Optimal Sensor Placement in Reduced-Order Models Using Modal Constraint Conditions

Sensor measurements of civil structures provide basic information on their performance. However, it is impossible to install sensors at every location owing to the limited number of sensors available. Therefore, in this study, we propose an optimal sensor placement (OSP) algorithm while reducing the system order by using the constraint condition between the master and slave modes from the target modes. The existing OSP methods are modified in this study, and an OSP approach using a constrained dynamic equation is presented. The validity and comparison of the proposed methods are illustrated by utilizing a numerical example that predicts the OSPs of the truss structure. It is observed that the proposed methods lead to different sensor layouts depending on the algorithm criteria. Thus, it can be concluded that the OSP algorithm meets the measurement requirements for various methods, such as structural damage detection, system identification, and vibration control.

On the Distributional Characterization of Graph Models of Water Distribution Networks in Wasserstein Spaces

This paper is focused on two topics very relevant in water distribution networks (WDNs): vulnerability assessment and the optimal placement of water quality sensors. The main novelty element of this paper is to represent the data of the problem, in this case all objects in a graph underlying a water distribution network, as discrete probability distributions. For vulnerability (and the related issue of re-silience) the metrics from network theory, widely studied and largely adopted in the water research community, reflect connectivity expressed as closeness centrality or, betweenness centrality based on the average values of shortest paths between all pairs of nodes. Also network efficiency and the related vulnerability measures are related to average of inverse distances. In this paper we propose a different approach based on the discrete probability distribution, for each node, of the node-to-node distances. For the optimal sensor placement, the elements to be represented as dis-crete probability distributions are sub-graphs given by the locations of water quality sensors. The objective functions, detection time and its variance as a proxy of risk, are accordingly represented as a discrete e probability distribution over contamination events. This problem is usually dealt with by EA algorithm. We’ll show that a probabilistic distance, specifically the Wasserstein (WST) distance, can naturally allow an effective formulation of genetic operators. Usually, each node is associated to a scalar real number, in the optimal sensor placement considered in the literature, average detection time, but in many applications, node labels are more naturally expressed as histograms or probability distributions: the water demand at each node is naturally seen as a histogram over the 24 hours cycle. The main aim of this paper is twofold: first to show how different problems in WDNs can take advantage of the representational flexibility inherent in WST spaces. Second how this flexibility translates into computational procedures.

Optimal sensor placement to detect ruptures in pipeline systems subject to uncertainty using an Adam-mutated genetic algorithm

Pipelines in critical engineered facilities, such as petrochemical and power plants, conduct important roles of fire extinguishing, cooling, and related essential tasks. Therefore, failure of a pipeline system can cause catastrophic disaster, which may include economic loss or even human casualty. Optimal sensor placement is required to detect and assess damage so that the optimal amount of resources is deployed and damage is minimized. This paper presents a novel methodology to determine the optimal location of sensors in a pipeline network for real-time monitoring. First, a lumped model of a small-scale pipeline network is built to simulate the behavior of working fluid. By propagating the inherent variability of hydraulic parameters in the simulation model, uncertainty in the behavior of the working fluid is evaluated. Sensor measurement error is also incorporated. Second, predefined damage scenarios are implemented in the simulation model and estimated through a damage classification algorithm using acquired data from the sensor network. Third, probabilistic detectability is measured as a performance metric of the sensor network. Finally, a detectability-based optimization problem is formulated as a mixed integer non-linear programming problem. An Adam-mutated genetic algorithm (AMGA) is proposed to solve the problem. The Adam-optimizer is incorporated as a mutation operator of the genetic algorithm to increase the capacity of the algorithm to escape from the local minimum. The performance of the AMGA is compared with that of the standard genetic algorithm. A case study using a pipeline system is presented to evaluate the performance of the proposed sensor network design methodology.