Surrogate Modeling of Ultrasonic Nondestructive Evaluation Simulations

Ultrasonic testing (UT) is used to detect internal flaws in materials or to characterize material properties. Computational simulations are an important part of the UT process. Fast models are essential for UT applications such as inverse design or model-assisted probability of detection. This paper presents investigations of using surrogate modeling techniques to create fast approximate models of UT simulator responses. In particular, we propose to use data-driven surrogate modeling techniques (kriging interpolation), and physics-based surrogate modeling techniques (space mapping), as well a mixture of the two approaches. These techniques are investigated for two cases involving UT simulations of metal components immersed in a water bath during the inspection process

Surrogate modeling of ultrasonic simulations using data-driven methods

Ultrasonic testing (UT) is used to detect internal flaws in materials and to characterize material properties. In many applications, computational simulations are an important part of the inspection-design and analysis processes. Having fast surrogate models for UT simulations is key for enabling efficient inverse analysis and model-assisted probability of detection (MAPOD). In many cases, it is impractical to perform the aforementioned tasks in a timely manner using current simulation models directly. Fast surrogate models can make these processes computationally tractable. This paper presents investigations of using surrogate modeling techniques to create fast approximate models of UT simulator responses. In particular, we propose to integrate data-driven methods (here, kriging interpolation with variable-fidelity models to construct an accurate and fast surrogate model. These techniques are investigated using test cases involving UT simulations of solid components immersed in a water bath during the inspection process. We will apply the full ultrasonic solver and the surrogate model to the detection and characterization of the flaw. The methods will be compared in terms of quality of the responses

Multifidelity Modeling of Ultrasonic Testing Simulations with Cokriging

Multifidelity methods are introduced to the nondestructive evaluation (NDE) of measurement systems. In particular, Cokriging interpolation metamodels of physics-based ultrasonic testing (UT) simulation responses are utilized to accelerate the uncertainty propagation in model-assisted NDE. The proposed approach is applied to a benchmark test case of UT simulations and compared with the current state-of-the-art techniques. The results show that Cokriging captures the physics of the problem well and is able to reduce the computational burden by over one order of magnitude compared to the state of the art. To the best of the author\u27s knowledge, this the first time multifidelity methods are applied to model-assisted NDE problems

Model-assisted probability of detection of flaws in aluminum blocks using polynomial chaos expansions

Probability of detection (POD) is widely used for measuring reliability of nondestructive testing (NDT) systems. Typically, POD is determined experimentally, while it can be enhanced by utilizing physics-based computational models in combination withmodel-assisted POD (MAPOD) methods. With the development of advanced physics-basedmethods, such as ultrasonic NDTtesting, the empirical information,needed for POD methods, can bereduced. However, performing accurate numerical simulationscan be prohibitivelytime-consuming, especially as part of stochastic analysis. In this work, stochastic surrogate models for computational physics-based measurement simulations are developed for cost savings of MAPOD methods while simultaneously ensuring sufficient accuracy. The stochastic surrogate is used to propagate the random input variables through thephysics-basedsimulation model to obtain the joint probability distribution of the output. The POD curves are then generated based on those results. Here, the stochastic surrogates are constructed using nonintrusive polynomial chaos (NIPC) expansions. In particular, the NIPC methods used are the quadrature, ordinary leastsquares (OLS), and least-angle regression sparse (LARS) techniques. The proposed approach is demonstrated on the ultrasonic testing simulation of a flat bottom hole flaw inanaluminum block. The results show that the stochastic surrogates have at least two orders of magnitude faster convergence on the statistics than direct Monte Carlo sampling (MCS). Moreover, the evaluation of the stochastic surrogate models is over three orders of magnitude faster than the underlying simulation modelfor this case,which is the UTSim2 model

Model-Assisted Probability of Detection of Flaws in Aluminum Blocks using Polynomial Chaos Expansions

Probability of detection (POD) is widely used for measuring reliability of nondestructive testing (NDT) systems. Typically, POD is determined experimentally, while it can be enhanced by utilizing physics-based computational models in combination with model-assisted POD (MAPOD) methods. With the development of advanced physics-based methods, such as ultrasonic NDT testing, the empirical information, needed for POD methods, can be reduced. However, performing accurate numerical simulations can be prohibitively time-consuming, especially as part of stochastic analysis. In this work, stochastic surrogate models for computational physics-based measurement simulations are developed for cost savings of MAPOD methods while simultaneously ensuring sufficient accuracy. The stochastic surrogate is used to propagate the random input variables through the physics-based simulation model to obtain the joint probability distribution of the output. The POD curves are then generated based on those results. Here, the stochastic surrogates are constructed using non-intrusive polynomial chaos (NIPC) expansions. In particular, the NIPC methods used are the quadrature, ordinary least-squares (OLS), and least-angle regression sparse (LARS) techniques. The proposed approach is demonstrated on the ultrasonic testing simulation of a flat bottom hole flaw in an aluminum block. The results show that the stochastic surrogates have at least two orders of magnitude faster convergence on the statistics than direct Monte Carlo sampling (MCS). Moreover, the evaluation of the stochastic surrogate models is over three orders of magnitude faster than the underlying simulation model for this case, which is the UTSim2 model

Surrogate Modeling of Ultrasonic Simulations using Data-Driven Methods

Ultrasonic testing (UT) is used to detect internal flaws in materials and to characterize material properties. In many applications, computational simulations are an important part of the inspection-design and analysis processes. Having fast surrogate models for UT simulations is key for enabling efficient inverse analysis and model-assisted probability of detection (MAPOD). In many cases, it is impractical to perform the aforementioned tasks in a timely manner using current simulation models directly. Fast surrogate models can make these processes computationally tractable. This paper presents investigations of using surrogate modeling techniques to create fast approximate models of UT simulator responses. In particular, we propose to integrate data-driven methods (here, kriging interpolation with variable-fidelity models to construct an accurate and fast surrogate model. These techniques are investigated using test cases involving UT simulations of solid components immersed in a water bath during the inspection process. We will apply the full ultrasonic solver and the surrogate model to the detection and characterization of the flaw. The methods will be compared in terms of quality of the responses

Multifidelity Modeling by Polynomial Chaos-Based Cokriging to Enable Efficient Model-Based Reliability Analysis of NDT Systems

This work proposes a novel multifidelity metamodeling approach, the polynomial chaos-based Cokriging (PC-Cokriging). The proposed approach is used for fast uncertainty propagation in a reliability analysis of nondestructive testing systems using model-assisted probability of detection (MAPOD). In particular, PC-Cokriging is a multivariate version of polynomial chaos-based Kriging (PC-Kriging), which aims at combining the advantages of the regression-based polynomial chaos expansions and the interpolation-based Kriging metamodeling methods. Following a similar process as Cokriging, the PC-Cokriging advances PC-Kriging by enabling the incorporation of multifidelity physics information. The proposed PC-Cokriging is demonstrated on two analytical functions and three ultrasonic testing MAPOD cases. The results show that PC-Cokriging outperforms the state-of-the-art metamodeling approaches when providing the same number of training points. Specifically, PC-Cokriging reduces the high-fidelity training sample cost of the Kriging and PCE metamodels by over one order of magnitude, and the PC-Kriging and conventional Cokriging multifidelity metamodeling by up to 50 % to reach the same accuracy level (defined by the root mean squared error being no greater than 1 % of the standard deviation of the testing points). The accuracy and robustness of the proposed method of the key MAPOD metrics versus various detection thresholds are investigated and satisfactory results are obtained

UTSim2 validation

The Center for NDE (CNDE) at Iowa State University has a long history of developing physics models for NDE and packaging these models into simulation tools which make the modeling capabilities accessible to CNDEs industrial sponsors. Recent work at CNDE has led to the development of a new ultrasonic simulation package, UTSim2, which aims to continue this tradition of supporting industrial application of CNDE models. In order to meet this goal, UTSim2 has been designed as an extensible software package which can support previously-developed physics models as well as future models yet to be developed. Initial work has focused on the implementation of a Gauss-Hermite beam model, a paraxial approximation, which is implemented as part of the Thompson-Gray measurement model. This paper will present recent validation results and include comparisons against both previously-validated model output and newly-performed experiments

Incorporation of composite defects from ultrasonic NDE into CAD and FE models

Fiber-reinforced composites are widely used in aerospace industry due to their combined properties of high strength and low weight. However, owing to their complex structure, it is difficult to assess the impact of manufacturing defects and service damage on their residual life. While, ultrasonic testing (UT) is the preferred NDE method to identify the presence of defects in composites, there are no reasonable ways to model the damage and evaluate the structural integrity of composites. We have developed an automated framework to incorporate flaws and known composite damage automatically into a finite element analysis (FEA) model of composites, ultimately aiding in accessing the residual life of composites and make informed decisions regarding repairs. The framework can be used to generate a layer-by-layer 3D structural CAD model of the composite laminates replicating their manufacturing process. Outlines of structural defects, such as delaminations, are automatically detected from UT of the laminate and are incorporated into the CAD model between the appropriate layers. In addition, the framework allows for direct structural analysis of the resulting 3D CAD models with defects by automatically applying the appropriate boundary conditions. In this paper, we show a working proof-of-concept for the composite model builder with capabilities of incorporating delaminations between laminate layers and automatically preparing the CAD model for structural analysis using a FEA software