# Browsing by Subject "Uncertainty (Information theory)"

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Item Optimal draining of fluid networks with parameter uncertainty(2007-12) Buke, Burak, 1980-; Hasenbein, John J.; Morton, David P.Show more Fluid networks are useful tools for analyzing complex manufacturing environments especially in semiconductor wafer fabrication. The makespan of a fluid network is defined as the time to drain the system, when there is fluid present in the buffers initially. Based on this definition, the question of determining the allocation of resources so as to minimize the makespan of a fluid network is known as the makespan problem. In the deterministic version of the makespan problem, it is assumed that the parameters of the system, such as incoming rates, service rates and initial inventory, are known deterministically. The deterministic version of the makespan problem for reentrant lines and multiclass fluid networks has been investigated in the literature and an analytical solution for the problem is well-known. In this work, we provide another formulation for the deterministic makespan problem and prove that the problem can be solved for each station separately. Optimal solutions for the deterministic makespan problem have been used as a guide to develop heuristics methods to solve makespan scheduling problem in the job-shop context in the literature. This provides one motivation for further investigation of the fluid makespan problem. In this work our main focus is solving the makespan problem when the problem parameters are uncertain. This uncertainty may be caused by various factors such as the unpredictability of the arrival process or randomness in machine availability due to failures. In the presence of parameter uncertainty, the decision maker's goal is to optimally allocate the capacity in order to minimize the expected value of the makespan. We assume that the decision maker has distributional information about the parameters at the time of decision making. We consider two decision making schemes. In the first scheme, the controller sets the allocations before observing the parameters. After the initial allocations are set, they cannot be changed. In the second scheme, the controller is allowed a recourse action after a data collection process. It is shown that in terms of obtaining the optimal control, both schemes differ considerably from the deterministic version of the problem. We formulate both schemes using stochastic programming techniques. The first scheme is easier to analyze since the resulting model is convex. Unfortunately, under the second decision scheme, the objective function is non-convex. We develop a branch-and-bound methodology to solve the resulting stochastic non-convex program. Finally, we identify some special cases where the stochastic problem is analytically solvable. This work uses stochastic programming techniques to formulate and solve a problem arising in queueing networks. Stochastic programming and queueing systems are two major areas of Operations Research that deal with decision making under uncertainty. To the best of our knowledge, this dissertation is one of the first works that brings these two major areas together.Show more Item Simulation of dynamic systems with uncertain parameters(2004) Zhang, Fu; Longoria, Raul G.Show more This dissertation describes numerical methods for representation and simulation of dynamic systems with time invariant uncertain parameters. Simulation is defined as computing a boundary of the system response that contains all the possible behaviors of an uncertain system. This problem features many challenges, especially those associated with minimizing the computational cost due to global optimization. To reduce computational cost, an approximation or surrogate of the original system model is constructed by employing Moving Least Square (MLS) Response Surface Method for non-convex global optimization. For more complicated systems, a gradient enhanced moving least square (GEMLS) response surface is used to construct the surrogate model more accurately and efficiently. This method takes advantage of the fact that parametric sensitivity of an ODE system can be calculated as a by-product with less computational cost when solving the original system. Furthermore, global sensitivity analysis for monotonic testing can be introduced in some cases to further reduce the number of samples. The proposed method has been applied to two engineering applications. The first is hybrid system verification by reachable set computing/approximation. First, the computational burden of using polyhedron for reachable set approximation is reviewed. It is then proven that the boundary of a reachable set is formed only by the trajectories from the boundary of an initial state region. This result reduces the search space from R n to R n−1 . Finally, the GEMLS method proposed is integrated with oriented rectangular hull for reachable set representation and an approximation with improved accuracy and efficiency can be achieved. Another engineering application is model-based fault detection. In this case, a fault free system is modeled as a parametric uncertain system whose parameters belong to a given bounded set. The performance boundary of a fault free system can be acquired by using the proposed approach and then employed as an adaptive threshold. A fault is defined when system parameters do not belong to the set due to malfunction or degradation. Once such a fault occurs, the monitored system performance will extend beyond the normal system boundary predicted.Show more