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

Abstract

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.

A New Processing Method for the Nonlinear Signals Produced by Electromagnetic Flowmeters in Conditions of Pipe Partial Filling

“…When the induced EMF output by the electromagnetic flowmeter sensor is E j ðj ¼ 1; 2; Á Á Á ; nÞ and the corresponding fluid flow rate is q j ðj ¼ 1; 2; Á Á Á ; nÞ, q ¼ f ðEÞ can be described by the following B-spline curve fitting equation [21][22][23]…”

“…B-spline curve fitting [19][20][21][22][23] is an approach that performs a nonlinear fit of data based on a limited selection of these data. As the B-spline curve method is a simple calculation procedure with fast calculation speed and geometric invariance, it is widely used in engineering practice, such as for the geometric definition of various industrial products and nonlinear curve reconstruction.…”

“…Xu et al [21] rebuilt the strain field of multiple elements by using the B-spline curve and inverse finite element methods to prove that the proposed algorithm can significantly improve the accuracy of reconstruction displacement. Jiang et al [22] reconstructed the under-sampling flow velocity distribution of partially filled pipes using the B-spline curve method, showing that this method effectively reduces the number of measurement data. Ravari et al [23] improved the B-spline curve method by using the group test theory to effectively enhance the low data processing efficiency of the B-spline curve fitting method.…”