Sensor Placement Methodology Research Articles

E. Torroja’s bridge: Tailored experimental setup for SHM of a historical bridge with a reduced number of sensors

This paper presents the design of an experimental setup with a reduced number of sensors for the structural health monitoring of the historical bridge of Posadas (Córdoba, Spain), designed by the eminent engineer Eduardo Torroja in 1957. The motivation of this study stems from the need for safeguarding this piece of cultural heritage. In particular, the singularity of this historical construction, a steel–concrete composite typology consisting of a concrete deck slab and inverted bowstring steel trusses, makes continuous in-service condition assessment essential for its maintenance. Nevertheless, the application of existing continuous monitoring systems to such large-scale structures entails considerable investments as well as complex signal processing algorithms. Whereby the optimization of the number of sensors and their location is of the utmost interest. In this line, this work presents the application of an Optimal Sensor Placement (OSP) methodology to tailor an experimental setup for a cost-efficient continuous monitoring of the E. Torroja’s bridge. Due to the fact that most OSP approaches are model-based, it is essential to count on a sufficiently accurate numerical model. To this aim, an extensive vibration-based operational modal analysis is first conducted with a large number of accelerometers. Afterward, a three-dimensional finite element model of the E. Torroja’s bridge is updated on the basis of the experimentally identified dynamic properties with a genetic optimization algorithm. Finally, an optimal sensor placement methodology is utilized to design an experimental setup with a limited number of sensors for long-term monitoring purposes. The results demonstrate that few sensors are needed to accurately assess the main resonant frequencies and mode shapes.

Bayesian optimal sensor placement for crack identification in structures using strain measurements

A Bayesian framework is presented for finding the optimal locations of strain sensors in a plate with a crack with the goal of identifying the crack properties, such as crack location, size, and orientation. Sensor grids of different type and size are considered. The Bayesian optimal sensor placement framework is rooted in information theory, and the optimal grid is the one which maximizes the expected information gain (Kullback–Liebler divergence) between the prior and posterior probability density functions of the crack parameters. The uncertainty in the crack parameters is accounted for naturally within the Bayesian framework through the prior probability density functions. The framework is demonstrated for a thin plate with crack, subjected to static loading. A finite element model is used to simulate the strain distributions in the plate given the crack properties. To verify the effectiveness of the proposed optimal sensor placement methodology, the estimated optimal sensor grids are used to perform Bayesian crack identification using simulated data. Parametric analyses are carried out giving emphasis on the effect of the number of sensors, grid type, and experimental data noise levels in the identification results.

Sensor Placement for Combined Sewer System Monitoring in the Besòs River Basin

In this paper, a sensor placement methodology for sewer systems monitoring in order to measure direct discharge to the river during intense rainfall events is presented. During these events, Combined Sewer Overflows (CSOs) may occur, causing serious problems of contamination of the corresponding receiving waters. The current national regulation compels sewer systems’ managers to monitor and quantify direct discharge to these receiving waters, in order to track these events. Hence, the selection of the appropriate sensor set in order to monitor the critical outlets of the network is of paramount importance to adequately monitor CSOs and minimize their effect by using the information gathered from these measurements. Here, a methodology considering relevant characteristics of each potential monitoring point —e.g. number of discharges, volume discharged or percentage of polluted mass— is defined to select the final sensor set. The presented methodology is applied to three different combined sewer systems in the Besòs river basin nearby Barcelona city area in Catalonia (Spain), i.e. Granollers, La Llagosta and Montornès systems.

Multi-scale model updating of a timber footbridge using experimental vibration data

PurposeThe purpose of this paper is to capture the actual structural behavior of the longest timber footbridge in Spain by means of a multi-scale model updating approach in conjunction with ambient vibration tests.Design/methodology/approachIn a first stage, a numerical pre-test analysis of the full bridge is performed, using standard beam-type finite elements with isotropic material properties. This approach offers a first structural model in which optimal sensor placement (OSP) methodologies are applied to improve the system identification process. In particular, the effective independence (EFI) method is used to determine the optimal locations of a set of sensors. Ambient vibration tests are conducted to determine experimentally the modal characteristics of the structure. The identified modal parameters are compared with those values obtained from this preliminary model. To improve the accuracy of the numerical predictions, the material response is modeled by means of a homogenization-based multi-scale computational approach. In a second stage, the structure is modeled by means of three-dimensional solid elements with the above material definition, capturing realistically the full orthotropic mechanical properties of wood. A genetic algorithm (GA) technique is adopted to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.FindingsAn overall good agreement is found between the results of the updated numerical simulations and the corresponding experimental measurements. The longitudinal and transverse Young's moduli, sliding and rolling shear moduli, density and natural frequencies are computed by the present approach. The obtained results reveal the potential predictive capabilities of the present GA/multi-scale/experimental approach to capture accurately the actual behavior of complex materials and structures.Originality/valueThe uniqueness and importance of this structure leads to an intensive study of its structural behavior. Ambient vibration tests are carried out under environmental excitation. Extraction of modal parameters is obtained from output-only experimental data. The EFI methodology is applied for the OSP on a large-scale structure. Information coming from several length scales, from sub-micrometer dimensions to macroscopic scales, is included in the material definition. The strong differences found between the stiffness along the longitudinal and transverse directions of wood lumbers are incorporated in the structural model. A multi-scale model updating approach is carried out by means of a GA technique to calibrate the micromechanical parameters which are either not well-known or susceptible to considerable variations when measured experimentally.

Optimal pressure sensor placement and assessment for leak location using a relaxed isolation index: Application to the Barcelona water network

Water distribution networks are large complex systems affected by leaks, which often entail high costs and may severely jeopardise the overall water distribution performance. Successful leak location is paramount in order to minimize the impact of these leaks when occurring. Sensor placement is a key issue in the leak location process, since the overall performance and success of this process highly depends on the choice of the sensors gathering data from the network. Common problems when isolating leaks in large scale highly gridded real water distribution networks include leak mislabelling and the obtention of large number of possible leak locations. This is due to similarity of leak effect in the measurements, which may be caused by topological issues and led to incomplete coverage of the whole network. The sensor placement strategy may minimize these undesired effects by setting the sensor placement optimisation problem with the appropriate assumptions (e.g. geographically cluster alike leak behaviors) and by taking into account real aspects of the practical application, such as the acceptable leak location distance. In this paper, a sensor placement methodology considering these aspects and a general sensor distribution assessment method for leak diagnosis in water distribution systems is presented and exemplified with a small illustrative case study. Finally, the proposed method is applied to two real District Metered Areas (DMAs) located within the Barcelona water distribution network.

Optimal sensor placement methodology for uncertainty reduction in the assessment of structural condition

This paper introduces a novel approach for selecting sensor positions for uncertainty reduction in the assessment of structural condition, where the main difficulty is how to quantify the uncertainty. In order to tackle this problem, a condition index, which is a linear combination of the finite-element model parameters, is defined. By taking the multiplying coefficient equal to the vulnerability index corresponding to each model parameter, the linearized condition index is able to reflect the influence of local damage on the global damage condition. The uncertainty in the estimate of this linearized condition index can be readily quantified from the uncertainty in the updated model parameters. Bayesian finite-element model updating is applied for uncertainty quantification in the model parameters. The procedure of the proposed method is illustrated by designing the optimal sensor configuration for a truss structure model. The simulated damage and condition assessment of the truss structure shows that the proposed method is effective in reducing the uncertainty in the condition assessment. Furthermore, it is demonstrated that the proposed method is useful for a more important reason: it can reduce the uncertainty in the damage assessment of vulnerable substructure. Copyright © 2016 John Wiley & Sons, Ltd.

Sensor Placement for Structural Monitoring of Transmission Line Towers

Transmission line towers are usually analyzed using linear elastic idealized truss models. Due to the assumptions used in the analysis, there are discrepancies between the actual results obtained from full scale prototype testing and the analytical results. Therefore, design engineers are interested in assessing the actual stress levels in transmission line towers. Since it is costly to place sensors on every member of a tower structure, the best locations for sensors need to be carefully selected. This study evaluates a methodology for sensor placement in transmission line towers. The objective is to find optimal locations for sensors such that the real behavior of the structure can be explained from measurements. The methodology is based on the concepts of entropy and model falsification. Sensor locations are selected based on maximum entropy such that there is maximum separation between model instances that represent different possible combinations of parameter values which have uncertainties. The performance of the proposed algorithm is compared to that of an intuitive method in which sensor locations are selected where the forces are maximum. A typical 220 kV transmission tower is taken as case study in this paper. It is shown that the intuitive method results in much higher number of non-separable models compared to the optimal sensor placement algorithm. Thus the intuitive method results in poor identification of the system.

Robust sensor placement for leak location: analysis and design

In this paper, a nominal sensor placement methodology for leak location in water distribution networks is presented. To reduce the size and the complexity of the optimization problem a clustering technique is combined with the nominal sensor placement methodology. Some of the pressure sensor placement methods for leak detection and location in water distribution networks are based on the pressure sensitivity matrix analysis. This matrix depends on the network demands, which are nondeterministic, and the leak magnitudes, that are unknown. The robustness of the nominal sensor placement methodology is investigated against the fault sensitivity matrix uncertainty. Providing upon the dependency of the leak location procedure on the network operating point, the nominal sensor placement problem is then reformulated as a multi-objective optimization for which Pareto optimal solutions are generated. The robustness study as well as the resulting robust sensor placement methodology are illustrated by means of a small academic network as well as a district metered area in the Barcelona water distribution network.

Optimal Sensor Placement for Time-Dependent Systems: Application to Wind Studies around Buildings

Warm climates pose challenges to building energy consumption and pedestrian comfort. Knowledge of the wind flow around buildings can help address these issues through improving natural ventilation, energy use, and outdoor thermal comfort. Computational fluid dynamics (CFD) simulations are widely used to predict wind flow around buildings, despite the large discrepancies that often occur between model predictions and actual measurements. Wind speed and direction exhibit a high degree of variability that adds uncertainties in modeling and measurements. Although some studies focus on methods to evaluate and minimize modeling uncertainties, sensor placement has been mostly based on subjective judgment and intuition; no systematic methodology is available to identify optimal sensor locations prior to field measurement. This work proposes a methodology for systematic sensor placement for situations when no measurement data are available and knowledge of the wind environment around buildings is limited. Sequential sensor placement algorithms and criteria are used to identify sensor configurations based on CFD simulation predictions at plausible locations. Optimal sensor configurations are compared for their ability to improve wind speed predictions at another location where no measurements are taken. The methodology is applied to two full-scale building systems of varying size. Results show that the methodology can be applied prior to field measurement to identify optimal configurations of a limited number of sensors that improve wind speed predictions at unmeasured locations.

Optimal Pressure Sensor Placement for Leak Localisation Using a Relaxed Isolation Index: Application to the Barcelona Water Network

Water distribution networks are large complex systems that are affected by leaks, which often entail high costs and may severely jeopardize the overall water distribution performance. Successful leak localisation is paramount in order to minimize the impact of these leaks when occurring. Sensor placement is a key issue in the leak localisation process, since the overall performance and success of the leak isolation method highly depends on the choice of the sensors gathering data from the network. Common problems when leak isolating in large scale highly-gridded real water distribution networks include leak mislabelling and large isolation areas obtention due to similarity of the measurements, which may be caused by topological issues and led to incomplete coverage of the whole network. The sensor placement strategy may minimize these undesired effects by setting the sensor placement optimisation problem with the appropriate assumptions e.g. geographically cluster alike leak behaviors, taking into account real aspects of the practical application such as the acceptable isolation distance. Here, a sensor placement methodology considering these assets and a general sensor distribution assessment method for leak diagnosis in water distribution systems is presented for a real District Metered Area (DMA) located within the Barcelona water distribution network.

Comparison of demand calibration in water distribution networks using pressure and flow sensors

Water distribution network models are used by water companies in a wide range of applications. A good calibration of these models is required in order to improve the confidence of the application results. Pressure and flow measurements are the main source of information when calibrating a hydraulic model. The selection of both the type and location of the sensors is crucial to guarantee a good calibration. This paper describes a sensor placement methodology based on the analysis of pressure and flow sensitivity using the Singular Value Decomposition. A comparison of demand calibration in a real network with synthetic data is presented. Three sets of sensors are considered: pressure sensors, flow sensors, and a combination of both.

An integrated approach for sensor placement in linear dynamic systems

This paper investigates the sensor placement in linear dynamic systems for fault detectability and isolability. A linear system is modelled by a bond graph (BG) that can be associated in a natural way with a set of linear differential-algebraic equations (DAEs). Simultaneously, possible sensor locations are modelled as junctions on the BG. Causal paths capture cause–effect relationships of a linear system and provide a means to analyze what subset of junctions contributes to fault detectability and isolability. Furthermore, this paper exploits DAEs associated with a BG and proves a necessary and sufficient condition of sensor placement to fulfill fault detectability. Based on the fault detectability condition, a necessary condition of sensor placement to achieve two-fault distinguishability is developed in the DAEs model and serves as the basis of formulating the sensor placement problem with regard to a fault set F. For efficiency, a dedicated dynamic programming (DP) algorithm is devised to attain the optimal set of junctions for fault isolability. The two-tank system is employed to illustrate the sensor placement steps in a linear system. The optimal set(s), computed by the proposed sensor placement methodology, is/are validated by deriving primary analytical redundancy relations (ARRs) of the two-tank system.

Knowledge driven sensor placement in multi-station manufacturing processes

This paper presents a novel methodology for sensor placement in case of multi station manufacturing processes to reduce the dimensional variation in the manufactured product. The proposed methodology integrates knowledge about sensor placement problem with data mining methods. In this paper, sensor placement is termed as design alternative and a set of possible sensor locations as design space. The proposed methodology has four basic steps, i.e.: 1 uniform selection of design alternatives from design space a set of all possible sensor locations/measurement points; 2 selection of computationally simpler feature functions which can characterise the goodness of a sensor placement; 3 construction of design library based on clustering approach; 4 classification of alternatives present in design library to form design selection rules. An assembly example i.e., side frame of a sports utility vehicle has been considered to illustrate the methodology. Moreover, efficiency of the proposed knowledge driven methodology is demonstrated by comparing it with exchange algorithm and other random search approaches which are predominantly used for sensor placement problem.

Robustness Analysis of Sensor Placement for Leak Detection and Location under Uncertain Operating Conditions

Some pressure sensor placement methods for leak detection and location in water distribution networks are based on the pressure sensitivity matrix analysis. This matrix depends on the network demands, which are nondeterministic, and the leak magnitudes, which are unknown. In this paper, the robustness of a sensor placement methodology against the fault sensitivity matrix uncertainty is studied. The robustness study is illustrated by means of a small academic network as well as a district metered area in the Barcelona water distribution network. Results reveal that this uncertainty should be taken into account in the sensor placement methodology.

Robustness of optimal sensor placement under parametric uncertainty

This paper examines the influence of parametric uncertainties on the optimal sensor placement methodologies for the modal analysis of a truss bridge. Four classical sensor location methodologies are employed: two based on the Fisher information matrix and the other two based on energy matrix rank optimization. Young's modulus, mass density and cross sectional dimensions are considered as uncertain parameters. The independent and cumulative effects of these uncertain variables on the sensor placement are studied. The optimal locations of sensors under parametric uncertainty are assessed with three different criteria: the Fisher matrix determinant, the modal assurance criterion error and the condition number. Furthermore, the robustness of this configuration is investigated for the case of random and bias errors. The numerical results show the parametric uncertainties have significant influence on the optimal sensor configuration of a truss bridge.

Model falsification diagnosis and sensor placement for leak detection in pressurized pipe networks

Pressurized pipe networks used for fresh-water distribution can take advantage of recent advances in sensing technologies and data-interpretation to evaluate their performance. In this paper, a leak-detection and a sensor placement methodology are proposed based on leak-scenario falsification. The approach includes modeling and measurement uncertainties during the leak detection process. The performance of the methodology proposed is tested on a full-scale water distribution network using simulated data. Findings indicate that when monitoring the flow velocity for 14 pipes over the entire network (295 pipes) leaks are circumscribed within a few potential locations. The case-study shows that a good detectability is expected for leaks of 50L/min or more. A study of measurement configurations shows that smaller leak levels could also be detected if additional pipes are instrumented.

An H2 norm approach for the actuator and sensor placement in vibration control of a smart structure

In active vibration control of smart structures, the actuator and sensor placement is a key point of the control system design. Even the most robust control logics could easily make a structure unstable if the actuators and sensors were not correctly positioned. The objective of this paper is to propose an H2 norm approach for the actuator and sensor placement. Unlike most modal H2 norm actuator and sensor placement methodologies, this work aims not only to maximize the norms of the controlled modes but also to reduce spillover problems by taking into account the residual modes and minimizing their H2 norms. It discusses the optimal actuator and sensor configuration in a finite element model of a square plate fixed on three sides with piezoelectric patch actuators and acceleration sensors. Finally, downstream of the actuator and sensor positioning, IMSC, PPF and NDF controls have been tested and discussed.

Optimal Sensor Placement for Leakage Detection and Isolation in Water Distribution Networks

In this paper, the problem of leakage detection and isolation in water distribution networks is addressed applying an optimal sensor placement methodology. The chosen technique is based on structural models and thus it is suitable to handle non-linear and large scale systems. A drawback of this technique arises when costs are assigned uniformly. A main contribution of this paper is the proposal of an iterative methodology that focuses on identifying essential sensors which ultimately leads to an improvement of the optimal search efficiency. The algorithm presented in this work is successfully applied to a District Metered Area (DMA) in the Barcelona water distribution network.

Optimal Damage Detection Sensor Placement Using PSO

An optimal damage detection sensor placement methodology is presented. The techniques utilize a Particle Swarm Optimization (PSO) algorithm. The proposed method is iterative in nature and it permits the use of incomplete measurements. Also, it allows diversity of damage detection algorithms to be used to generate the PSO required fitness function. However, in this work Linear Matrix Inequalities are used as the damage detection schemes. Computer simulations of a cantilevered beam will be used to demonstrate the effectiveness of the methodology.

Methodology for leakage isolation using pressure sensitivity analysis in water distribution networks

Leaks are present to some extent in all water-distribution systems. This paper proposes a leakage localisation method based on the pressure measurements and pressure sensitivity analysis of nodes in a network. The sensitivity analysis using analytical tools is not a trivial job in a real network because of the huge non-explicit non-linear systems of equations that describe its dynamics. Simulations of the network in the presence and the absence of leakage may provide an approximation of this sensitivity. This matrix is binarised using a threshold independent of the node. The binary matrix is assumed as a signature matrix for leakages. However, there is a trade-off between the resolution of the leakage isolation procedure and the number of available pressure sensors. In order to maximise the isolability with a reasonable number of sensors, an optimal sensor placement methodology, based on genetic algorithms, is also proposed. These methodologies have been applied to the Barcelona Network using PICCOLO simulator. The sensor placement and the leakage detection and localisation methodologies are applied to several district management areas (DMA) in simulation and in reality.