Sensitivity and uncertainty analysis are becoming increasingly widespread in many fields of engineering and sciences, encompassing practically all of the experimental data processing activities and many computational modeling and process simulation activities. There are many methods, based either on deterministic or statistical concepts, for performing sensitivity and uncertainty analysis. However, a precise, unified terminology, across all methods, does not seem to exist yet; often, identical words (e. g., “sensitivity”) may not necessarily describe identical quantities, particularly when stemming from conceptually distinct (statistical versus deterministic) methods. Furthermore, the relative strengths and weaknesses of the various methods do not seem to have been reviewed comparatively in the literature published thus far. This Report presents the current state-of-the-art regarding the deterministic and statistical methods for performing sensitivity and uncertainty analysis of physical and engineering problems. In particular, this Report focuses on reviewing comparatively the salient features of the statistical and deterministic methods currently used for local and global sensitivity and uncertainty analysis of both large-scale computational models and indirect experimental measurements. The deterministic methods are analyzed in Part I, while the statistical methods are highlighted in Part II of this Report, respectively. Section1 of this Report commences by highlighting the deterministic methods for computing local sensitivities, namely: the so-called brute-force method (based on recalculations), the direct method (including the decoupled direct method), the Green’s function method, the forward sensitivity analysis procedure (FSAP), and the adjoint sensitivity analysis procedure (ASAP). Except for the brute-force method, it is emphasized that local sensitivities can be computed exactly and exhaustively only by using deterministic methods. Furthermore, it is noted that the direct method and the FSAP require at least as many model-evaluations as there are parameters, while the ASAP requires a single model-evaluation of an appropriate adjoint model, whose source term is related to the response under investigation. If this adjoint model is developed simultaneously with the original model, then the adjoint model requires relatively modest additional resources to develop and implement. If, however, the adjoint model is constructed a posteriori, considerable skills may be required for its successful development and implementation. Nevertheless, the ASAP is the most efficient method to use for computing local sensitivities of large-scale systems, where the number of parameters, and parameter variations, exceed the number of responses of interest. The global adjoint sensitivity analysis procedure (GASAP) is also highlighted, as it appears to be the only deterministic method, published thus far, for performing genuinely global analysis of nonlinear systems. The GASAP uses both the forward and the adjoint sensitivity systems to explore, exhaustively and efficiently, the entire phase-space of system parameters and dependent variables, in order to obtain complete information about the important global features of the physical system, namely the critical points of the response and the bifurcation branches and/or turning points of the system’s state variables. Section 2 of this Report highlights the salient features of the most popular statistical methods currently used for local and global sensitivity and uncertainty analysis of both large-scale computational models and indirect experimental measurements. These statistical procedures include: sampling-based methods (random sampling, stratified importance sampling, and Latin Hypercube sampling), first- and second-order reliability algorithms (FORM and SORM, respectively), variance-based methods (correlation ratio-based methods, the Fourier amplitude sensitivity test, and Sobol’s method), screening design methods (classical one-at-a-time experiments, global one-at-a-time design methods, systematic fractional replicate designs, and sequential bifurcation designs), use of chaos-polynomials, and, finally, the CIAU method. It is emphasized that all statistical uncertainty and sensitivity analysis procedures first commence with the “uncertainty analysis” stage, and only subsequently proceed to the “sensitivity analysis” stage; this path is the exact reverse of the conceptual path underlying the methods of deterministic sensitivity and uncertainty analysis, where the sensitivities are determined prior to using them for uncertainty analysis. By comparison to deterministic methods, statistical methods for uncertainty and sensitivity analysis are relatively easier to develop and use, but cannot yield exact values of the local sensitivities. Furthermore, current statistical methods have two major inherent drawbacks, as follows: (i) since many thousands of simulations are needed to obtain reliable results, statistical methods are at best expensive (for small systems), or, at worst, impracticable (e.g., for large time-dependent systems); and (ii) since the response sensitivities and parameter uncertainties are inherently and inseparably amalgamated in the results produced by these methods, improvements in parameter uncertainties cannot be directly propagated to improve response uncertainties; rather, the entire set of simulations and statistical post-processing must be repeated anew. In particular, a “fool-proof” statistical method for analyzing correctly models involving highly correlated parameters does not seem to exist currently, so that particular care must be used when interpreting regression results for such models. By addressing computational issues and particularly challenging open problems and knowledge gaps, this Report aims at providing a comprehensive basis for further advancements and innovations in the field sensitivity and uncertainty analysis. Section 3 presents the CIAU (Code with capability of Internal Assessment of Uncertainty) Method proposed by the University of Pisa is described including ideas at the basis and results from applications. The CIAU method exploits the idea of the “status approach” for identifying the thermal-hydraulic conditions of an accident in any Nuclear Power Plant (NPP). Errors in predicting the status of the NPP are derived from the comparison between predicted and measured quantities and, in the stage of the application of the method, are used to compute the uncertainty. Two approaches are distinguished that are characterized as “propagation of code input uncertainty” and “propagation of code output errors”. For both methods, the thermal-hydraulic code is at the centre of the process of uncertainty evaluation: in the former case the code itself is adopted to compute the error bands and to propagate the input errors, in the latter case the errors in code application to relevant measurements are used to derive the error bands. An activity in progress at the International Atomic Energy Agency (IAEA) is also considered.
State of the Art Report on Sensitivity and Uncertainty Analysis (SP4)
D'Auria Francesco Saverio
Co-primo
Writing – Review & Editing
2006-01-01
Abstract
Sensitivity and uncertainty analysis are becoming increasingly widespread in many fields of engineering and sciences, encompassing practically all of the experimental data processing activities and many computational modeling and process simulation activities. There are many methods, based either on deterministic or statistical concepts, for performing sensitivity and uncertainty analysis. However, a precise, unified terminology, across all methods, does not seem to exist yet; often, identical words (e. g., “sensitivity”) may not necessarily describe identical quantities, particularly when stemming from conceptually distinct (statistical versus deterministic) methods. Furthermore, the relative strengths and weaknesses of the various methods do not seem to have been reviewed comparatively in the literature published thus far. This Report presents the current state-of-the-art regarding the deterministic and statistical methods for performing sensitivity and uncertainty analysis of physical and engineering problems. In particular, this Report focuses on reviewing comparatively the salient features of the statistical and deterministic methods currently used for local and global sensitivity and uncertainty analysis of both large-scale computational models and indirect experimental measurements. The deterministic methods are analyzed in Part I, while the statistical methods are highlighted in Part II of this Report, respectively. Section1 of this Report commences by highlighting the deterministic methods for computing local sensitivities, namely: the so-called brute-force method (based on recalculations), the direct method (including the decoupled direct method), the Green’s function method, the forward sensitivity analysis procedure (FSAP), and the adjoint sensitivity analysis procedure (ASAP). Except for the brute-force method, it is emphasized that local sensitivities can be computed exactly and exhaustively only by using deterministic methods. Furthermore, it is noted that the direct method and the FSAP require at least as many model-evaluations as there are parameters, while the ASAP requires a single model-evaluation of an appropriate adjoint model, whose source term is related to the response under investigation. If this adjoint model is developed simultaneously with the original model, then the adjoint model requires relatively modest additional resources to develop and implement. If, however, the adjoint model is constructed a posteriori, considerable skills may be required for its successful development and implementation. Nevertheless, the ASAP is the most efficient method to use for computing local sensitivities of large-scale systems, where the number of parameters, and parameter variations, exceed the number of responses of interest. The global adjoint sensitivity analysis procedure (GASAP) is also highlighted, as it appears to be the only deterministic method, published thus far, for performing genuinely global analysis of nonlinear systems. The GASAP uses both the forward and the adjoint sensitivity systems to explore, exhaustively and efficiently, the entire phase-space of system parameters and dependent variables, in order to obtain complete information about the important global features of the physical system, namely the critical points of the response and the bifurcation branches and/or turning points of the system’s state variables. Section 2 of this Report highlights the salient features of the most popular statistical methods currently used for local and global sensitivity and uncertainty analysis of both large-scale computational models and indirect experimental measurements. These statistical procedures include: sampling-based methods (random sampling, stratified importance sampling, and Latin Hypercube sampling), first- and second-order reliability algorithms (FORM and SORM, respectively), variance-based methods (correlation ratio-based methods, the Fourier amplitude sensitivity test, and Sobol’s method), screening design methods (classical one-at-a-time experiments, global one-at-a-time design methods, systematic fractional replicate designs, and sequential bifurcation designs), use of chaos-polynomials, and, finally, the CIAU method. It is emphasized that all statistical uncertainty and sensitivity analysis procedures first commence with the “uncertainty analysis” stage, and only subsequently proceed to the “sensitivity analysis” stage; this path is the exact reverse of the conceptual path underlying the methods of deterministic sensitivity and uncertainty analysis, where the sensitivities are determined prior to using them for uncertainty analysis. By comparison to deterministic methods, statistical methods for uncertainty and sensitivity analysis are relatively easier to develop and use, but cannot yield exact values of the local sensitivities. Furthermore, current statistical methods have two major inherent drawbacks, as follows: (i) since many thousands of simulations are needed to obtain reliable results, statistical methods are at best expensive (for small systems), or, at worst, impracticable (e.g., for large time-dependent systems); and (ii) since the response sensitivities and parameter uncertainties are inherently and inseparably amalgamated in the results produced by these methods, improvements in parameter uncertainties cannot be directly propagated to improve response uncertainties; rather, the entire set of simulations and statistical post-processing must be repeated anew. In particular, a “fool-proof” statistical method for analyzing correctly models involving highly correlated parameters does not seem to exist currently, so that particular care must be used when interpreting regression results for such models. By addressing computational issues and particularly challenging open problems and knowledge gaps, this Report aims at providing a comprehensive basis for further advancements and innovations in the field sensitivity and uncertainty analysis. Section 3 presents the CIAU (Code with capability of Internal Assessment of Uncertainty) Method proposed by the University of Pisa is described including ideas at the basis and results from applications. The CIAU method exploits the idea of the “status approach” for identifying the thermal-hydraulic conditions of an accident in any Nuclear Power Plant (NPP). Errors in predicting the status of the NPP are derived from the comparison between predicted and measured quantities and, in the stage of the application of the method, are used to compute the uncertainty. Two approaches are distinguished that are characterized as “propagation of code input uncertainty” and “propagation of code output errors”. For both methods, the thermal-hydraulic code is at the centre of the process of uncertainty evaluation: in the former case the code itself is adopted to compute the error bands and to propagate the input errors, in the latter case the errors in code application to relevant measurements are used to derive the error bands. An activity in progress at the International Atomic Energy Agency (IAEA) is also considered.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
