Optimal Sensor Location Research Articles

Employment of the bootstrap method for optimal sensor location considering uncertainties in a coupled hydro-mechanical application

Numerical simulations become an increasingly utilised tool for predicting soil behaviour in geotechnical engineering. However, these simulations require reliable soil parameters that have to be determined either by conducting laboratory experiments or by model parameter identification using in-situ measurements. To gain reliable and sufficiently informative measurement results for successful determination of the soil parameters while being still economic, an optimal experimental design is of crucial importance. This work presents a procedure of setting up a monitoring concept for a dike with uncertain material properties exposed to a rapid drawdown of the adjacent water level. The illustrative example is numerically modelled using a coupled hydro-mechanical analysis and the parameters that are most relevant for the dike stability are firstly identified via global sensitivity analysis. Subsequently, the global sensitivity analysis with respect to measurable outputs is employed to identify appropriate monitoring areas. Finally, bootstrapping is conducted to make possible to decide on the optimal observation sensor locations for reliable identification of the most influential soil parameters.

Dynamic Programming Approach to Load Estimation Using Optimal Sensor Placement and Model Reduction

A time-domain technique for estimating dynamic loads acting on a structure from structural response measured experimentally at a finite number of optimally placed sensors on the structure is presented. The technique relies on an existing solution method based on dynamic programming, which consists of a backward (inverse) time sweeping phase followed by a forward time sweeping phase. The dynamic programming method of load identification, similar to all other inverse methods, suffers from ill-conditioning. Small variations (noise) in response measurements can cause large errors in load estimates. The condition of the inverse problem, and hence the quality of load estimates, depends on the locations of sensors on the structure. There can be a large number of locations on a structure where sensors can potentially be mounted. A D-optimal design algorithm is used to arrive at optimal sensor locations such that the condition of the inverse problem is improved and precise load estimates are obtained. Another major limitation of the dynamic programming technique is that the computation time increases dramatically as the model size increases. To deal with this shortcoming, a technique based on Craig–Bampton model reduction is also proposed in this paper. Numerical results illustrate the effectiveness of the proposed technique in accurately recovering the loads imposed on discrete as well as continuous systems.

Genetic algorithm based optimal sensor placement forL1-regularized damage detection

Sparse recovery theory has been applied to damage detection by utilizing the sparsity feature of structural damage. The theory requires that the columns of the sensing matrix suffice certain independence criteria. In l1-regularized damage detection, the sensitivity matrix serves as the sensing matrix and is directly related to sensor locations. An optimal sensor placement technique is proposed such that the resulting sensitivity matrix is of the maximum independence in the columns or is of the least mutual coherence. Given a total number of sensors, the selection of sensor locations is a combinatorial problem. A genetic algorithm is thus used to solve this optimization problem, in which the mutual coherence of the sensitivity matrix is minimized. The obtained optimal sensor locations and associated sensitivity matrix are used in l1-regularized damage detection. An experimental cantilever beam and a three-storey frame are utilized to verify the effectiveness and reliability of the proposed sensor placement technique. Results show that using the modal data based on the optimal sensor placement can identify damage location and severity more accurately than using the ones based on uniformly selected sensor locations.

Sensor placement optimization applied to laminated composite plates under vibration

The location optimization of sensors is a essential problem in structural health monitoring systems. Taking the cost of sensors into account, it is uneconomical to install sensors on every part of a structure and moreover in aeronautical industry, the weight is a crucial factor. In this paper, a optimal placement optimization of sensor locations for structural health monitoring systems is studied. Several techniques of optimization of sensors are approached and applied in a shell structure. The structure, a laminate of carbon fiber, was modeled by the finite element method (FEM) and then subject to free vibration. Genetic algorithms (GAs) are then employed to locate the best sensor distribution to cover a specific number of low frequency modes. Numerical results have demonstrated the overall efficiency of sensor delivery methods. Specific problems occurred, especially regarding the method of effective independence, being less efficient and discrepant in relation to the other methods employed. In summary, the results obtained in this paper provide an optimal position for sensors in real SHM systems and experiments.

Approximate computational approaches for Bayesian sensor placement in high dimensions

Since the cost of installing and maintaining sensors is usually high, sensor locations should always be strategically selected to extract most of the information. For inferring certain quantities of interest (QoIs) using sensor data, it is desirable to explore the dependency between observables and QoIs to identify optimal placement of sensors. Mutual information is a popular dependency measure, however, its estimation in high dimensions is challenging as it requires a large number of samples. This also comes at a significant computational cost when samples are obtained by simulating complex physics-based models. Similarly, identifying the optimal design/location requires a large number of mutual information evaluations to explore a continuous design space. To address these challenges, two novel approaches are proposed. First, instead of estimating mutual information in high-dimensions, we map the limited number of samples onto a lower dimensional space while capturing dependencies between the QoIs and observables. We then estimate a lower bound of the original mutual information in this low dimensional space, which becomes our new dependence measure between QoIs and observables. Second, we use Bayesian optimization to search for optimal sensor locations in a continuous design space while reducing the number of lower bound evaluations. Numerical results on both synthetic and real data are provided to compare the performance of the lower bound with the estimate of mutual information in high dimensions, and a puff-based dispersion model is used to evaluate the sensor placement of the Bayesian optimization for a chemical release problem. The results show that the proposed approaches are both effective and efficient in capturing dependencies and inferring the QoIs.

End-User Software for Efficient Sensor Placement in Jacketed Wine Tanks

In food processing, temperature is a key parameter affecting product quality and energy consumption. The efficiency of temperature control depends on the data provided by sensors installed in the production device. In the wine industry, temperature sensor placement inside the tanks is usually predetermined by the tank manufacturers. Winemakers rely on these measurements and configure their temperature control accordingly, not knowing whether the monitored values really represent the wine’s bulk temperature. To address this problem, we developed an end-user software which 1. allows winemakers or tank manufacturers to identify optimal sensor locations for customizable tank geometries and 2. allows for comparisons between actual and optimal sensor placements. The analysis is based on numerical simulations of a user-defined cooling scenario. Case studies involving two different tanks showed good agreement between experimental data and simulations. Implemented based on the scientific Linux operating system gmlinux, the application solely relies on open-source software that is available free of charge.

Sparse-Sensor Placement for Wind Farm Control

The objective of this paper is to incorporate sparse sensor data to improve flow-field estimates in a wind farm, which can then be used to perform better online wind farm optimization and control. A sparse-sensing algorithm is used to determine the optimal locations of sensors to improve the overall estimation precision of the flow field within the wind farm. This algorithm takes advantage of the dominant atmospheric structures in a wind farm to reconstruct the flow field from point measurements in the field. These measurements, in their optimal locations, have the ability to improve the observability of a wind farm and thus provide faster, more accurate, state estimation.

Ensemble-Based State Estimator for Aerodynamic Flows

Regardless of the plant model, robust flow estimation based on limited measurements remains a major challenge in successful flow control applications. Aiming to combine the robustness of a high-dimensional representation of the dynamics with the cost efficiency of a low-order approximation of the state covariance matrix, a flow state estimator based on the ensemble Kalman filter is applied to two-dimensional flow past a cylinder and an airfoil at high angle of attack and low Reynolds number. For development purposes, the numerical algorithm is used as both the estimator and as a surrogate for the measurements. Estimation is successful using a reduced number of either pressure sensors on the surface of the body or sparsely placed velocity probes in the wake. Because the most relevant features of these flows are restricted to a low-dimensional manifold of the state space, asymptotic behavior of the estimator is shown to be achieved with a small ensemble size. The relative importance of each sensor location is evaluated by analyzing how they influence the estimated flowfield, and optimal locations for pressure sensors are determined. Covariance inflation is used to enhance the estimator performance in the presence of unmodeled freestream perturbations. A combination of parametric modeling and augmented state methodology is used to successfully estimate the forces on immersed bodies subjected to deterministic and random gusts.

Genetic Algorithm Based Optimum Semi-Active Control of Building Frames Using Limited Number of Magneto-Rheological Dampers and Sensors

Optimum semi-active control with a limited number of magneto-rheological (MR) dampers and measurement sensors has certain requirements. Most important of them is the accurate estimation of control forces developed in the MR dampers from the observations made in the structure. Therefore, the observation strategy should form an integral part of the optimization problem. The existing literature on the subject does not address this issue properly. The paper presents a computationally efficient optimization scheme for semi-active control of partially observed building frames using a limited number of MR dampers and sensors for earthquakes. The control scheme duly incorporates the locations of measurement sensors as variables into the genetic algorithm (GA) based optimization problem. A ten-storied building frame is taken as an illustrative example. The optimum control strategy utilizes two well-known control laws, namely, the linear quadratic Gaussian (LQG) with clipped optimal control and the bang-bang control to find the time histories of voltage to be applied to the MR dampers. The results of the numerical study show that the proposed scheme of sensor placement provides the optimum reduction of response with more computational efficiency. Second, optimal locations of sensors vary with the response quantities to be controlled, the nature of earthquake, and the control algorithm. Third, optimal locations of MR dampers are invariant of the response quantities to be controlled and the nature of earthquake.

A multiobjective sensor placement optimization for SHM systems considering Fisher information matrix and mode shape interpolation

Sensor placement optimization plays a key role in structural health monitoring (SHM) of large mechanical structures. Given the existence of an effective damage identification procedure, the problem arises as to how the acquisition points should be placed for optimal efficiency of the detection system. The global multiobjective optimization of sensor locations for structural health monitoring systems is studied in this paper. First, a laminated composite plate is modelled using Finite Element Method (FEM) and put into modal analysis. Then, multiobjective genetic algorithms (GAs) are adopted to search for the optimal locations of sensors. Numerical issues arising in the selection of the optimal sensor configuration in structural dynamics are addressed. A method of multiobjective sensor locations optimization using the collected information by Fisher Information Matrix (FIM) and mode shape interpolation is presented in this paper. The sensor locations are prioritized according to their ability to localize structural damage based on the eigenvector sensitivity method. The proposed method presented in this paper allows to distribute the points of acquisition on a structure in the best possible way so as to obtain both data of greater modal information and data for better modal reconstruction from a minimum point interpolation. Numerical example and test results show that the proposed method is effective to distribute a reduced number of sensors on a structure and at the same time guarantee the quality of information obtained. The results still indicate that the modal configuration obtained by multiobjective optimization does not become trivial when a set of modes is used in the construction of the objective function. This strategy is an advantage in experimental modal analysis tests, since it is only necessary to acquire signals in a limited number of points, saving time and operational costs.

Data-driven distributionally robust optimization approach for reliable travel-time-information-gain-oriented traffic sensor location model

Travel time is one of the most intuitive pieces of traffic information to help decision makers to control real-time traffic conditions and to guide travelers to choose a reasonable route. An optimal sensor location scheme can obtain reliable route travel time information. Most current travel-time-oriented sensor location models are deterministic and assume a given and correct travel time probability density function. Nevertheless, due to widespread observational and systematic errors, prior travel time information is not accurate or reliable. In our study, a novel data-driven link-based network sensor location method is proposed to maximize travel time information gain. The effect of route differentiation is considered, and the sensors are located at links rather than at nodes. In addition, to account for the uncertainty in the prior travel time distribution, the distributionally robust travel time information gain sensor location (DRTTIGSL) model is presented. The prior distribution information is taken into account based on a statistical measure called ϕ-divergence. The ϕ-divergence is used to construct the uncertainty set. The reformulation of DRTTIGSL is dependent on the choice of ϕ-divergence and is tractable. Extensive numerical experiments are conducted to verify the effectiveness of the DRTTIGSL model. Compared with the optimal solutions for the deterministic model, the optimal solutions for the DRTTIGSL model can reduce the worst-case situation with a small price of the average objective value, especially when the total budget is not large.

Reconstruction of unidirectional strain maps via iterative signal fusion for mesoscale structures monitored by a sensing skin

Abstract Flexible skin-like membranes have received considerable research interest for the cost-effective monitoring of mesoscale (large-scale) structures. The authors have recently proposed a large-area electronic consisting of a soft elastomeric capacitor (SEC) that transduces a structure’s change in geometry (i.e. strain) into a measurable change in capacitance. The SEC sensor measures the summation of the orthogonal strains (i.e. e x + e y ). It follows that an algorithm is required for the decomposition of the sensor signal into unidirectional strain maps. In this study, a new method enabling such decomposition, leveraging a dense sensor network of SECs and resistive strain gauges (RSGs), is proposed. This method, termed iterative signal fusion (ISF), combines the large-area sensing capability of SECs and the high-precision sensing capability of RSGs. The proposed ISF method adaptively fuses the different sources of signal information (e.g. from SECs and RSGs) to build a structure’s best fit unidirectional strain maps. Each step of ISF contains an update process for strain maps based on the Kriging model. To demonstrate the accuracy of the proposed method, an experimental test bench is developed, which is the largest deployment of the SEC-based sensing skin to date in terms of both size and sensor count. A network of 40 SECs deployed on a grid (5 × 8) is utilized and an optimal sensor placement algorithm is used to select the optimal RSG sensor locations within the network of SECs. Results show that the proposed ISF method is capable of reconstructing unidirectional strain maps for the experimental test plate. In addition to the experimental data, a numerical validation for the ISF method is provided through a finite element analysis model of the experimental test bench.

Development of a stochastic effective independence (SEFI) method for optimal sensor placement under uncertainty

Abstract Finding optimal sensor placement for data acquisition is an essential initial stage in the development of many engineered systems. For this purpose, the effective independence (EFI) method was developed and has been widely used. In this method, sensor locations are selected to maximize the linear independency of the target mode shape matrix. However, the EFI method lacks consideration of the uncertainty that is present in real applications. To overcome this limitation, in this study, a new stochastic EFI method is derived. The resultant equation is composed of the conventional deterministic term and an additional random term. Using the derived equation, optimal sensor locations are found. The results of stochastic EFI give the best linear independency of the mode shape matrix in the mean sense. In this paper, stochastic EFI is also extended to the energy-based EFI method. In the energy-based EFI method, the mass or stiffness matrix is weighted to have the kinetic or strain energy form of the EFI method. By decomposing the weighted matrix, the same form is obtained as in the EFI method; thus, its stochastic version follows naturally, as in the stochastic EFI method. Further, the stochastic sensor placement method is also derived for a different optimization criterion called the A-optimality criterion, which uses a matrix trace for its measure. Finally, the proposed method is validated using a truss bridge case. Its results are compared with the Monte Carlo simulation based method, which is another approach used to handle the system uncertainty. The case study indicates that the suggested method shows higher linear independency than the EFI method and the energy-based EFI method; it is also better with different optimality conditions.

A fast way to determine temperature sensor locations in thermal error compensation

With the improvement of machining accuracy, problems associated with the thermal deformation of the machine tool structure and the thermal error compensation technique have received more and more attention. However, the complexity of the predictive thermal model limits the application of the thermal error compensation technique. Appropriate temperature sensor locations could contribute to a better thermal model and greatly reduce the amount of time spent. This paper introduces a fast way to determine temperature sensor locations for thermal error compensation. A theoretical analysis of the heat transfer, heat exchange, and thermal deformation of a 1-D structure, i.e., a spindle, is discussed. A simulation of the heat transfers and exchange process for the spindle is performed, considering different heat flux coefficients and heat transfer coefficients. The results from the theoretical analysis and the simulation indicate that there is an optimal sensor location point on the 1-D structure and that the heat flux and transfer coefficients have little influence on the position of the optimal sensor location on the 1-D structure. The experimental results prove that optimal temperature sensor locations do exist, regarding which the temperature change and the spindle thermal deformation also have a nearly linear relationship without a time delay. Thus, a linear model can be obtained via interpolation of the experimental data. Finally, the optimal temperature sensor location method is successfully applied for the thermal error compensation of a high-speed spindle of a horizontal machining center.

Assessment of water quality monitoring for the optimal sensor placement in lake Yahuarcocha using pattern recognition techniques and geographical information systems.

Pollution and the eutrophication process are increasing in lake Yahuarcocha and constant water quality monitoring is essential for a better understanding of the patterns occurring in this ecosystem. In this study, key sensor locations were determined using spatial and temporal analyses combined with geographical information systems (GIS) to assess the influence of weather features, anthropogenic activities, and other non-point pollution sources. A water quality monitoring network was established to obtain data on 14 physicochemical and microbiological parameters at each of seven sample sites over a period of 13months. A spatial and temporal statistical approach using pattern recognition techniques, such as cluster analysis (CA) and discriminant analysis (DA), was employed to classify and identify the most important water quality parameters in the lake. The original monitoring network was reduced to four optimal sensor locations based on a fuzzy overlay of the interpolations of concentration variations of the most important parameters.

Sensor placement for structural health monitoring using hybrid optimization algorithm based on sensor distribution index and FE grids

Considering the adjustments for sensor selections attributed by different finite element (FE) grids, a hybrid optimization algorithm including FE grids updating for optimal sensor placement is proposed based on effective independence method and sensor distribution index, in order to improve the algorithm efficient and reduce the redundancy information simultaneously. This study takes into account of the relationship of FE grids, redundancy information, and optimal sensor placement performance by detailed statements. Furthermore, in order to reduce the redundancy information caused by too fine FE grids and too near measurements, the proposed sensor distribution index can synthetically deal with both cases of the nearer nodes and overall sensor distribution ranges. Moreover, by means of normalization and weighted factor, the constituted fitness function, which consists of Fisher information and sensor distribution index, can be more competitive by eliminating the gap of orders caused by the different fitness functions. Therefore, the economical FE grids are suggested, and the corresponding optimum sensor locations are simultaneously obtained by the hybrid optimization algorithm. Finally, the proposed method is verified by a deployable antenna module of space solar power satellite and a wing of reusable launch vehicle, respectively.

Inverse Conduction Heat Transfer and Kriging Interpolation Applied to Temperature Sensor Location in Microchips

Large thermal gradients represent major operational hazards in microprocessors; hence, there is a critical need to monitor possible hot spots both accurately and in real time. Thermal monitoring in microprocessors is typically performed using temperature sensors embedded in the electronic board. The location of the temperature sensors is primarily determined by the sensor space claim rather than the ideal location for thermal management. This paper presents an optimization methodology to determine the most beneficial locations for the temperature sensors inside of the microprocessors, based on input from high-resolution surface infrared thermography combined with inverse heat transfer solvers to predict hot spot locations. Specifically, the infrared image is used to obtain the temperature map over the processor surface, and subsequently delivers the input to a three-dimensional (3D) inverse heat conduction methodology, used to determine the temperature field within the processor. In this paper, simulated thermal maps are utilized to assess the accuracy of this method. The inverse methodology is based on a function specification method combined with a sequential regularization in order to increase accuracy in the results. Together with the number of sensors, the temperature field within the processor is then used to determine the optimal location of the temperature sensors using a genetic algorithm optimization combined with a Kriging interpolation. This combination of methodologies was validated against the finite element analysis of a chip incorporating heaters and temperature sensors. An uncertainty analysis of the inverse methodology and the Kriging interpolation was performed separately to assess the reliability of the procedure.

An efficient approach for optimal sensor placement and damage identification in laminated composite structures

This paper proposed an efficient approach for optimal sensor placement and damage identification in laminated composite structures. This approach first utilized a model reduction technique, namely iterated improved reduced system (IIRS) method, to develop a reduced order model for optimal sensor placement (OSP), and then the OSP strategy using Jaya algorithm is conducted by formulating and solving an optimization problem for finding the best sensor locations. The objective function of the optimization problem is defined based on the correlation between the flexibility matrix obtained from an original finite element model and the corresponding one calculated from IIRS method. Next, the approach uses the measured incomplete modal data from optimized sensor locations for detecting and assessing any stiffness reduction induced by damage. In order to do this, the damage identification problem is formulated as an optimization problem where the damage extent of elements and the modal flexibility change are taken as the continuous design variables and the objective function, respectively. The Jaya algorithm is again adopted to solve the optimization problem for determining the actual damage sites and extents. Numerical simulations of a three cross-ply (0°/90°/0°) beam and a four-layer (0°/90°/90°/0°) laminated composite plate are carried out to demonstrate the applicability and efficiency of the proposed approach.

Overview of Bridge Health Monitoring

Bridge operation safety is a key to national security and people’s livelihood. The importance and the urgency of bridge health monitoring and damage detection are introduced here. In the past, the health monitoring of bridges often relied on experienced engineers. They rely on their rich experience to detect and repair bridges. This method is inefficient and has low universality. Engineers can only detect and maintain the bridge they are familiar with. With the increasing importance of safety, durability and normal use of large bridges, the research and evaluation system of bridge health monitoring has been developed and achieved a wide range of achievements in the 20th century. This paper introduces the composition of the bridge health monitoring system. It consists of sensor subsystem, data acquisition and transmission subsystem, data processing and control subsystem. The key problems in sensor subsystem: sensor location optimization, data transmission mode and data processing method are also introduced. At the end, varies issues in existing systems and directions on the near future are analyzed and summarized.

Sensor Choice for Minimum Error Variance Estimation

A Kalman filter is optimal in that the variance of the error is minimized by the estimator. It is shown here, in an infinite-dimensional context, that the solution to an operator Riccati equation minimizes the steady-state error variance. This extends a result previously known for lumped parameter systems to distributed parameter systems. It is shown then that minimizing the trace of the Riccati operator is a reasonable criterion for choosing sensor locations. It is then shown that multiple 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. Optimal sensor location is then combined with estimator design. A framework for calculation of the best sensor locations using approximations is established and sensor location as well as choice is investigated with three examples. Simulations indicate that the sensor locations do affect the quality of the estimation and that multiple low-quality sensors can lead to better estimation than a single high-quality sensor.