Process Metamodel Research Articles

Assessment of the Choked Flow Model of RELAP5 for Application of Inverse Quantification Methods

In the framework of deterministic safety analysis, best estimate plus uncertainty methodologies can provide a more informative detailed analysis of transients than conservative approaches. However, one important step in the application of such methodologies is derivation of uncertainty of the physical models. Probability density functions of the physical model parameters are obtained by applying inverse uncertainty quantification (IUQ) methods to experimental data. The present work deals with evaluation of the experimental database and assessment of the simulation model, which are required steps prior to the application of IUQ methods. The U.S. Nuclear Regulatory Commission system code RELAP5 has been applied for simulation of three experimental databases on choked/critical flow: Sozzi-Sutherland, Super MobyDick, and Marviken Critical Flow Tests. First, the adequacy of the experimental data to the specific target domain is carried out, to then proceed to calibration of the input model parameters by combining the use of Gaussian Process metamodels and optimization schemes. The assessment of the simulation models is performed by evaluating independently accuracy, precision, and consistency through four statistical indicators, including a novel indicator to evaluate the consistency of the results. The final results indicate that the model is capable of reproducing the selected experimental database and overall average accuracy, precision, and consistency below the 10% threshold and can be used for application of IUQ methods.

A metamodel of the wire arc additive manufacturing process based on basis spline entities

A metamodel of the wire arc additive manufacturing process based on basis spline entities

Gaussian process metamodel and Markov chain Monte Carlo-based Bayesian inference framework for stochastic nonlinear model updating with uncertainties

The estimation of the posterior probability density function (PDF) of unknown parameters remains a challenge in stochastic nonlinear model updating with uncertainties; thus, a novel Bayesian inference framework based on the Gaussian process metamodel (GPM) and the advanced Markov chain Monte Carlo (MCMC) method is proposed in this paper. The instantaneous characteristics (ICs) of the decomposed measurement response, calculated using the Hilbert transform and the discrete analytical mode decomposition methodology, are extracted as nonlinear indices and further used to construct the likelihood function. Then, the posterior PDFs of structural nonlinear model parameters are derived based on the Bayesian theorem. To precisely calculate the posterior PDF, an advanced MCMC approach, i.e., delayed rejection adaptive Metropolis-Hastings (DRAM) algorithm, is adopted with the advantages of a high acceptance ratio and strong robustness. However, as a common shortage in most MCMC methods, the resampling technology is still applied, and numerous iterations of nonlinear simulations are conducted to ensure accuracy, thus directly reducing the computational efficiency of the DRAM. To address the abovementioned issue, a mathematical regression metamodel of the GPM with a polynomial kernel function is adopted in this paper instead of the traditional finite element model (FEM) to simulate a nonlinear response for the reduction of computational cost, and the hyperparameters are further estimated using the conjugate gradient optimization methodology. Finally, numerical simulations concerning a Giuffré–Menegotto–Pinto modeled steel-frame structure and a seven-storey base-isolated structure are conducted. Furthermore, a shake-table experimental test of a nonlinear steel framework is investigated to validate the accuracy of the Bayesian inference method. Both simulations and experiment demonstrate that the proposed GPM and DRAM-based Bayesian method effectively estimates the posterior PDF of unknown parameters and is appropriate for stochastic nonlinear model updating even with multisource uncertainties.

Assessment of adaptive optics‐corrected optical links statistics from integrated turbulence parameters through a Gaussian process metamodel

SummaryWith the development of free space optical links (FSO) for space‐ground communications comes the need to mitigate the effects of the atmospheric turbulence to guarantee a lossless connection. By having a network of addressable ground stations, we want to guarantee to always target a point where the link is available. Assuming atmospheric transmission is managed thanks to site diversity, we focus only on the influence of atmospheric turbulence on the signal injected into a single mode fiber on the downlink. The use of adaptive optics (AO) is assumed to avoid turbulence‐induced signal disruptions and enable a sufficiently high level of received signal for data transmission. Up to now, AO performance adequate assessment required the knowledge of high‐resolution and wind profiles. With the advent of integrated atmospheric parameters measurement instruments, we investigate here the possibility to estimate AO‐corrected performance from a limited number of integrated parameters. In this paper, we propose to use a Gaussian process metamodel to assess the statistics of the received optical power after an AO correction. Taking as input only four integrated parameters of the turbulence profile and associated wind profile, which can be measured with simple instruments, the estimation error on the value of the 1% quantile of the received optical power is inferior to . We also demonstrate the possibility to estimate the half correlation time of the received optical power using the same integrated parameters.

Efficient Bayesian automatic calibration of a functional-structural wheat model using an adaptive design and a metamodelling approach.

Functional-structural plant models are increasingly being used by plant scientists to address a wide variety of questions. However, the calibration of these complex models is often challenging, mainly because of their high computational cost, and, as a result, error propagation is usually ignored. Here we applied an automatic method to the calibration of WALTer: a functional-structural wheat model that simulates the plasticity of tillering in response to competition for light. We used a Bayesian calibration method to jointly estimate the values of five parameters and quantify their uncertainty by fitting the model outputs to tillering dynamics data. We made recourse to Gaussian process metamodels in order to alleviate the computational cost of WALTer. These metamodels are built from an adaptive design that consists of successive runs of WALTer chosen by an efficient global optimization algorithm specifically adapted to this particular calibration task. The method presented here performed well on both synthetic and experimental data. It is an efficient approach for the calibration of WALTer and should be of interest for the calibration of other functional-structural plant models.

Gaussian process metamodels for floating offshore wind turbine platforms

The dynamics of floating offshore wind turbines (FOWT) are quite complex as it involves interactions in multiple domains. The dynamic response of FOWT is numerically evaluated using coupled aero-hydro-servo-elastic analysis. In the design stages, the dynamic analysis of FOWT is carried out for different environmental conditions. These analyses can be time-consuming and computationally expensive. This paper proposes the use of metamodels based on the Gaussian process for representing the hydrodynamics and structural dynamics of the floating platform. The input to Gaussian process metamodels is taken as wave elevation, forces and moments at the interface of the tower and platform. The output of the metamodels is the displacements (surge, sway and heave) and the rotations (roll, pitch and yaw) of the platform. Three different Gaussian process metamodels are considered in this paper — Standard Gaussian Process, Variational Heteroscedastic Gaussian Process and Sparse Spectrum Gaussian Process. The construction of the metamodels is demonstrated for an NREL 5MW turbine supported on an ITI barge platform. The performance of the Gaussian metamodels is compared in terms of evaluation indices, convergence, residuals and computational efficiency. The sensitivity analysis of the metamodels is carried out to verify that the interdependence between the variables is captured accurately. All three Gaussian process metamodels are found to be effective in emulating the response of the platform. These models can be effectively used in situations where simple and computationally inexpensive models are required.

Partitioning the contributions of dependent offshore forcing conditions in the probabilistic assessment of future coastal flooding

Abstract. Getting a deep insight into the role of coastal flooding drivers is of great interest for the planning of adaptation strategies for future climate conditions. Using global sensitivity analysis, we aim to measure the contributions of the offshore forcing conditions (wave–wind characteristics, still water level and sea level rise (SLR) projected up to 2200) to the occurrence of a flooding event at Gâvres town on the French Atlantic coast in a macrotidal environment. This procedure faces, however, two major difficulties, namely (1) the high computational time costs of the hydrodynamic numerical simulations and (2) the statistical dependence between the forcing conditions. By applying a Monte Carlo-based approach combined with multivariate extreme value analysis, our study proposes a procedure to overcome both difficulties by calculating sensitivity measures dedicated to dependent input variables (named Shapley effects) using Gaussian process (GP) metamodels. On this basis, our results show the increasing influence of SLR over time and a small-to-moderate contribution of wave–wind characteristics or even negligible importance in the very long term (beyond 2100). These results were discussed in relation to our modelling choices, in particular the climate change scenario, as well as the uncertainties of the estimation procedure (Monte Carlo sampling and GP error).

Bayesian Inference With Gaussian Process Surrogates to Characterize Anisotropic Mechanical Properties of Skin From Suction Tests.

One of the intrinsic features of skin and other biological tissues is the high variation in the mechanical properties across individuals and different demographics. Mechanical characterization of skin is still a challenge because the need for subject-specific in vivo parameters prevents us from utilizing traditional methods, e.g., uniaxial tensile test. Suction devices have been suggested as the best candidate to acquire mechanical properties of skin noninvasively, but capturing anisotropic properties using a circular probe opening-which is the conventional suction device-is not possible. On the other hand, noncircular probe openings can drive different deformations with respect to fiber orientation and therefore could be used to characterize the anisotropic mechanics of skin noninvasively. We propose the use of elliptical probe openings and a methodology to solve the inverse problem of finding mechanical properties from suction measurements. The proposed probe is tested virtually by solving the forward problem of skin deformation by a finite element (FE) model. The forward problem is a function of the material parameters. In order to solve the inverse problem of determining skin properties from suction data, we use a Bayesian framework. The FE model is an expensive forward function, and is thus substituted with a Gaussian process metamodel to enable the Bayesian inference problem.

META-MODEL OF DESIGN OF INFORMATION TECHNOLOGY PROTOTYPE OF CLASSIFICATION OF OBJECTS BY IMAGE SHAPE USING GMDH NEURAL NETWORKS IN THE NOTATION OF A UNIFIED MODELING LANGUAGE

The article is devoted to the development of intelligent monitoring systems of technological processes based on the use of machine vision systems. The principles of object-oriented formalization of the process of designing information technology of the classification of objects by the geometric shape of the image obtained from the machine vision system are proposed in the article. The proposed information technology is based on the use of machine learning technologies and provides for the selection of the best structure of the classifier model from a set of candidate models. Construction of candidate models is based on the use of the group method of data handling, based on the principles of self-organization of models. The outline of the image of the object obtained from the intelligent monitoring system is the input information. The set of input data contains a set of morphometric parameters that describe the geometric shape of the figure formed by the contour of the image of the object, as well as the label of the class to which the object belongs. The formation of the set of input data is implemented in the block «Image Processing». The decisive rule of classification is built in the block of synthesis of models of information technology of classification. GMDH neural networks were used as an algorithm for model synthesis. The choice of the best structure of the model is performed by a set of criteria. The information technology for constructing the classifier model is implemented by supplementing the block of algorithms for synthesis of MSUA models with the block «Class of models», which implements the process of selecting the class of functions for building models, and the block «Verification of models», which implements the best model structure. Construction of the meta-model of the design process was performed using a unified modeling language. The functional meta-model is represented by a use case diagram.

(Invited) Combining Machine Learning, DFT, EFM, and Modeling to Design Nanodielectric Behavior

Polymer Nanodielectrics are class of materials with intriguing combinations of properties. Predicting and designing the properties, however, is complex due to the number of parameters controlling the properties. This makes it difficult to compare results across groups, validate models, and develop a design methodology. This presentation will share a recent approach to developing a data driven design methodology grounded in physics-based models and experimental calibration. We combine finite element modeling of dielectric constant and loss functions with a Monte Carlo multi-scale simulation of carrier hopping to predict break down strength. Filler dispersion, filler geometry, isotropy and interface properties are explicitly taken into to account to compute objective functions for ideal nanodielectric insulators. Further, we have used machine learning to develop an EFM technique for directly measuring the dielectric constant of the nanoscale interfacial region as critical input to our models. Ultimately, we calculate the Pareto frontier with respect to nanocomposite constitute properties and geometry to optimize properties.The finite element approach can be used to forward predict properties based on the properties of the interfacial region and filler dispersion, or as an inverse tool to calculate interface properties or develop optimized filler morphologies. The breakdown strength model critically depends on the energy distribution of trap states that inhibit space charge motion. We have developed an ab initio approach to determine the trap states at amorphous interfaces, and have used that to do a systematic analyses of trap distributions in composites with functionalized particle interfaces. The models all use 3D particle distributions based on 2D imaging (TEM) of the composites and publicly available tools for binarization and characterization of filler morphology. Finally, we use a design of experiment approach (Latin Hybercube Design) to sample the complete experimental design space, and using calibrated models and morphologies, create a data set spanning the full set of parameters. We use the data from the DOE to train a Gaussian Process metamodel and a genetic algorithm to determine which designs fulfill the design parameters. The talk will present several case studies as examples.The data for this work was accessed from a new data resource, MaterialsMine, using FAIR (Findable, Accessible, Interoperable, and Reusable) principles. MaterialsMine is an open source data repository, and resource. It includes unique visualization tools as well as modeling and characterization resources.

(Invited) Combining Machine Learning, DFT, EFM, and Modeling to Design Nanodielectric Behavior

Predicting and designing the properties of polymer nanodielectrics is challenging due to the number of parameters controlling properties and the breadth of scale (from electronic to mm). This paper summarizes a preliminary study using elongated semiconducting nanoparticles with an extrinsic interface that enhanced carrier trapping to attempt to find a parameter space that allows for improved permittivity and breakdown strength without increasing loss. We combine finite element modeling of dielectric constant with a Monte Carlo multi-scale simulation of carrier hopping to predict break down strength. Filler dispersion, filler geometry, isotropy and interface trapping properties are explicitly taken into account to compute design objectives associated with dielectric constant and mobility. Ultimately, we trained a latent variable Gaussian Process (LVGP) metamodel that can take both qualitative (e.g., orientation and dispersion states) and quantitative variables (e.g., microstructure descriptors) as inputs to predict properties over a broader range with observed tradeoffs.

Metamodeling of a deep drawing process using conditional Generative Adversarial Networks

Optimization tasks as well as quality predictions for process control require fast responding process metamodels. A common strategy for sheet metal forming is building fast data driven metamodels based on results of Finite Element (FE) process simulations. However, FE simulations with complex material models and large parts with many elements consume extensive computational time. Hence, one major challenge in developing metamodels is to achieve a good prediction precision with limited data, while these predictions still need to be robust against varying input parameters. Therefore, the aim of this study was to evaluate if conditional Generative Adversarial Networks (cGAN) are applicable for predicting results of FE deep drawing simulations, since cGANs could achieve high performance in similar tasks in previous work. This involves investigations of the influence of data required to achieve a defined precision and to predict e.g. wrinkling phenomena. Results show that the cGAN used in this study was able to predict forming results with an averaged absolute deviation of sheet thickness of 0.025 mm, even when using a comparable small amount of data.

Iterative method for tuning complex simulation code

Tuning a complex simulation code refers to the process of improving the agreement of a code calculation with respect to a set of experimental data by adjusting parameters implemented in the code. This process belongs to the class of inverse problems or model calibration. For this problem, the approximated nonlinear least squares (ANLS) method based on a Gaussian process (GP) metamodel has been employed by some researchers. A potential drawback of the ANLS method is that the metamodel is built only once and not updated thereafter. To address this difficulty, we propose an iterative algorithm in this study. In the proposed algorithm, the parameters of the simulation code and GP metamodel are alternatively re-estimated and updated by maximum likelihood estimation and the ANLS method. This algorithm uses both computer and experimental data repeatedly until convergence. A study using toy-models including inexact computer code with bias terms reveals that the proposed algorithm performs better than the ANLS method and the conditional-likelihood-based approach. Finally, an application to a nuclear fusion simulation code is illustrated.

Machine Learning Surrogate Modeling for Meshless Methods: Leveraging Universal Approximation

This paper presents a machine learning (ML) surrogate modeling for fast processing in meshless/ meshfree methods. The main idea is to leverage the universal approximation (UA) propriety of supervised ML models (shallow/ deep learning and other regression models) to surrogate the heavy shape function construction in meshless methods. The resulting ML metamodel preserves the same accuracy of the meshless interpolation while avoiding costly matrix inversion operations. The total computation time for solving 3D test simulation problems (using more than 20[Formula: see text]k nodes) is reduced by a factor of 1[Formula: see text]k in the case of the Gaussian process (GP) metamodel.

Uncertainty quantification and prediction for mechanical properties of graphene aerogels via Gaussian process metamodels

Graphene aerogels (GAs), a special class of 3D graphene assemblies, are well known for their exceptional combination of high strength, lightweightness, and high porosity. However, due to microstructural randomness, the mechanical properties of GAs are also highly stochastic, an issue that has been observed but insufficiently addressed. In this work, we develop Gaussian process metamodels to not only predict important mechanical properties of GAs but also quantify their uncertainties. Using the molecular dynamics simulation technique, GAs are assembled from randomly distributed graphene flakes and spherical inclusions, and are subsequently subject to a quasi-static uniaxial tensile load to deduce mechanical properties. Results show that given the same density, mechanical properties such as the Young’s modulus and the ultimate tensile strength can vary substantially. Treating density, Young’s modulus, and ultimate tensile strength as functions of the inclusion size, and using the simulated GA results as training data, we build Gaussian process metamodels that can efficiently predict the properties of unseen GAs. In addition, statistically valid confidence intervals centered around the predictions are established. This metamodel approach is particularly beneficial when the data acquisition requires expensive experiments or computation, which is the case for GA simulations. The present research quantifies the uncertain mechanical properties of GAs, which may shed light on the statistical analysis of novel nanomaterials of a broad variety.

The ICSCREAM Methodology: Identification of Penalizing Configurations in Computer Experiments Using Screening and Metamodel—Applications in Thermal Hydraulics

In the framework of risk assessment in nuclear accident analysis, best-estimate computer codes associated with probabilistic modeling of uncertain input variables are used to estimate safety margins. Often, a first step in such uncertainty quantification studies is to identify the critical configurations (or penalizing, in the sense of a prescribed safety margin) of several input parameters (called scenario inputs) under the uncertainty of the other input parameters. However, the large CPU-time cost of most of the computer codes used in nuclear engineering, as the ones related to thermal-hydraulic accident scenario simulations, involves developing highly efficient strategies. This work focuses on machine learning algorithms by way of a metamodel-based approach (i.e., a mathematical model that is fitted on a small sample of simulations). To achieve it with a very large number of inputs, a specific and original methodology called Identification of penalizing Configurations using SCREening And Metamodel (ICSCREAM) is proposed. The screening of influential inputs is based on an advanced global sensitivity analysis tool (Hilbert-Schmidt Independence Criterion importance measures). A Gaussian process metamodel is then sequentially built and used to estimate within a Bayesian framework the conditional probabilities of exceeding a high-level threshold according to the scenario inputs. The efficiency of this methodology is illustrated with two high-dimensional (around a hundred inputs) thermal-hydraulic industrial cases simulating an accident of primary coolant loss in a pressurized water reactor. For both use cases, the study focuses on the peak cladding temperature (PCT), and critical configurations are defined by exceeding the 90%-quantile of the PCT. In both cases, using only around one thousand code simulations, the ICSCREAM methodology allows one to estimate the impact of the scenario inputs and their critical areas of values.

Uncertainty analysis of curing-induced dimensional variability of composite structures utilizing physics-guided Gaussian process meta-modeling

Composite manufacturing process involves a suite of complex and inter-related procedures that span across multiple physics domains and scales. A variety of uncertainties that inevitably exist may degrade the quality of composites produced. Quantitatively characterizing the effect of uncertainties in such process hence becomes critically important. In this study, we establish a systematic framework for uncertainty analysis of composite manufacturing process. A finite element processing model has been developed to characterize the multi-physics and multi-scale nature of composite manufacturing process, based upon which a Gaussian process (GP) meta-model has been synthesized for efficient uncertainty quantification. By leveraging the well-trained GP meta-model, an importance ranking analysis of uncertainties was then carried out using a series of metrics, i.e., Pearson coefficient, Sobol index and Shapley Additive exPlanations (SHAP). Since the physics-based processing model involves several simplifying assumptions and empirical relations, modeling errors were also considered in the uncertainty analysis. Comprehensive case studies, which aim at elucidating the causes of composite spring-in angles, were conducted to examine the feasibility and validity of this new framework. Specifically, the mean error of GP predictions is smaller than 2%, and the uncertainty importance ranking can be obtained with high confidence in both cases with and without modeling errors.

Adaptive batching for Gaussian process surrogates with application in noisy level set estimation

AbstractWe develop adaptive replicated designs for Gaussian process metamodels of stochastic experiments. Adaptive batching is a natural extension of sequential design heuristics with the benefit of replication growing as response features are learned, inputs concentrate, and the metamodeling overhead rises. Motivated by the problem of learning the level set of the mean simulator response, we develop five novel schemes: Multi‐Level Batching (MLB), Ratchet Batching (RB), Adaptive Batched Stepwise Uncertainty Reduction (ABSUR), Adaptive Design with Stepwise Allocation (ADSA), and Deterministic Design with Stepwise Allocation (DDSA). Our algorithms simultaneously (MLB, RB, and ABSUR) or sequentially (ADSA and DDSA) determine the sequential design inputs and the respective number of replicates. Illustrations using synthetic examples and an application in quantitative finance (Bermudan option pricing via Regression Monte Carlo) show that adaptive batching brings significant computational speed‐ups with minimal loss of modeling fidelity.

Evaluating Gaussian process metamodels and sequential designs for noisy level set estimation

We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic simulators, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student-t observations; (ii) Student-t processes (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1–6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.

Targeted Reduction of p-Boxes in Risk Assessments With Mixed Aleatory and Epistemic Uncertainties

Abstract The treatment of uncertainty using extra-probabilistic approaches, like intervals or p-boxes, allows for a clear separation between epistemic uncertainty and randomness in the results of risk assessments. This can take the form of an interval of failure probabilities; the interval width W being an indicator of “what is unknown.” In some situations, W is too large to be informative. To overcome this problem, we propose to reverse the usual chain of treatment by starting with the targeted value of W that is acceptable to support the decision-making, and to quantify the necessary reduction in the input p-boxes that allows achieving it. In this view, we assess the feasibility of this procedure using two case studies (risk of dike failure, and risk of rupture of a frame structure subjected to lateral loads). By making the link with the estimation of excursion sets (i.e., the set of points where a function takes values below some prescribed threshold), we propose to alleviate the computational burden of the procedure by relying on the combination of Gaussian process (GP) metamodels and sequential design of computer experiments. The considered test cases show that the estimates can be achieved with only a few tens of calls to the computationally intensive algorithm for mixed aleatory/epistemic uncertainty propagation.