Bond Graph Representation of Standard Interconnection Model

International audienceThe study of the robustness of a system's parametric uncertainties is based on state representations which separate the nominal part of the system from the uncertain part. The most used form is the standard interconnection model. Recent works have been formulated so as to find this representation graphically by the bond graph approach. A new procedure is proposed in this paper to determine an uncertain model adapted to the study of robustness and for robust control. The advantage of this procedure is in simplifying the resulting graphical model

Fault evaluation and adaptive threshold detection of helicopter pilot using bond graph method

Hitherto, in the field of aerospace science and industry, some acceptable results from control behavior of human operator (pilot), are caught using usual methods. However, very fewer research, has been done based on personal characteristics. The performed investigations, show that many of happened faults (especially in helicopter), would result to the loss of natural behavior of system, and eventually some fatal accidents. Therefore, development of tools of assessment of pilot in this dynamical system, is one of the vital necessities. The tools of management of system, should be such that, can show the fault. The object of this paper is assessment of the modelled pilot in a simulator, in presence of standard fly inputs. For this purpose the performance of the pilot for collective and cyclic control of the helicopter, is investigated. The used methods are based on mathematical models and by bond graph modeling method. The existence of uncertainties in the simulator system and the modeled pilot’s behavior, causes creation of fault threshold, for human behavior of pilot. By having these fault thresholds, the improper actions of the pilot, cause creation of behavioral reminders, which can perform the assessment of the pilot. By other speech, using fault detection and isolation (FDI), by bond graph method in state space, the assessment is performed and a non-zero reminder shows existence of fault in the system. Therefore, in this paper there is the novelties for modeling the pilot’s body performance and the helicopter’s systems integrally and designing a fault detection system for it that shows the source of the fault, and obviously it can be useful in aviation industry.Keywords: Helicopter Control, Fault Detection and Isolation, Human Fault, Bond Grap

Option Pricing with Transaction Costs Using a Markov Chain Approximation

An e cient algorithm is developed to price European options in the pres- ence of proportional transaction costs, using the optimal portfolio frame- work of Davis (1997). A fair option price is determined by requiring that an in nitesimal diversion of funds into the purchase or sale of options has a neutral e ect on achievable utility. This results in a general option pricing formula, in which option prices are computed from the solution of the investor's basic portfolio selection problem, without the need to solve a more complex optimisation problem involving the insertion of the op- tion payo into the terminal value function. Option prices are computed numerically using a Markov chain approximation to the continuous time singular stochastic optimal control problem, for the case of exponential utility. Comparisons with approximately replicating strategies are made. The method results in a uniquely speci ed option price for every initial holding of stock, and the price lies within bounds which are tight even as transaction costs become large. A general de nition of an option hedg- ing strategy for a utility maximising investor is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed

A New Hybrid Robust Fault Detection of Switching Systems by Combination of Observer and Bond Graph Method

In this paper, the problem of robust Fault Detection (FD) for continuous time switched system is tackled using a hybrid approach by combination of a switching observer and Bond Graph (BG) method. The main criteria of an FD system including the fault sensitivity and disturbance attenuation level in the presence of parametric uncertainties are considered in the proposed FD system. In the first stage, an optimal switching observer based on state space representation of the BG model is designed in which simultaneous fault sensitivity and disturbance attenuation level are satisfied using H=H1 index. In the second stage, the Global Analytical Redundancy Relations (GARRs) of the switching system are derived based on the output estimation error of the observer, which is called Error-based Global Analytical Redundancy Relations (EGARRs). The parametric uncertainties are included in the EGARRs, which define the adaptive thresholds on the residuals. A constant term due to the effect of disturbance is also considered in the thresholds. In fact, a two-stage FD system is proposed wherein some criteria may be considered in each stage. The efficiency of the proposed method is shown for a two-tank system

Option pricing with transaction costs using a Markov chain approximation

An efficient algorithm is developed to price European options in the presence of proportional transaction costs, using the optimal portfolio framework of Davis (in: Dempster, M.A.H., Pliska, S.R. (Eds.), Mathematics of Derivative Securities. Cambridge University Press, Cambridge, UK). A fair option price is determined by requiring that an infinitesimal diversion of funds into the purchase or sale of options has a neutral effect on achievable utility. This results in a general option pricing formula, in which option prices are computed from the solution of the investor's basic portfolio selection problem, without the need to solve a more complex optimisation problem involving the insertion of the option payoff into the terminal value function. Option prices are computed numerically using a Markov chain approximation to the continuous time singular stochastic optimal control problem, for the case of exponential utility. Comparisons with approximately replicating strategies are made. The method results in a uniquely specified option price for every initial holding of stock, and the price lies within bounds which are tight even as transaction costs become large. A general definition of an option hedging strategy for a utility maximising investor is developed. This involves calculating the perturbation to the optimal portfolio strategy when an option trade is executed

Implementation of a Cascade Fault Tolerant Control and Fault Diagnosis Design for a Modular Power Supply

The main objective of this research work was to develop reliable and intelligent power sources for the future. To achieve this objective, a modular stand-alone solar energy-based direct current (DC) power supply was designed and implemented. The converter topology used is a two-stage interleaved boost converter, which is monitored in closed loop. The diagnosis method is based on analytic redundancy relations (ARRs) deduced from the bond graph (BG) model, which can be used to detect the failures of power switches, sensors, and discrete components such as the output capacitor. The proposed supervision scheme including a passive fault-tolerant cascade proportional integral sliding mode control (PI-SMC) for the two-stage boost converter connected to a solar panel is suitable for real applications. Most model-based diagnosis approaches for power converters typically deal with open circuit and short circuit faults, but the proposed method offers the advantage of detecting the failures of other vital components. Practical experiments on a newly designed and constructed prototype, along with simulations under PSIM software, confirm the efficiency of the control scheme and the successful recovery of a faulty stage by manual isolation. In future work, the automation of this reconfiguration task could be based on the successful simulation results of the diagnosis method.This research was funded by the Tunisian Ministry of Higher Education and Scientific Research

Peridynamic Galerkin methods for nonlinear solid mechanics

Simulation-driven product development is nowadays an essential part in the industrial digitalization. Notably, there is an increasing interest in realistic high-fidelity simulation methods in the fast-growing field of additive and ablative manufacturing processes. Thanks to their flexibility, meshfree solution methods are particularly suitable for simulating the stated processes, often accompanied by large deformations, variable discontinuities, or phase changes. Furthermore, in the industrial domain, the meshing of complex geometries represents a significant workload, which is usually minor for meshfree methods. Over the years, several meshfree schemes have been developed. Nevertheless, along with their flexibility in discretization, meshfree methods often endure a decrease in accuracy, efficiency and stability or suffer from a significantly increased computation time. Peridynamics is an alternative theory to local continuum mechanics for describing partial differential equations in a non-local integro-differential form. The combination of the so-called peridynamic correspondence formulation with a particle discretization yields a flexible meshfree simulation method, though does not lead to reliable results without further treatment.\newline In order to develop a reliable, robust and still flexible meshfree simulation method, the classical correspondence formulation is generalized into the Peridynamic Galerkin (PG) methods in this work. On this basis, conditions on the meshfree shape functions of virtual and actual displacement are presented, which allow an accurate imposition of force and displacement boundary conditions and lead to stability and optimal convergence rates. Based on Taylor expansions moving with the evaluation point, special shape functions are introduced that satisfy all the previously mentioned requirements employing correction schemes. In addition to displacement-based formulations, a variety of stabilized, mixed and enriched variants are developed, which are tailored in their application to the nearly incompressible and elasto-plastic finite deformation of solids, highlighting the broad design scope within the PG methods. Extensive numerical validations and benchmark simulations are performed to show the impact of violating different shape function requirements as well as demonstrating the properties of the different PG formulations. Compared to related Finite Element formulations, the PG methods exhibit similar convergence properties. Furthermore, an increased computation time due to non-locality is counterbalanced by a considerably improved robustness against poorly meshed discretizations

Bond-based nonlocal models by nonlocal operator method in symmetric support domain

This paper is concerned with the energy decomposition of various nonlocal models, including elasticity, thin plates, and gradient elasticity, to arrive at bond-based nonlocal models in which the bond force depends only on the deformation of a single bond. By assuming an appropriate form of bond force and using energy equivalence between local and nonlocal models, several very concise bond-based models are derived. We also revisit the nonlocal operator methods and study the simplified form of second-order NOM in the symmetric support domain. A bent-bond consisting of three points is proposed to describe the curvature and moment. To model the damage, a rule based on Griffith theory for the critical normal strain of the bond is proposed in analogy to the phase field model, which can be applied individually to each bond and provides strain localization. With this rule, the crack direction can be automatically predicted by simply cutting the bond, giving comparable results to the phase field method. At the same time, a damage rule for critical shear strains in shear fractures is proposed. Furthermore, an incremental form of the plasticity model for bond reaction force is derived. Several numerical examples are presented to further validate the nonlocal bond-based models

Increasing the robustness of autonomous systems to hardware degradation using machine learning

Autonomous systems perform predetermined tasks (missions) with minimum supervision. In most applications, the state of the world changes with time. Sensors are employed to measure part or whole of the world’s state. However, sensors often fail amidst operation; feeding as such decision-making with wrong information about the world. Moreover, hardware degradation may alter dynamic behaviour, and subsequently the capabilities, of an autonomous system; rendering the original mission infeasible. This thesis applies machine learning to yield powerful and robust tools that can facilitate autonomy in modern systems. Incremental kernel regression is used for dynamic modelling. Algorithms of this sort are easy to train and are highly adaptive. Adaptivity allows for model adjustments, whenever the environment of operation changes. Bayesian reasoning provides a rigorous framework for addressing uncertainty. Moreover, using Bayesian Networks, complex inference regarding hardware degradation can be answered. Specifically, adaptive modelling is combined with Bayesian reasoning to yield recursive estimation algorithms that are robust to sensor failures. Two solutions are presented by extending existing recursive estimation algorithms from the robotics literature. The algorithms are deployed on an underwater vehicle and the performance is assessed in real-world experiments. A comparison against standard filters is also provided. Next, the previous algorithms are extended to consider sensor and actuator failures jointly. An algorithm that can detect thruster failures in an Autonomous Underwater Vehicle has been developed. Moreover, the algorithm adapts the dynamic model online to compensate for the detected fault. The performance of this algorithm was also tested in a real-world application. One step further than hardware fault detection, prognostics predict how much longer can a particular hardware component operate normally. Ubiquitous sensors in modern systems render data-driven prognostics a viable solution. However, training is based on skewed datasets; datasets where the samples from the faulty region of operation are much fewer than the ones from the healthy region of operation. This thesis presents a prognostic algorithm that tackles the problem of imbalanced (skewed) datasets

Pairwise MRF Calibration by Perturbation of the Bethe Reference Point

We investigate different ways of generating approximate solutions to the pairwise Markov random field (MRF) selection problem. We focus mainly on the inverse Ising problem, but discuss also the somewhat related inverse Gaussian problem because both types of MRF are suitable for inference tasks with the belief propagation algorithm (BP) under certain conditions. Our approach consists in to take a Bethe mean-field solution obtained with a maximum spanning tree (MST) of pairwise mutual information, referred to as the \emph{Bethe reference point}, for further perturbation procedures. We consider three different ways following this idea: in the first one, we select and calibrate iteratively the optimal links to be added starting from the Bethe reference point; the second one is based on the observation that the natural gradient can be computed analytically at the Bethe point; in the third one, assuming no local field and using low temperature expansion we develop a dual loop joint model based on a well chosen fundamental cycle basis. We indeed identify a subclass of planar models, which we refer to as \emph{Bethe-dual graph models}, having possibly many loops, but characterized by a singly connected dual factor graph, for which the partition function and the linear response can be computed exactly in respectively O(N) and $O(N^2)$ operations, thanks to a dual weight propagation (DWP) message passing procedure that we set up. When restricted to this subclass of models, the inverse Ising problem being convex, becomes tractable at any temperature. Experimental tests on various datasets with refined $L_0$ or $L_1$ regularization procedures indicate that these approaches may be competitive and useful alternatives to existing ones.Comment: 54 pages, 8 figure. section 5 and refs added in V