Moment-independent Global Sensitivity Analysis Research Articles

Stability Evaluation of Slope Based on Global Sensitivity Analysis

The uncertainty of parameters will have a significant impact on slope stability, where sensitivity analysis is a commonly used method in uncertainty research. However, traditional sensitivity analysis method costs much computation time. When calculating the sensitivity index of one parameter, all other parameters are taken as fixed values, and the uncertainty of all parameters cannot be considered simultaneously. Therefore, the variance-based and the moment-independent global sensitivity analysis (GSA) methods are both introduced to determine the influence of geotechnical parameters on slope stability in this study. To solve the importance index of GSA, the least angle regression algorithm, the kernel density estimation, and orthogonal polynomial estimation methods are developed to obtain variance-based importance index and the moment-independent importance index, respectively. The proposed methods allow all variables to change simultaneously within their variation range and have high computational efficiency. The results are in good at with those obtained by the variance-based Monte Carlo simulation method, which is considered as the exact solution forobtaining the importance index. The influence of the correlation between the shear strength parameters (c and φ) on the importance index is also studied, which indicates that the negative correlation will have a great impact on the importance index, which in turn affects the safety assessment of slope. Three engineering cases have been studied for engineering application, and the compared results indicate that the impact of the geotechnical parameters uncertainty on the safety factor (Fs) and failure probability (pf) are different. Therefore, the approaches based on GSA which can integrate the Fs with pf will be a promising approach for slope stability evaluation.

A Bayesian multi-model inference methodology for imprecise moment-independent global sensitivity analysis of rock structures

Traditional global sensitivity analysis (GSA) neglects the epistemic uncertainties associated with the probabilistic characteristics (i.e. type of distribution type and its parameters) of input rock properties emanating due to the small size of datasets while mapping the relative importance of properties to the model response. This paper proposes an augmented Bayesian multi-model inference (BMMI) coupled with GSA methodology (BMMI-GSA) to address this issue by estimating the imprecision in the moment-independent sensitivity indices of rock structures arising from the small size of input data. The methodology employs BMMI to quantify the epistemic uncertainties associated with model type and parameters of input properties. The estimated uncertainties are propagated in estimating imprecision in moment-independent Borgonovo's indices by employing a reweighting approach on candidate probabilistic models. The proposed methodology is showcased for a rock slope prone to stress-controlled failure in the Himalayan region of India. The proposed methodology was superior to the conventional GSA (neglects all epistemic uncertainties) and Bayesian coupled GSA (B-GSA) (neglects model uncertainty) due to its capability to incorporate the uncertainties in both model type and parameters of properties. Imprecise Borgonovo's indices estimated via proposed methodology provide the confidence intervals of the sensitivity indices instead of their fixed-point estimates, which makes the user more informed in the data collection efforts. Analyses performed with the varying sample sizes suggested that the uncertainties in sensitivity indices reduce significantly with the increasing sample sizes. The accurate importance ranking of properties was only possible via samples of large sizes. Further, the impact of the prior knowledge in terms of prior ranges and distributions was significant; hence, any related assumption should be made carefully.

Mutual information for explainable deep learning of multiscale systems

Timely completion of design cycles for complex systems ranging from consumer electronics to hypersonic vehicles relies on rapid simulation-based prototyping. The latter typically involves high-dimensional spaces of possibly correlated control variables (CVs) and quantities of interest (QoIs) with non-Gaussian and possibly multimodal distributions. We develop a model-agnostic, moment-independent global sensitivity analysis (GSA) that relies on differential mutual information to rank the effects of CVs on QoIs. The data requirements of this information-theoretic approach to GSA are met by replacing computationally intensive components of the physics-based model with a deep neural network surrogate. Subsequently, the GSA is used to explain the surrogate predictions, and the surrogate-driven GSA is deployed as an uncertainty quantification emulator to close design loops. Viewed as an uncertainty quantification method for interrogating the surrogate, this framework is compatible with a wide variety of black-box models. We demonstrate that the surrogate-driven mutual information GSA provides useful and distinguishable rankings via a validation step for applications of interest in energy storage. Consequently, our information-theoretic GSA provides an “outer loop” for accelerated product design by identifying the most and least sensitive input directions and performing subsequent optimization over appropriately reduced parameter subspaces.

A novel single-loop simulation method and its combination with adaptive kriging for moment-independent global sensitivity analysis

The moment-independent global sensitivity (MIGS) analysis can help decision makers to efficiently reduce the uncertainty of model output. This article proposes a novel single-loop simulation (NSLS) method for MIGS analysis. Through an interval discretization strategy, estimation of probability density functions (PDFs) in existing methods is transformed to estimation of the marginal probability of the input, the marginal probability of the output and the joint probability of the inputs–output in NSLS, which avoids the computational complexity and error resulting from PDF estimation in MIGS analysis. To drastically reduce the computational cost of NSLS to estimate the MIGS index, an NSLS-based adaptive kriging (NSLS-AK) method is subsequently developed. In NSLS-AK, a rough global kriging model is first constructed, then this kriging model is adaptively updated until the convergent condition is satisfied for accurately and efficiently predicting the responses of the samples in estimating the MIGS index.

Time-dependent reliability moment-independent global sensitivity analysis of planar motion mechanisms

The planar motion mechanisms are widely applied in aerospace field to realize the scheduled output. A moment-independent global sensitivity analysis method (MIGSA) is developed for time-dependent reliability of planar motion mechanisms. The defined sensitivity index can indicate the influence of the uncertainty of the input variables in the entire uncertain region on time-dependent reliability of the planar motion mechanisms. An active learning Kriging (ALK) model is established to solve time-dependent failure probability as well as sensitivity index efficiently. A representative rack-and-pinion steering linkage example is investigated for validating its significance of the time-dependent reliability MIGSA method in this paper, and the efficiency of ALK method for approximating the time-dependent reliability MIGSA index.

Exploring the direct influence of control parameters of experimental facility for fuel cells based on improved generalized regression neural network

The exploration of the control parameters for experimental facility in terms of their coupling effects can provide direct guidance for experimental research of fuel cells. In this study, a model based on an improved generalized regression neural network (GRNN) is proposed to study the coupling effect of control parameters that can be set and adjusted directly during the experiment. In addition, the expectation-maximization algorithm and the ensemble filter algorithm are introduced to preprocess data; the adaptive learning factor and the differential evolution strategy are introduced to improve the GRNN. Moreover, a moment-independent global sensitivity analysis is introduced to apply for sensitivity analysis by the dimensional reduction technique and principle of maximum entropy. The results indicated that the improved model can accurately predict performance in a dynamic environment; the relative error was <1.7%, the prediction errors were, respectively, reduced by 35.61%, 19.78%, 60.99%, and 37.55% as compared with the GRNN model, demonstrating the effectiveness of the improvement strategy; the back pressure and inlet temperatures, dew point, and cell temperatures were classified as sensitive factors; when the anodic back pressure was approximately 1 atm, the cathodic back pressure had little influence, the performance conforms to the maximum level.

Improvement of the uncertainty method with model treatment and optimized global sensitivity analysis and its application to pressurized water reactor

Best estimate plus uncertainty methodology is an advanced technology for licensing application of the nuclear power plants, but some aspects can still be improved in the conventional input-driven methodologies. For instance, uncertainties of the closure models are not properly handled; local sensitivity analysis methods not suitable for complex nuclear systems are still widely utilized; the sensitivity analysis process needs to be performed again every time new parameters are identified. Optimization researches were carried out in the study. A structural method was proposed to quantify the uncertainties of the closure models, and a low-cost moment-independent global sensitivity analysis method was developed to improve the sensitivity analysis framework. By integrating the improvements into the conventional input-driven framework, an uncertainty method with model treatment and improved sensitivity analysis was obtained. Finally, the method was validated through a large break loss of coolant accident in a three-loop pressurized water reactor.

Parameter importance ranking for SBLOCA of CPR1000 with moment-independent sensitivity analysis

The phenomenon identification and ranking table (PIRT) is an important basis in the nuclear power plant (NPP) thermal-hydraulic analysis. This study focuses on the importance ranking of the input parameters when lacking the PIRT, and the target scenario is the small break loss of coolant accident (SBLOCA) in a pressurized water reactor (PWR) CPR1000. A total of 54 input parameters which might have influence on the figure of merit (FOM) were identified, and the sensitivity measure of each input on the FOM was calculated through an optimized moment-independent global sensitivity analysis method. The importance ranking orders of the parameters were transformed into the Savage scores, and the parameters were categorized based on the Savage scores. A parameter importance ranking table for the SBLOCA scenario of the CPR1000 reactor was obtained, and the influences of some important parameters at different break sizes and different accident stages were analyzed.

Optimization of sensitivity analysis in best estimate plus uncertainty and the application to large break LOCA of a three-loop pressurized water reactor

The best estimate plus uncertainty (BEPU) methodology is developed to carry out realistic safety analysis of the nuclear power plant. However, the sensitivity analysis in the conventional methodologies often leads to inaccurate results when lacking of the phenomenon identification and ranking table (PIRT) or adopting the local sensitivity analysis methods. As the initial inputs determined in short of the PIRT may neglect some important parameters or identify some unimportant parameters, and the local methods are not appropriate for complex and non-linear systems. In this study, an optimized moment-independent global sensitivity analysis method with very low computational cost was utilized to improve the sensitivity analysis framework of the BEPU methodology. The reliability as well as the applicability of the method were assessed through some tests and a large break loss of coolant accident (LBLOCA) of the LOFT facility. The improved sensitivity analysis framework was then applied to the BEPU analysis of a typical three-loop pressurized water reactor CPR1000, and the reliability of the optimized moment-independent method was further confirmed by comparing the sensitivity analysis result of the method to the results of the BEMUSE project and the Spearman method. Besides, two new parameters were identified to have great influence on the PCT, and the two parameters should be taken into consideration in the uncertainty analysis of the BEPU methodology.

Fatigue dynamic reliability and global sensitivity analysis of double random vibration system based on Kriging model

ABSTRACT In this paper, the dynamic reliability and global sensitivity analysis method of double random vibration system is proposed, considering structure uncertainty and excitation uncertainty of complex mechanical and structural systems under random load. Based on the Miner criterion of fatigue failure of structures, the dynamic responses of structures under the condition of double random vibration are analyzed, and the dynamic reliability analysis method is established. Furthermore, the moment-independent global sensitivity index of random structures is proposed, which can quantitatively reflect the effects of random structure parameters on dynamic reliability under random excitation and provide reference for structure reliability optimization design. Based on the proposed dynamic reliability moment-independent global sensitivity analysis (GSA) index, this paper combines the computationally efficient active learning Kriging (ALK) method to establish the solving method. Finally, the rationality and correctness of the dynamic reliability GSA index and the ALK method proposed in this paper are illustrated by comparing the results with those gained by Monte Carlo simulation (MCS) method. The results prove that the GSA has significantly guided meaning and referenced value in the dynamic reliability design and optimization for the double random vibration system, especially for the engineering practice.

Dynamic Reliability and Global Sensitivity Analysis for Hydraulic Pipe Based on Sparse Grid Integral Method

Abstract Due to the extremely rough working environment, aero-hydraulic pipes face serious dynamic failure problems in applications for practical engineering. This paper proposes a dynamic reliability and moment-independent global sensitivity analysis (GSA) method to evaluate the dynamic reliability and the effects of random input variables on the dynamic reliability of aero-hydraulic pipes. Based on the Miner criterion for the cumulative damage of structural fatigue, this paper establishes the dynamic reliability analysis method under the condition of double random vibration. In order to further analyze the influence of the uncertainty of each random variable of pipe on its dynamic reliability, a moment-independent global sensitivity index for dynamic reliability based on cumulative distribution function is proposed in this paper. The index can reflect the effects of random variables on dynamic reliability quantitatively. Based on the proposed GSA method of dynamic reliability, a sparse grid integral (SGI) method is introduced to solve the dynamic reliability and moment-independent global sensitivity index, with high computational efficiency. Finally, the effects of clamp supports, diameters, and curvature of curved pipe on the dynamic reliability and GSA are analyzed through a hydraulic piping example.

Resonance risk and global sensitivity analysis of a straight–curved combination pipe based on active learning Kriging model

The resonance failure of straight–curved combination pipes conveying fluid which are widely used in engineering is becoming a serious issue. But there are only few studies available on the resonance failure of combination pipes. The resonance failure probability and global sensitivity analysis of straight–curved combination pipes conveying fluid are studied by the active learning Kriging method proposed in this article. Based on the Euler–Bernoulli beam theory, the dynamic stiffness matrices of straight and curved pipes are derived in the local coordinate system, respectively. Then the dynamic stiffness matrix and characteristic equation of a straight–curved combination pipe conveying fluid are assembled under a global coordinate system. The natural frequency is calculated based on the characteristic equation. A resonance failure performance function is established based on the resonance failure mechanism and relative criterions. The active learning Kriging model based on expected risk function is introduced for calculating the resonance failure probability and moment-independent global sensitivity analysis index. The importance rankings of input variables are obtained with different velocities. According to the results, it is shown that the method proposed in this article provides a lot of guidance for resonance reliability analysis and anti-resonance design in combination pipes conveying fluid.

An efficient method for moment-independent global sensitivity analysis by dimensional reduction technique and principle of maximum entropy

Probability density function (PDF)-based and failure probability (FP)-based moment-independent global sensitivity indices can commendably reflect the influence of model input on the whole distribution and partial distribution (or called FP) of model output respectively, yet how to efficiently and accurately estimate these two indices for guiding the engineering practice still remains an essential and challenging problem. In this paper, a novel PDF estimation based method is proposed, which equivalently transforms the computation of these two indices into that of the unconditional and conditional fractional moments of model output. To estimate them, an efficient and simple way is introduced based on a multiplicative version of the dimensional reduction method. The proposed method remarkably reduces the computational cost and can obtain these two indices simultaneously by reusing the information in the integration grid. Results of three case studies demonstrate the effectiveness of the proposed method and its good engineering application.

A review of global sensitivity analysis for uncertainty structure

This paper mainly reviews some widely used global sensitivity analysis methods for uncertainty structure, in which the uncertainty is described by probability theory. Global sensitivity analysis can be divided into single output global sensitivity analysis and multivariate global sensitivity analysis based on the number of output response of the structure. The single output global sensitivity analysis has been studied by many researchers and obtains widely development. Due to the different ways of representing uncertainty in probability theory (variance, probability density function, cumulative distribution function, etc.), different global sensitivity analysis methods (variance based method, moment-independent method, etc.) have been proposed. For example, the variance based global sensitivity analysis method can reflect the structure of the model itself and has been widely studied and applied in engineering; while the moment independent global sensitivity analysis method has a more comprehensive description of the uncertainty and reflects more uncertainty information. The multivariate output global sensitivity analysis is developed based on the single output global sensitivity analysis and it mainly focuses on the effects of input variables on the uncertainty of the whole multivariate output. For the models with multivariate outputs, the correlation between different outputs exists and it should be considered when performing the global sensitivity analysis. Comparing to the single output global sensitivity analysis, the multivariate output global sensitivity analysis is much more complicated and computational demanding since there are more uncertainty information for the multivariate outputs. The basic theories of different global sensitivity analysis methods are described in detail in order to have better understanding of these methods. Numerical examples are also used to compare these different methods. Through the comparison, the advantages and shortage of different global sensitivity analysis methods are obtained.

Comparison of variance-based and moment-independent global sensitivity analysis approaches by application to the SWAT model

Global Sensitivity Analysis (GSA) is an essential technique to support the calibration of environmental models by identifying the influential parameters (screening) and ranking them.In this paper, the widely-used variance-based method (Sobol') and the recently proposed moment-independent PAWN method for GSA are applied to the Soil and Water Assessment Tool (SWAT), and compared in terms of ranking and screening results of 26 SWAT parameters. In order to set a threshold for parameter screening, we propose the use of a “dummy parameter”, which has no influence on the model output. The sensitivity index of the dummy parameter is calculated from sampled data, without changing the model equations. We find that Sobol' and PAWN identify the same 12 influential parameters but rank them differently, and discuss how this result may be related to the limitations of the Sobol' method when the output distribution is asymmetric.

An efficient Kriging method for global sensitivity of structural reliability analysis with non-probabilistic convex model

The convex model which only needs to know the variation bound of the uncertainty domain is competent to deal with the reliability analysis for the engineering problems lacking sufficient information. However, compared with the researches in solving non-probabilistic reliability index with convex model, the non-probabilistic reliability sensitivity analysis is less available. In this article, the moment-independent global sensitivity analysis of the basic variable based on convex model is performed for investigating the effect of non-probabilistic variable of the structure or system on the dangerous degree in reliability engineering. The proposed sensitivity index inherits the advantages of the traditional moment-independent global sensitivity index. For the problems of which the computational cost of the Monte Carlo simulation is too high, an active learning Kriging solution is established to solve the global sensitivity index. Several examples are adopted to illustrate the correctness of this global reliability sensitivity describing the effect on the reliability of the structure system of the convex model variable and the applicability and feasibility of the active learning Kriging–based solution.

Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations

summary Real world models of seawater intrusion (SWI) require high computational efforts. This creates computational difficulties for the uncertainty propagation (UP) analysis of these models due the need for repeated numerical simulations in order to adequately capture the underlying statistics that describe the uncertainty in model outputs. Moreover, despite the obvious advantages of moment-independent global sensitivity analysis (SA) methods, these methods have rarely been employed for SWI and other complex groundwater models. The reason is that moment-independent global SA methods involve repeated UP analysis which further becomes computationally demanding. This study proposes the use of non-intrusive polynomial chaos expansions (PCEs) as a means to significantly accelerate UP analysis in SWI numerical modeling studies and shows that despite the highly non-linear and non-smooth input/output relationship that exists in SWI models, non-intrusive PCEs provide a reliable and yet computationally efficient surrogate of the original numerical model. The study illustrates that for the considered two and six dimensional UP problems, PCEs offer a more accurate estimation of the statistics describing the uncertainty in model outputs compared to Monte Carlo simulations based on the original numerical model. This study also shows that the use of non-intrusive PCEs in the estimation of the moment-independent sensitivity indices (i.e. delta indices) decreases the computational time by several orders of magnitude without causing significant loss of accuracy. The use of non-intrusive PCEs for the generation of SWI hazard maps is proposed to extend the practical applications of UP analysis in coastal aquifer management studies.