Observability analysis and optimal sensor placement in stereo radar odometry

Accurate localization is a critical task in underwater navigation. Typical localization methods use a set of acoustic sensors and beacons to estimate relative position, whose geometric configuration has a significant impact on the localization accuracy. Although there is much effort in the literature to define optimal 2D or 3D sensor placement, the optimal sensor placement in irregular and constrained 3D surfaces, such as autonomous underwater vehicles (AUVs) or other structures, is not exploited for improving localization. Additionally, most applications using AUVs employ commercial acoustic modems or compact arrays, therefore the optimization of the placement of spatially independent sensors is not a considered issue. This article tackles acoustic sensor placement optimization in irregular and constrained 3D surfaces, for inverted ultra-short baseline (USBL) approaches, to improve localization accuracy. The implemented multi-objective memetic algorithm combines an evaluation of the geometric sensor's configuration, using the Cramer-Rao Lower Bound (CRLB), with the incidence angle of the received signal. A case study is presented over a simulated homing and docking scenario to demonstrate the proposed optimization algorithm.

Optimal sensor placement is an important yet unsolved problem in control theory. In biological organisms, genetic activity is often highly nonlinear, making it difficult to design libraries of promoters to act as reporters of the cell state. We make use of the Koopman observability gramian to develop an algorithm for optimal sensor (or reporter) placement for discrete time nonlinear dynamical systems to ease the difficulty of design of the promoter library. This ease is enabled due to the fact that the Koopman operator represents the evolution of a nonlinear system linearly by lifting the states to an infinite-dimensional space of observables. The Koopman framework ideally demands high temporal resolution, but data in biology are often sampled sparsely in time. Therefore we compute what we call the temporally fine-grained Koopman operator from the temporally coarse-grained Koopman operator, the latter of which is identified from the sparse data. The optimal placement of sensors then corresponds to maximizing the observability of the fine-grained system. We demonstrate the algorithm on a simulation example of a circadian oscillator.

This report summarizes the achievements and final results of this program. The objective of this program is to develop a general model-based sensor network design methodology and tools to address key issues in the design of an optimal sensor network configuration: the type, location and number of sensors used in a network, for online condition monitoring. In particular, the focus in this work is to develop software tools for optimal sensor placement (OSP) and use these tools to design optimal sensor network configuration for online condition monitoring of gasifier refractory wear and radiant syngas cooler (RSC) fouling. The methodology developed will be applicable to sensing system design for online condition monitoring for broad range of applications. The overall approach consists of (i) defining condition monitoring requirement in terms of OSP and mapping these requirements in mathematical terms for OSP algorithm, (ii) analyzing trade-off of alternate OSP algorithms, down selecting the most relevant ones and developing them for IGCC applications (iii) enhancing the gasifier and RSC models as required by OSP algorithms, (iv) applying the developed OSP algorithm to design the optimal sensor network required for the condition monitoring of an IGCC gasifier refractory and RSC fouling. Two key requirements for OSP for condition monitoring are desired precision for the monitoring variables (e.g. refractory wear) and reliability of the proposed sensor network in the presence of expected sensor failures. The OSP problem is naturally posed within a Kalman filtering approach as an integer programming problem where the key requirements of precision and reliability are imposed as constraints. The optimization is performed over the overall network cost. Based on extensive literature survey two formulations were identified as being relevant to OSP for condition monitoring; one based on LMI formulation and the other being standard INLP formulation. Various algorithms to solve these two formulations were developed and validated. For a given OSP problem the computation efficiency largely depends on the “size” of the problem. Initially a simplified 1-D gasifier model assuming axial and azimuthal symmetry was used to test out various OSP algorithms. Finally these algorithms were used to design the optimal sensor network for condition monitoring of IGCC gasifier refractory wear and RSC fouling. The sensors type and locations obtained as solution to the OSP problem were validated using model based sensing approach. The OSP algorithm has been developed in a modular form and has been packaged as a software tool for OSP design where a designer can explore various OSP design algorithm is a user friendly way. The OSP software tool is implemented in Matlab/Simulink© in-house. The tool also uses few optimization routines that are freely available on World Wide Web. In addition a modular Extended Kalman Filter (EKF) block has also been developed in Matlab/Simulink© which can be utilized for model based sensing of important process variables that are not directly measured through combining the online sensors with model based estimation once the hardware sensor and their locations has been finalized. The OSP algorithm details and the results of applying these algorithms to obtain optimal sensor location for condition monitoring of gasifier refractory wear and RSC fouling profile are summarized in this final report.

A novel tensor-based modal decomposition method for reduced order modeling and optimal sparse sensor placement

In an increasing number of scientific and commercial mission scenarios at sea, it is required to simultaneously localize a group of underwater targets. The latter may include moored systems, autonomous vehicles, and even human divers. For reasons that have to do with the unavailability of Global Positioning System underwater, cost reduction, and simplicity of operation, there is currently a surge of interest in the development of range-based multiple target localization systems that rely on the computation of the distances between the targets and a number of sensor nodes deployed at the ocean surface, equipped with acoustic range measuring devices. In the case of a single target, there is a wealth of literature on the problem of optimal acoustic sensor placement to maximize the information available for target localization using trilateration methods. In the case of multiple targets, however, the literature is scarce. Motivated by these considerations, we address the problem of optimal sensor placement for multiple underwater target positioning. In this setup, we are naturally led to a multiple objective optimization problem, the solution of which allows for the analysis of the trade-offs involved in the localization of the targets simultaneously. To this end, we resort to tools from estimation theory and multi-objective optimization. For each target, the function to be minimized (by proper choice of the sensor configuration) is related to the determinant of the corresponding Fisher information matrix, which yields information on the minimum possible covariance of the error with which the position of the target can be estimated using any non-biased estimator. To deal with the fact that more than one target is involved, we exploit the concept of multiple objective Pareto-optimal solutions to characterize the best possible accuracy with which each of the targets can be positioned, given constraints on the desired positioning accuracy of the other targets. Simulation examples illustrate how, for a three-sensor network and two targets, it is possible to define an optimal sensor configuration that yields large positioning accuracy for both targets simultaneously, using convex optimization tools. When more than two targets are involved, however, more than three sensors are required to exploit an adequate trade-off of the accuracy with which each target can be positioned by resorting to non-convex and Pareto-optimization tools. We show how in this case the optimal sensor configurations depend on the Pareto weights assigned to each of the targets, as well as on the number of sensors, the number of targets, and the uncertainty with which the positions of the targets are known a priori.

The optimal placement method of sensors is carried out based on improved genetic algorithm for solving the sensors optimal placement problem of the health monitoring system for long-span railway bridge. Dual structure coding method is introduced to improve the individual encoding method in the Genetic Algorithm. Adaptive partial matching crossover and inversus mutation method is adopted in the optimal preservation strategy, and the probabilities of crossover and mutation are changed automatically according to the fitness value for obtaining the global optimal solution of the sensor placement. So some defects in other Genetic Algorithm applied in the optimal placement of sensors for major bridge structure, such as slow convergence speed and easily falling into local optimum etc., are overcome, and the convergence is ensured. Then the optimal sensors placement of the health monitoring system for one certain long-span railway steel truss cable-stayed bridge is taken as the example to verify the proposed improved genetic algorithm. The result shows that the proposed method has better global optimization, computational efficiency and reliability in compare with the Simple Genetic Algorithm and General Genetic Algorithm, and can be applied to the actual railway cable-stayed bridge health monitoring system for the optimal sensors placement.

This article addresses the problem of moving source localization in 3-D using the time-difference-of-arrival and frequency-difference-of-arrival measurements without accurate sensor location information. Different from the previous studies, we focus on improving the localization performance by introducing two approaches with a limited number of sensors, including optimal sensor placement and velocity configuration, as well as successive measurements for a time period. This article first determines the sensor placement and velocity (including speed and orientation) configuration to achieve optimal localization based on a criterion devised from the Fisher information matrix, in which the restrictions for the two-stage weighted-least-squares (TSWLS) positioning algorithm and the geographical conditions are taken into considerations. Then, to utilize successive measurements while the source is in motion, we separate the sensor velocity into two components for achieving the localization optimality and compensating the source motion, and propose a practical sensor placement and velocity configuration strategy. Finally, combining with the TSWLS-based prelocalization, Kalman filtering and the proposed sensor motion strategy, we develop a source tracking scheme that simultaneously obeys the optimal sensor placement and velocity configuration during tracking. Mathematical analyses and numerical simulations validate the optimal sensor placement and the efficiencies of the source tracking scheme.

This paper considers the optimal sensor placement problem for angle-of-arrival (AOA) target localization in the 2D plane with a Gaussian prior. Optimal sensor locations are analytically determined for a single AOA sensor using the D- and A-optimality criteria and an approximation of the Bayesian Fisher information matrix (BFIM). Optimal sensor placement is shown to align with the minor axis of the prior covariance error ellipse for both optimality criteria. The approximate BFIM is argued to be valid for a sufficiently small prior covariance compared with the target range. Optimal sensor placement results obtained for Bayesian target localization are extended to manoeuvring target tracking. For sensor trajectory optimization subject to turn-rate constraints, numerical search methods based on the D- and A-optimality criteria as well as a new closed-form projection algorithm that aims to achieve alignment with the minor axis of the prior error ellipse are proposed. It is observed that the two optimality criteria generate significantly different optimal sensor trajectories despite having the same optimal sensor placement for the localization of a stationary target. Analysis results and the performance of the sensor trajectory optimization methods are demonstrated with simulation examples. It is observed that the new closed-form projection algorithm achieves superior tracking performance compared with the two numerical search methods.

Performance-based optimal sensor placement method for single-layer reticulated shells considering modal observability and damage identifiability

The Environmental Awareness for Sensor and Emitter Employment (EASEE) software is designed to help in surveillance planning by predicting detection performance of sensors and optimizing sensor selection and placement for intrusion detection around any controlled area, including power plants, dams, borders, prisons, military bases, combat outposts, etc. By its flexible, object-oriented software architecture, EASEE can simulate the performance of a wide variety of sensor modalities-including optical, acoustic, seismic, magnetic, radio-frequency, chemical, and biological-in the realistic terrain and weather conditions of the surveillance environment. EASEE characterizes complex terrain and weather effects on target signatures, signal propagation, and sensor systems, using an expansive library of realistic physics models. Statistical methodologies are also used to account for uncertainties from random signal-generation and propagation mechanisms. A built-in sensor placement algorithm optimizes sensor selections and placements based on sensor supply limitations, coverage priorities, overlapping sensor coverage preferences, and wireless sensor communication requirements.

Structural health monitoring plays an increasingly significant role in detecting damages for large and complex structures to ensure their serviceability and sustainability. Optimal sensor placement is critical in the structural health monitoring system as the sensor configuration directly impacts the quality of collected data used for structural health diagnosis. Therefore, this study presents a comprehensive review of computational methodologies for optimal sensor placement in structural health monitoring. The problem formulation of optimal sensor placement is first introduced, including commonly used evaluation criteria for sensor configurations. Then, various existing optimization methodologies for sensor placement are summarized and introduced in detail, especially for the evolutionary algorithms and their improved variants. Finally, the suitability of computational methods for specific structural health monitoring applications is also discussed. The main goal of this study is to deliver a comprehensive reference of computational methodologies for optimal sensor placement in structural health monitoring studies and applications. This article is concluded by highlighting the most widely utilized evaluation criteria and optimization methodologies for sensor configuration determination.

Structural health monitoring (SHM) is gaining more attention, particularly for bridge structures to continuously evaluate their structural performance and assure their serviceability and safety throughout their service life. To assure reliable SHM systems, optimal sensor placement (OSP) is a cornerstone since it directly influences the quality of obtained data and, thus, the accuracy of the diagnosis. Hence, determining the optimal sensor configuration is a critical step to acquire the maximum information on the structural behavior. Of the available OSP methods, the effective independence method (EFI), which aims to assure that the mode shapes identified from the recorded vibrations are orthogonal to each other, is popular and widely used in literature. Despite its popularity, there are no clear guidelines on how to select the modes that will be included in the OSP application. This chapter evaluates the impact of various parameters including the selected number of mode shapes and sensors on the results of OSP using EFI.KeywordsOptimal sensor placementEffective independence methodStructural health monitoringFinite element modelingModal mass participation

Blasts can produce, in a very short time, an overload much greater than the design load of a building. The blast explosion nearby or within structures causes catastrophic damage to the building both externally and internally. This study intends to model a Cold-Formed Steel (CFS) building using Finite Element Method (FEM) in which material properties of the model are defined according to results of performed laboratory tests. Then accelerograph record of a standard blast was applied to the Finite Element (FE) model. Furthermore, various Optimal Sensor Placement (OSP) algorithms were used and Genetic Algorithm (GA) was selected to act as the solution of the optimization formulation in selection of the best sensor placement according to the blast loading response of the system. In this research a novel numerical algorithm was proposed for OSP procedure which utilizes the exact value of the structural response under blast excitation. Results show that with a proper OSP method for Structural Health Monitoring (SHM) can detect the weak points of CFS structures in different parts efficiently.

Modern health and productivity concerns related to air pollutant exposure in buildings have sparked the need for occupant-centric monitoring and ventilation control. The existing personal exposure monitoring is often restricted to stationary air quality sensors and static occupancy. This study aims to identify optimal stationary sensor placement that best represents exposure to CO2, PM2.5, and PM10 under static and dynamic office occupancies. A total of 48 controlled chamber experiments were executed in four office layouts with variation of occupant numbers (2, 4, 6 or 8), activities (sitting/standing and static/dynamic), ventilation strategies (mixing/displacement) and air change rates (0.5–0.7 h−1, 2.4–2.6 h−1, and 3.8–4.2 h−1). The breathing zone concentration of a reference occupant was monitored with concurrent measurements at seven stationary locations: front edge of the desk, sides of two desks, two sidewalls, and two exhaust vents. The proximity of sensors to the reference occupant and ventilation rate/strategy were important determinants of personal exposure detection. Regression analyses showed that the wall- and desk-mounted CO2 sensors near the occupant (<1 m) best captured CO2 exposure under dynamic–standing activities (R2∼0.4). The wall immediately behind the seated occupant and the ceiling-mounted exhaust near the standing occupant (<1–1.5 m) were the best sensor placements for capturing exposure to particles (R2=0.8–0.9). Separating static from dynamic occupancy activities resulted in improved exposure prediction by 1.4-6.1× . This study is a step towards provision of practical guidelines on stationary air quality sensor placement indoors with the consideration of dynamic occupancy profiles.

It has been of great practical value to optimize sensors' locations and number for the self-diagnostic smart structures. Based on damage detection, Least Square Support Vector Machine (LS-SVM) is proposed to establish the performance function of damage detection for the piezoelectric smart structures, and then quantum genetic algorithm (QGA) is applied to optimize the performance function. To enhance the algorithm speed, LS-SVMs adopted as parallel mode are combined with QGA, that is, a parallel QGA integrated LS-SVMs is constructed to realize optimal sensor placement corresponding to its primal sensor placement. For the more sensors' primal placement, the number of sensors can be reduced effectively through the method of parallel QGA integrated LS-SVMs, and thus leads to cost savings. Compared with traditional GA, QGA possesses the better searching ability and the faster convergence speed.