Efficient Model-Assisted Probability of Detection and Sensitivity Analysis for Ultrasonic Testing Simulations Using Stochastic Metamodeling

2019 ◽  
Vol 2 (4) ◽  
Author(s):  
Xiaosong Du ◽  
Leifur Leifsson ◽  
William Meeker ◽  
Praveen Gurrala ◽  
Jiming Song ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Computational Efficiency ◽  
Ultrasonic Testing ◽  
Measurement Model ◽  
Monte Carlo Sampling ◽  
Ordinary Least Squares ◽  
Probability Of Detection ◽  
Truncation Scheme ◽  
Physics Model ◽  
Polynomial Chaos Expansions

Abstract Model-assisted probability of detection (MAPOD) and sensitivity analysis (SA) are important for quantifying the inspection capability of nondestructive testing (NDT) systems. To improve the computational efficiency, this work proposes the use of polynomial chaos expansions (PCEs), integrated with least-angle regression (LARS), a basis-adaptive technique, and a hyperbolic truncation scheme, in lieu of the direct use of the physics-based measurement model in the MAPOD and SA calculations. The proposed method is demonstrated on three ultrasonic testing cases and compared with Monte Carlo sampling (MCS) of the physics model, MCS-based kriging, and the ordinary least-squares (OLS)-based PCE method. The results show that the probability of detection (POD) metrics of interests can be controlled within 1% accuracy relative to using the physics model directly. Comparison with metamodels shows that the LARS-based PCE method can provide up to an order of magnitude improvement in the computational efficiency.

Efficient uncertainty propagation for MAPOD via polynomial chaos-based Kriging

2019 ◽  
Vol 37 (1) ◽  
pp. 73-92 ◽  
Author(s):  
Xiaosong Du ◽  
Leifur Leifsson
Keyword(s):  
Polynomial Chaos ◽  
State Of The Art ◽  
Uncertainty Propagation ◽  
Kriging Model ◽  
Probability Of Detection ◽  
Kriging Interpolation ◽  
Benchmark Problems ◽  
Content Type ◽  
Order Of Magnitude ◽  
Polynomial Chaos Expansions

Purpose Model-assisted probability of detection (MAPOD) is an important approach used as part of assessing the reliability of nondestructive testing systems. The purpose of this paper is to apply the polynomial chaos-based Kriging (PCK) metamodeling method to MAPOD for the first time to enable efficient uncertainty propagation, which is currently a major bottleneck when using accurate physics-based models. Design/methodology/approach In this paper, the state-of-the-art Kriging, polynomial chaos expansions (PCE) and PCK are applied to “a^ vs a”-based MAPOD of ultrasonic testing (UT) benchmark problems. In particular, Kriging interpolation matches the observations well, while PCE is capable of capturing the global trend accurately. The proposed UP approach for MAPOD using PCK adopts the PCE bases as the trend function of the universal Kriging model, aiming at combining advantages of both metamodels. Findings To reach a pre-set accuracy threshold, the PCK method requires 50 per cent fewer training points than the PCE method, and around one order of magnitude fewer than Kriging for the test cases considered. The relative differences on the key MAPOD metrics compared with those from the physics-based models are controlled within 1 per cent. Originality/value The contributions of this work are the first application of PCK metamodel for MAPOD analysis, the first comparison between PCK with the current state-of-the-art metamodels for MAPOD and new MAPOD results for the UT benchmark cases.

Capacity Expansion in Stochastic Flow Networks

1992 ◽  
Vol 6 (1) ◽  
pp. 99-118 ◽  
Author(s):  
Christos Alexopoulos ◽  
George S. Fishman
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Upper Bound ◽  
Network Flow ◽  
Water Distribution ◽  
Water Distribution Network ◽  
Monte Carlo Sampling ◽  
Data Set ◽  
Flow Capacity ◽  
Single Data

Sensitivity analysis represents an important aspect of network flow design problems. For example, what is the incremental increase in system flow of increasing the diameters of specified pipes in a water distribution network? Although methods exist for solving this problem in the deterministic case, no comparable methodology has been available when the network's arc capacities are subject to random variation. This paper provides this methodology by describing a Monte Carlo sampling plan that allows one to conduct a sensitivity analysis for a variable upper bound on the flow capacity of a specified arc. The proposed plan has two notable features. It permits estimation of the probabilities of a feasible flow for many values of the upper bound on the arc capacity from a single data set generated by the Monte Carlo method at a single value of this upper bound. Also, the resulting estimators have considerably smaller variancesthan crude Monte Carlo sampling would produce in the same setting. The success of the technique follows from the use of lower and upper bounds on each probability of interest where the bounds are generated from an established method of decomposing the capacity state space.

scholarly journals Informed Proposal Monte Carlo

2021 ◽  
Author(s):  
Sarouyeh Khoshkholgh ◽  
Andrea Zunino ◽  
Klaus Mosegaard
Keyword(s):  
Monte Carlo ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Model Space ◽  
Monte Carlo Sampling ◽  
External Information ◽  
Proposal Distribution ◽  
Highly Nonlinear ◽  
Sampling Algorithms ◽  
Physics Model

Summary Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a consequence of the No-Free-Lunch Theorem, the only way we can ensure a significantly better performance of search and sampling algorithms is to build in as much external information about the problem as possible. In the special case of Markov Chain Monte Carlo sampling (MCMC) we review how this is done through the choice of proposal distribution, and we show how this way of adding more information about the problem can be made particularly efficient when based on an approximate physics model of the problem. A highly nonlinear inverse scattering problem with a high-dimensional model space serves as an illustration of the gain of efficiency through this approach.

scholarly journals High-Dimensional, Small-Sample Product Quality Prediction Method Based on MIC-Stacking Ensemble Learning

2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Jiahao Yu ◽  
Rongshun Pan ◽  
Yongman Zhao
Keyword(s):  
Product Quality ◽  
Ensemble Learning ◽  
Measurement Model ◽  
Learning Model ◽  
Ordinary Least Squares ◽  
Small Sample ◽  
Small Samples ◽  
High Dimensional ◽  
Quality Prediction ◽  
Maximal Information Coefficient

Accurate quality prediction can find and eliminate quality hazards. It is difficult to construct an accurate quality mathematical model for the production of small samples with high dimensionality due to the influence of quality characteristics and the complex mechanism of action. In addition, overfitting scenarios are prone to occur in high-dimensional, small-sample industrial product quality prediction. This paper proposes an ensemble learning and measurement model based on stacking and selects eight algorithms as the base learning model. The maximal information coefficient (MIC) is used to obtain the correlation between the base learning models. Models with low correlation and strong predictive power were chosen to build stacking ensemble models, which effectively avoids overfitting and obtains better predictive performance. To improve the prediction performance as the optimization goal, in the data preprocessing stage, boxplots, ordinary least squares (OLS), and multivariate imputation by chained equations (MICE) are used to detect and replace outliers. The CatBoost algorithm is used to construct combined features. Strong combination features were selected to construct a new feature set. Concrete slump data from the University of California Irvine (UCI) machine learning library were used to conduct comprehensive verification experiments. The experimental results show that, compared with the optimal single model, the minimum correlation stacking ensemble learning model has higher precision and stronger robustness, and a new method is provided to guarantee the accuracy of final product quality prediction.

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