Scientia et Technica Año XXVI, Vol. 26, No. 01, marzo de 2021. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214

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 Abstract— Flow rate is a necessary variable in industrial

processes and, therefore, there is a wide variety of instruments

designed to measure it. However, the most accepted measuring

opportunities for the indirect measurement of this magnitude. The

methodology for this review was made up by three stages: revision,

analysis and discussion, performed over a wide set of documents

published between 2004 and 2020. The analyzed information

shows the phenomenological relationship between the features of

the vibrations in a pipe and the flow rate magnitude circulating

through it, which can be used for metrological purposes. However,

several studies report limitations that suggest improvement needs,

related to acquisition routines, calibration tests and uncertainty

analysis, as well as time-frequency explorations. A promising line

Index Terms— Indirect measurement method, flow rate, soft

metrology, soft sensor.

Resumen— El caudal es una variable necesaria en procesos

industriales, por lo que existe gran variedad de instrumentos para

su medición. Sin embargo, las alternativas mejor aceptadas de

registro presentan inconvenientes por lo invasivo o intrusivo que

requiere ser el medidor para su confiabilidad. El reto científico y

tecnológico consiste en lograr la medición explotando todas las

posibilidades fenomenológicas mediante un mecanismo no

franciscovilla67634@correo.itm.edu.co).

Cherlly Sánchez is with the Acuatubos SAS, Quality Engineering Student,

Instituto Tecnológico Metropolitano ITM, Medellín, Colombia (e-mail:

cherllysanchez200214@correo.itm.edu.co).

intrusivo, de fácil instalación, portátil y de bajo costo. Este artículo

presenta una revisión del estado del arte sobre el uso del análisis

de vibraciones en sistemas metrológicos de caudal a fin de

identificar oportunidades de investigación para su medición

indirecta. La metodología para esta revisión, se compuso de tres

etapas: revisión, análisis y discusión, sobre un conjunto amplio de

rutinas de adquisición, pruebas de calibración y análisis de la

incertidumbre, así como exploraciones de tiempo-frecuencia. Se

encontró una línea de trabajo promisoria basada en soft sensores

para caudal que, con el análisis de vibraciones de la tubería

integrado a rutinas de inteligencia computacional, permite inferir

el valor del caudal. Los hallazgos impulsan a seguir con nuevas

apuestas técnico-científicas.

Palabras claves— Caudal, método de medición indirecta, soft

metrología, soft sensor.

of the following drawbacks: they are intrusive sensors that need

to be installed within the pipe [2][3], they require a complex

installation procedure that is not suitable for portable measuring

systems [1], or they are expensive [4]. These disadvantages are

critical in specific applications, such as the contexts where

A 354, Medellín, Colombia (e-mail: edilsondelgado@itm.edu.co).

Corresponding author: Marcela Vallejo (Phone: +57 4 4405100 Opc. 9 Ext.

3213, e-mail: marcelavallejo@itm.edu.co).

F

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portable measuring systems are required, when a large number

of sensors most be installed, or when flow rate in going to be

measured in adverse conditions, like in the case of corrosive or

very dense fluids

Literature reports new trends in the development of flow rate

flow rate soft metrology systems using the measurement of

representational characteristics derived from the vibrations that

are produced on a pipe when a fluid is passing through it. This

approach has shown promising results to achieve non-invasive

and precise flow rate measurement at low cost [6]. Although

pipe vibrational analysis has been proposed as a mean to

achieve flow rate measurement since de 1990’s, this type of

indirect measurement systems is still under development and

need to achieve better precision, stability and consistency in the

measurement in order to guarantee the reliability of the method.

processing and the analysis used to infer the flow rate value.

Finally, results obtained for different authors in the literature

are discussed.

II. REVIEW METHODOLOGY

The research methodology is qualitative and is made up by

three stages, as depicted in Fig. 1.

The following sources of information were used:

IEEEXplore and SCOPUS. The thesaurus and the number of

documents retrieved in each database are shown in Table I.

measurement from vibration analysis. The papers that were

considered to be relevant were analyzed in two senses: search

for important papers cited and search for those that were

frequently cited by the initial selection.

Because of the subject analyzed in this review is relatively

new and the number of papers that directly address the

development of flow rate inference based on vibrational

features is limited, some papers related to the development of

soft sensors, machine learning techniques and sensor

characteristics were used to provide context.

developments for flow rate measurement using pipe vibrational

analysis were identified. The classification and selection of the

flow rate soft sensors, as well as the determination of the most

commonly used approaches in each one of the stages that

Scientia et Technica Año XXVI, Vol. 26, No. 01, marzo de 2021. Universidad Tecnológica de Pereira

flow rate. This initial result motivated an additional study, that

was fund by the same laboratory and focused in the study of the

correlation between vibration and flow rate with metrological

purposes [6].

Different alternatives have been proposed in the field of flow

2011

Initial Test and Design of a Soft

Sensor Flow Estimation Using

Conference

2013

A Nonintrusive and Single-Point

Infrastructure-Mediated Sensing

Approach for Water-Use Activity

Recognition [34]

Water-use activity recognition, machine

learning, infrastructure-mediated sensing

Conference

10.1109/HPCC.and.EU

C.2013.304.

Estimatión of Flow Rate Through

10.2478/ama-2018-

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along axial, 

is the shear stress in the pipe. In order to

establish a direct mathematical relation between vibration and

flow rate, in [7], a third order root function of the water flow

rate , expressed by (2), was successfully tested.

Although several studies in the literature use a variety of

methodological structures for relating flow rate with vibrations,

it is possible to deduce a general structure based on signal

processing, the construction of representation spaces and

inference by machine learning techniques, as shown in Fig. 2.

There are manly three types of sensors (see Table III) that have

been used to acquire signals that capture the vibrational features

on a pipe: accelerometers, which are attached to the pipe wall

vibrations associated with acoustic dynamics, where promising

results have been accomplished [12] [13] [14] [15].

acquisition, and have been used in a variety of applications such

the integrity analysis of structures and machinery [16] [17],

water leak localization [18][19], helicopter transmission

diagnostics [20] [21] and detecting incipient damage on rotating

machines [22], among others. The fact that accelerometers

usually measure the vibrational characteristics in three axes

provides a more complete representation of the system

dynamics, which allows constructing a better inference space,

piezoelectric accelerometer have shown a noise spectral density

that increases with decreasing frequency. In contrast, MEMS

accelerometers are less expensive and they exhibit a good

response at low frequencies, but they have a smaller bandwidth

and present higher noise levels [24][25].

LDVs have been used since 1964 in several different

applications, such as structural health monitoring [26], the

analysis of propagation and scattering properties of ultrasonic

waves in solids [27] and condition monitoring of wind turbines

[28]. One of the advantages of this type of sensor is that the

biomedical applications [33], among others. Similar to LDV,

acoustic sensors do not need to be indirect contact with the

Scientia et Technica Año XXVI, Vol. 26, No. 01, marzo de 2021. Universidad Tecnológica de Pereira

measured surface, but in this case line of sight is not necessary.

signal spectrum [1][10][11][13][14], but the central frequency

propose the use of the RMS value of the signal [1] [11] [13].

signal energy, the signal must be time invariant and wide-sense

In 2018, Göksu propose the use of Wavelet Packet Analysis

mean absolute error was of 3.99E−04 L/s.

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machine learning algorithm that can learn the relationship

between the features and the flow rate using a labeled data set.

Many of the works have proposed a simple linear mode

obtained with least squares fit [1][4][9][10], but some others

have proposed nonlinear models, such as polynomial regression

[12]. ANN is one of the most popular alternatives in soft

metrology systems [5] and soft sensor development and has

in the case of flow rate estimation, both for linear and not linear

regression. Popular linear machine learning approaches in soft

metrology are Multiple Linear Regression (MLR) [39] [40] [37]

[41], Principal Component Regression (PCR) [37] [42], Partial

Least Squares (PLS) [43] [44] [45] [38] [46], Ridge Regression

(RR) [77], Least Absolute Shrinkage Selection Operator

(LASSO) [40] [47] and Gaussian Process Regression (GPR)

[40] [38]. In nonlinear regression, some of the alternatives are

Support Vector Regression (SVR) [48], K Nearest Neighbor

(KNN) regression [49] and Extreme Learning Machine (ELM)

disadvantages of the methods that have been used in the

literature for flow rate estimation.

Finally, there are some approaches that do not focus on

precisely measure flow rate, but only try to identify patterns in

the flow rate associated to activities such as bathing or cooking.

In this case, the inference model is replaced with a classification

algorithm, like Support Vector Machines [34].

Results reported in the literature, that have been obtained with

the implementations described in the previous section, are

operation parameters have in each soft sensor model, such as

pipe material and diameter [4], sensor placement [14], temporal

duration of the analyzed signals [2][3] and the operation

pipe [10].

Campagna et al tested the influence of the pipe diameter and

found that increasing it causes a decrease in the sensitivity in

the relation between the amplitude of the first harmonic of the

signal and the flow rate [4]. They also found that another

parameter that has an effect in the relationship between

vibrations and flow rate is the pipe material, performing tests in

PVC and galvanized steel pipes. They found that the vibrational

peaks were greater for PVC than for steel pipes with the same

that the slope of the curve in the relation between the standard

deviation of the acceleration signal an the flow rate decreased

when the density and stiffness of the material were increased

rate [10]. Medeiros et al investigated the effect of varying the

duration of the analyzed signals, and stated that 10 seconds is

the optimum time to estimate flow rate [2][3]. Venkata &

Navada performed test with two different fluids: water and

sugar solution. Their proposed model was valid for both fluid,

with no need for adjusting parameters [8].

Likewise, Safari & Travasoli studied the effect of changing

the placement of the sensor and concluded that the position of

the sensor changed the type of correlation between flowrate and

vibration. They found a quadratic model when the sensor was

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placed in the long horizontal pipe and a linear model when it

was placed in the pipe knee [14].

Another difficulty in the literature results comparison is that

different authors have used different parameters to express the

proposed model accuracy. Some authors report results in terms

of the statistical parameter 

[6], Root Mean Squared Error

(RMSE) or mean absolute error [7][12][13], while others do not

report measurement accuracy parameters, but concentrate only

on proving that there is a deterministic relation between

vibration characteristics and flow rate, and test the effect of

some parameters, such as the pipe characteristics [10][4]. Table

V shows some results in the literature that report specific

performance results.

The studies in the literature do not discriminate the results

proposal regarding the uncertainty estimation for the soft

sensor, where they state that the components that must be

considered are the uncertainty associated with the regression

algorithm and the one associated with the sensors, including the

sensor that registers the vibrational characteristics and the flow

rate sensor used to obtain the reference values necessary to train

the inference algorithm [2] [3].

This paper is a literature review of the metrological advantages

of applying vibration analysis to the inference of pipeline flow

vibrational analysis in pipes opens a door to new research

associated to the parameterization, adjustment and installation

of the sensor, in relation to signal processing techniques

regarding useful vibration dynamics correlated to flow rate

change, in addition to linear or nonlinear approaches to

inference.

suggest that the structures and acquisition schemes present

notable difficulties in terms of mechanisms that reduce

showed that the system parameters that influence the

of external influence affect the estimation in different

proportions, and it is not always possible to distinguish all the

variables with their influence weights.

As for the construction of the feature space that represents

the vibratory dynamics, the different approaches reviewed

are difficult to observe directly, is becoming an important trend

computational intelligence in the context of the fourth industrial

revolution. Therefore, it is necessary to define precise, stable

and consistent procedures for estimating the measurement,

including new ways of estimating uncertainty measures under

procedures that use abstract and multivariate representations.

The uncertainty analysis in soft sensor is still an open field in

the literature where only few studies have been made [5].

This work was supported by the Instituto Tecnológico

Metropolitano ITM of Medellín. Additionally, the authors

would like to thank the Measurement Analysis and Decision

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10.1109/JSEN.2016.2630008.

[22] S. Schmidt, A. Mauricio, P. S. Heyns, and K. C. Gryllias, “A

[24] M. Varanis, A. Silva, A. Mereles, and R. Pederiva, “MEMS

10.1177/1475921716636336.

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