A note on the inverse mode shape problem for bars, beams, and plates

Motivated by the idea of designing a structure for a desired mode shape, intended towards applications such as resonant sensors, actuators and vibration confinement, we present the inverse mode shape problem for bars, beams and plates in this work. The objective is to determine the cross-sectional profile of these structures, given a mode shape, boundary condition and the mass. The contribution of this article is twofold: (i) A numerical method to solve this problem when a valid mode shape is provided in the finite element framework for both linear and nonlinear versions of the problem. (ii) An analytical result to prove the uniqueness and existence of the solution in the case of bars. This article also highlights a very important question of the validity of a mode shape for any structure of given boundary conditions.

Active Sequential Hypothesis Testing with Application to a Visual Search Problem

We consider a visual search problem studied by Sripati and Olson where the objective is to identify an oddball image embedded among multiple distractor images as quickly as possible. We model this visual search task as an active sequential hypothesis testing problem (ASHT problem). Chernoff in 1959 proposed a policy in which the expected delay to decision is asymptotically optimal. The asymptotics is under vanishing error probabilities. We first prove a stronger property on the moments of the delay until a decision, under the same asymptotics. Applying the result to the visual search problem, we then propose a ``neuronal metric'' on the measured neuronal responses that captures the discriminability between images. From empirical study we obtain a remarkable correlation (r = 0.90) between the proposed neuronal metric and speed of discrimination between the images. Although this correlation is lower than with the L-1 metric used by Sripati and Olson, this metric has the advantage of being firmly grounded in formal decision theory.

Rendezvous of Multiple UAVs with Collision Avoidance Using Consensus

This paper addresses the problem of multiple unmanned aerial vehicle (UAV) rendezvous when the UAVs have to perform maneuvers to avoid collisions with other UAVs. The proposed solution consists of using velocity control and a wandering maneuver, if needed, of the UAVs based on a consensus among them on the estimated time of arrival at the point of the rendezvous. This algorithm, with a slight modification is shown to be useful in tracking stationary or slowly moving targets with a standoff distance. The proposed algorithm is simple and computationally efficient. The simulation results demonstrate the efficacy of the proposed approach. DOI: 10.1061/(ASCE)AS.1943-5525.0000145. (C) 2012 American Society of Civil Engineers.

Relay Selection for Geographical Forwarding in Sleep-Wake Cycling Wireless Sensor Networks

Our work is motivated by geographical forwarding of sporadic alarm packets to a base station in a wireless sensor network (WSN), where the nodes are sleep-wake cycling periodically and asynchronously. We seek to develop local forwarding algorithms that can be tuned so as to tradeoff the end-to-end delay against a total cost, such as the hop count or total energy. Our approach is to solve, at each forwarding node enroute to the sink, the local forwarding problem of minimizing one-hop waiting delay subject to a lower bound constraint on a suitable reward offered by the next-hop relay; the constraint serves to tune the tradeoff. The reward metric used for the local problem is based on the end-to-end total cost objective (for instance, when the total cost is hop count, we choose to use the progress toward sink made by a relay as the reward). The forwarding node, to begin with, is uncertain about the number of relays, their wake-up times, and the reward values, but knows the probability distributions of these quantities. At each relay wake-up instant, when a relay reveals its reward value, the forwarding node's problem is to forward the packet or to wait for further relays to wake-up. In terms of the operations research literature, our work can be considered as a variant of the asset selling problem. We formulate our local forwarding problem as a partially observable Markov decision process (POMDP) and obtain inner and outer bounds for the optimal policy. Motivated by the computational complexity involved in the policies derived out of these bounds, we formulate an alternate simplified model, the optimal policy for which is a simple threshold rule. We provide simulation results to compare the performance of the inner and outer bound policies against the simple policy, and also against the optimal policy when the source knows the exact number of relays. Observing the good performance and the ease of implementation of the simple policy, we apply it to our motivating problem, i.e., local geographical routing of sporadic alarm packets in a large WSN. We compare the end-to-end performance (i.e., average total delay and average total cost) obtained by the simple policy, when used for local geographical forwarding, against that obtained by the globally optimal forwarding algorithm proposed by Kim et al. 1].

On the Erdos-Szekeres n-interior point problem

The n-interior point variant of the Erdos-Szekeres problem is to show the following: For any n, n-1, every point set in the plane with sufficient number of interior points contains a convex polygon containing exactly n-interior points. This has been proved only for n-3. In this paper, we prove it for pointsets having atmost logarithmic number of convex layers. We also show that any pointset containing atleast n interior points, there exists a 2-convex polygon that contains exactly n-interior points.

Optimal control problem for the time-dependent Kirchhoff-Love plate in a domain with rough boundary

In this paper, we study the asymptotic behavior of an optimal control problem for the time-dependent Kirchhoff-Love plate whose middle surface has a very rough boundary. We identify the limit problem which is an optimal control problem for the limit equation with a different cost functional.

An efficient hybrid approach for design of automotive wheel bearings

Wheel bearings play a crucial role in the mobility of a vehicle by minimizing motive power loss and providing stability in cornering maneuvers. Detailed engineering analysis of a wheel bearing subsystem under dynamic conditions poses enormous challenges due to the nonlinearity of the problem caused by multiple factional contacts between rotating and stationary parts and difficulties in prediction of dynamic loads that wheels are subject to. Commonly used design methodologies are based on equivalent static analysis of ball or roller bearings in which the latter elements may even be represented with springs. In the present study, an advanced hybrid approach is suggested for realistic dynamic analysis of wheel bearings by combining lumped parameter and finite element modeling techniques. A validated lumped parameter representation serves as an efficient tool for the prediction of radial wheel load due to ground reaction which is then used in detailed finite element analysis that automatically accounts for contact forces in an explicit formulation.

A novel Q-learning algorithm with function approximation for constrained Markov decision processes

We present a novel multi-timescale Q-learning algorithm for average cost control in a Markov decision process subject to multiple inequality constraints. We formulate a relaxed version of this problem through the Lagrange multiplier method. Our algorithm is different from Q-learning in that it updates two parameters - a Q-value parameter and a policy parameter. The Q-value parameter is updated on a slower time scale as compared to the policy parameter. Whereas Q-learning with function approximation can diverge in some cases, our algorithm is seen to be convergent as a result of the aforementioned timescale separation. We show the results of experiments on a problem of constrained routing in a multistage queueing network. Our algorithm is seen to exhibit good performance and the various inequality constraints are seen to be satisfied upon convergence of the algorithm.

Exact internal controllability for a hyperbolic problem in a domain with highly oscillating boundary

In this paper, by using the Hilbert Uniqueness Method (HUM), we study the exact controllability problem described by the wave equation in a three-dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities whose size depends on a small parameter epsilon > 0, and with a fixed height. Our aim is to obtain the exact controllability for the homogenized equation. In the process, we study the asymptotic analysis of wave equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Efficient method of moving shadow detection and vehicle classification

Moving shadow detection and removal from the extracted foreground regions of video frames, aim to limit the risk of misconsideration of moving shadows as a part of moving objects. This operation thus enhances the rate of accuracy in detection and classification of moving objects. With a similar reasoning, the present paper proposes an efficient method for the discrimination of moving object and moving shadow regions in a video sequence, with no human intervention. Also, it requires less computational burden and works effectively under dynamic traffic road conditions on highways (with and without marking lines), street ways (with and without marking lines). Further, we have used scale-invariant feature transform-based features for the classification of moving vehicles (with and without shadow regions), which enhances the effectiveness of the proposed method. The potentiality of the method is tested with various data sets collected from different road traffic scenarios, and its superiority is compared with the existing methods. (C) 2013 Elsevier GmbH. All rights reserved.

Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure

The random eigenvalue problem arises in frequency and mode shape determination for a linear system with uncertainties in structural properties. Among several methods of characterizing this random eigenvalue problem, one computationally fast method that gives good accuracy is a weak formulation using polynomial chaos expansion (PCE). In this method, the eigenvalues and eigenvectors are expanded in PCE, and the residual is minimized by a Galerkin projection. The goals of the current work are (i) to implement this PCE-characterized random eigenvalue problem in the dynamic response calculation under random loading and (ii) to explore the computational advantages and challenges. In the proposed method, the response quantities are also expressed in PCE followed by a Galerkin projection. A numerical comparison with a perturbation method and the Monte Carlo simulation shows that when the loading has a random amplitude but deterministic frequency content, the proposed method gives more accurate results than a first-order perturbation method and a comparable accuracy as the Monte Carlo simulation in a lower computational time. However, as the frequency content of the loading becomes random, or for general random process loadings, the method loses its accuracy and computational efficiency. Issues in implementation, limitations, and further challenges are also addressed.

Design and Evaluation of a Robust Optical Beam-Interruption-Based Vehicle Classifier System

This paper presents the design and development of a novel optical vehicle classifier system, which is based on interruption of laser beams, that is suitable for use in places with poor transportation infrastructure. The system can estimate the speed, axle count, wheelbase, tire diameter, and the lane of motion of a vehicle. The design of the system eliminates the need for careful optical alignment, whereas the proposed estimation strategies render the estimates insensitive to angular mounting errors and to unevenness of the road. Strategies to estimate vehicular parameters are described along with the optimization of the geometry of the system to minimize estimation errors due to quantization. The system is subsequently fabricated, and the proposed features of the system are experimentally demonstrated. The relative errors in the estimation of velocity and tire diameter are shown to be within 0.5% and to change by less than 17% for angular mounting errors up to 30 degrees. In the field, the classifier demonstrates accuracy better than 97.5% and 94%, respectively, in the estimation of the wheelbase and lane of motion and can classify vehicles with an average accuracy of over 89.5%.

On the Erdos-Szekeres n-interior-point problem

The n-interior-point variant of the Erdos Szekeres problem is the following: for every n, n >= 1, does there exist a g(n) such that every point set in the plane with at least g(n) interior points has a convex polygon containing exactly n interior points. The existence of g(n) has been proved only for n <= 3. In this paper, we show that for any fixed r >= 2, and for every n >= 5, every point set having sufficiently large number of interior points and at most r convex layers contains a subset with exactly n interior points. We also consider a relaxation of the notion of convex polygons and show that for every n, n >= 1, any point set with at least n interior points has an almost convex polygon (a simple polygon with at most one concave vertex) that contains exactly n interior points. (C) 2013 Elsevier Ltd. All rights reserved.

Higher-Dimensional Analogues of the Map Coloring Problem

After a brief discussion of the history of the problem, we propose a generalization of the map coloring problem to higher dimensions.

Hardness results for computing optimal locally Gabriel graphs

Delaunay and Gabriel graphs are widely studied geo-metric proximity structures. Motivated by applications in wireless routing, relaxed versions of these graphs known as Locally Delaunay Graphs (LDGs) and Lo-cally Gabriel Graphs (LGGs) have been proposed. We propose another generalization of LGGs called Gener-alized Locally Gabriel Graphs (GLGGs) in the context when certain edges are forbidden in the graph. Unlike a Gabriel Graph, there is no unique LGG or GLGG for a given point set because no edge is necessarily in-cluded or excluded. This property allows us to choose an LGG/GLGG that optimizes a parameter of interest in the graph. We show that computing an edge max-imum GLGG for a given problem instance is NP-hard and also APX-hard. We also show that computing an LGG on a given point set with dilation ≤k is NP-hard. Finally, we give an algorithm to verify whether a given geometric graph G= (V, E) is a valid LGG.