Ultrasonic concentration measurement of aqueous solutions using PLS regression

doi:10.1016/j.ultras.2006.05.204

Ultrasonics

Volume 44, Supplement, 22 December 2006, Pages e947-e950

https://doi.org/10.1016/j.ultras.2006.05.204 Get rights and content

Abstract

This work demonstrates the use of a multivariate statistical technique called partial least squares (PLS) to extract material related data by analyzing spectra of ultrasonic pulses. We show how PLS can be used to estimate the concentration of sodium chloride in an aqueous solution. The paper describes the use of PLS and discusses pre-processing of ultrasonic data, the PLS algorithm as well as model validation. The measured concentrations are compared to reference values. The influence of disturbances and parameter changes is highlighted. The proposed method is easily adaptable to similar applications and permits a cost-saving implementation using existing and approved hardware.

Introduction

Modern industrial process control requires a high availability of accurate in situ measurement data. Additionally, rough conditions like extreme temperatures or aggressive substances induce a demand on robust measurement techniques. Ultrasonic solutions have become standard in this field of applications [1]. The focus is generally set to time-of-flight measurements as it is known from flowmeter or levelmeter devices, while amplitude information is often ignored. The amplitude information is related to mechanical properties of the propagation medium, which permits material characterization based on analyzing amplitude variations.

Material properties have become more and more important control variables for industrial processes. In addition to cost aspects one reason that limits the use of ultrasonic NDT/NDE application in process control might be the complexity of the systems, resulting in unmanageable or inaccurate physical models. One remedy to this problem is statistical modeling. This means finding a connection between some responses Y that are not directly measurable by studying some directly measurable descriptor variables, X, using Multiple Linear Regression (MLR), so that $Y = X \cdot A .$

In this paper, we use partial least squares (PLS) to model the variations in spectra of ultrasonic pulses transmitted through aqueous solutions of sodium chloride (NaCl), for varying concentrations of NaCl. The PLS Regression (PLSR) delivers the coefficients A.

Section snippets

Physical background

Changing the concentration of a dissolved specimen in an aqueous solution causes changes in the mechanical properties of the fluid, in terms of density and bulk modulus. This affects the shape of an ultrasonic pulse transmitted through the fluid in several ways. Variations cause changes in acoustic impedance of the fluid Z_l, while the acoustic impedance of the transducer Z_t remains unchanged. Reflections at the transducer/fluid interface are determined by a reflection coefficient r = r(Z_t,Z_l) [2]

Experiment description

This section describes a representative experiment, conducted to estimate the concentration of NaCl in an aqueous solution. N = 50 measured concentrations c_n are covering a range of 0–5% (by weight).

A Tektronix AWG520 arbitrary waveform generator was used to form short sine pulses with a fundamental frequency of 1 MHz. These were converted into pressure pulses by an emitting transducer. The transmitted pulses were then recorded at a receiving transducer, opposite to the first one. A Data

Discussion

For aqueous solutions of NaCl concentrations in the observed measurement range, variations of the wave shape are visible as attenuation changes as well as a varying sound velocity. The results presented in the previous section were obtained using only one pulse transmitted through the medium, and thus no knowledge about the energy transmitted by the transducer was available. This prevents estimation of the absolute attenuation of the medium, and only relative changes, due to changes in sodium

Conclusion

In this paper we demonstrate how PLS regression can be used to accurately estimate the concentration of sodium chloride in an aqueous solution using spectra of ultrasound pulses. A reliable model could be found, using a cross-validation technique. The applied method affords a separation of several mechanisms affecting the wave shape. That is, a direct interrelation of concentration and characteristic wave shape could be found. An important requirement is, however, considering temperature as

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Ultrasonic concentration measurement of aqueous solutions using PLS regression

Abstract

Introduction

Section snippets

Physical background

Experiment description

Discussion

Conclusion

Chemometrics Intell. Lab. Syst.

Application of ultrasonic sensors in the process industry

Meas. Sci. Tech.

Ultraschalltechnik Grundlagen und Anwendungen

New equivalent circuits for elementary piezoelectric transducers

Electron. Lett.

On the determination of phase and group velcocities of dispersive waves in solids

J. Appl. Phys