Scientia et Technica Año XXVI, Vol. 26, No. 01, marzo de 2021. Universidad Tecnológica de Pereira. ISSN 0122-1701 y ISSN-e: 2344-7214
28
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
devices have the problem of being invasive or intrusive. The
scientific and technological challenge is to achieve measurement
by exploiting all the phenomenological possibilities using a non-
intrusive, easy-to-install, portable and low-cost mechanism. This
paper presents a literature review on the use of vibration analysis
in flow rate metrological systems in order to identify research
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
of work was found based on soft flow rate sensors that use the
analysis of pipeline vibrations integrated into computational
intelligence routines, which allows inference of the flow rate value.
The findings promote to continue with new technical and scientific
challenges.
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
This manuscript was sent on May 28, 2020 and accepted on February 05,
2021.This work was supported by the Instituto Tecnológico Metropolitano ITM
of Medellín, Colombia.
Francisco Villa is with the Acuatubos SAS, Quality Engineering Student,
Instituto Tecnológico Metropolitano ITM, Medellín, Colombia (e-mail:
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
documentos publicados entre 2004 y 2020. La información
analizada muestra la relación fenomenológica entre las
características de la vibración en una tubería y la magnitud del
caudal circulante en ella, lo cual puede ser usado con propósitos
metrológicos. Sin embargo, varios estudios reportan limitaciones
que sugieren necesidades de mejoramiento, relacionadas con
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.
I. INTRODUCTION
LOW rate measurement is a relevant issue in many different
contexts, such as processes control and potable water
distribution networks [1]. Nowadays, there is a wide variety of
measuring instruments for this variable that have excellent
precision. However, most of these devices have one or several
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
Marcela Vallejo is with the AMYSOD Lab, Department of Electronics and
Telecommunications, Instituto Tecnológico Metropolitano ITM, CL 54A No.
30-01, Medellín, Colombia (e-mail: marcelavallejo@itm.edu.co).
Edilson Delgado-Trejos is with the CM&P Research Group, AMYSOD Lab,
Associate Professor, Instituto Tecnológico Metropolitano ITM, CL 73 No. 76
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).
Metrological Advantages of Applying Vibration
Analysis to Pipelines: A Review
M. Vallejo-Valencia ;F.L. Villa-Restrepo ;C. Sanchez-Gonzalez ;E. Delgado Trejos
DOI: https://doi.org/10.22517/23447214.24351
Artículo de revisión
Aprovechamiento Metrológico de la Aplicación del Análisis de Vibraciones a
Tuberías: Estado del Arte
F
Scientia et Technica Año XXVI, Vol. 26, No. 01, marzo de 2021. Universidad Tecnológica de Pereira
29
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
measurement systems that are easy to install, non-intrusive and
not expensive, usually based in the use of soft metrology
systems or soft sensors, which are indirect measurement
systems that infer the value of the variable of interest from
measures of other related variables that are easier to measure
[5]. One of the most relevant approaches is the development of
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.
This paper presents a literature review on the use of pipe
vibrational analysis applied to flow rate measurement with de
aim of identifying research opportunities in this area. A general
structure for this type of system has been identified, along with
the main techniques and methods used in the development
process, encompassing the sensor selection, the signal
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.
Several types of documents were retrieved, including journal
papers, conferences proceedings and transactions. These
documents were further filtered in order to analyze only those
that were focused on systems intended to infer a flow rate
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.
The final selection of documents has a time window from
2004 to 2020. These papers were analyzed in the light of the
following research questions:
¿What features have been proposed for establishing
the phenomenological relation between flow rate and
pipe vibrations?
¿What are the external parameters that influence the
relation between flow rate and vibrational features?
¿What are the strengths and weaknesses of approaches
for the flow rate inference processes from a
metrological performance perspective?
¿What is the performance of the methods that have
used pipe vibrational analysis with metrological
purposes and how has this performance been
measured?
With these research questions, the documentation of the main
developments for flow rate measurement using pipe vibrational
analysis were identified. The classification and selection of the
information led to the identification of a general structure for
flow rate soft sensors, as well as the determination of the most
commonly used approaches in each one of the stages that
compose such structure. Finally, it was possible to discuss the
parameters of influence in flow rate inference models and the
strengths, restrictions and limitations. Table II shows the
documents that were considered to be the most relevant for the
subject of the review.
TABLE I
REPRESENTATIVE SENSORS IN THE LITERATURE
Keywords
IEEEXplore
flow rate” + “indirect measurement
2
“flow rate” + “soft sensor”
5
"flow rate" + "vibration analysis"
4
"flow rate" + "soft sensor"
15
flow rate estimation” + “vibration”
2
“flow rate” + “accelerometer
18
“flow rate” + “acoustic sensor”
4
“flow rate” + LDV
5
Fig. 1. Stages in the review methodology.
Revision
Documents concerning flow
rate estimation from
vibrational analysis are
considered.
This revision uses research
questions for constraining the
analysis directions
Analysis
Correlation between flow rate
and vibration features
Inference system structure
Types of sensor
Information representation
Methods and algorithms used
in the inference process
Performance metrics
Issues that influence the
performance
Discussion
Restrictions and limitations
of the existing methods
Research opportunities
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III. CONTENT
A. Flow rate and vibrations
The correlation between vibrations and flow rate on a pipe has
been studied since the 1990’s, but it is still a field in
development and there are not commercial developments yet.
In 1992, INEEL (Idaho National Engineering and
Environmental Laboratory) performed a series of loss-of-fluid
tests that considered several measurements, including an
accelerometer attached to the pipe. The measurement analysis
revealed that the standard deviation of the signal increased with
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
rate indirect measurement techniques. In the literature, the
experimental correlation between the fluid flow rate through a
pipe (
) and the acceleration affecting the pipe wall in the radial
direction
has been described with a series of linear
relations (), expressed by (1) [4][1].
TABLE II
MORE RELEVANT DOCUMENTS FOUND REGARDING FLOW RATE ESTIMATION USING VIBRATIONAL ANALYSIS
AÑO
Title
Key words
Data base
Type of publication
DOI
2004
Flow Rate Measurements Using Flow-
induced Pipe Vibration [6]
Flow measurement, instrumentation, pipe
flow, noise
Scopus
Journal Q1
10.1115/1.1667882
2008
NAWMS: Nonintrusive Autonomous
Water Monitoring System [7]
Adaptive sensor calibration, machine
learning, water flow rate estimation,
nonintrusive and spatially distributed
sensing, tiered information architecture,
parameter estimation via optimization
Scopus
Conference
proceedings
10.1145/1460412.1460
443
2011
Initial Test and Design of a Soft
Sensor Flow Estimation Using
Vibration Measurements [14]
Microphones, frequency domain analysis,
fluid flow measurement, estimation,
vibrations, pollution measurement,
accuracy
IEEE
Conference
10.1109/ICCIAutom.20
11.6356765
2013
Fluid Flow Rate Estimation Using
Acceleration Sensor [10]
Vibrations measurement, flow rate
measurement in pipes, accelerometer,
LDV.
IEEE
Conference
10.1109/ICSensT.2013.
6727646
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
IEEE
Conference
10.1109/HPCC.and.EU
C.2013.304.
2015
Fluid Flow Measurements by Means of
Vibration Monitoring [5]
Flowmeter, acceleration measurement,
micro-accelerometer, signal processing,
laser Doppler vibrometer
Scopus
Journal Q1
10.1088/0957-
0233/26/11/115306.
2015
Correlating Sound and Flow Rate at a
Tap [13]
Flow rate, Sound, water use
Scopus
Conference
proceedings
doi:10.1016/j.proeng.2
015.08.953.
2015
Nonintrusive Method for Measuring
Water Flow in Pipes [2]
Flow measurement, pipe vibration,
piezoelectric accelerometer.
Scopus
Conference
proceedings
2016
Optimization of Flow Rate
Measurement Using Piezoelectric
Accelerometers: Application in Water
Industry [3]
Second order calibration uncertainty, pipe
vibration, flow induced vibration,
piezoelectric accelerometer, water flow
rate measurement
Scopus
Journal Q1
10.1016/j.measurement
.2016.05.101
2018
Vibrational Signal Processing for
Characterizatión of Fluid in Pipes [1]
Fluid flow measurements, flowmeter,
vibration measurements, laser Doppler
vibrometer, vibration signal processing,
fast fourier transform, root mean square
value, random signals
Scopus
Journal Q1
10.1016/j.measurement
.2017.06.040.
2018
Flow Measurement by Wavelet Packet
Analysis of Sound Emissions [12]
Acoustic emissions, flow measurement,
fluids, multilayer perceptron, norm
entropy, wavelet packet analysis
Scopus
Journal Q4
10.1177/002029401876
8340
2018
Estimatión of Flow Rate Through
Analysis of Pipe Vibration [8]
Accelerometer, estimation, frequency
response, flow rate, neural network,
vibration
Scopus
Journal Q3
10.2478/ama-2018-
0045
2018
Non-invasive Estimation of Domestic
Hot Water Usage with Temperature and
Vibration Sensors [9]
Hot water flow estimation, Smart water
heaters, Smart grid
Scopus
Journal Q2
10.1016/j.flowmeasinst
.2018.07.003.
2020
Smart Water Grid: A Smart
Methodology to Detect Leaks in Water
Distribution Networks [11]
Smart city, smart water grid, vibration
measurement, laser Doppler vibrometry,
water leaks, smart sensing
Scopus
Journal Q1
10.1016/j.measurement
.2019.107260.
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
(1)
Where, is the cross-sectional area of the pipe,
is the
averaged flow velocity,
is the flow velocity fluctuations
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.

 
  
  (2)
Where,
is the measured vibration, and , , and are
function parameters that must be adjusted according to the
study case. These relationships given by (1) and (2) have
allowed the development of soft sensors that use measurements
of pipe vibrational features to infer the value of the flow rate.
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.
B. Signal acquisition
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
and register the acceleration that affects in in several axes [2]
[3] [6] [8] [9] [7]; Laser Doppler Vibrometer (LDV), that use
a laser and an interferometer to measure the vibration
amplitude and frequency based on the Doppler shift of the laser
reflected on the pipe surface [1] [4] [10] [11]; and acoustic
sensors, which have been used on works that focus on
vibrations associated with acoustic dynamics, where promising
results have been accomplished [12] [13] [14] [15].
Accelerometers are popular sensors in vibrational signal
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,
increasing the soft sensor accuracy [23].
Piezoelectric and MEMS accelerometers have been used in
flow rate soft sensors. Piezoelectric accelerometers have low
noise levels and wide frequency responses but they are more
expensive and they suffer from significant attenuation and
phase shifts at low frequencies. Also studies in some
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
instrument does not require direct contact with the analyzed
pipe surface. However, that characteristic may be an
inconvenient in the cases where there is limited access or not
line of sight [29].
Acoustic sensors have been used in machine and structural
monitoring [30], leak detection systems [31], the detection of
solid particles in water-conveying pipe flow [32] and
biomedical applications [33], among others. Similar to LDV,
acoustic sensors do not need to be indirect contact with the
TABLE III
REPRESENTATIVE SENSORS IN THE LITERATURE
Sensor
Authors
Accelerometer
Evans et al. 2004 [6], Kim et al. 2008 [7], Hu et al.
2013 [34], Medeiros et al. 2016 [3], Venkata &
Navada 2018 [8], Pirow et al.2018 [9].
LVD
Dinardo et al. 2013[10], Campagna et al. 2015. [4],
Dinardo et al. 2018 [1], Fabbiano et al. 2020 [11].
Acoustic sensor
Safary & Travassoli 2011 [14], Kakuta et al. 2012
[15], Jacobs et al. 2015[13], Goksu 2018 [12]
•Accelerometer
•LVD
Acoustic sensor
•Filtering
•Frequency analysis
•Time analysis
•Time-frequency
analysis
•Relevance analysis
•Linear model
•Quadratic model
•Regression by parts
•Artificial neural
networks
Vibration
s
Signal
acquisition
Signal
preprocessing
Representation
space
Machine
learning
routines
Flow rate
estimation
Flow rate soft sensor
Fig. 2. Flow rate soft sensor structure.
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measured surface, but in this case line of sight is not necessary.
C. Signal preprocessing
Before processing the sensor signal to obtain a set of
representation features suitable for the inference process, some
of the papers in the literature include a previous pre-processing
stage. Such stage regards basically with a filtering procedure,
to remove interferences and disturbances that the signal may
contain, such as noise from the electrical network, measurement
devices or the booster pump, in order to reduce the effect of
noise on the representation space. In the pre-processing stage
implementation, different types of filters have been used, such
as Butterworth and “notch comb” digital filters [2] [3], Sallen-
Key architectures [8], median filters [34] and Wavelet
transform based filters [1], which have demonstrated good
performance for this type of signals.
D. Representation space
After the preprocessing stage, an assemble of signal
deconstruction algorithms must be structured trough indexes
and transforms that can capture the vibrational dynamics to
build a feature space from the sensor signals and allow an
estimation space for the inference algorithm. In this aspects,
literature shows three approaches:
1) Approaches based on frequency analysis
This approach is based in the idea that the fundamental natural
frequency of a pipe containing a flowing fluid decreases as the
flow rate increases [6], and thus, some authors have used the
spectrum of the signal as an input to the inference algorithm [8].
Usually, the spectrum of the signal is calculated and analyzed
to look for parameters that are related to the flow rate. The main
parameter used is the amplitude of the first harmonic of the
signal spectrum [1][10][11][13][14], but the central frequency
of the first harmonic has been used too [6]. In all the cases in
the literature, only one feature has been used to represent the
system dynamic and, thus, no relevance analysis has been
performed optimize the representation space.
Some of the authors report that the changes in natural
frequency are usually very small, and for this reason a technique
based frequency analysis would not work well for small flow
rates [6]. This has led to the use of other types of analysis. The
frequency analysis approach has been used in systems that use
either an LDV or acoustic sensors.
2) Approaches based on time analysis
The vibration sound in water-conveying pipe flow can be
analyzed as a loudness intensity and characterized in terms of
the signal amplitude in the time domain [13]. Also, a statistical
parameter can be computed over the time signal and used in the
inference process. Some authors have used the standard
deviation of the vibrational signal [2] [3] or of the frequency
domain average time series signal [6] [9], and some other
propose the use of the RMS value of the signal [1] [11] [13].
For the RMS value to be a suitable indicator of the vibrational
signal energy, the signal must be time invariant and wide-sense
stationary [1]. In the same way as for frequency analysis, the
works that have used this approach have developed
representations with only one feature. The time analysis
approach has been used in systems that use accelerometers or
microphones as sensors.
3) Approaches based on time-frequency analysis
This approach is based in the use of decomposition techniques
that analyze both the time and frequency characteristics of the
signals, such as wavelets.
In 2018, Göksu propose the use of Wavelet Packet Analysis
(WPA), which has the advantage of enabling the analysis of
stationary and non-stationary signals [12]. This is an approach
that relies on multiple features to represent the system dynamics
and includes a relevance analysis, using norm entropy, to obtain
an effective representation space. Using this kind of features, a
mean absolute error was of 3.99E−04 L/s.
The time-frequency analysis has been used in systems that
use microphones as sensors. Experimental results indicate that
wavelet transform is a good candidate for flow measurement by
acoustic analysis and there are open issues to improvement by
varying window width and wavelet basis function.
E. Machine learning routines
Once the signal processing has been performed and the
representation space has been constructed, the obtained features
are used as the input for an inference algorithm that is going to
compute the flow rate value. The inference model is usually a
TABLE IV
MACHINE LEARNING TECHNIQUES USED IN FLOW RATE INFERENCE
Technique
Advantages
Disadvantages
Linear
regression
Well-known
•Low complexity
Good interpretability
•Good performance when
outputs are linearly
independent from inputs
Many real world
problems can be
simplified
Can identify only linear
relations
•Low performance with
highly collinear data
•Sensitive to outliers
Assumes normally
distributed data
Polynomial
regression
•Low computational
complexity
Very flexible for
empirical developments
Broad range of functions
can be fit
Polynomial fit a wide
range of curvature
Strong sensitive to
outliers
•Low performance with
highly collinear data
Prone to overfitting
Fewer model validation
tools
Regression
by parts
Very flexible
Combines all the
strengths of linear and
polynomial regression
Prior knowledge of the
nature of the data for a
good selection of parts
•Sensitive to outliers
Unsuitable for highly
collinear data
Prone to overfitting
ANN
• Bypasses the feature
selection /extraction stage
•Good performance for
highly nonlinear
processes
High generalization
capability
Nonlinear mapping in
large datasets
•Possibilities for
probabilistic assignment
No prior knowledge of
the nature of the data
•Training is
computationally
demanding
•Latent probability of
overfitting
•A lot of parameters to be
adjusted
•Low performance if the
number of descriptors
exceeds the number of
observations
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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
[2] [3][6][14] and a third order square root curve [7]. Also,
regression by parts has been used, combining linear and
quadratic fits or third degree polynomial regression and
quadratic regression [2] [3].
Some other authors have used Artificial Neural Networks
(ANN), which can learn more complex nonlinear models [8]
[12]. ANN is one of the most popular alternatives in soft
metrology systems [5] and soft sensor development and has
been used in a variety of applications [35] [36] [37] [38].
However, there is a lot of machine learning algorithms that are
commonly used in soft metrology that have not been explored
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)
[50] [51].
As for the relationship between the sensor selection and the
type of inference model, the works that use LDVs have always
proposed linear models while the ones using accelerometers or
microphones have proposed different approaches in the
inference model. Table IV is a compendium of advantages and
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].
F. Flow rate estimation
Results reported in the literature, that have been obtained with
the implementations described in the previous section, are
diverse and the comparison between them implicates high
levels of difficulty because the conditions in which each system
has been tested are different in terms of magnitudes, installation
parameters, equipment characteristics, data acquisition and
sampling, among other issues. Concerning these diverse
conditions, some authors have proved the influence that certain
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
characteristics of the mechanism that boost the fluid through the
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
diameter and that the sensitivity was greater for PVC pipes than
for steel and this effect was more evident for bigger diameters
[4]. This last fact was also observed by Evans et al, who stated
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
[6].
Dinardo et al studied a hydraulic system that had a turbo-
pump with variable revolution and they performed tests varying
the rpm of the pump. They found models with different
parameter for each rpm value, which indicates that this variable
also has an effect on the relationship between vibration and flow
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
TABLE V
LITERATURE RESULTS
Authors
Results
Evans et al., 2004 [6]
PVC pipe:

Stainless steel pipe:

Aluminum pipe :

Kim et al., 2008 [7]
Tested in several pipes. One of the cases
had a mean error of  with
standard deviation of  in a 
duration experiment. In general, the
results gave an estimation error below
Safari & Tavassoli, 2011
[14]
The absolute accuracy is presented as a
function of real flowrate, which is
approx. between  and 
Jacobs et al., 2015 [13]
Mean error of , with of readings
with less than 6 error
Medeiros et al., 2016 [3]
With  accelerometer:
 

With  accelerometer:
 

Dinardo et al., 2018 [1]
  

Göksu, 2018 [12]
 of mean measurement
accuracy with  mean
absolute error that corresponds to
 relative error
Venkata & Navada, 2018 [8]
A different error percentage in
presented for each flow rate value, with
a mean value of  and a maximum
error of 
Pirow et al., 2018 [9]
A figure presents an analysis of error
( vs. flow rate. Values vary in a wide
range, but errors below 10 are
reported for the study cases.
Scientia et Technica Año XXVI, Vol. 26, No. 01, marzo de 2021. Universidad Tecnológica de Pereira
34
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
during the training phase of the model and the posterior
validation, and for this reason it is not possible to estimate the
generalization ability of the proposed models. Additionally,
some of the studies have several measurement points with low
statistical sufficiency (3 to 5 instances of analysis).
One of the papers reviewed in the literature presents a
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].
IV. CONCLUSIONS
This paper is a literature review of the metrological advantages
of applying vibration analysis to the inference of pipeline flow
rate, showing that there is a phenomenological relationship
between the characteristics of the vibrations in a pipe and the
magnitude of the flow circulating through it. This fact suggests
that there are important opportunities for the development of
new alternatives of soft sensors that support the estimation in
flow rate measurement. Consequently, the metrological use of
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.
Although most semi-analytical methods are accurate and can
be used in static or dynamic nonlinear systems, or where the
flow signal is not completely static, the data provided for the
analysis is affected by fluctuations, outliers and even erroneous
data. Therefore, the development of this type of systems
requires that data acquisition be improved, as published papers
suggest that the structures and acquisition schemes present
notable difficulties in terms of mechanisms that reduce
disturbances and noise. Additionally, the literature reviewed
showed that the system parameters that influence the
measurement estimation require compensation, self-test or
calibration procedures to improve the measurement precision
and reliability. The difficulty lies in the fact that the variables
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
report restrictions associated with low sensitivity for low flow
rate levels and the need for the analyzed signals to be time
invariant and stationary, at least in a broad sense. In this sense,
it is evident that time-frequency methods have not been widely
explored in this context.
The use of soft sensors for the analysis of measurements that
are difficult to observe directly, is becoming an important trend
in nanotechnology, robotics, analysis of big data and
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].
ACKNOWLEDGMENTS
This work was supported by the Instituto Tecnológico
Metropolitano ITM of Medellín. Additionally, the authors
would like to thank the Measurement Analysis and Decision
Support Laboratory (AMYSOD Lab) of Parque i, Medellin,
Colombia.
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Francisco Luis Villa Restrepo, received
his Bachelor of Technology degree in
Quality from the Instituto Tecnológico
Metropolitano in 2016.
Since October of 2017, he has been a
Metrologist at the ACUATUBOS S.A.S,
where he has been in charge of performing
flow measurements under accreditation norms and
requirements by ONAC, in Colombia. He has obtained
certifications in the following norms: NTC ISO/IEC
17025:2017, NTC-ISO 4064-1 and NTC-ISO 4064-2. His
current research interests include indirect measurement
methods, signal processing and soft metrology.
ORCID: http://orcid.org/0000-0002-6183-9577
Cherlly Sánchez González received his
Bachelor of Technology degree in Quality
from the Instituto Tecnológico
Metropolitano, in 2017.
Since June of 2013, he has been a
Metrology Assistant at the ACUATUBOS
S.A.S., where he has been in charge of
supporting the laboratory accreditations
under the NTC-ISO 17025 norm, 2015 and 2017 versions. He
completed internships at Instituto Nacional de Metrología, in
2014 and 2016. In addition, he has obtained certifications in the
following norms: NTC-ISO 17025:2005, NTC-ISO
17025:2017 and NTC-ISO/IEC 4064:2016. His current
research interests include indirect measurement methods, signal
processing and soft metrology.
ORCID: http://orcid.org/0000-0001-9637-360X
Marcela Vallejo received her B.Eng.
degree in Electronic Engineering and an
M.Eng. degree in Electronics, from
Universidad de Antioquia, in 2008 and
2013, respectively.
She is currently a Lecturer and Researcher
at the Instituto Tecnológico Metropolitano
ITM, Medellín, Colombia. Her current
research interests include pattern recognition, machine
learning, artificial neural networks, signal processing and soft
metrology.
ORCID: http://orcid.org/0000-0002-9724-3169
Edilson Delgado-Trejos received a
B.Eng. degree in Electronic
Engineering, a M.Eng. degree in
Industrial Automation, and a Ph.D.
degree in Engineering Sciences from the
Universidad Nacional de Colombia, in
2000, 2003, and 2008, respectively.
Since August of 2008, he has been a full-
time Lecturer/Researcher at the Instituto Tecnológico
Metropolitano (ITM), Medellín-Colombia, where he has been
Director of the Research Center (2009 to 2011), Dean for the
Faculty of Engineering (2013 to 2015) and Vice Chancellor of
the Research and Academic Extension (2017 to 2019).
Currently, he is an Associate Professor and a Senior Researcher
at the same institute. He has published more than 50 papers, 10
book chapters and 3 books in indexed scientific journals and
editorials. His current research interests include pattern
recognition, machine learning, multivariate data analysis,
nonlinear analysis, signal processing and soft metrology.
ORCID: http://orcid.org/0000-0002-4840-478X