A review of techniques for parameter sensitivity analysis of environmental models

Mathematical models are utilized to approximate various highly complex engineering, physical, environmental, social, and economic phenomena. Model parameters exerting the most influence on model results are identified through a ‘sensitivity analysis’. A comprehensive review is presented of more than a dozen sensitivity analysis methods. This review is intended for those not intimately familiar with statistics or the techniques utilized for sensitivity analysis of computer models. The most fundamental of sensitivity techniques utilizes partial differentiation whereas the simplest approach requires varying parameter values one-at-a-time. Correlation analysis is used to determine relationships between independent and dependent variables. Regression analysis provides the most comprehensive sensitivity measure and is commonly utilized to build response surfaces that approximate complex models.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42691/1/10661_2004_Article_BF00547132.pd

Analytical calculations of neutron slowing down and transport in the constant-cross-section problem

Aspects of the problem of neutron slowing down and transport in an infinite medium consisting of a single nuclide that scatters elastically and isotropically and has energy-independent cross sections were investigated. The method of singular eigenfunctions was applied to the Boltzmann Equation governing the Laplace transform (with respect to the lethargy variable) of the neutron flux. A new sufficient condition for the convergence of the coefficients of the expansion of the scattering kernel in Legendre polynomials was rigorously derived for this energy-dependent problem. Formulas were obtained for the lethargy-dependent spatial moments of the scalar flux that are valid for medium to large lethargies. Use was made of the well-known connection between the spatial moments of the Laplace-transformed scalar flux and the moments of the flux in the ''eigenvalue space.'' The calculations were aided by the construction of a closed general expression for these ''eigenvalue space'' moments. Extensive use was also made of the methods of combinatorial analysis and of computer evaluation of complicated sequences of manipulations. For the case of no absorption it was possible to obtain for materials of any atomic weight explicit corrections to the age-theory formulas for the spatial moments M/sub 2n/(u) of the scalar flux that are valid through terms of the order of u/sup -5/. The evaluation of the coefficients of the powers of n, as explicit functions of the nuclear mass, represent one of the end products of this investigation. In addition, an exact expression for the second spatial moment, M/sub 2/(u), valid for arbitrary (constant) absorption, was derived. It is now possible to calculate analytically and rigorously the ''age'' for the constant-cross-section problem for arbitrary (constant) absorption and nuclear mass. 5 figures, 1 table

Appliction of sensitivity theory for extrema of functionals to a transient reactor thermal-hydraulics problem. [LMFBR]

A generalized sensitivity theory based on adjoint functions has been recently developed for systems governed by coupled nonlinear equations and nonlinear responses, and has been successfully applied to several reactor thermal-hydraulics sample problems. This theory has now been significantly extended to include treatment of a new class of responses which are extrema (in phase-space variables) of functionals of the system's state vector and input parameters. Examples of such responses - of great interest in reactor safety and design - are the maximum clad and maximum fuel temperatures. A practical application of this theory is presented

Best-Estimate Model Calibration and Prediction through Experimental Data Assimilation—II: Application to a Blow-down Benchmark Experiment

This work presents a paradigm application of a new methodology for simultaneously calibrating (adjusting) model parameters and responses, through assimilation of experimental data, to the benchmark transient thermal-hydraulic experiment IC1, performed at London's Imperial College. Following the description of the experimental setup, the corresponding mathematical model is developed and solved numerically. The sensitivities of typically important responses (e.g., temperatures, pressures) to model parameters are computed by applying both the forward and the adjoint sensitivity analysis procedures. These sensitivities not only identify the most important model parameters but also propagate, within the data assimilation procedure, parameter uncertainties for obtaining predictive best-estimate quantities, with reduced best-estimate uncertainties (i.e., “smaller” values for the variance-covariance matrices). This assimilation procedure also provides a quantitative indication of the degree of agreement between computations and experiments. In particular, the paradigm application presented in this work indicates the path for validating and calibrating thermal-hydraulic computational models used for reactor safety analyses. The concluding remarks highlight several important open issues, the resolution of which would significantly advance the area of predictive best-estimate modeling, while opening new avenues for applications in nuclear reactor engineering and safety

Deterministic Sensitivity and Uncertainty Methodology for Best Estimate System Codes applied in Nuclear Technology

Nuclear Power Plant (NPP) technology has been developed based on the traditional defense in depth philosophy supported by deterministic and overly conservative methods for safety analysis. In the 1970s [1], conservative hypotheses were introduced for safety analyses to address existing uncertainties. Since then, intensive thermal-hydraulic experimental research has resulted in a considerable increase in knowledge and consequently in the development of best-estimate codes able to provide more realistic information about the physical behaviour and to identify the most relevant safety issues allowing the evaluation of the existing actual margins between the results of the calculations and the acceptance criteria. However, the best-estimate calculation results from complex thermal-hydraulic system codes (like Relap5, Cathare, Athlet, Trace, etc..) are affected by unavoidable approximations that are un-predictable without the use of computational tools that account for the various sources of uncertainty. Therefore the use of best-estimate codes (BE) within the reactor technology, either for design or safety purposes, implies understanding and accepting the limitations and the deficiencies of those codes. Taking into consideration the above framework, a comprehensive approach for utilizing quantified uncertainties arising from Integral Test Facilities (ITFs, [2]) and Separate Effect Test Facilities (SETFs, [3]) in the process of calibrating complex computer models for the application to NPP transient scenarios has been developed. The methodology proposed is capable of accommodating multiple SETFs and ITFs to learn as much as possible about uncertain parameters, allowing for the improvement of the computer model predictions based on the available experimental evidences. The proposed methodology constitutes a major step forward with respect to the generally used expert judgment and statistical methods as it permits a) to establish the uncertainties of any parameter characterizing the system, based on a fully mathematical approach where the experimental evidences play the major role and b) to calculate an improved estimate of the computed response and relative improved (i.e. reduced) uncertainty

Limit cycles and bifurcations in nuclear systems

This work provides a basis for scoping calculations to determine the dynamic behavior - both linear and nonlinear - of BWRs. Additional work is now underway to establish the feasibility of routine operation of nuclear systems in the nonlinear (limit-cycle) regime

Developments in sensitivity theory

A review of recent developments in sensitivity theory is presented with an emphasis on (a) extensions to new areas such as thermal hydraulics, reactor depletion, multi-constraint and extrema problems, and (b) recent mathematical refinements to and extensions of the basic theory. The diverse new areas of application are discussed from a unified theoretical viewpoint based on nonlinear functional analysis. Several new applications of sensitivity theory are presented for problems in constrained reactor physics calculations, irradiation experiment analysis, reactor burnup calculations, and transient thermal-hydraulic analysis. Future directions of the research are suggested