Density-based Sensitivity Analysis Research Articles

Assessing safety functionalities in the design and validation of driving automation

This paper aims to contribute to the comprehensive and systematic safety assessment of Automated Driving Systems (ADSs) by identifying unknown hazardous areas of operation. The current methodologies employed in this domain typically involve estimating the distributions of situational variables based on human-centered field test, crash databases, or expert knowledge of critical values. However, due to the lack of a-priori knowledge regarding the influential factors, their critical ranges, and their distributions, these approaches may not be entirely suitable for the assessment of emerging automated driving technologies. To deal with this challenging problem, here we propose a testing methodology incorporating realistic yet unobserved driving conditions, distinguished by numerous situational variables, so to encompass unknown unsafe conditions comprehensively. Our methodology utilizes stochastic simulation and uncertainty modeling techniques to account for the variability of realistic driving conditions and their impact on ADSs' performances. By doing so, we aim to identify unsafe operational regions and triggering conditions that can lead to hazardous behaviors, thus improving the development and safety of automated driving functions. For our purposes, the Latin Hypercube Sampling technique and the recently proposed PAWN density-based sensitivity analysis method are employed. We apply this methodology for the first time in the specific field of ADSs design and validation, using an exemplificative use case. We discuss and compare the results obtained from our approach with those obtained from a traditional approach.

Forward-reverse switch between density-based and regional sensitivity analysis

Global sensitivity analysis is a widely used tool for uncertainty apportionment and is very useful for decision making, risk assessment, model simplification, optimal design of experiments, etc. Density-based sensitivity analysis and regional sensitivity analysis are two widely used approaches. Both of them can work with a given sample set of model input-output pairs. One significant difference between them is that density-based sensitivity analysis analyzes output distributions conditional on input values (forward), while regional sensitivity analysis analyzes input distributions conditional on output values (reverse). In this paper, we study the relationship between these two approaches and show that regional sensitivity analysis (reverse), when focusing on probability density functions of input, converges towards density-based sensitivity analysis (forward) as the number of classes for conditioning model outputs in the reverse method increases. Similar to the existing general form of forward sensitivity indices, we derive a general form of the reverse sensitivity indices and provide the corresponding reverse given-data method. Due to the shown equivalence, the reverse given-data method provides an efficient way to approximate density-based sensitivity indices. Two test examples are used to verify this connection and compare the results. Finally, we use the reverse given-data method to perform sensitivity analysis in a carbon dioxide storage benchmark problem with multiple outputs, where forward analysis of density-based indices would be impossible due to the high-dimensionality of its model outputs.

An Approach to the Sensitivity Analysis in Variation Simulations considering Form Deviations

In tolerance and variation simulations, sensitivity analyses are used to assess the influences of tolerance specifications and geometrical deviations on the assembly key characteristics and to support product and process developers in deriving more suitable tolerancing decisions and in optimizing manufacturing and assembly processes. However, established methods to the sensitivity analysis in the context of variation simulations disregard important statistical dependencies, which occur when considering form deviations. To overcome these shortcomings, an approach to the density-based sensitivity analysis in variation simulations considering form deviations based on Skin Model Shapes is presented. The method is highlighted and discussed employing a typical tolerance analysis case study.

Robust global sensitivity analysis of a river management model to assess nonlinear and interaction effects

Abstract. The simulation of routing and distribution of water through a regulated river system with a river management model will quickly result in complex and nonlinear model behaviour. A robust sensitivity analysis increases the transparency of the model and provides both the modeller and the system manager with a better understanding and insight on how the model simulates reality and management operations. In this study, a robust, density-based sensitivity analysis, developed by Plischke et al. (2013), is applied to an eWater Source river management model. This sensitivity analysis methodology is extended to not only account for main effects but also for interaction effects. The combination of sensitivity indices and scatter plots enables the identification of major linear effects as well as subtle minor and nonlinear effects. The case study is an idealized river management model representing typical conditions of the southern Murray–Darling Basin in Australia for which the sensitivity of a variety of model outcomes to variations in the driving forces, inflow to the system, rainfall and potential evapotranspiration, is examined. The model outcomes are most sensitive to the inflow to the system, but the sensitivity analysis identified minor effects of potential evapotranspiration and nonlinear interaction effects between inflow and potential evapotranspiration.

Sampling strategies in density-based sensitivity analysis

Decision and policy-makers benefit from the utilization of computer codes in an increasing number of areas and applications. Several authorities and agencies recommend the utilization of proper sensitivity analysis methods in order to confidently entrust model results. In this respect, density-based techniques have recently attracted interest among academicians and practitioners, for their property to characterize uncertainty in terms of the entire distribution of an output variable. However, their estimation is a challenging task and, without a proper methodical approach, errors in the estimates can lead to misleading conclusions. In this work, we propose sampling plans for reducing the computational burden of sensitivity estimates while improving and controlling the accuracy in the estimation. We compare designs based on column substitutions and designs based on permutations. We investigate their behaviour in terms of type I and type II errors. We apply the methods to the Level E model, a computational tool developed by the Nuclear Energy Agency of the OECD for the assessment of nuclear waste disposal sites. Results show that application of the proposed sampling plans allows one to obtain confidence in the sensitivity estimates at a number of model runs several orders of magnitude lower than a brute-force approach. This assessment, based upon the entire distribution of the model output, provides us with ways to effectively reduce uncertainty in the model output, either by prioritizing the model factors that need to be better known or by prioritizing the areas where additional modelling efforts are needed.