This work presents a method for predicting vibration at any location along the span of a pipeline using a model constructed from experimental data. The hybrid approach involves the construction of an initial model using system identification techniques of experimental data, and a modified model using Linear Quadratic Estimator (LQE) and Linear Quadratic Regulator (LQR) approach. The combination of the two approaches resulted in a system that is capable of predicting vibration at random locations along the span of the pipe section using minimal feedback from physical system. Change in vibration signature at any location on the pipeline can be used as an early warning against damage at that location. The proposed method can be utilized as a practical damage detection technique of underground pipelines and buried structures. The validity of the propose approach has been examined experimentally and the results are presented

Ameen Hussein El-Sinawi

Yongxiang Wang

English

Vibroengineering PROCEDIA

  © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. OCT 2015, VOLUME 6. ISSN 2345-0533 93 
Constructing a dynamic model for damage detection of 
pipelines using a hybrid modeling approach 
Yongxiang Wang1, Ameen Hussein El-Sinawi2 
The Petroleum Institute, Abu Dhabi, United Arab Emirates 
1Corresponding author 
E-mail: 1yowang@pi.ac.ae, 2aelsinawi@pi.ac.ae 
(Accepted 5 August 2015) 
Abstract. This work presents a method for predicting vibration at any location along the span of 
a pipeline using a model constructed from experimental data. The hybrid approach involves the 
construction of an initial model using system identification techniques of experimental data, and 
a modified model using Linear Quadratic Estimator (LQE) and Linear Quadratic Regulator (LQR) 
approach. The combination of the two approaches resulted in a system that is capable of predicting 
vibration at random locations along the span of the pipe section using minimal feedback from 
physical system. Change in vibration signature at any location on the pipeline can be used as an 
early warning against damage at that location. The proposed method can be utilized as a practical 
damage detection technique of underground pipelines and buried structures. The validity of the 
propose approach has been examined experimentally and the results are presented. 
Keywords: system identification, dynamic model, pipeline, damage detection, LQE, LQR, hybrid 
modeling approach. 
1. Introduction 
Research on vibration-based damage detection is increasingly gaining momentum due to 
factors like economic and technical advantages. The basic principle is that modal parameters such 
as natural frequencies, mode shapes and modal damping are functions of the system’s physical 
properties namely, mass, damping, and stiffness. Hence, changes in physical properties manifest 
itself as changes in modal properties which depend on the nature, location and severity of the 
damage [1]. Therefore, damages can be quantified from changes in modal frequencies and mode 
shapes. 
At the initial stage, an accurate dynamic model of the system under study is needed to predict 
its dynamic response over time. However, in some situations, structures to be tested or diagnosed 
are not accessible for measurements, and/or modeling conditions are not properly identified or too 
complex to model. Examples of such models are, underground pipelines, subsea tunnels and 
pipelines and underground foundations. These and similar situations, present a modelling 
challenge where obtaining a working model can be tedious and time consuming. Therefore, system 
identification is an effective and practical approach to build a dynamic model. System 
identification is a black box method which is based on experimental data only. In this approach, 
there are no prior requirements and assumptions related to structural parameters, properties and 
boundary conditions [2]. Generically, system identification techniques use the method of least 
square fit to identify system parameters. They can be classified into two categories: deterministic 
and statistical, where both can be used to identify system parameters, such as a damping and modal 
frequencies of the system [3]. 
Chang, Baek [4] obtained a baseline structure first using FEM and then modified it using SI to 
get the related perturbations. Mastorocostas and Theocharis [5] introduced a kind of fuzzy neural 
model for dynamic system identification. The recurrent models are similar as closed loop systems 
whose feedback paths introduce dynamics to the model. This model can learn the system dynamics 
without any basic knowledge about the structure of the system. Chen, Kurt [6] performed a method 
about nonlinear system identification which is used for structural health monitoring and damage 
detection based on measured acceleration signals. The method used in this research is presented 
in the following sections. 
CONSTRUCTING A DYNAMIC MODEL FOR DAMAGE DETECTION OF PIPELINES USING A HYBRID MODELING APPROACH.  
YONGXIANG WANG, AMEEN HUSSEIN EL-SINAWI 
94 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. OCT 2015, VOLUME 6. ISSN 2345-0533  
2. System modelling 
2.1. System identification methodology and procedures 
System identification of vibrating system is to develop a parametrized model based on 
measured excitation and/or response signals. In this work, an instrumented hammer is used to 
provide the input impulse force while accelerometers measure the response at different locations 
on the pipe span. System identification toolbox in MATLAB is utilized to obtain and initial model 
from raw experimental data. General identification procedure is outlined in Fig. 1. 
 
Fig. 1. General identification procedure 
In this work, many types of models were test and validated against experimental data and the 
Box-Jenkins model which belongs to polynomial model class is found to have the best 
performance. The principle formula of Box-Jenkins model class is shown below: 
ݕ ൌ ൤ܤܨ൨ ݑ ൅ ൤
ܥ
ܦ൨ ݁, (1)
where ݕ represents the output; ݑ represents the input and ݁ represents the error predicted. Models 
with various best fits can be obtained when the parameters ܤ, ܨ, ܥ, ܦ are adjusted [7-9]. The 
polynomial model generated is converted to discrete state-space format such that the dynamic 
system of the pipeline is: 
ݔሺ݊ ൅ 1ሻ ൌ ܣ௜ݔሺ݊ሻ ൅ ܤ௜ݑሺ݊ሻ, ݕሺ݊ሻ ൌ ܥ௜ݔሺ݊ሻ ൅ ܦ௜ݑሺ݊ሻ, (2)
where quadruple ܣ௜,  ܤ௜,  ܥ௜,  ܦ௜  represents the state-space model obtained using system 
identification toolbox. 
2.2. Construction of the hybrid model 
The hybrid model presented in this work uses the initial state-space model from system 
identification shown in Eq. (2) and the LQE and LQR techniques to generate optimal estimates of 
the system’s states such that the associated cost functions are minimized. The generic form of the 
cost function is for LQR is: 
ܬ ൌ නሺݔ்ܳݔ ൅ ݑ்ܴݑሻ݀ݐ
ஶ
଴
, (3)
where ݔ  and ݑ  represent the states and control inputs, respectively. The choice of ܳ  and ܴ 
depends on the transient response and measurement qualities [7-10]. The hybrid model is shown 
in Fig. 3. 
3. Experimental and simulation results 
The experimental setup is shown Fig. 2 in which Accelerometers (a) is located at the right side 
of the pipe section, (b) is at the middle and (c) is at the left. An instrumented hammer applies the 
excitation force at the right end of the pipe. DSpace and its data acquisition system measures 
CONSTRUCTING A DYNAMIC MODEL FOR DAMAGE DETECTION OF PIPELINES USING A HYBRID MODELING APPROACH.  
YONGXIANG WANG, AMEEN HUSSEIN EL-SINAWI 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. OCT 2015, VOLUME 6. ISSN 2345-0533 95 
hammer force as well as the accelerometers’ responses and utilize them in a hardware-in-the-loop 
format in as shown in Fig. 3, to produce an optimal estimate of pipe vibration at any desired 
location. It is worth mentioning that, in this experimental work, only one accelerometer 
measurement is used to update the model (i.e., feedback signal), the remaining accelerometers are 
used for comparison with estimates at corresponding locations. 
 
Fig. 2. Experimental setup 
 
Fig. 3. Schematic of the hybrid model 
Fig. 4 show the system identification (SysID) main window, and the model match to 
experimental results. It is also worth mentioning that 70 % of the data points are used to construct 
the model while the remaining 30 % are used for SysID model verification.  
 
Fig. 4. Constructing model based on Box-Jenkins model 
CONSTRUCTING A DYNAMIC MODEL FOR DAMAGE DETECTION OF PIPELINES USING A HYBRID MODELING APPROACH.  
YONGXIANG WANG, AMEEN HUSSEIN EL-SINAWI 
96 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. OCT 2015, VOLUME 6. ISSN 2345-0533  
Comparison between estimated response and actual response using only SysID model, in 
frequency domain, are showed in Fig. 5 (solid line is actual response and dashed line is estimated). 
It is clear that the SysID model poorly predicts the actual vibration of the pipeline at the 
corresponding locations. 
a) 
 
b) 
Fig. 5. Comparison of spectrogram between estimated and actual results  
(middle and right accelerometers) using SysID model 
However, implementing the hybrid model approach shows that the model is capable of 
predicting the vibration fairly accurately with minimal discrepancies and exact resonant 
frequencies match as shown in Fig. 6. The amplitude scaling is related to hardware bias. 
 
Fig. 6. Comparison of spectrogram between estimated and actual results  
(middle and right accelerometers) using hybrid model 
4. Conclusions 
In this work, a novel approach for predicting vibration of a buried pipeline or structures is 
presented. An initial system identification model is constructed from impulse response data of the 
structure. The initial model is then improved in a hybrid approach format such that, an optimal 
estimator is constructed and actual measurement are used to improve estimates of the structural 
vibration at desired location. The number of actual measurements needed to update the initial 
model is kept at minimal to mimic real-life applications where few measurements of the structural 
vibration can be afforded. The hybrid approach improved the model significantly and the integrity 
of the model is verified experimentally. The model succeeded in predicting the vibration at any 
location of choice with good accuracy. 
Frequency (Hz)
 dB
W
 / H
z
 0 100 200 300 400 500
-100
-80
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0
Estimated response
Actual response
Frequency (Hz)
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W
 / H
z
 
 
0 100 200 300 400 500
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Estimated response
Actual response
Frequency (Hz)
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m 
/ H
z
 
 
0 100 200 300 400 500
-60
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-40
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-10
0
10
Estimated response
Actual response
Frequency (Hz)
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m 
/ H
z
 
 
0 100 200 300 400 500
-50
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0
Estimated response
Actual response
CONSTRUCTING A DYNAMIC MODEL FOR DAMAGE DETECTION OF PIPELINES USING A HYBRID MODELING APPROACH.  
YONGXIANG WANG, AMEEN HUSSEIN EL-SINAWI 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. OCT 2015, VOLUME 6. ISSN 2345-0533 97 
Acknowledgement 
Authors acknowledge the support of the Petroleum Institute. 
References 
[1] Doebling S. W., Farrar C. R., Prime M. B. A summary review of vibration-based damage 
identification methods. Shock and Vibration Digest, Vol. 30, Issue 2, 1998, p. 91-105. 
[2] Le Ber L., et al. IDENT 1D – a novel software tool for an easy identification of material constitutive 
parameters. Nuclear Engineering and Design, Vol. 186, Issue 3, 1998, p. 343-352. 
[3] Jovanović O. Identification of dynamic system using neural network. The Scientific Journal Facta 
Universitatis Series: Architecture and Civil Engineering, Vol. 31, 1997, p. 525-532. 
[4] Chang S., et al. Structural system identification using degree of freedom-based reduction and 
hierarchical clustering algorithm. Journal of Sound and Vibration, 2015. 
[5] Mastorocostas P., Theocharis J. B. A recurrent fuzzy-neural model for dynamic system 
identification. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol. 32, 
Issue 2, 2002, p. 176-190. 
[6] Chen H., et al. Experimental system identification of the dynamics of a vibro-impact beam with a 
view towards structural health monitoring and damage detection. Mechanical Systems and Signal 
Processing, Vol. 46, Issue 1, 2014, p. 91-113. 
[7] Ljung L. System Identification Toolbox for Use with MATLAB. 2007. 
[8] Fassois S. Identification, Model Based Methods. Academic Press, 2001, p. 673-686. 
[9] Ljung L. System Identification Toolbox: User’s Guide. Citeseer, 1995. 
[10] Lewis F. L., D. L. Vrabie, V. L. Syrmos Optimal Control of Discrete – Time Systems. Optimal 
Control, Third Edition, 1986, p. 19-109. 


Constructing a dynamic model for damage detection of pipelines using a hybrid modeling approach

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Constructing a dynamic model for damage detection of pipelines using a hybrid modeling approach

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