Optimum estimation of the mean flow velocity for the multi-electrode inductance flowmeter

Xu, Lijun; Li, X M; Dong, Feng; Wang, Y; Xu, Lijun

doi:10.1088/0957-0233/12/8/321

Cited by 31 publications

(10 citation statements)

References 5 publications

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“…The parameters v * and σ 2 mean,v can be chosen based on a priori knowledge about the possible range of the mean velocity of the flow, and σ 2 in,v and l can be chosen based on the expected range of changes of the velocity field around the mean and smoothness of it.…”

Section: (B) Prior Modelmentioning

confidence: 99%

See 1 more Smart Citation

Reconstruction of velocity fields in electromagnetic flow tomography

Lehtikangas¹,

Karhunen²,

Vauhkonen³

2016

Phil. Trans. R. Soc. A.

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Electromagnetic flow meters (EMFMs) are the gold standard in measuring flow velocity in process industry. The flow meters can measure the mean flow velocity of conductive liquids and slurries. A drawback of this approach is that the velocity field cannot be determined. Asymmetric axial flows, often encountered in multiphase flows, pipe elbows and T-junctions, are problematic and can lead to serious systematic errors. Recently, electromagnetic flow tomography (EMFT) has been proposed for measuring velocity fields using several coils and a set of electrodes attached to the surface of the pipe. In this work, a velocity field reconstruction method for EMFT is proposed. The method uses a previously developed finite-element-based computational forward model for computing boundary voltages and a Bayesian framework for inverse problems. In the approach, the vz-component of the velocity field along the longitudinal axis of the pipe is estimated on the pipe cross section. Different asymmetric velocity fields encountered near pipe elbows, solids-in-water flows in inclined pipes and in stratified or multiphase flows are tested. The results suggest that the proposed reconstruction method could be used to estimate velocity fields in complicated pipe flows in which the conventional EMFMs have limited accuracy. This article is part of the themed issue 'Supersensing through industrial process tomography'.

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Section: (B) Prior Modelmentioning

confidence: 99%

“…(Online version in colour. )where σ2 in,v is the variance of the spatially varying part and l describes the correlation length affecting the smoothness of the velocity field. The spatially constant part is modelled as…”

mentioning

confidence: 99%

Reconstruction of velocity fields in electromagnetic flow tomography

Lehtikangas¹,

Karhunen²,

Vauhkonen³

2016

Phil. Trans. R. Soc. A.

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“…An adaptive weighted fusion algorithm based on minimum mean square error (MMSE) is generally used in multisensor systems to obtain the optimal observation value. 14,15 We employed this strategy here to obtain the weights of each regression coefficient of PLS submodels. Suppose that the mean squares of calibration errors of the PLS submodels are σ 2 , σ 2 2 , …, σ K 2 individually, based on the MMSE strategy, and the weights of the PLS submodels w i ( i = 1, 2, …, K ) with constraint Σ K i=1 w i = 1 are obtained by…”

Section: Theorymentioning

confidence: 99%

Weighted Fusion of Multiple Models for Wavelength Selection

et al. 2013

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A new method based on the weighted fusion of multiple models is presented for wavelength selection in multivariate calibration of spectral data. It fuses the regression coefficients of multiple models with weights based on minimum mean square error to improve the accuracy and stability of the wavelength selection. To validate the performance of the proposed method, it was applied to the partial least squares (PLS) modeling of three near-infrared spectral datasets and compared with full-spectrum PLS, genetic algorithm-based PLS, and uninformative variable elimination-based PLS methods. Results show that the proposed method can effectively select the informative wavelength and enhance the prediction ability of the PLS model. On account of its simpler algorithm and higher efficiency, it can be widely used in practical applications.

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“…In the aspect of reconstructing the original eld in the case of undersampled, a series of studies have been carried out and many theoretical methods have been also put forward, such as ordered-subsets expectation-maximization method [17], Least squares tting algorithm [18,19], NURBS curve tting method [20,21], B-spline curve tting method [22,23], etc. Because the B-spline curve method has excellent properties such as geometric invariance, convex hull, and local support, this method is o en used in scienti c research and engineering applications, such as data analysis and distribution reconstruction [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of Velocity Distribution in Partially-Filled Pipe Based on Non-Uniform Under-Sampling

Jiang

Qing-min

Ding

2020

Advances in Mathematical Physics

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In the process of research on the flow velocity distribution in a partially filled pipe, the under-sampling of measurement data often occurs. For the first time, this problem is solved by the improved non-uniform B-spline curve fitting approximation (NBSC) method. The main innovation of this method is to reconstruct the flow velocity distribution fitting curve with a small amount of non-uniform feature points containing flow velocity information. First, the curvature of a whole discrete sampled data is analyzed, then the weighted threshold is set, and the sampled points that satisfy the threshold are extracted as the initial velocity distribution feature points. Next the node vectors were constructed according to the initial feature points, and the initial interpolation fitting curves are generated. Secondly, by using the relative deviation between the initial approximation curve and each sampled point, new feature points were added where the curve allowable deviation exceeded the specified tolerance, and then a new interpolation fitting curve was obtained. The above procedure was repeated until the fitting curve reached expected accuracy, thus the appropriate feature points were determined. Experimental results showed that, in the case of the same approximation deviation, the proposed NBSC method can solve the problem of under-sampling of measurement data better.

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Optimum estimation of the mean flow velocity for the multi-electrode inductance flowmeter

Cited by 31 publications

References 5 publications

Reconstruction of velocity fields in electromagnetic flow tomography

Reconstruction of velocity fields in electromagnetic flow tomography

Weighted Fusion of Multiple Models for Wavelength Selection

Reconstruction of Velocity Distribution in Partially-Filled Pipe Based on Non-Uniform Under-Sampling

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