Sur les techniques de modélisation des expériences numériques.

Abstract

In order to study any phenomenon and develop technological systems, researchers use certain experiments. However, the reduction in the number of experiments to be carried out with a view to inferring conclusions remains fundamental because it allows a saving of time and productivity; Hence the value of design of experiments. Sir Roland Fisher (1890-1962) proposed experimental configurations based on rigorous statistical models. This is the starting point of the theoretical method of the design experiments. The classic techniques of experimental plans such as incomplete plans, balanced plans, ANOVA; cannot account for the complexity of certain systems and processes. It was necessary to develop modeling techniques. On the other hand, the availability of computers made possible models and numerical simulation techniques to analyze very complex systems containing a large number of parameters. The theory of numeric experimental plans responds perfectly to these needs with modern methods or techniques such as the least squares method, neural networks, data*mining, kriging, sensitivity analysis, operational research, etc. In this thesis, our work concerns the adaptation and use of certain modeling techniques to the following problems: 1 - We have designed and implemented a recognition system of spoken words to control robotic systems. The recognition system is based on Neural Nets (MLP-NN) multi-layer Perceptron. The minimum number of tests required to reduce learning time has also been studied experimentally, ensuring a success rate comparable to other studies. 2 - In the field of dynamic modeling and simulation of the slider-crank mechanism; We have mathematically formulated the problem within the framework of the theory of multi-body systems constrained using the Euler-Lagrange approach. The problem is expressed in the form of a set of differential algebraic equations (DAE). We used the index reduction method for AEDs. We have derived a dynamic model based on two variables for easier analysis and implementation. We have successfully solved the DAE problem with the Matlab function (ode15s) which is dedicated to the resolution of rigid ordinary differential equations (ODEs). The simulation results obtained allowed to analyze the behavior of the crank-crank mechanism with different parameters and to provide physical interpretations of its functioning. 3 - In the framework of the studies on anaerobic bioreactors and the estimation of the quantity of methane released, a mathematical model corresponding to the biotechnological processes of the biphasic anaerobic digestion was implemented on the basis of model AM2. It was used to simulate the operations of the batch bioreactor. The model obtained is a system of coupled and nonlinear differential equations. It has been found, for the initial conditions and parameters of our ODE system, that its integration by the function (ode45) of Matlab is not always possible because the system becomes rigid. It was then necessary to use ode15s which is suitable for rigid ODEs. To estimate the amount of methane produced by the bioreactor, we used simulation using the AM2 model. We also examined the cumulative estimated methane production using a modified Gompertz equation for discontinuous digesters. 4 - In the field of renewable energies, we sought to select the theoretical model of the solar radiation most appropriate for our region among the models: CAPDEROU, R.SUN and LIU and JORDAN. Each of the models uses special equations to estimate global solar radiation as a function of geometric parameters and atmospheric parameters. Experimental measurements were obtained using a pyranometer in the Constantine region. We found that the CAPDEROU model gives a better estimate of the solar radiation at the Constantine site compared to the other models. As a general conclusion, we have found that numerical experiments modeling techniques actually provide science and technology with economical, powerful and flexible methods that can be effectively adapted to solve problems. Some of these methods have been adapted to our problems and have led to the successful modeling and simulation of analytical processes and systems to be developed.