A survey of surrogate modeling techniques for global sensitivity analysis in hybrid simulation

Hybrid simulation is a method used to investigate the dynamic response of a system subjected to a realistic loading scenario. The system under consideration is divided into multiple individual loading-rate-sensitive substructures, out of which one or more are tested physically, whereas the remaining are simulated numerically. The coupling of all substructures forms the so-called hybrid model. Although hybrid simulation has been extensively used across various engineering disciplines, it is often the case that the hybrid model and related excitation is conceived as deterministic. However, associated uncertainties are present whilst simulation deviation due to their presence could be significant. To this regard, global sensitivity analysis based on Sobol' indices can be used to determine the sensitivity of the hybrid model response due to the presence of the associated uncertainties. Nonetheless, estimation of the Sobol' sensitivity indices requires unaffordable amount of hybrid simulation evaluations. Therefore, surrogate modeling techniques are used to alleviate this burden. In this paper, three different surrogate modeling methods are examined, namely polynomial chaos expansion, Kriging and polynomial chaos Kriging. A case study encompassing a virtual hybrid model is employed and hybrid model response quantities of interest are selected. Their respective surrogates are developed using all three aforementioned techniques. The Sobol' indices obtained utilizing each examined surrogate are compared with each other and results highlight potential deviations.

Download Full-text

A Comparison of Surrogate Modeling Techniques for Global Sensitivity Analysis in Hybrid Simulation

Machine Learning and Knowledge Extraction ◽

10.3390/make4010001 ◽

2021 ◽

Vol 4 (1) ◽

pp. 1-21

Author(s):

Nikolaos Tsokanas ◽

Roland Pastorino ◽

Božidar Stojadinović

Keyword(s):

Sensitivity Analysis ◽

Hybrid Model ◽

Polynomial Chaos ◽

Global Sensitivity Analysis ◽

Hybrid Simulation ◽

Surrogate Modeling ◽

Sobol Indices ◽

Global Sensitivity ◽

Model Response ◽

Modeling Techniques

Hybrid simulation is a method used to investigate the dynamic response of a system subjected to a realistic loading scenario. The system under consideration is divided into multiple individual substructures, out of which one or more are tested physically, whereas the remaining are simulated numerically. The coupling of all substructures forms the so-called hybrid model. Although hybrid simulation is extensively used across various engineering disciplines, it is often the case that the hybrid model and related excitation are conceived as being deterministic. However, associated uncertainties are present, whilst simulation deviation, due to their presence, could be significant. In this regard, global sensitivity analysis based on Sobol’ indices can be used to determine the sensitivity of the hybrid model response due to the presence of the associated uncertainties. Nonetheless, estimation of the Sobol’ sensitivity indices requires an unaffordable amount of hybrid simulation evaluations. Therefore, surrogate modeling techniques using machine learning data-driven regression are utilized to alleviate this burden. This study extends the current global sensitivity analysis practices in hybrid simulation by employing various different surrogate modeling methodologies as well as providing comparative results. In particular, polynomial chaos expansion, Kriging and polynomial chaos Kriging are used. A case study encompassing a virtual hybrid model is employed, and hybrid model response quantities of interest are selected. Their respective surrogates are developed, using all three aforementioned techniques. The Sobol’ indices obtained utilizing each examined surrogate are compared with each other, and the results highlight potential deviations when different surrogates are used.

Download Full-text

A Global Sensitivity Analysis Framework for Hybrid Simulation

10.31224/osf.io/wnqgb ◽

2021 ◽

Author(s):

Giuseppe Abbiati ◽

Stefano Marelli ◽

Nikolaos Tsokanas ◽

Bruno Sudret ◽

Bozidar Stojadinovic

Keyword(s):

Sensitivity Analysis ◽

Hybrid Model ◽

Polynomial Chaos ◽

Global Sensitivity Analysis ◽

Hybrid Simulation ◽

Polynomial Chaos Expansion ◽

Chaos Expansion ◽

Analysis Framework ◽

Global Sensitivity ◽

Sensitivity Indices

Hybrid Simulation is a dynamic response simulation paradigm that merges physical experiments and computational models into a hybrid model. In earthquake engineering, it is used to investigate the response of structures to earthquake excitation. In the context of response to extreme loads, the structure, its boundary conditions, damping, and the ground motion excitation itself are all subjected to large parameter variability. However, in current seismic response testing practice, Hybrid Simulation campaigns rely on a few prototype structures with fixed parameters subjected to one or two ground motions of different intensity. While this approach effectively reveals structural weaknesses, it does not reveal the sensitivity of structure's response. This thus far missing information could support the planning of further experiments as well as drive modeling choices in subsequent analysis and evaluation phases of the structural design process.This paper describes a Global Sensitivity Analysis framework for Hybrid Simulation. This framework, based on Sobol' sensitivity indices, is used to quantify the sensitivity of the response of a structure tested using the Hybrid Simulation approach due to the variability of the prototype structure and the excitation parameters. Polynomial Chaos Expansion is used to surrogate the hybrid model response. Thereafter, Sobol' sensitivity indices are obtained as a by-product of polynomial coefficients, entailing a reduced number of Hybrid Simulations compared to a crude Monte Carlo approach. An experimental verification example highlights the excellent performance of Polynomial Chaos Expansion surrogates in terms of stable estimates of Sobol' sensitivity indices in the presence of noise caused by random experimental errors.

Download Full-text

A global sensitivity analysis framework for hybrid simulation with stochastic substructures

10.31224/osf.io/kjnec ◽

2021 ◽

Author(s):

Nikolaos Tsokanas ◽

Xujia Zhu ◽

Giuseppe Abbiati ◽

Stefano Marelli ◽

Bruno Sudret ◽

...

Keyword(s):

Sensitivity Analysis ◽

Hybrid Model ◽

Global Sensitivity Analysis ◽

Hybrid Simulation ◽

Hybrid Models ◽

Analysis Framework ◽

Global Sensitivity ◽

Sensitivity Indices ◽

Model Response ◽

Realistic Situation

Hybrid simulation is used to investigate the experimental dynamic response of a component or sub-assembly of a prototype structure using a hybrid model. The latter comprises both physically-tested and numerically-simulated substructures interacting with each other in a real-time feedback loop. In this study, we extend our previous work on metamodel-based sensitivity analysis of deterministic hybrid models to the practically more relevant case of stochastic hybrid models. The aim is to cover a more realistic situation where the physical substructure response is not deterministic. A generalized lambda surrogate model recently developed by some of the authors is proposed to surrogate the hybrid model response, and Sobol' sensitivity indices are computed for substructure quantity of interest response quantiles. The effectiveness of the proposed hybrid simulation global sensitivity analysis framework is demonstrated using an experiment.

Download Full-text

A Global Sensitivity Analysis Framework for Hybrid Simulation with Stochastic Substructures

Frontiers in Built Environment ◽

10.3389/fbuil.2021.778716 ◽

2021 ◽

Vol 7 ◽

Author(s):

Nikolaos Tsokanas ◽

Xujia Zhu ◽

Giuseppe Abbiati ◽

Stefano Marelli ◽

Bruno Sudret ◽

...

Keyword(s):

Sensitivity Analysis ◽

Hybrid Model ◽

Surrogate Model ◽

Global Sensitivity Analysis ◽

Hybrid Simulation ◽

Hybrid Models ◽

Analysis Framework ◽

Global Sensitivity ◽

Sensitivity Indices ◽

Realistic Situation

Hybrid simulation is an experimental method used to investigate the dynamic response of a reference prototype structure by decomposing it to physically-tested and numerically-simulated substructures. The latter substructures interact with each other in a real-time feedback loop and their coupling forms the hybrid model. In this study, we extend our previous work on metamodel-based sensitivity analysis of deterministic hybrid models to the practically more relevant case of stochastic hybrid models. The aim is to cover a more realistic situation where the physical substructure response is not deterministic, as nominally identical specimens are, in practice, never actually identical. A generalized lambda surrogate model recently developed by some of the authors is proposed to surrogate the hybrid model response, and Sobol’ sensitivity indices are computed for substructure quantity of interest response quantiles. Normally, several repetitions of every single sample of the inputs parameters would be required to replicate the response of a stochastic hybrid model. In this regard, a great advantage of the proposed framework is that the generalized lambda surrogate model does not require repeated evaluations of the same sample. The effectiveness of the proposed hybrid simulation global sensitivity analysis framework is demonstrated using an experiment.

Download Full-text

Time-Dependent Global Sensitivity Analysis for Long-Term Degeneracy Model Using Polynomial Chaos

Advances in Mechanical Engineering ◽

10.1155/2014/719825 ◽

2014 ◽

Vol 6 ◽

pp. 719825 ◽

Cited By ~ 2

Author(s):

Jianbin Guo ◽

Shaohua Du ◽

Yao Wang ◽

Shengkui Zeng

Keyword(s):

Sensitivity Analysis ◽

Polynomial Chaos ◽

Global Sensitivity Analysis ◽

Time Dependent ◽

Accurate Information ◽

Test Case ◽

Sobol Indices ◽

Global Sensitivity ◽

Mechanism Model

Global sensitivity is used to quantify the influence of uncertain model inputs on the output variability of static models in general. However, very few approaches can be applied for the sensitivity analysis of long-term degeneracy models, as far as time-dependent reliability is concerned. The reason is that the static sensitivity may not reflect the completed sensitivity during the entire life circle. This paper presents time-dependent global sensitivity analysis for long-term degeneracy models based on polynomial chaos expansion (PCE). Sobol’ indices are employed as the time-dependent global sensitivity since they provide accurate information on the selected uncertain inputs. In order to compute Sobol’ indices more efficiently, this paper proposes a moving least squares (MLS) method to obtain the time-dependent PCE coefficients with acceptable simulation effort. Then Sobol’ indices can be calculated analytically as a postprocessing of the time-dependent PCE coefficients with almost no additional cost. A test case is used to show how to conduct the proposed method, then this approach is applied to an engineering case, and the time-dependent global sensitivity is obtained for the long-term degeneracy mechanism model.

Download Full-text

Uncertainty Propagation and Global Sensitivity Analysis in Hybrid Simulation using Polynomial Chaos Expansion

Proceedings of the Fourth International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering ◽

10.4203/ccp.109.23 ◽

2015 ◽

Cited By ~ 1

Author(s):

G. Abbiati ◽

S. Marelli ◽

O.S. Bursi ◽

B. Sudret ◽

B. Stojadinovic

Keyword(s):

Sensitivity Analysis ◽

Polynomial Chaos ◽

Global Sensitivity Analysis ◽

Uncertainty Propagation ◽

Hybrid Simulation ◽

Polynomial Chaos Expansion ◽

Chaos Expansion ◽

Global Sensitivity

Download Full-text

Variance-based global sensitivity analysis and beyond in life cycle assessment: an application to geothermal heating networks

The International Journal of Life Cycle Assessment ◽

10.1007/s11367-021-01921-1 ◽

2021 ◽

Author(s):

Marc Jaxa-Rozen ◽

Astu Sam Pratiwi ◽

Evelina Trutnevyte

Keyword(s):

Sensitivity Analysis ◽

Life Cycle Assessment ◽

Environmental Impacts ◽

Spectral Clustering ◽

Global Sensitivity Analysis ◽

Sobol Indices ◽

Global Sensitivity ◽

Geothermal Heating ◽

Trade Offs ◽

Heating Networks

Abstract Purpose Global sensitivity analysis increasingly replaces manual sensitivity analysis in life cycle assessment (LCA). Variance-based global sensitivity analysis identifies influential uncertain model input parameters by estimating so-called Sobol indices that represent each parameter’s contribution to the variance in model output. However, this technique can potentially be unreliable when analyzing non-normal model outputs, and it does not inform analysts about specific values of the model input or output that may be decision-relevant. We demonstrate three emerging methods that build on variance-based global sensitivity analysis and that can provide new insights on uncertainty in typical LCA applications that present non-normal output distributions, trade-offs between environmental impacts, and interactions between model inputs. Methods To identify influential model inputs, trade-offs, and decision-relevant interactions, we implement techniques for distribution-based global sensitivity analysis (PAWN technique), spectral clustering, and scenario discovery (patient rule induction method: PRIM). We choose these techniques because they are applicable with generic Monte Carlo sampling and common LCA software. We compare these techniques with variance-based Sobol indices, using a previously published LCA case study of geothermal heating networks. We assess eight environmental impacts under uncertainty for three design alternatives, spanning different geothermal production temperatures and heating network configurations. Results In the application case on geothermal heating networks, PAWN distribution-based sensitivity indices generally identify influential model parameters consistently with Sobol indices. However, some discrepancies highlight the potentially misleading interpretation of Sobol indices on the non-normal distributions obtained in our analysis, where variance may not meaningfully describe uncertainty. Spectral clustering highlights groups of model results that present different trade-offs between environmental impacts. Compared to second-order Sobol interaction indices, PRIM then provides more precise information regarding the combinations of input values associated with these different groups of calculated impacts. PAWN indices, spectral clustering, and PRIM have a computational advantage because they yield stable results at relatively small sample sizes (n = 12,000), unlike Sobol indices (n = 100,000 for second-order indices). Conclusions We recommend adding these new techniques to global sensitivity analysis in LCA as they give more precise as well as additional insights on uncertainty regardless of the distribution of the model outputs. PAWN distribution-based global sensitivity analysis provides a computationally efficient assessment of input sensitivities as compared to variance-based global sensitivity analysis. The combination of clustering and scenario discovery enables analysts to precisely identify combinations of input parameters or uncertainties associated with different outcomes of environmental impacts.

Download Full-text

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4041622 ◽

2019 ◽

Vol 14 (2) ◽

Cited By ~ 1

Author(s):

Souransu Nandi ◽

Tarunraj Singh

Keyword(s):

Sensitivity Analysis ◽

Linear Systems ◽

Global Sensitivity Analysis ◽

Benchmark Problems ◽

Model Parameters ◽

Parameter Uncertainties ◽

Sobol Indices ◽

Global Sensitivity ◽

Time Invariant ◽

The Impact

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

Download Full-text