Blockage detection in networks : The area reconstruction method

In this note we present a reconstructive algorithm for solving the cross-sectional pipe area from boundary measurements in a tree network with one inaccessible end. This is equivalent to reconstructing the first order perturbation to a wave equation on a quantum graph from boundary measurements at all network ends except one. The method presented here is based on a time reversal boundary control method originally presented by Sondhi and Gopinath for one dimensional problems and later by Oksanen to higher dimensional manifolds. The algorithm is local, so is applicable to complicated networks if we are interested only in a part isomorphic to a tree. Moreover the numerical implementation requires only one matrix inversion or least squares minimization per discretization point in the physical network. We present a theoretical solution existence proof, a step-by-step algorithm, and a numerical implementation applied to two numerical experiments.Peer reviewe

On Wave-Defect Interaction in Pressurized Conduits

Pressurized conduits transporting liquids such as freshwater, storm-water, wastewater, oil and gas often experience partial blockages or leakages during their life time due to physical and/or chemical processes. In water supply, these anomalies result in about 30% of water loss and more than 30% of energy waste. Transient-based defect detection methods are highly promising, but require in-depth understanding of wave-defect-turbulence interaction in conduits. This paper develops a two-dimensional compressible flow model, based on the axial symmetry assumption, to investigate the interaction between transient waves and the flow structure in the vicinity of a leak or a blockage. An explicit Finite Volume Scheme (FVS) based on Riemann solvers is used to solve the hyperbolic part of the 2D axi-symmetric compressible Navier-Stokes equations for transient flow in a pipe. The parabolic (viscous and turbulence) part are modeled by a central differential scheme. Several boundary conditions are studied including (i) sudden closure of a valve, (ii) pulse wave and (iii) strong shock waves. Preliminary tests show that the scheme has good accuracy, efficiency and convergence characteristics. Detailed study of the scheme are ongoing and will entail comparisons with other schemes such as implicit factorized scheme and Lax-Wendroff schemes as well as experimental data. Thus far, the focus has been on laminar flows, but the physics of turbulence will be added in the near future and will involve the use of Bardina Large Eddy Simulation mode

SINGLE EXTENDED BLOCKAGE IDENTIFICATION USING A MODEL-BASED MATCHED-FIELD PROCESSING APPROACH

International audienceA new transient-based approach for single blockage detection is proposed which requires two measurement stations at both ends of a single pipe system. The method uses the frequency response and gives satisfactory results using low frequency bandwidth. The first advantage of the proposed technique is to obtain the location and length of the blockage independently from the blockage's area. The second advantage is that the method uses information not only from the eigen-frequencies, but also from the whole frequency spectrum. This brings more accuracy especially when the identification of the resonant frequencies and their corresponding mode number are not accurate. Moreover, the method has the ability of tolerating noise as long as it is Gaussian of zero-mean and has a well-known structure. Comparison with other blockage detection methods is given and the benefits and drawbacks of the proposed method are discussed

Mathematical methodology for optimization of the clamping forces accounting for workpiece vibratory behaviour

This paper addresses the problem of determining the minimum clamping forces that ensure the dynamic fixturing stability. The clamping force optimization problem is formulated as a bi-level nonlinear programming problem and solved using a computational intelligence technique called particle swarm optimization (PSO). Indeed, we present an innovative simulation methodology that is able to study the effects of fixture-workpiece system dynamics and the continuously change due to material removal on fixturing stability and the minimum required clamping forces during machining. The dynamic behaviour of the fixtured workpiece subjected to time-and space-varying machining loads is simulated using a forced vibration model based on the regenerative vibrations of the cutter and workpiece excited by the dynamic cutting forces. Indeed, Material removal significantly affects the fixture-workpiece system dynamics and subsequently the minimum clamping forces required for achieving fixturing dynamic stability