Implications of Energy Profile and Storage on Energy Harvesting Sensor Link Performance

Energy harvesting sensors (EHS), which harvest energy from the environment in order to sense and then communicate their measurements over a wireless link, provide the tantalizing possibility of perpetual lifetime operation of a sensor network. The wireless communication link design problem needs to be revisited for these sensors as the energy harvested can be random and small and not available when required. In this paper, we develop a simple model that captures the interactions between important parameters that govern the communication link performance of a EHS node, and analyze its outage probability for both slow fading and fast fading wireless channels. Our analysis brings out the critical importance of the energy profile and the energy storage capability on the EHS link performance. Our results show that properly tuning the transmission parameters of the EHS node and having even a small amount of energy storage capability improves the EHS link performance considerably.

Joint Power Control, Scheduling and Routing for Multihop Energy Harvesting Sensor Networks

We study wireless multihop energy harvesting sensor networks employed for random field estimation. The sensors sense the random field and generate data that is to be sent to a fusion node for estimation. Each sensor has an energy harvesting source and can operate in two modes: Wake and Sleep. We consider the problem of obtaining jointly optimal power control, routing and scheduling policies that ensure a fair utilization of network resources. This problem has a high computational complexity. Therefore, we develop a computationally efficient suboptimal approach to obtain good solutions to this problem. We study the optimal solution and performance of the suboptimal approach through some numerical examples.

Steady compressible flow of granular materials through a wedge-shaped hopper: The smooth wall, radial gravity problem

A continuum model based on the critical state theory of soil mechanics is used to generate stress and density profiles, and to compute discharge velocities for the plane flow of cohesionless materials. Two types of yield loci are employed, namely, a yield locus with a corner, and a smooth yield locus. The yield locus with a corner leads to computational difficulties. For the smooth yield locus, results are found to be relatively insensitive to the shape of the yield locus, the location of the upper traction-free surface and the density specified on this surface. This insensitivity arises from the existence of asymptotic stress and density fields, to which the solution tends to converge on moving down the hopper. Numerical and approximate analytical solutions are obtained for these fields and the latter is used to derive an expression for the discharge velocity. This relation predicts discharge velocities to within 13% of the exact (numerical) values. While the assumption of incompressibility has been frequently used in the literature, it is shown here that in some cases, this leads to discharge velocities which are significantly higher than those obtained by the incorporation of density variation.

Optimisation problems in wireless sensor networks

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating–dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating–dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs – these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating–dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

Particle filters for structural system identification using multiple test and sensor data: A combined computational and experimental study

The problem of structural system identification when measurements originate from multiple tests and multiple sensors is considered. An offline solution to this problem using bootstrap particle filtering is proposed. The central idea of the proposed method is the introduction of a dummy independent variable that allows for simultaneous assimilation of multiple measurements in a sequential manner. The method can treat linear/nonlinear structural models and allows for measurements on strains and displacements under static/dynamic loads. Illustrative examples consider measurement data from numerical models and also from laboratory experiments. The results from the proposed method are compared with those from a Kalman filter-based approach and the superior performance of the proposed method is demonstrated. Copyright (C) 2009 John Wiley & Sons, Ltd.

Model Based Target Tracking in a Wireless Network of Passive Infrared Sensor Nodes

We consider the problem of tracking an intruder in a plane region by using a wireless sensor network comprising motes equipped with passive infrared (PIR) sensors deployed over the region. An input-output model for the PIR sensor and a method to estimate the angular speed of the target from the sensor output are proposed. With the measurement model so obtained, we study the centralized and decentralized tracking performance using the extended Kalman filter.

Tunable Locally-Optimal Geographical Forwarding in Wireless Sensor Networks with Sleep-Wake Cycling Nodes

We consider a wireless sensor network whose main function is to detect certain infrequent alarm events, and to forward alarm packets to a base station, using geographical forwarding. The nodes know their locations, and they sleep-wake cycle, waking up periodically but not synchronously. In this situation, when a node has a packet to forward to the sink, there is a trade-off between how long this node waits for a suitable neighbor to wake up and the progress the packet makes towards the sink once it is forwarded to this neighbor. Hence, in choosing a relay node, we consider the problem of minimizing average delay subject to a constraint on the average progress. By constraint relaxation, we formulate this next hop relay selection problem as a Markov decision process (MDP). The exact optimal solution (BF (Best Forward)) can be found, but is computationally intensive. Next, we consider a mathematically simplified model for which the optimal policy (SF (Simplified Forward)) turns out to be a simple one-step-look-ahead rule. Simulations show that SF is very close in performance to BF, even for reasonably small node density. We then study the end-to-end performance of SF in comparison with two extremal policies: Max Forward (MF) and First Forward (FF), and an end-to-end delay minimising policy proposed by Kim et al. 1]. We find that, with appropriate choice of one hop average progress constraint, SF can be tuned to provide a favorable trade-off between end-to-end packet delay and the number of hops in the forwarding path.

Bounds on the Lifetime of Wireless Sensor Networks Employing Multiple Data Sinks

Employing multiple base stations is an attractive approach to enhance the lifetime of wireless sensor networks. In this paper, we address the fundamental question concerning the limits on the network lifetime in sensor networks when multiple base stations are deployed as data sinks. Specifically, we derive upper bounds on the network lifetime when multiple base stations are employed, and obtain optimum locations of the base stations (BSs) that maximize these lifetime bounds. For the case of two BSs, we jointly optimize the BS locations by maximizing the lifetime bound using a genetic algorithm based optimization. Joint optimization for more number of BSs is complex. Hence, for the case of three BSs, we optimize the third BS location using the previously obtained optimum locations of the first two BSs. We also provide simulation results that validate the lifetime bounds and the optimum locations of the BSs.

Delay constrained optimal relay placement for planned wireless sensor networks

In this paper, we study the problem of wireless sensor network design by deploying a minimum number of additional relay nodes (to minimize network design cost) at a subset of given potential relay locationsin order to convey the data from already existing sensor nodes (hereafter called source nodes) to a Base Station within a certain specified mean delay bound. We formulate this problem in two different ways, and show that the problem is NP-Hard. For a problem in which the number of existing sensor nodes and potential relay locations is n, we propose an O(n) approximation algorithm of polynomial time complexity. Results show that the algorithm performs efficiently (in over 90% of the tested scenarios, it gave solutions that were either optimal or exceeding optimal just by one relay) in various randomly generated network scenarios.

Performance Evaluation of Distance-Hop Proportionality on Geometric Graph Models of Dense Sensor Networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes on a region in Euclidean space, e.g., the unit square. After deployment, the nodes self-organise into a mesh topology. In a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this paper, we analyse the performance of this approximation. We show that nodes with a certain hop distance from a fixed anchor node lie within a certain annulus with probability approach- ing unity as the number of nodes n → ∞. We take a uniform, i.i.d. deployment of n nodes on a unit square, and consider the geometric graph on these nodes with radius r(n) = c q ln n n . We show that, for a given hop distance h of a node from a fixed anchor on the unit square,the Euclidean distance lies within [(1−ǫ)(h−1)r(n), hr(n)],for ǫ > 0, with probability approaching unity as n → ∞.This result shows that it is more likely to expect a node, with hop distance h from the anchor, to lie within this an- nulus centred at the anchor location, and of width roughly r(n), rather than close to a circle whose radius is exactly proportional to h. We show that if the radius r of the ge- ometric graph is fixed, the convergence of the probability is exponentially fast. Similar results hold for a randomised lattice deployment. We provide simulation results that il- lustrate the theory, and serve to show how large n needs to be for the asymptotics to be useful.

Optimal Sleep-Wake Scheduling for Quickest Intrusion Detection using wireless sensor Networks

We consider the problem of quickest detection of an intrusion using a sensor network, keeping only a minimal number of sensors active. By using a minimal number of sensor devices,we ensure that the energy expenditure for sensing, computation and communication is minimized (and the lifetime of the network is maximized). We model the intrusion detection (or change detection) problem as a Markov decision process (MDP). Based on the theory of MDP, we develop the following closed loop sleep/wake scheduling algorithms: 1) optimal control of Mk+1, the number of sensors in the wake state in time slot k + 1, 2) optimal control of qk+1, the probability of a sensor in the wake state in time slot k + 1, and an open loop sleep/wake scheduling algorithm which 3) computes q, the optimal probability of a sensor in the wake state (which does not vary with time),based on the sensor observations obtained until time slot k.Our results show that an optimum closed loop control onMk+1 significantly decreases the cost compared to keeping any number of sensors active all the time. Also, among the three algorithms described, we observe that the total cost is minimum for the optimum control on Mk+1 and is maximum for the optimum open loop control on q.

An analog MVUE for a wireless sensor network

An analog minimum-variance unbiased estimator(MVUE) over an asymmetric wireless sensor network is studied.Minimisation of variance is cast into a constrained non-convex optimisation problem. An explicit algorithm that solves the problem is provided. The solution is obtained by decomposing the original problem into a finite number of convex optimisation problems with explicit solutions. These solutions are then juxtaposed together by exploiting further structure in the objective function.

Connectivity-aware Routing in Sensor Networks

Sensor network applications such as environmental monitoring demand that the data collection process be carried out for the longest possible time. Our paper addresses this problem by presenting a routing scheme that ensures that the monitoring network remains connected and hence the live sensor nodes deliver data for a longer duration. We analyze the role of relay nodes (neighbours of the base-station) in maintaining network connectivity and present a routing strategy that, for a particular class of networks, approaches the optimal as the set of relay nodes becomes larger. We then use these findings to develop an appropriate distributed routing protocol using potential-based routing. The basic idea of potential-based routing is to define a (scalar) potential value at each node in the network and forward data to the neighbor with the highest potential. We propose a potential function and evaluate its performance through simulations. The results show that our approach performs better than the well known lifetime maximization policy proposed by Chang and Tassiulas (2004), as well as AODV [Adhoc on demand distance vector routing] proposed by Perkins (1997).

An Efficient Scheme for Establishing Pairwise Keys for Wireless Sensor Networks

This paper addresses the problem of secure path key establishment in wireless sensor networks that uses the random key pre-distribution technique. Inspired by the recent proxy-based scheme in the work of Ling and Znati (2005) and Li et al. (2005), we introduce a friend-based scheme for establishing pairwise keys securely. We show that the chances of finding friends in a neighbourhood are considerably more than that of finding proxies, leading to lower communication overhead. Further, we prove that the friend-based scheme performs better than the proxy-based scheme both in terms of resilience against node capture as well as in energy consumption for pairwise key establishment, making our scheme more feasible.

Optimizing Delay in Sequential Change Detection on Ad Hoc Wireless Sensor Networks

We consider the classical problem of sequential detection of change in a distribution (from hypothesis 0 to hypothesis 1), where the fusion centre receives vectors of periodic measurements, with the measurements being i.i.d. over time and across the vector components, under each of the two hypotheses. In our problem, the sensor devices ("motes") that generate the measurements constitute an ad hoc wireless network. The motes contend using a random access protocol (such as CSMA/CA) to transmit their measurement packets to the fusion centre. The fusion centre waits for vectors of measurements to accumulate before taking decisions. We formulate the optimal detection problem, taking into account the network delay experienced by the vectors of measurements, and find that, under periodic sampling, the detection delay decouples into network delay and decision delay. We obtain a lower bound on the network delay, and propose a censoring scheme, where lagging sensors drop their delayed observations in order to mitigate network delay. We show that this scheme can achieve the lower bound. This approach is explored via simulation. We also use numerical evaluation and simulation to study issues such as: the optimal sampling rate for a given number of sensors, and the optimal number of sensors for a given measurement rate