Optimal sensor placement for state estimation of flexible shell structures

Weickgenannt, Martin; Neuhaeuser, Stefan; Henke, Benjamin; Sobek, Werner; Sawodny, Oliver

doi:10.1109/fpm.2011.6045791

Cited by 6 publications

(5 citation statements)

References 16 publications

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“…Other researchers have used the eigenvalues of the observability Gramian in the cost functional for systems with linear dynamics [17,18]. Here, however, the goal is to incorporate nonlinear dynamics into the sensor placement problem.…”

Section: B Observability Gramianmentioning

confidence: 98%

“…The optimal sensor placement problem has received widespread attention in diverse areas such as mobile senor networks [15,16], civil structure health monitoring [17,18], robotic navigation [19,20], power grid monitoring [21], and chemical processes [22]. Avariety of cost functions have been used to select optimal sensor locations in these and related works.…”

Section: Introductionmentioning

confidence: 99%

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Observability-Based Optimal Sensor Placement for Flapping Airfoil Wake Estimation

Hinson

Morgansen

2014

Journal of Guidance, Control, and Dynamics

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This work considers the optimal sensor placement problem for a general nonlinear system using the eigenvalues of the observability Gramian in the cost function. The problem is formulated as a mixed-integer convex optimization problem. Using the empirical observability Gramian, the input data to this optimization problem are computed from a simulation of the nonlinear system with no analytical model required. A piecewise linear approximation to the observability Gramian is proposed using special ordered sets of type two, allowing a coarser sensor location mesh and thus fewer binary variables and shorter solution times compared with standard gridded approaches. The solution methodology is applied to vortex estimation in the wake of a flapping airfoil using velocity sensors on the surface of the airfoil, which is modeled using unsteady potential flow and a Joukowski conformal mapping. Resulting optimal sensor sets are found near the trailing edge in pairs on the upper and lower surface. Although the observability Gramian is computed from the linearized system, the optimal sensor sets yield improved performance of an unscented Kalman filter estimating wake vortex structure on the nonlinear dynamics; the optimal sets outperform more than 99% of the sampled feasible sensor sets, thus validating the observability eigenvalues as a measure of nonlinear estimator performance. Nomenclature A, B, C = linearized system dynamics matrices a = Joukowski cylinder radius E = expectation operator F = Fisher information matrix f = nonlinear dynamics model H = linear measurement model h = nonlinear measurement model k = discrete time step k r = reduced frequency P = covariance matrix p = number of desired sensors r = number of candidate sensors s i = sensor location for sensor i u = control input u = control linearization deviation u 0 = control linearization trajectory v = measurement noise W = observability Gramiañ W = empirical observability Gramian W = interpolated observability Gramian W d = discrete-time observability Gramian w j = special ordered set weight vector for sensor j x = state vector x = state linearization deviation x 0 = state linearization trajectory

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Section: B Observability Gramianmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Observability-Based Optimal Sensor Placement for Flapping Airfoil Wake Estimation

Hinson

Morgansen

2014

Journal of Guidance, Control, and Dynamics

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“…(10). Then a state space model is generated using mode shapes to generate the reference displacement r S and reference strain.…”

Section: Dstmentioning

confidence: 99%

“…But it just roughly described the sensors' layout, rather than give the specific optical methods. Literature [10] studied both numbers and locations of sensors for reconstructing the flexible shell structure with modal transformation approach and simulated-annealing algorithms. Although the quantity and placement of sensors were ascertained by finite element simulation and analysis, it also did not give the specific experimental verification and analysis results.…”

Section: Introductionmentioning

confidence: 99%

Optimal placement of FBG sensors for reconstruction of flexible plate structures using modal approach

Zhu

Zhang

et al. 2015

2015 34th Chinese Control Conference (CCC)

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An optimization method based on mode approach and improved genetic algorithms is developed for optimal FBG sensors placement in health monitoring and reconstruction of flexible thin-plate structure. The optimization objective is to obtain a kind of placement of FBG sensors which has the best reconstruction effects. The structure is modeled using Finite Element methods and modal analysis is carried out to create a modal space which provides data for both shape-reconstruction and error-calculation. The optimization is performed by improved genetic algorithm that uses the mean square error of reconstruction for the comparison of different optimal solution candidates. FBG sensors were arranged on the structural surface and experiment with an optimized sensor placement were performed to verify the effectiveness of the method and the simulation results.

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“…The problem of optimal sensor placement for state estimation has attracted a large body of practical and theoretical research. On the practical side, sensor placement has been investigated with respect to state estimation in complex dynamical systems like electric power grids (Cho et al., 2001; Dua et al., 2008), biochemical reaction networks (Liu et al., 2013), structural systems (Safizadeh & Darus, 2010; van der Linden et al., 2011; Weickgenannt et al., 2011), weather systems (Guestrin et al., 2005), and contaminant monitoring in soil and groundwater (Castello et al., 2010; Reed et al., 2000). While application areas are diverse, these studies share the common goal of designing sensor networks that can optimally infer system states from limited observed data—for instance, estimating line voltages in an electrical grid from data collected at generating stations.…”

Section: Introductionmentioning

confidence: 99%

Observability‐Based Sensor Placement Improves Contaminant Tracing in River Networks

Bartos

Kerkez

2021

Water Resources Research

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Global river health is in a state of crisis. In the United States, roughly 46% of river length is classified as being in poor biological condition (US EPA, 2017). Survey results indicate similar trends worldwide (Vörösmarty et al., 2010). The main drivers of surface water impairment are nonpoint-source pollutants like sewage, nutrients, and sediments (Rowny & Stewart, 2012). Sewer overflows release pathogens that are attributable to roughly 3,400-5,600 cases of illness annually in the United States (US EPA, 2004). At the same time, excessive nutrient loads from agriculture result in harmful algal blooms that impair aquatic ecosystems and render water unsafe to drink (

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Optimal sensor placement for state estimation of flexible shell structures

Cited by 6 publications

References 16 publications

Observability-Based Optimal Sensor Placement for Flapping Airfoil Wake Estimation

Observability-Based Optimal Sensor Placement for Flapping Airfoil Wake Estimation

Optimal placement of FBG sensors for reconstruction of flexible plate structures using modal approach

Observability‐Based Sensor Placement Improves Contaminant Tracing in River Networks

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