Optimal sensor placement for structural response estimation

A methodology, termed estimation error minimization(EEM) method, was proposed to determine the optimal number and locations of sensors so as to better estimate the vibration response of the entire structure. Utilizing the limited sensor measurements, the entire structure response can be estimated based on the system equivalent reduction-expansion process(SEREP) method. In order to compare the capability of capturing the structural vibration response with other optimal sensor placement(OSP) methods, the effective independence(EI) method, modal kinetic energy(MKE) method and modal assurance criterion(MAC) method, were also investigated. A statistical criterion, root mean square error(RMSE), was employed to assess the magnitude of the estimation error between the real response and the estimated response. For investigating the effectiveness and accuracy of the above OSP methods, a 31-bar truss structure is introduced as a simulation example. The analysis results show that both the maximum and mean of the RMSE value obtained from the EEM method are smaller than those from other OSP methods, which indicates that the optimal sensor configuration obtained from the EEM method can provide a more accurate estimation of the entire structure response compared with the EI, MKE and MAC methods.

Optimal sensor placement in health monitoring of suspension bridge

Structural health monitoring(SHM) provides an effective approach to ensure the safety of structures.However,with the restriction of the cost of sensor system and data processing,only a small number of sensors could be available in the health monitoring system(HMS).In order to obtain the best identification of structural characteristics,optimal sensor placement(OSP) becomes an inevitable task in the design of HMS.This paper introduces the process for determining the OSP in HMS of a suspension bridge,in which four different OSP methods have been investigated,including the effective independence(EI) method,the effective independence driving-point residue(EFI-DPR) method,the minimized modal assurance criterion(minMAC) method and the principal subset selection-based extended EI(PSS-EI) method.Then,three criteria,which are modal assurance matrix(MAC),condition number(CN) of mode shape matrix and determinant of Fisher information matrix(FIM),were employed to evaluate the effect of the OSP methods respectively.The result showed that the PSS-EI method developed has the ability to guarantee the highest determinant of FIM,a relatively small off-diagonal term of MAC and agreeable CN,as well as the deployment of sensors in a uniform and symmetric fashion for the studied bridge.Finally,the scheme obtained by PSS-EI was adopted in the HMS.

An interval effective independence method for optimal sensor placement based on non-probabilistic approach

This paper presents an interval effective independence method for optimal sensor placement, which contains uncertain structural information. To overcome the lack of insufficient statistic description of uncertain parameters, this paper treats uncertainties as non-probability intervals. Based on the iterative process of classical effective independence method, the proposed study considers the eliminating steps with uncertain cases. Therefore, this method with Fisher information matrix is extended to interval numbers, which could conform to actual engineering. As long as we know the bounds of uncertainties, the interval Fisher information matrix could be obtained conveniently by interval analysis technology. Moreover, due to the definition and calculation of the interval relationship, the possibilities of eliminating candidate sensors in each iterative process and the final layout of sensor placement are both presented in this paper. Finally, two numerical examples, including a five-storey shear structure and a truss structure are proposed respectively in this paper. Compared with Monte Carlo simulation, both of them can indicate the veracity of the interval effective independence method.

Multi-type sensor placement and response reconstruction for building structures: Experimental investigations

Estimation of lateral displacement and acceleration responses is essential to assess safety and serviceability of high-rise buildings under dynamic loadings including earthquake excitations. However, the measurement information from the limited number of sensors installed in a building structure is often insufficient for the complete structural performance assessment. An integrated multi-type sensor placement and response reconstruction method has thus been proposed by the authors to tackle this problem. To validate the feasibility and effectiveness of the proposed method, an experimental investigation using a cantilever beam with multi-type sensors is performed and reported in this paper. The experimental setup is first introduced. The finite element modelling and model updating of the cantilever beam are then performed. The optimal sensor placement for the best response reconstruction is determined by the proposed method based on the updated FE model of the beam. After the sensors are installed on the physical cantilever beam, a number of experiments are carried out. The responses at key locations are reconstructed and compared with the measured ones. The reconstructed responses achieve a good match with the measured ones, manifesting the feasibility and effectiveness of the proposed method. Besides, the proposed method is also examined for the cases of different excitations and unknown excitation, and the results prove the proposed method to be robust and effective. The superiority of the optimized sensor placement scheme is finally demonstrated through comparison with two other different sensor placement schemes： the accelerometer-only scheme and non-optimal sensor placement scheme. The proposed method can be applied to high-rise buildings for seismic performance assessment.

Sensor placement of long-term health monitoring for large bridges based on the real-time correction of finite element model

The process of optimized placement of long-term health monitoring sensors for large bridges generally begins with finite element models, but there will arise great discrepancies between theoretically-calculated results and actual measurements.Therefore, rectified finite element models need to be rectified by virtue of model rectifying technology. Firstly, the result of construction monitoring and finished state load test is used to real-time modification of finite element model. Subsequently, an accurate finite element model is established. Secondly, the optimizing the layout of sensor with following orthogonality guarantees orthogonal property and linear independence for the measured data. Lastly, the effectiveness and feasibility of method in the paper is tested by real-time modifying finite element model and optimizing the layout of sensor for Nujiang Bridge.

Design of Resilient Sensor Networks Balancing Resilience and Efficiency

In recent years,the notion of resilience has been developed and applied in many technical areas,becoming exceptionally pertinent to disaster risk science.During a disaster situation,accurate sensing information is the key to efficient recovery efforts.In general,resilience aims to minimize the impact of disruptions to systems through the fast recovery of critical functionality,but resilient design may require redundancy and could increase costs.In this article,we describe a method based on binary linear programming for sensor network design balancing efficiency with resilience.The application of the developed framework is demonstrated for the case of interior building surveillance utilizing infrared sensors in both twoand three-dimensional spaces.The method provides optimal sensor placement,taking into account critical functionality and a desired level of resilience and considering sensor type and availability.The problem formulation,resilience requirements,and application of the optimization algorithm are described in detail.Analysis of sensor locations with and without resilience requirements shows that resilient configuration requires redundancy in number of sensors and their intelligent placement.Both tasks are successfully solved by the described method,which can be applied to strengthen the resilience of sensor networks by design.The proposed methodology is suitable for large-scale optimization problems with many sensors and extensive coverage areas.

Placement optimization of actuator and sensor and decentralized adaptive fuzzy vibration control for large space intelligent truss structure

Large space truss structure is widely used in spacecrafts.The vibration of this kind of structure will cause some serious problems.For instance,it will disturb the work of the payloads which are supported on the truss,even worse,it will deactivate the spacecrafts.Therefore,it is highly in need of executing vibration control for large space truss structure.Large space intelligent truss system(LSITS) is not a normal truss structure but a complex truss system consisting of common rods and active rods,and there are at least one actuator and one sensor in each active rod.One of the key points in the vibration control for LSITS is the location assignment of actuators and sensors.The positions of actuators and sensors will directly determine the properties of the control system,such as stability,controllability,observability,etc.In this paper,placement optimization of actuators and sensors(POAS) and decentralized adaptive fuzzy control methods are presented to solve the vibration control problem.The electro-mechanical coupled equations of the active rod are established,and the optimization criterion which does not depend upon control methods is proposed.The optimal positions of actuators and sensors in LSITS are obtained by using genetic algorithm(GA).Furthermore,the decentralized adaptive fuzzy vibration controller is designed to control LSITS.The LSITS dynamic equations with considering those remaining modes are derived.The adaptive fuzzy control scheme is improved via sliding control method.One T-typed truss structure is taken as an example and a demonstration experiment is carried out.The experimental results show that the GA is reliable and valid for placement optimization of actuators and sensors,and the adaptive fuzzy controller can effectively suppress the vibration of LSITS without control spillovers and observation spillovers.

Horizontal convergence reconstruction in the longitudinal direction for shield tunnels based on conditional random field

Tunnel horizontal convergence monitoring is essential to ensure the operation safety.However,only a few representative tunnel sec-tions are chosen for monitoring due to the cost limitation.It is difficult to capture the horizontal convergence of each tunnel ring with limited measurements.Confronted with this difficulty,the paper proposes a horizontal convergence reconstruction method based on the measurements of deployed sensors.The tunnel horizontal convergence along the longitudinal direction is seen as a one-dimensional sta-tionary and ergodic random field.The reconstruction problem is then transformed into the generation of conditional random fields.Monte Carlo simulation is adopted to generate possible realizations and the mean of realizations is considered as the maximum likeli-hood reconstruction.Error analysis proves the effectiveness of the proposed reconstruction method.The proposed method is proved to be applicable in reconstructing the time-variant horizontal convergence and is verified by the monitoring results of the shield tunnel of Shanghai Metro Line 2.The effect of sensor numbers is parametrically studied,and an optimal sensor placement scheme is decided.Additional sensors placed at the deformation drastically changed location can significantly improve the performance of the proposed method.

DAMAGE DETECTION STRATEGY FOR RETICULATED STRUCTURES BASED ON INCOMPLETE STRAIN MODE

Damage detection based on strain responses of vibration is highly attractive for monitoring long-span reticulated structures.However,there are a lot of structure members in reticulated structures and it is impossible to install strain sensors in each member.Therefore,how to locate and quantify damages with the incomplete mode shapes obtained from few strain sensors is a challenge topic.A new strategy,named incomplete strain mode damage detection（ISMDD） strategy,is proposed in this paper.In the strategy,the distribution of the strain sensors in the reticulated structures can be optimized through sensitive analysis on strain mode perturbation matrix,which can be obtained by perturbation theory.Mode assurance criterion（MAC） value is applied in damage location,and the members with relative large MAC values are defined as damage members.In addition,damage index obtained by solving the perturbation equation is used for damage quantification.Numerical analysis on a long-span reticulated structure,including damage location and quantification for single-and multi-member damages,detection for different damage quantity,the effect analysis of sensor quantity,are performed to verify the effectiveness of the proposed ISMDD strategy.It can be shown from the analysis that the ISMDD strategy is effective in damage location and quantification for both single-and multi-member damages.And the quantity of strain sensors has effect on damage location,but has no obvious influence on damage quantification.Additionally,the anti-noise pollution ability analysis of the ISMDD strategy is carried out,which shows that the ISMDD strategy has excellent anti-noise pollution ability for both single-and multi-damaged members.