| Research Abstract |
In many fields of engineering, science, sociology, etc., the sensitivity analysis is a key technique for system design/operation and verification of suitability of mathematical models explaining natural or sociological phenomena. Many researchers, however, had studied on it independently, who lived in different countries, whose themes were widely spread, whose terminologies were quite different (e.g., conjugate system, adjoint system, perturbation computation). As a result, each of them had separately "found" almost same idea in the different contexts. Our research aims were (1) unification and systematization of the proposed ideas, (2) construction of "synthetic theory on sensitivity analysis" with fast automatic differentiation, (3) establishment of a general algorithm, (4) development of software system for the algorithm, and (5) evaluation through computational experiments.
We have obtained the following expected results. Firstly, we proposed a new theory for the sensitivity analysis on nonlinear systems, and established an algorithm which could be generally applied to any model. It can perform the sensitivity analysis as well as analyzing the mathematical model. In particular its complexity was the same order as that for analyzing the model alone. Secondly, we unified the concepts referred as adjoint system, conjugate system, etc. with a numerical computational approach. We are developing an experimental system by which we can treat interval numbers, floating-point numbers with variable length of exponent, automatic differentiation numbers, etc. Finally, we have recognized an issue for characterizing system structures whose sensitivity can be easily analyzed, i.e., by which influences of perturbation of elements to the whole system can be easily anticipated, giving the structure of the serial-parallel system as an example. This recognition is significance in engineering in order to design "structure" of system through system analysis.
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