Payman Sadegh

Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation

The simultaneous perturbation stochastic approximation (SPSA) algorithm has recently attracted considerable attention for optimization problems where it is difficult or impossible to obtain a direct gradient of the objective (say, loss) function. The approach is based on a highly efficient simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo process. The objective is to minimize the mean square error of the estimate. We also consider maximization of the likelihood that the estimate be confined within a bounded symmetric region of the true parameter. The optimal distribution for the components of the simultaneous perturbation vector is found to be a symmetric Bernoulli in both cases. We end the paper with a numerical study related to the area of experiment design.

A methodology for predicting service life and design of reliability experiments

This paper summarizes a methodology for reliability prediction of new products where field data are sparse, and the allowed number & length of experiments are limited. The methodology relies on estimating a set where the unknown parameters are most likely to be found, calculation of an upper bound for the reliability metric of interest conditioned that the parameters reside in the estimated set, and tightening the bounds via design of experiments. Models of failure propagation, failure acceleration, system operations, and time/cycle to failure at various levels of fidelity & expert elicited information may be incorporated to enhance the accuracy of the predictions. The application of the model is illustrated through numerical studies.

A framework for unified design of fault detection & isolation and optimal maintenance policies

Fault detection and isolation (FDI) and design of optimal maintenance policies have been traditionally studied separately by the control community and domain experts on the one hand and the operations research community on the other. The objective of this paper is to provide a unified approach where maintenance decisions are driven by real-time FDI signals. Such an approach allows systematic analysis and design of FDI with the objective of minimizing the overall costs of operations and maintenance (O&M). Our approach relies on the following steps. First, the information about the assets, their likely failure modes (as generated by failure modes and effects analysis or from historical service data), service business processes, and costs associated with fixing the assets are captured from designers or practitioners. The Unified Modeling Language (UML) is used as an expressive way to capture and display such information. Next, this information is used to arrive at a representation of the asset degradation and maintenance process as a Markov process. Finally, the asset management problem is formulated as an optimal control over the Markov process. We show how the fundamental properties of FDI drive the O&M costs and the solution to the control problem through their impact on transition probabilities of the Markov process. We illustrate the approach by a numerical example for maintaining proper refrigerant charge levels in Rankine cycle equipment

Optimal sensor configuration for complex systems with application to signal detection in structures

The paper considers the problem of sensor configuration for complex systems. The contribution of the paper is twofold. Firstly, we define an appropriate criterion that is based on maximizing overall sensor responses while minimizing redundant information as measured by correlations between multiple sensor outputs. Secondly, we describe an efficient and practical algorithm to achieve the optimization goals, based on simultaneous perturbation stochastic approximation (SPSA). SPSA avoids the need for detailed modeling of the sensor response by simply relying on observed responses as obtained by limited experimentation with test sensor configurations. We illustrate the application of the approach to optimal placement of acoustic sensors for signal detection in structures. This includes both a computer simulation study for an aluminum plate, and real experimentations on a steel I-beam.

Correction to "Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation"

The numbering of references in the article noted by the title (ibid., vol. 43, pp. 1480-1484, Oct. 1998) is incorrect. A corrected reference list is provided.

A maximum feasible subset algorithm with application to radiation therapy

Consider a set of linear one sided or two sided inequality constraints on a real vector X. The problem of interest is selection of X so as to maximize the number of constraints that are simultaneously satisfied, or equivalently, combinatorial selection of a maximum cardinality subset of feasible inequalities. Special classes of this problem are of interest in a variety of areas such as pattern recognition, machine learning, operations research, and medical treatment planning. This problem is generally solvable in exponential time. A heuristic polynomial time algorithm is presented in this paper. The algorithm relies on an iterative constraint removal procedure where constraints are eliminated from a set proposed by solutions to minmax linear programs. The method is illustrated by a simulated example of a linear system with double sided bounds and a case from the area of radiation therapy.