansions

Journal of Computational Science ◽

10.1016/j.jocs.2020.101287 ◽

2021 ◽

pp. 101287

Author(s):

Laura Lyman ◽

Gianluca Iaccarino

Keyword(s):

Polynomial Chaos ◽

Polynomial Chaos Expansions

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Cost-effectiveness of TAS-102 plus bevacizumab versus TAS-102 monotherapy in patients with metastatic colorectal cancer

BMC Gastroenterology ◽

10.1186/s12876-021-01771-z ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Kiyoaki Sugiura ◽

Yuki Seo ◽

Takayuki Takahashi ◽

Hideyuki Tokura ◽

Yasuhiro Ito ◽

...

Keyword(s):

Colorectal Cancer ◽

Health Care ◽

Sensitivity Analysis ◽

Cost Effectiveness ◽

Combination Therapy ◽

Metastatic Colorectal Cancer ◽

Cost Effective ◽

Model Parameters ◽

Combination Regimen ◽

The Cost

Abstract Background TAS-102 plus bevacizumab is an anticipated combination regimen for patients who have metastatic colorectal cancer. However, evidence supporting its use for this indication is limited. We compared the cost-effectiveness of TAS-102 plus bevacizumab combination therapy with TAS-102 monotherapy for patients with chemorefractory metastatic colorectal cancer. Method Markov decision modeling using treatment costs, disease-free survival, and overall survival was performed to examine the cost-effectiveness of TAS-102 plus bevacizumab combination therapy and TAS-102 monotherapy. The Japanese health care payer’s perspective was adopted. The outcomes were modeled on the basis of published literature. The incremental cost-effectiveness ratio (ICER) between the two treatment regimens was the primary outcome. Sensitivity analysis was performed and the effect of uncertainty on the model parameters were investigated. Results TAS-102 plus bevacizumab had an ICER of $21,534 per quality-adjusted life-year (QALY) gained compared with TAS-102 monotherapy. Sensitivity analysis demonstrated that TAS-102 monotherapy was more cost-effective than TAS-102 and bevacizumab combination therapy at a willingness-to-pay of under $50,000 per QALY gained. Conclusions TAS-102 and bevacizumab combination therapy is a cost-effective option for patients who have metastatic colorectal cancer in the Japanese health care system.

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