Nonlinear

Cette these est principalement consacree a l'association des methodes de points interieurs et des techniques de l'optimisation DC et DCA pour resoudre les problemes d'optimisation non convexes de grande taille. La these comporte trois parties : la premiere partie est consacree aux techniques d'optimisations locales et s'articule autour des methodes de points interieurs et de la programmation DC. Nous y developpons deux algorithmes. Apres une presentation non exhaustive de la programmation DC, des methodes de points interieurs et des proprietes essentielles de la classe des matrices quasi-definies au chapitre un, nous presentons au chapitre deux un nouvel algorithme base sur une reformulation des conditions d'optimalite de Karush-Kuhn-Tucker. Le troisieme chapitre est consacre a l'integration des techniques d'optimisation DC dans un schema de points interieurs, c'est l'algorithme IPDCA. La seconde partie de la these est consacree aux solutions ...

Background Nonlinear relationships are common in the environmental discipline. Spreadsheet packages such as Microsoft Excel come with an add-on for nonlinear regression, but parameter uncertainty estimates are not yet available. The purpose of this paper is to use Monte Carlo and bootstrap methods to estimate nonlinear parameter uncertainties with a Microsoft Excel spreadsheet. As an example, uncertainties of two parameters (α and n) for a soil water retention curve are estimated. Results The fitted parameters generally do not follow a normal distribution. Except for the upper limit of α using the bootstrap method, the lower and upper limits of α and n obtained by these two methods are slightly greater than those obtained using the SigmaPlot software which linearlizes the nonlinear model. Conclusions Since the linearization method is based on the assumption of normal distribution of parameter values, the Monte Carlo and bootstrap methods may be preferred to the linearization method.

A study of an existing B-pillar was conducted to examine the changes required to increase the lateral load carrying capability by a factor of ten. A finite element optimization package was used to adjust the geometric and material characteristics simultaneously while minimizing weight. The results show that the weight and cost necessary for the ten-fold improvement in lateral load carrying capability were very low. Further, the results illustrate how structural design optimization with finite element modeling can be effectively utilized to create cost effective elements for use in an integrated occupant protection system.

Cylindrical compression spring behavior has been described in the literature using an efficient analytical model. Conical compression spring behavior has a linear phase but can also have a nonlinear phase. The rate of the linear phase can easily be calculated but no analytical model exists to describe the nonlinear phase precisely. This nonlinear phase can only be determined by a discretizing algorithm. The present paper presents analytical continuous expressions of length as a function of load and load as a function of length for a constant pitch conical compression spring in the nonlinear phase. Whal’s basic cylindrical compression assumptions are adopted for these new models (Wahl, A. M., 1963, Mechanical Springs, Mc Graw-Hill, New York). The method leading to the analytical expression involves separating free and solid/ground coils, and integrating elementary deflections along the whole spring. The inverse process to obtain the spring load from its length is assimilated to solve...

This paper describes the design of an adaptive controller based on model reference adaptive PID control (MRAPIDC) to stabilize a two-tank process when large variations of parameters and external disturbances affect the closed-loop system. To achieve that, an innovative structure of the adaptive PID controller is defined, an additional PI is designed to make sure that the reference model produces stable output signals and three adaptive gains are included to guarantee stability and robustness of the closed-loop system. Then, the performance of the model reference adaptive PID controller on the behaviour of the closed-loop system is compared to a PI controller designed on MATLAB when both closed-loop systems are under various conditions. The results demonstrate that the MRAPIDC performs significantly better than the conventional PI controller. Keywords: Adaptive Linearization MIT MRAPIDC Nonlinear Parameters Stability This is an open access article under the CC BY-SA license. 1. INTRODUCTION Adaptive control of uncertain processes has become more and more important in industry. Adaptive controllers differ from ordinary ones, because their parameters are variable, and there is a mechanism for adjusting these parameters online based on signals in the system [1]. The design of an adaptive PI controller to stabilize a mass damper-spring system under parameters' uncertainties was proposed in [2]. The designed adaptive PI controller adjusts to parameters' variations, and the output of the process follows the set points, regardless of the values of the parameters. But it does not guarantee stability when external disturbances and large variations of parameters occur. In [3], the design of a PID controller on MATLAB to maintain the level of liquid constant in a coupled-tank system (CTS) was proposed. The control parameters were found using the trial and error methodology and the results were analysed in MATLAB/Simulink environments. Proportional (P), proportional integral (PI), proportional derivative (PD) and proportional integral derivative (PID) controllers were applied on the process and their performances were compared to select the most suitable control solution. The PID controller showed superior results, but it did not guarantee stability to disturbances and variations of plant parameters. Adaptive controllers, as opposed to conventional constant gain controllers (PID controllers), are very effective in handling situations where the variations of parameters and environmental changes are very frequent with the application of model reference adaptive control scheme in a first order system [4].

Terrestrial heat flow is considered an important parameter in studying the regional geotectonic and geodynamic evolutionary history of any region. However, its distribution is still very uneven. There is hardly any information available for many geodynamically important areas. In the present study, we provide a methodology to predict the surface heat flow in areas, where detailed seismic information such as depth to the lithosphere-asthenosphere boundary (LAB) and crustal structure is known. The tool was first tested in several geotectonic blocks around the world and then used to predict the surface heat flow for the 2001 Bhuj earthquake region of Kachchh, India, which has been seismically active since historical times and where aftershock activity is still continuing nine years after the 2001 main event. Surface heat flow for this region is estimated to be about 61.3 mW m-2. Beneath this region, heat flow input from the mantle as well as the temperatures at the Moho are quite high at around 44 mW m-2 and 630 °C, respectively, possibly due to thermal restructuring of the underlying crust and mantle lithosphere. In absence of conventional data, the proposed tool may be used to estimate a first order heat flow in continental regions for geotectonic studies, as it is also unaffected by the subsurface climatic perturbations that percolate even up to 2000 m depth.

Received Mar 31, 2020 Revised Jun 20, 2020 Accepted Jul 6, 2020 This paper describes the design of an adaptive controller based on model reference adaptive PID control (MRAPIDC) to stabilize a two-tank process when large variations of parameters and external disturbances affect the closed-loop system. To achieve that, an innovative structure of the adaptive PID controller is defined, an additional PI is designed to make sure that the reference model produces stable output signals and three adaptive gains are included to guarantee stability and robustness of the closed-loop system. Then, the performance of the model reference adaptive PID controller on the behaviour of the closed-loop system is compared to a PI controller designed on MATLAB when both closed-loop systems are under various conditions. The results demonstrate that the MRAPIDC performs significantly better than the conventional PI controller.

Chatter is an instability condition in machining processes characterized by nonlinear behavior, such as the presence of limit cycles, jump phenomenon, subcritical Hopf and period doubling bifurcations. Although the use of nonlinear techniques has provided a better understanding of chatter, neither a unifying model nor an exact solution has yet been developed due to the intricacy of the problem. This work proposes a weakly nonlinear model with square and cubic terms in both structural stiffness and regenerative terms, to represent self-excited vibrations in machining. An approximate solution is derived by using the method of multiple scales. In addition, a qualitative analysis of the effect of the nonlinear parameters on the stability of the system is performed. The structural cubic term gives a better representation of the nonlinear behavior, whereas the square term represents a distant attractor in the stability chart. Instability due to subcritical Hopf bifurcations is established in terms of the eigenvalues of the model in normal form. An important contribution of this analysis is the representation of hysteresis in terms of new lobes within the conventional stability limits, useful in restoring stability. This analysis leads to a further understanding of the nonlinear behavior of regenerative chatter.

The response of an electrochemical reacting system to potential perturbations during electrochemical impedance spectrum measurement is investigated using numerical simulation. Electrochemical metal dissolution via an adsorbed intermediate species is analyzed and it is shown that applying the potential perturbation causes the average surface coverage to drift. For high frequency perturbations, the final value of the average surface coverage depends mainly on the kinetic parameters and the amplitude of the applied perturbation. Acquiring the data during the first few cycles of perturbations leads to an incorrect calculation of the impedance, particularly for large amplitude perturbations. Repeating the experiments will not identify this drift, while Kramers–Kronig Transform (KKT) can successfully detect this problem. The correct experimental methodology to overcome this effect and obtain the impedance spectra is also described. Another reaction with two adsorbed intermediates is also investigated and it is shown that in certain cases, the violations of linearity criteria can also be detected by KKT. The results illustrate the importance of validating the impedance data with KKT before further analysis.► EIS response of reaction via adsorbed intermediates analyzed. Numerical simulation. ► Surface coverage drifts during measurement. Analytical solution confirms results. ► Correct experimental strategy to overcome the drift effect identified. ► Kramers–Kronig Transforms identify the drift and in certain cases, nonlinearities.

The complexity in the tsunami phenomenon makes the available warning systems not much effective in the practical situations. The problem arises due to the time lapsed in the data transfer, processing and modeling. The modeling and simulation needs the input fault geometry and mechanism of the earthquake. The estimation of these parameters and other aprior information increases the utilized time for making any warning. Here, the wavelet analysis is used to identify the tsunamigenesis of an earthquake. The frequency content of the seismogram in time scale domain is examined using wavelet transform. The energy content in high frequencies is calculated and gives a threshold for tsunami warnings. Only first few minutes of the seismograms of the earthquake events are used for quick estimation. The results for the earthquake events of Andaman Sumatra region and other historic events are promising.

The purpose of this paper is to present a new perspective of the linear-nonlinear thinking style and its critical role in knowledge management education. Previous works in this field identified linear thinking as being rational, logic and analytic, and nonlinear thinking as ...