Optimal Attitude Sensor Placement and Modal Frequency Identification of Large Space Structure

The current work aims at determining optimal sensor configurations for the modal identification of a post-tensioned timber frame structure. The objective is to maximise the information gained from the structural testing, while keeping the number of necessary sensors to a minimum. Three different and widely used optimal sensor placement (OSP) methods are investigated and evaluated based on appropriate metrics, namely the effective independence method, the modal kinetic energy method and the information entropy (IE) method. An enhanced IE variant is adopted, which resolves the problem of close positioning of sensors, which forms a common issue when sensor positions are selected from a dense grid. In terms of the adopted metrics, three different options are investigated, namely, the information entropy index, the Modal Assurance Criterion and a newly introduced metric, the relative dispersion index. For the quantification of trade-offs among the selected metrics a Pareto Front scheme is realised. The study indicates that the evaluation of different OSP configurations is strongly dependent on the employed metric. It is therefore of vital importance to select the appropriate metric when determining optimal sensor positions.

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.

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 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.

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

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.

Localization is the key perceptual process closing the loop of autonomous navigation, allowing self-driving vehicles to operate in a deliberate way. To ensure robust localization, autonomous vehicles have to implement redundant estimation processes, ideally independent in terms of the underlying physics behind sensing principles. This paper presents a stereo radar odometry system, which can be used as such a redundant system, complementary to other odometry estimation processes, providing robustness for long-term operability. The presented work is novel with respect to previously published methods in that it contains: (i) a detailed formulation of the Doppler error and its associated uncertainty; (ii) an observability analysis that gives the minimal conditions to infer a 2D twist from radar readings; and (iii) a numerical analysis for optimal vehicle sensor placement. Experimental results are also detailed that validate the theoretical insights.

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.

In modal testing, the quality of vibration signals and clarity of peak points to extract the natural frequencies, corresponding mode shapes and damping ratio depend on the number and location of the sensors. High measurement costs are required for structural identification and long-term structural health monitoring in large structures, which require a high number of sensors. Therefore, the minimum number of sensors should be placed at appropriate locations on the system during experimental measurements to ensure both information of sufficient quality and cost reductions. The aim of this study is to perform cost-efficient non-destructive modal tests for a laminated composite and steel cantilever beams using an optimal sensor placement approach. Finite element models of the sample beams are constituted in ANSYS® software to determine the initial candidate set of sensor locations. Then, ambient vibration tests are conducted. Based on the experimental modal amplitudes and mode shapes, optimal sensor locations are determined using the effective independence method, and measurements are repeated. The study shows that there is good agreement between the natural frequencies and mode shapes obtained from the initial measurements and those obtained using the limited number of sensors.

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.

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.

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

Modal parameter identification is an important content for the research on dynamic behavior of civil engineering structures. For the conventional modal parameter identification techniques, excitation signal and response signal are necessary. But excitations can not be measured for structures under natural loading conditions, or excited by random forces. So, the operational modal parameter identification approaches are developing to identify structural modal parameters by using vibration response signal directly. In this paper, a new method for modal parameter identification depending on ambient excitation response signal is proposed based on independent component analysis (ICA). For modal coordinates independent of each other, ICA can extract modal coordinates of structure and estimate mode shape matrix using vibration response signal directly. The free vibration responses can be obtained by random decrement technique (RDT) from modal coordinates which are random processes, and then the natural frequencies and damping ratios are calculated by Hilbert transform. Numerical simulation results indicate that this method is effective and suitable for output-only structural modal parameter identification.

A variant of the genetic algorithm is used to place sensors optimally on a large space structure for the purpose of modal identification. The selection and reproduction schemes of the genetic algorithm are modified and a new operator called forced mutation is introduced. These changes are shown to improve the convergence of the algorithm and to lead to near-optimal sensor locations. Simulated results are also compared with previous results obtained by the effective independent method. The genetic algorithm based sensor configuration estimates the target mode response more accurately. >

Structural modal parameter identification with the Power-Exponential window function