Optimal Sensor Location Research Articles

On Identification of Parallel Cascade Serial Systems

AbstractWe consider identification of systems with a parallel serial (cascade) structure with multiple-input and multiple-output signals. The statistical properties of estimated models are studied with respect to input signals and possible sensor locations. The quality of the estimates are analyzed by means of the asymptotic covariance matrix of the estimated parameters. This is an extension of previous work on identification of cascaded linear systems. The key result concerns systems where the sub-systems have common dynamics. An interesting observation is that for this case the variance for the parameters belonging to the unmeasured subsystem always is larger than for the other sub-systems. This is not true for general parameters. The variance results can be used for optimal input and sensor location design. The results are illustrated by some simple FIR examples and numerical evaluations.

Design of Sensor Placement for an Integral Pressurized Water Reactor Using Fault Diagnostic Observability and Reliability Criteria

Fault diagnosis is an important area in the nuclear industry for effective and continuous operation of power plants. All the approaches for fault diagnosis depend critically on the sensors that measure important process variables in the system. The locations of these sensors determine the effectiveness of the diagnostic methods. However, the emphasis of most fault diagnosis approaches is primarily on procedures to perform fault detection and isolation (FDI) given a set of sensors. Little attention has been given to the actual allocation of sensors for achieving efficient FDI performance. A graph-based approach, the directed graph (DG), is proposed in this paper as a solution for the optimization of sensor locations for efficient fault identification. The application of the DG modeling in deciding the locations of sensors based on the concepts of observability and fault resolution is introduced. A reliability maximization-based optimization framework for sensor placement from a fault diagnosis perspective is described. The helical coil steam generator unit of the International Reactor Innovative and Secure system is outlined to underscore the utility of the algorithms for large systems.

Optimal measurement allocation for parametric model identification of electrical networks

In this paper we develop optimal sensor siting methods along the edges of a large network of electrical oscillators to identify a parametric model for the network using dynamic measurements of electrical signals corrupted with Gaussian noise. We pose the identification problem as estimation of four essential parameters for each edge in the network, namely the real and imaginary components of the edge-weight, or equivalently, the resistance and reactance of the tie-line connecting any two oscillators, and the inertias of the oscillators connected by this edge. We then formulate the Cramer-Rao bounds for the estimates of these four unknown parameters using three fundamental outputs - namely, the magnitude, the phase angle and the frequency of the voltage phasor along each edge, and show that the bounds are functions of the sensor locations on the edges as well as of the contribution of each variable in the combined output. We finally state the condition for finding the optimal sensor location and the optimal signal combination to achieve the tightest Cramer-Rao bound. The problem is first addressed for open-loop networks and, thereafter, for networks where outputs measured at desired locations on the edges are fed back to the nodes to improve transient performance. We show that unlike the first case where the open-loop configuration allows us to optimize the bounds in a distributed fashion for each individual edge, for the latter situation the problem no longer has a decoupled structure under the influence of feedback, and must be carried out in a centralized fashion.

Using reactive tracers to detect flow field anomalies in water treatment reactors

The hydraulics of water and wastewater treatment reactors has a major impact on their performance and control. The residence time distribution as a measure for the hydraulics represents macroscopic mixing in an integrated way with no spatial information. However, with regard to optimal sensor location for process control and for process optimisation measures, spatial information about macro-mixing is helpful. Spatially distributed measurements of reactive tracers can provide this information. In this paper we generally discuss how reactive tracers can be used to detect and characterize distinct large scale flow structures. It is shown that tracer substances are particularly suited if their reaction time scale is similar to the time scale of the large scale flow structure. For nitrifying activated sludge systems, ammonium is identified to be a suitable tracer. In a comprehensive experimental study at a real aeration tank, two distinct large scale flow features were identified by distributed ammonium measurements. Flow velocity measurements using acoustic Doppler velocimetry clearly supported the nature of these flow field anomalies. Ion-selective electrodes are a well suited device for ammonium measurements providing the temporal resolution that is needed for such an analysis.

Determining optimal sensor locations in freeway using genetic algorithm-based optimization

Travel time is the most intuitive measure of effectiveness for road users and transportation agency operators. However, travel times derived from speed data measured at fixed point sensors often varies from actual travel time. This is, in part, due to the intentional positioning of sensors to avoid lane changing and/or to inadequate numbers of sensors capturing the dynamic characteristics inherent in freeway traffic flow. This paper presents an approach that optimizes the location of sensors in a freeway to support more accurate estimations of travel times than those obtained from conventionally deployed fixed point sensors. Evaluation results, under varying traffic conditions, including incidents, showed that the proposed approach produced average travel time estimation errors within 10% and performed much better than the conventional approach. Thus, the proposed approach provides a promising tool to support re-positioning of the existing non-intrusive point sensors (e.g., video sensors) or deployment of new sets of point sensors for improving travel time estimation.

Wing box transonic-flutter suppression using piezoelectric self-sensing actuators attached toskin

The main objective of this research is to study the capability of piezoelectric (PZT)self-sensing actuators to suppress the transonic wing box flutter, which is a flow–structureinteraction phenomenon. The unsteady general frequency modified transonic smalldisturbance (TSD) equation is used to model the transonic flow about the wing. The wingbox structure and piezoelectric actuators are modeled using the equivalent plate method,which is based on the first order shear deformation plate theory (FSDPT). Thepiezoelectric actuators are bonded to the skin. The optimal electromechanical couplingconditions between the piezoelectric actuators and the wing are collected from previouswork. Three main different control strategies, a linear quadratic Gaussian (LQG) whichcombines the linear quadratic regulator (LQR) with the Kalman filter estimator (KFE), anoptimal static output feedback (SOF), and a classic feedback controller (CFC), are studiedand compared. The optimum actuator and sensor locations are determined using thenorm of feedback control gains (NFCG) and norm of Kalman filter estimatorgains (NKFEG) respectively. A genetic algorithm (GA) optimization technique isused to calculate the controller and estimator parameters to achieve a targetresponse.

Optimization Criteria for Optimal Placement of Piezoelectric Sensors and Actuators on a Smart Structure: A Technical Review

This article presents in a unified way, the various optimization criteria used by researchers for optimal placement of piezoelectric sensors and actuators on a smart structure. The article discusses optimal placement of piezoelectric sensors and actuators based upon six criteria: (i) maximizing modal forces/moments applied by piezoelectric actuators, (ii) maximizing deflection of the host structure, (iii) minimizing control effort/maximizing energy dissipated, (iv) maximizing degree of controllability, (v) maximizing degree of observability, and (vi) minimizing spill-over effects. Optimal piezoelectric sensor and actuator locations on beam and plate structures for each criterion and modes of interest are presented in a tabular form. This technical review has two objectives: (i) practicing engineers can pick the most suitable philosophy for their end application and (ii) researchers can come to know about potential gaps in this area.

Structural analysis of near-optimal sensor locations for a stochastic large-scale network

Finding a set of optimal sensor locations in terms of estimated demand uncertainty minimization for a sensor network is a network design problem. This paper presents a multi-objective model, which considers link information gains (weights of each link, in order to correct a priori origin–destination demands) and origin–destination demand coverage to locate a minimal number of passive point sensors in a roadway network constrained by available resources (e.g., budget limits). We discuss a conceptual link framework for structural analysis, which involves network observability (mean of eigenvolume) and uncertainty (variance of eigenvolume). The general idea behind this method is that the first few installed sensors will account for most of the uncertainty of the origin–destination flow if sensors have substantial correlations among each other (e.g., if each link has a sensor installed). The link structure analysis explores the theoretical structure for understanding the essentials of considering network uncertainty and demand coverage simultaneously in the sensor location problem, as well as providing search directions in the hereafter solution procedure. Consequently, a bi-objective model that balances the trade-off between reducing the network uncertainty and covering demand under a budgetary constraint in the context of traffic dynamics is proposed. A heuristic procedure, the hybrid Greedy Randomized Adaptive Search Procedure (HGRASP), is applied to find Pareto optimal solutions. A case study on the CHART (Washington, DC–Baltimore, Maryland corridor) network was used to demonstrate the proposed methodology.

A mixed-integer linear program for optimizing sensor locations along freeway corridors

How to optimally allocate limited freeway sensor resources is of great interest to transportation engineers. In this paper, we focus on the optimal allocation of point sensors, such as loop detectors, to minimize performance measurement errors. Although it has been shown that the minimization problem can be intuitively formulated as a nonlinear program, the formulation is so complex that only heuristic approaches can be used to solve the problem. In this paper, we transform the nonlinear program into an equivalent mixed-integer linear model. The linearized model is shown to have a graphical interpretation and can be solved using resource constrained shortest path algorithms. A customized Branch-and-Bound technique is then proposed to solve the resource constrained shortest path problem. Numerical experiments along an urban freeway corridor demonstrate that this sensor location model is successful in allocating loop detectors to improve the accuracy of travel time estimation.

Optimal location of measurements for parameter estimation of distributed parameter systems

Systematic methodologies for the optimal location of spatial measurements, for efficient estimation of parameters of distributed systems, are investigated. A review of relevant methods in the literature is presented, and a comparison between the results obtained with three distinctive existing techniques is given. In addition, a new approach based on the Proper Orthogonal Decomposition (POD), to address this important problem is introduced and discussed with the aid of illustrative benchmark case studies from the literature. Based on the results obtained here, it was observed that the method based on the Gram determinant evolution ( Vande Wouwer et al., 2000), does not always produce accurate results. It is strongly dependent on the behaviour of sensitivity coefficients and requires extensive calculations. The method based on max–min optimisation ( Alonso, Kevrekidis, Banga, & Frouzakis, 2004) assigns optimal sensor locations to the positions where system outputs reach their extrema values; however, in some cases it produces more than one optimal solution. The D-optimal design method, Uciński (2003, June 18–20), produces as results the optimal number and spatial positions of measurements based on the behaviour (rather than the magnitude) of the sensitivity functions. Here we show that the extrema values of POD modes can be used directly to compute optimal sensor locations (as opposed e.g. to Alonso, Kevrekidis, et al., 2004, where PODs are merely used to reduce the system and further calculations are needed to compute sensor locations). Furthermore, we demonstrate the equivalence between the extrema of POD modes and of sensitivity functions. The added value of directly using PODs for the computation of optimal sensor locations is the computational efficiency of the method, side-stepping the tedious computation of sensitivity coefficient Jacobian matrices and using only system responses and/or experimental results directly. Furthermore, the inherent combination of model reduction and sensor location estimation in this method becomes more important as the complexity of the original distributed parameter system increases.

A Systematic Approach for the Design of Optimal Monitoring Systems for Large Scale Processes

In this work a new concept for designing an efficient monitoring system for large scale chemical plants is presented. It is considered that the monitoring problem must be solved integrated with the optimal sensor location together with the plant-wide control structure design. The solution of these problems involves deciding among a great number of possible combinations between the input-output variables. It is done supported by the application of genetic algorithm (GA). The key new idea is to propose an adequate objective function, within the GA, that takes into account a fault detectability index based on combined statistics. Additionally, by using a specific penalty function, it is possible to drive the search to the less expensive structure, that is by using the lowest number of sensors. The well-known benchmark case of the Tennessee Eastman plant (TE) is chosen for testing this methodology and for discussion purposes. Since several authors have studied the TE case, the results obtained here can be rigorously compared with those already published. All of the previous works considered that every TE output variables were available for the abnormal events detection for designing the monitoring system.

Sensitivity Analysis as a Tool of Optimal Sensors Location for Solidification Parameters Estimation

The paper deals with the inverse problems appearing in the thermal theory of foundry processes. In particular, the problems connected with identification of casting and mould thermophysical parameters can be considered. To estimate the parameters determining heat transfer processes in the system casting-mould, the additional information concerning the changes of temperature at the points selected from the domain considered is necessary. The localization of sensors should assure the best conditions of identification process. Generally speaking, the sensor should be located at the point for which the sensitivity of temperature field with respect to parameter estimated achieves maximum. In the case of simultaneous identification of several parameters, the proper choice of sensors localization is more complicated. The main goal of the paper is to discuss a theoretical base connected with the problem formulated, to present the possibilities of numerical methods application, to solve the problem, and finally to show the examples of inverse problems solutions (in particular, the latent heat of binary alloy will be estimated).

Risk-Based Sensor Placement for Contaminant Detection in Water Distribution Systems

A method for optimizing sensor locations to effectively and efficiently detect contamination in a water distribution network is presented here. The problem is formulated and solved as a twin-objective optimization problem with the objectives being the minimization of the number of sensors and minimization of the risk of contamination. Unlike past approaches, the risk of contamination is explicitly evaluated as the product of the likelihood that a set of sensors fails to detect contaminant intrusion and the consequence of that failure (expressed as volume of polluted water consumed prior to detection). A novel importance-based sampling method is developed and used to effectively determine the relative importance of contamination events, thus reducing the overall computation time. The above problem is solved by using the nondominated sorting genetic algorithm II. The methodology is tested on a case study involving the water distribution system of Almelo (The Netherlands) and the potential intrusion of E. co...

Process Monitoring of Tubular Microreactors using Particle Filter

Microreactors consist of tens to hundreds of micrometer-scale channels. The residence time of a fluid can be set exactly and backmixing can be minimized. Particularly, very short residence time can be achieved. In addition, it is possible to precisely control the reaction temperature due to large surface to volume ratio of channels. These features of microreactors make it possible to realize the production of specialty chemicals, which cannot be handled in conventional reactors. The most recognized problem in microreactors is channel blockage. The catalyst deterioration is also an inevitable problem for catalyst reactions in microreactors. To realize stable long-term operation of microreactors, it is necessary to detect such problems as early as possible. Since miniaturized sensors are expensive and their direct installation inside channels may disturb the flow, it is indispensable to develop a process monitoring system using a few indirect measurements. In this research, a state and parameter estimation system for tubular microreactors (TMRs) is developed to detect process faults. In the developed system, a process model is derived from the first-principle model of TMRs. Particle Filter (PF) or Extended Kalman Filter (EKF) or Ensemble Kalman Filter (EnKF) is designed to obtain the unknown parameters such as catalyst efficiency from a single wall temperature sensor. To achieve high estimation performance, the optimal sensor location is determined on the basis of the observability. The numerical examples illustrate that the blockage and the catalyst deterioration of TMRs can be detected more rapidly and accurately by using PF, as compared with EnKF and EKF.

A Bayesian methodology for crack identification in structures using strain measurements

A Bayesian system identification methodology is presented for estimating the crack location, size and orientation in a structure using strain measurements. The Bayesian statistical approach combines information from measured data and analytical or computational models of structural behaviour to predict estimates of the crack characteristics along with the associated uncertainties, taking into account modelling and measurement errors. An optimal sensor location methodology is also proposed to maximise the information that is contained in the measured data for crack identification problems. For this, the most informative, about the condition of the structure, data are obtained by minimising the information entropy measure of the uncertainty in the crack parameter estimates. Both crack identification and optimal sensor location formulations lead to highly non-convex optimisation problems in which multiple local and global optima may exist. A hybrid optimisation method, based on evolutionary strategies and gradient-based techniques, is used to determine the global minima. The effectiveness of the proposed methodologies is illustrated using simulated data from a single crack in a thin plate subjected to static loading.

Plant-Wide Control Based on Minimum Square Deviation

In this work a new systematic and generalized strategy to solve the MIMO plant-wide control problem is proposed. The methodology called Minimum Square Deviation (MSD) considers several points such as the optimal sensor location (OSL) based on the sum of square deviation (SSD) and the control structure selection (CSS) based on net load evaluation (NLE) problems simultaneously. Particularly, this work focuses on selecting the best MIMO control structure by using a new steady-state index called NLE. Thus, alternative control structures can be obtained through different interaction levels and defining a corresponding performance improvement. Two well-known chemical process are proposed here for testing this methodology. In addition, a robust stability analysis applying the classical μ-tool is performed by considering both parametric and unmodeled dynamic uncertainties.

Estimation of Distribution Algorithms: Applications to the Design of Process Sensor Networks

The optimal location of sensors involves the selection of type, number and location of sensorsfrom a set of available instruments with certain values of cost, precision and reliability. Theoptimal design not only satisfies economic criteria, but also some requirements on the qualityof key variable estimates. In this work, a methodology for solving the sensor network designproblem based on Estimation of Distribution Algorithms is presented. These algorithms areincluded in the Evolutionary Computation paradigm and substitute the probability distributionestimation of a population composed by potential solutions and its subsequent sampling forthe use of the classic crossover and mutation operators. The performance of the new strategyis evaluated and compared with that provided by other evolutionary techniques for the case ofa steam metering network of a methanol synthesis plant.

Optimized finite element model updating method for damage detection using limited sensor information

Limited, noisy data in vibration testing is a hindrance to the development of structural damage detection. This paper presents a method for optimizing sensor placement and performing damage detection using finite element model updating. Sensitivity analysis of the modal flexibility matrix determines the optimal sensor locations for collecting information on structural damage. The optimal sensor locations require the instrumentation of only a limited number of degrees of freedom. Using noisy modal data from only these limited sensor locations, a method based on model updating and changes in the flexibility matrix successfully determines the location and severity of the imposed damage in numerical simulations. In addition, a steel cantilever beam experiment performed in the laboratory that considered the effects of model error and noise tested the validity of the method. The results show that the proposed approach effectively and robustly detects structural damage using limited, optimal sensor information.

Optimal Sensor Location Design for Reliable Fault Detection in Presence of False Alarms

To improve fault detection reliability, sensor location should be designed according to an optimization criterion with constraints imposed by issues of detectability and identifiability. Reliability requires the minimization of undetectability and false alarm probability due to random factors on sensor readings, which is not only related with sensor readings but also affected by fault propagation. This paper introduces the reliability criteria expression based on the missed/false alarm probability of each sensor and system topology or connectivity derived from the directed graph. The algorithm for the optimization problem is presented as a heuristic procedure. Finally, a boiler system is illustrated using the proposed method.

Sensor Network Optimization for a Passive Sensing Impact Detection Technique

An investigation was performed to develop a sensor placement method to maximize the performance of a structural health monitoring (SHM) system with a minimal number of sensors for detection of impact in structures, particularly for structures made of fiber-reinforced composite materials. The performance of the SHM system is evaluated based on the probability of detection (POD). This optimization problem was formulated to maximize the POD through selection of optimal sensor locations for a given sensor network. A genetic algorithm was adopted and integrated with the SHM system to perform the optimization process. Numerical simulations on two composite panels showed that the selection of sensor network configuration is crucial for the performance of the SHM system. For a targeted POD, the proposed method can be used to configure an SHM system with a minimal number of sensors to identify impact forces that are greater than a pre-defined critical value.