Optimal Sensor Location Problem Research Articles

Optimal Sensor Location and Mobile Sensor Crowd Modeling for Environmental Monitoring

In this paper, the optimal sensor location problem is first discussed for environmental monitoring of physical phenomena governed by some advection-diffusion partial-differential equations. In particular, the exact derivation of the observability Gramian of an advection-diffusion PDE is investigated. Based on the optimality criteria derived from this analysis, a conservation law governing the behavior of a crowd of mobile sensors is proposed to ensure convergence of the sensor density towards an optimal location. The monitoring of pollution on a 2D domain is the case study used throughout the paper to illustrate the effectiveness of the proposed approach.

A multi-objective optimization approach to optimal sensor location problem in IGCC power plants

Integrated Gasification Combined Cycle (IGCC) power plants provide a cleaner and more efficient way to obtain energy from coal. In order to operate an IGCC power plant in a safe and stable manner, several input and output process parameters need to be monitored. However, due to economic and operational constraints, it is infeasible to place sensors at every input and output process parameter location. Hence, it becomes important to select the most effective sensor locations which lead to maximum information gain about the plant conditions. Practical issues present in an IGCC power plant, such as harsh physical conditions and variability in process parameters, make the optimal sensor location problem an especially complicated one. Further, sensors can have multiple objectives and they can produce uncertainties due to measurement errors. This work considers hybrid hardware and virtual sensing for advanced power systems with multiple objectives. In order to solve this real world large scale problem, we use a novel algorithm called Better Optimization of Nonlinear Uncertain Systems (BONUS). BONUS works in probability distribution space and avoids sampling for each optimization and derivative calculations iterations. A new algorithm for multi-objective optimization is also developed specifically for problem. The result of this nonlinear stochastic multi-objective problem is the non-dominated, or Pareto set, which provides trade-offs between various objectives like observability, cost, and thermal efficiency. This is the first attempt at solving the problem of optimal sensor deployment in advanced power plants, with consideration of hybrid hardware and virtual sensing and incorporation of uncertainty with multiple objectives.

Effect of Sensor Noise on Estimation of Diffusion

A Kalman filter is commonly used for state estimation. It is optimal in that the variance of the error is minimized by the estimator. In this paper the problem of optimal sensor location is combined with estimator design to obtain a sensor placement that minimizes the error variance. The question of whether of a larger number of inaccurate sensors, that is those with large noise variance, can provide as good an estimate as a single highly accurate (but probably more expensive) sensor. This question can be investigated with the assumption that all the selected sensors are placed optimally. Estimation of the state of a one-dimensional diffusion equation with three different disturbances is examined in this context. Despite the difference among disturbances, similar proportional relations between the sensor noise variance and the estimation error are observed in numerical simulations. Furthermore, it appears that multiple low quality sensors can lead to better estimation than a single high quality sensor, provided that enough sensors are used.

Solutions and Approximations to the Riccati Integral Equation with Values in a Space of Compact Operators

In this paper, we present conditions that ensure the existence of Bochner integrable solutions of infinite dimensional Riccati integral equations. In particular, we focus on $\mathscr{I}_p$-valued continuous solutions. We formulate an optimal sensor location problem that is based on optimal filtering and show that when the underlying system is of convection-diffusion type the Riccati integral equation has Bochner integrable solutions. We use these results to approximate the sensor placement problem by using a simple quadrature rule. A numerical example is given to illustrate the results.

On Computation of the Design Function Gradient for the Sensor-Location Problem in Variational Data Assimilation

The optimal sensor-location problem is considered in the framework of variational data assimilation for a large-scale dynamical model governed by partial differential equations. This problem is formulated as an optimization problem for the design function defined on the limited-memory approximation of the inverse Hessian of the data assimilation cost function. The expression for the gradient of the design function with respect to the sensor-location coordinates is derived via the adjoint to the Hessian derivative. An efficient algorithm for the gradient evaluation suitable for large-scale applications is suggested. This algorithm exploits the special structure of the limited-memory inverse Hessian defined by a small number of Ritz pairs obtained by the Lanczos method. If additional memory is allocated and certain data are stored during the computation of the Ritz pairs, no additional runs of the tangent linear model are required to evaluate the gradient. The accuracy of the gradients is checked in the numerical experiments. These gradients can be used for the gradient-based optimization of the design function within the chosen global optimization procedure.

Optimal Sensor Placement Based on Particle Swarm Optimization

In order to dispose sensors to reasonable freedom degrees, and reflect adequately the dynamic characteristics of tested structure, the sensor locations of dynamic testing must be optimized. In this paper, taking MAC matrix, Fisher information matrix (FIM), and their combinations as optimization criteria respectively, the particle swarm optimization (PSO) was applied to the optimal sensor location problem (OSLP). The effect of optimization criteria and optimal method to optimal sensor locations were discussed. According to the optimized results, we can arrived at the following conclusions: using MAC and FIM as optimal criteria, introducing the PSO into the OSLP, the optimal sensor locations can ensure the better linear independence of the mode shape vectors and the better estimation of the experimental modal parameters.

Optimal sensor location for distributed-sensor systems using multivariate regression

The performance of monitoring and control techniques for distributed-sensor systems is affected by the choice of the measurement sensor location. In this paper a methodology is suggested to solve the optimal sensor location problem. The suggested algorithm does not require any explicit knowledge of the plant model, and is based upon a sequential procedure selecting at each iteration the most informative measurement input, and updating the input and output spaces by subtracting the information explained by the computed regressor. The effectiveness of the proposed algorithm is assessed by means of two simulated case studies concerning the location of sensors in tubular reactors where product composition need to be estimated from temperature measurements.

Selection of optimal sensor position in a tubular reactor using robust degree of observability criteria

Robust selection criteria for the optimal location for in-process concentration or temperature sensors along the length of a tubular reactor for the partial oxidation of Benzene to Maleic Anhydride are developed. A model of the reactor is constructed by rewriting the Pde's describing the mass and heat balances into a set of Ode's through the method of lines on a grid defined over the reactor length. The linearized model is described as a continuous, time-invariant state-space model where the state is formed by temperature and concentration profiles on the grid points. The best sensor location for the reactor is found by specifying scalar measures on the observability Gramian integral from the linear least-squares state estimation problem. New robust criteria for a degree of observability are specified. The scores on these criteria are determined by the amount of signal received by a sensor for a specific system configuration. These new selection criteria are compared with known measures for degree of observability for the optimal sensor location problem from the literature.

Optimal measurement trajectories for distributed parameter systems

The paper deals with the optimal sensor location problem associated with minimax filtering for linear distributed parameter systems under the moving sensors. The problem of optimal choice of a measurement trajectory is treated here as an H ∞- optimal control one under phase constraints with the objective to minimize a given ‘weak’ performance index under ‘worst’ possible disturbances. Existence of a solution to such a problem is established for the case of quadratic constraints on the disturbances and necessary conditions for optimally are derived on the basis of constructing a sequence of suboptimal solutions associated, in turn, with a sequence of finite-dimensional maximum principles.

Optimal sensor location for detecting changes in dynamical behavior

We address the problem of optimal sensor location for monitoring the eigenstructure of a multivariable dynamical system. The criterions which are optimized are the power of new tests designed for detecting and diagnosing changes in the eigencharacteristics of a system [3], [12]. The key points are the choice of the parameterization for computing the criterion and the comparison of designs with a different number of sensors. The discussion of the numerical results for sensor location includes the analysis of the effect of the geometry of the unknown excitation.

Existence and comparison theorems for partial differential equations of Riccati type

In this paper, we discuss the partial differential equation of Riccati type that describes the optimal filtering error covariance function for a linear distributed-parameter system with pointwise observations. Since this equation contains the Dirac delta function, it is impossible to apply directly the usual methods of functional analysis to prove existence and uniqueness of a bounded solution. By using properties of the fundamental solution and the classical technique of successive approximation, we prove the existence and uniqueness theorem. We then prove the comparison theorem for partial differential equations of Riccati type. Finally, we consider some applications of these theorems to the distributed-parameter optimal sensor location problem.

Optimal sensor location problem for a linear distributed parameter system

This paper studies an optimal sensor location problem for a linear distributed parameter system. It is assumed that a criterion for the optimal sensor location is to minimize the trace of the optimal filtering error covariance function. The existence and uniqueness theorem concerning a solution of the optimal filtering error covariance function for the pointwise observation case is considered. Then by using the existence and uniqueness theorem, the comparison theorem for the partial differential equations of Riccati type is proved. By using the theorems obtained here, the existence theorem concerning a solution of the optimal sensor location problem is proved and the necessary and sufficient conditions for optimality are derived. Finally, some numerical examples for the optimal sensor location problem are illustrated.

Optimal location of measurements for distributed parameter estimation

The problem of optimal measurement locations for state estimation in linear distributed parameter systems is considered. It has previously been shown that the optimal sensor location problem for distributed systems can be posed as an optimal control problem for a system described by the infinite-dimensional matrix Riccati equation for the filter covariance. A more efficient approach based on an upper bound of the filter covariance is developed in the present study. The relationship between the present approach and that of minimizing a measure of the filter covariance is studied. A detailed example is considered, and the results of the two approaches are compared.

Optimal Sensor Location in a Linear Distributed Parameter System

In this paper, we treat the optimal sensor location problem by using functional analysis. Thus, the partial differential equations are embedded into the ordinary differential equations in Hilbert spaces. It is assumed that a criterion for the sensor location is to minimize the trace of the estimation error covariance operator described by the operator-valued differential equations of Riccati type plus the measurement cost. We prove the existence and uniqueness theorem concerning the solution of the estimation error covariance operator by using the theory of the evolution operator and Picard's method. Furthermore, we prove the comparison theorem for the operator-valued differential equations. Based on the theorems, we derive the sufficient condition for the optimal sensor location and then derive the necessary condition. Finally, some numerical examples for the optimal sensor locations are shown.