Sensitivity analysis and model optimization for reaction-diffusion systems

This paper presents a computational framework for the optimization and sensitivity analysis of a process whose state depends upon several parameter functions. Assuming that the process is described by a system of quasilinear, parabolic, partial differential equations, we show how determining the problem parameters so as to improve an associated objective functional is directly related to knowing the state function sensitivities. An expression for the gradient of the objective functional in terms of the solutions of an adjoint system enables one to bypass the calculation of state function sensitivities. These concepts are illustrated for a simple model of cooperative processes in chemical kinetics. Since sensitivity analysis and model optimization are important tools for investigating parameter dependence and validating mathematical models, research developments in such diverse fields as optimal design theory, chemical kinetics, and parameter identification are important motivations for this paper.This author would like to gratefully acknowledge Dr. M. Delle Donne, EGG, for several helpful discussions.This author was partially supported by NSF Grant No. CMS-80-05677.     

脉冲激光离子源飞行时间质谱计的设计与研制

目前国内外的飞行时间质谱计，大多采用双电场加速的方式改善其质谱分辨率。通过较详尽的计算，讨论了双电场飞行时间质谱计中各参数对质谱分辨率和灵敏度的影响及其选择的方向，并在此基础上选定了仪器的主要参量，为飞行时间质谱计的设计与改进提供了依据。还介绍了在此基础上设计与建立的脉冲激光离子源飞行时间质谱计。     

光纤光栅弹簧管压力传感器的压力和温度特性

本文利用弹簧管对于压力的机械放大作用,将弹簧管与光纤光栅悬臂梁调谐技术相结合,研制了一种新颖的光纤光栅弹簧管压力传感器,大大提高了光纤布喇格光栅对压力测量的灵敏度,压力灵敏度系数可达-1.79×10^-4/MPa,比裸光栅提高了两个数量级,在0～12MPa的压力范围内,光纤布喇格光栅中心反射波长的改变与压力成良好的线性关系.同时由于悬臂梁热膨胀效应的影响,光纤光栅的温度灵敏度提高为裸光栅的7倍.     

Sensitivity analysis in multiobjective optimization

Sensitivity analysis in multiobjective optimization is dealt with in this paper. Given a family of parametrized multiobjective optimization problems, the perturbation map is defined as the set-valued map which associates to each parameter value the set of minimal points of the perturbed feasible set in the objective space with respect to a fixed ordering convex cone. The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivatives for set-valued maps. Particularly, it is shown that the sensitivity is closely related to the Lagrange multipliers in multiobjective programming.This research was made while the author stayed at the International Institute for Applied Systems Analysis, Laxenburg, Austria.The author would like to thank an anonymous referee for his helpful suggestions; particularly, he pointed out that Proposition 2.2 and Theorem 2.1 are valid also in infinite-dimensional spaces.     

Studies on thermionic ionisation detection in comprehensive two-dimensional gas chromatography

This study explores the application of specific thermionic ionisation detection in comprehensive 2-D GC (GC x GC) and represents the first report of GC x GC with nitrogen phosphorus detection (GC x GC-NPD). Of particular interest is the performance of the NPD with respect to peak parameters of asymmetry and sensitivity. Since GC x GC produces much narrower peaks than obtained with fast GC (e.g. 100 ms vs. <1 s) the effect of detector response time and any lack of symmetry arising from the detection step is important if peak separation (resolution) is to be maintained. It was observed that detector gas flows had a significant impact on peak asymmetry and peak magnitude, and that optimisation of the detector was critical, particularly for complex sample analysis by GC x GC-NPD. Peak asymmetries ranging from As = 1.8 to 8.0 were observed under different conditions of detector gas flows. Comparison of GC x GC-NPD with GC x GC-flame ionisation detection (FID) showed the former to be approximately 20 times more sensitive for the detection of nitrogen-containing methoxypyrazines analytes, and GC x GC-NPD had a larger linear detection range compared to GC x GC-FID. Furthermore, comparison of GC x GC-NPD and GC x GC-TOFMS chromatograms for the analysis of coffee head-space demonstrated the benefits of selective detection, ultimately realised in a comparatively simplified contour plot.     

Level set method for the inverse elliptic problem in nonlinear electromagnetism

An inverse problem of inhomogeneity identification inside a nonlinear magnetic material from the local measurements of the magnetic induction is investigated. The representation of the shape of the inhomogeneity and its evolution during an iterative reconstruction process is achieved by the level set method. The reconstruction is realized by the minimization of a cost function using the steepest descent method. The gradient directions are evaluated using the sensitivity equation and the adjoint variable method. Simulations has been performed showing the robustness of the algorithm and its ability to reconstruct single inhomogeneities, convex and non-convex, as well as multiple inhomogeneities.     

Generalized linear fractional programming under interval uncertainty

Data in many real-life engineering and economical problems suffer from inexactness. Herein we assume that we are given some intervals in which the data can simultaneously and independently perturb. We consider a generalized linear fractional programming problem with interval data and present an efficient method for computing the range of optimal values. The method reduces the problem to solving from two to four real-valued generalized linear fractional programs, which can be computed in polynomial time using an appropriate interior point method solver.     

What drives value creation in investment projects? An application of sensitivity analysis to project finance transactions

Evaluating the economic attractiveness of large projects often requires the development of large and complex financial models. Model complexity can prevent management from obtaining crucial information, with the risk of a suboptimal exploitation of the modelling efforts. We propose a methodology based on the so-called “differential importance measure (D)$(D)$” to enhance the managerial insights obtained from financial models. We illustrate our methodology by applying it to a project finance case study. We show that the additivity property of D grants analysts and managers full flexibility in combining parameters into any group and at the desired aggregation level. We analyze investment criteria related to both the investors’s and lenders’ perspectives. Results indicate that exogenous factors affect investors (sponsors and lenders) in different ways, whether exogenous variables are considered individually or by groups.     

Sensitivity analysis on the priority of the objective functions in lexicographic multiple objective linear programs

This paper deals with a class of multiple objective linear programs (MOLP) called lexicographic multiple objective linear programs (LMOLP). In this paper, by providing an efficient algorithm which employs the preceding computations as well, it is shown how we can solve the LMOLP problem if the priority of the objective functions is changed. In fact, the proposed algorithm is a kind of sensitivity analysis on the priority of the objective functions in the LMOLP problems.