Parameter Global Sensitivity Analysis And Its Application To Determinstic Complex Dynamic System Modelling

As long as the dramatical improvement of infomation science especially computer science, mathematical modeling becomes more and more crucial and popular for the analysis of a wide range of real-world phenomena ranging from physics and engineering to chemistry, biology and economics. Determinstic model only has important theoretical significance but also has potential practical value. It has many important advantages:people can more easily focus on the essential characteristics of the analytical systems while modeling. Deterministic model results can be used to indirectly verify the correctness of stochastic models and methods, and thus to promote the further research of stochastic model. Deterministic dynamic system model is the one of the most common model in modeling study.The definition of sensitivity analysis can be:The study of how uncertainty in the output of a model can be apportioned to different sources of uncertainty in the model input. Modelling of natural phenomena is always facing several sources of unvertainty which should be considered qualitatively and quantitatively for modelers. Sensitivity analysis is necessary for providing such gurantee for modeling.When the initial basic concept of sensitivity analysis was proposed, except in the field of economic modeling analysis, modeling in other areas did not get the attention it deserves. The main use of the method is the most simple local analysis. In the 1990s, when several important sensitivity analysis method proposed, the improvement made sensitivity analysis of this important analytical tool was quickly extended to areas outside the economic model and allow more and more researchers recognize its modeling importance. More and more close combination of the mathematical model with different areas started, like ecological modeling, agricultural research, the field of chemical analysis,etc. It drives more interdisciplinary research field, in which sensitivity analysis are more and more frequently mentioned.To this end, the main objective of this thesis is to study global sensitivity analysis method and strategy for determinstic complex dynamic systems. Specifically, as one type of typical determinstic complex dynamic system, our practice case would be: functional structural plant model, FSPM. This research was funded by the French National Institute of Information and Automation (INRIA Saclay Ile-de-France), Paris Central School (Ecole Centrale Paris) joint with Wuhan University.In order to face the challenge of the computing cost and to meet the necessity of using Sobol's indices for the quantitative information about sensitivity of models, especially the interaction information, we improved a computing method so that the model evaluations can be made best use of. We derived an estimator of the error of sensitivity indices evaluation with respect to the sampling size for this generic type of computational methods so that better control of the convergence of the estimations of Sobol's indices can be achieved.We designed a methodology adapted to determinstic complex dynamic systems. We first discussed the use of non-linearity assessment to identify the occurrence of particular biological phenomena, and then processed a strategy to conduct module by module analysis' in order to comprehensively integrate different SA methods and indices when a complex biophysical system characterized by the interaction of several processes described by sub-models/modules is analyzed.We applied the developed methodology of sensitivity analysis to 3 FSPMs with different levels of complexity, and inferred in each case what information can be drawn from this analysis. Better understanding of source-sink dynamics and internal driving forces during plant growth are achieved. Especially for NEMA model,module by module analysis' helped to understanding the model behavior from the classical simulation approach.