Evaluation of Different System Identification Methods for Assessment of RC Structures in Aggressive Environments, Afshin KALANTARI

6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Evaluation of different system
identification methods for
assessment of deteriorated RC
structures in aggressive
environments
Afshin Kalantari,International Institute of Earthquake Engineering and Seismology,Iran
Omid Bahar,International Institute of Earthquake Engineering and Seismology,Iran
Benyamin Abbasi Feshki, University Of Science and Culture,Iran

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1. Introduction
• Lack of information like how to build or injury or decline in
materials in buildings, bridges, oil platforms and other structural
systems over the life of structures as a result of various factors are
causing unknown the behavior of structures. More fetal damage
that can be corrected with early studies of structures status and
thus, prevent The spread of damage in structures and buildings
crumble and the risk of critical structures such as bridges can also
be reduced. In general identification of structural systems means
extracting modal parameters (frequency, damping, mode shape)
through testing and dynamic measurements. . For this purpose, a
numerical model of a bridge structure under chloride ion attack is
developed in Opensees software. Simulated response of the
corroded structure ambient vibration is calculated under ambient
vibration and the results of system identification methods are
calculated.

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2. System identification methods used in this study
• In this paper, 4 system identification methods are applied at a
bridge whose characteristics has been changed due to corrosion.
The identification methods include: Fourier transformation,
Wavelet transformations,Peak picking method & Frequency domain
decompositioin (FDD)method.
2.1. Fourier transformation method
• This method uses time data to the frequency domain and offers
input signal frequency content. Fourier transformation generally
defined by the following equation:
• 𝐹 𝜔 = −∞
+∞
𝑓(𝑡)𝑒−𝑖𝜔𝑡 𝑑𝑡 (1)
• The result is Fourier coefficients F(ω) by multiplying the sine wave
of the frequency corresponding to the frequency of the signal
frequency content. In cases where the frequency behavior of
structures is important, Fourier transform is particularly effective
and successful.

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• In addition to functionality, simplicity and other advantages of the
Fourier transform, this method would not be achievable on the
basis of the frequency signal timing information. According to the
Fourier transform of a signal can never suggest that a special event
happened at what time.
2.2. Wavelet transformation method
• Wavelet transformation supply solutions to the time-scale analysis
by separating signals into a superposition of shifted and scaled
versions of the mother wavelet.
• On the expected application of wavelet, a variety of mother
wavelets are produced. A number of these mother wavelets are
displayed in Figure 1.

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Fig 1: Some types of the mother wavelet[Rooijakkers et al,2012]
• The dilated and translated functions derived from the mother
wavelet are called daughter wavelets or simply wavelets. these
daughter wavelets have the same shape as their mother wavelet.
the functional relationship between daughter and mother wavelet
in the scale "s" and displacement "τ" , is expressed as
Eq(2)[Chinarro,D,2014]:
• 𝜓 𝑠, 𝜏 = (𝑡
1
𝑠
𝜓(𝑡)(
𝑡−𝜏
𝑠
) (2)

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• To convert scale to frequency, the following equation was presented
by yoon et al in 2000:
• f =
fs
3
2
1
a
(3)
where fs= sampling frequency and a= scale.
2.3. Peak picking method:
• The easiest way to approximate the modal parameters of a
structure exposed to ambient loading is peak picking method. In
this method the average normalized power spectral density(ANPSD)
peaks are considered as natural frequencies. Mode shape
components are determined by values of transfer function in the
natural frequencies[Peeters et al,1999].

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• Transfer function in forced vibration test is the ratio of responses
obtained to the input power. While in ambient vibration test this
function is obtained from ratio of responses measured in the
motion sensor to reference sensor.
2.4. Frequency domain decomposition method:
• In this section a new frequency domain technique is introduced for
the modal identification of output-only systems, i.e. in the case
where the modal parameters must be estimated without knowing
the input exciting the system[Brincker et al,2001]. first all extremes
𝑟𝑘, both peaks and valleys, on the correlation function are found.
the logarithmic decrement δ is then given by Eq(4)[Brincker et
al,2001]:
• 𝛿 =
2
𝑘
𝑙𝑛(
𝑟0
𝑟 𝑘
) (4)

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• where r0 is the initial value of the correlation function and rk is the
k'th extreme, and the damping ratio is given by the Eq(5)[Brincker
et al,2001]:
• 𝜉 =
𝛿
𝛿2+4𝜋2
(5)
• The frequency is found by making a linear regression on the
crossing times corresponding to the extremes and using that the
damped natural frequency fd and the undamped natural frequency f
is related by:
• 𝑓 =
𝑓 𝑑
1−𝜉2
(6)
• Now, according to given description in this study, system
identification of a RC bridge subjected to corrosion is performed
using fourier transformation method, pick peaking , wavelet
transformation method and FDD method.

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2.5. Bridge description
• Under studied bridge in this paper has 2 spans with length of 20
meters and piers at a height of 6 , was modeled in Opensees
software. The following figure shows schematically the bridge. In
order to model the corroded structure the environmental condition
of Persian Gulf has been applied in a period of 50 years.
• A simulation of structural system identification under ambient
vibration has been performed applying a white noise to the
numerical model and analyzing the response.
Fig2:bridge schematic view
6m
20m

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2.5.1. Results of applying the system identification methods:
• In this study, after the implementation of system identification
methods on the bridge which studied in this paper; It was observed
that the frequency parameter has changed due to corrosion in the
structure.
2.5.2. Sound structure results:
• Results of system identification methods in this structure has been
shown in table 1.
Table1: Identified frequency in different methods
Frequency(Hz)Method
3.4Fourier transformation(Fig3)
2.5Wavelet transformation(Fig4)
2.7Peak picking(Fig5)
2.73FDD(Fig6)

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Fig3:Fourier transformation of sound structure

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Fig4:Wavelet transformation of sound structure

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Fig5: Power spectrum density of sound structure

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Fig6:Frequency Domain Decomposition output of sound structure

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2.5.3. corroded structure(after 50 years) results:
Results of system identification methods in this structure has been
shown in table 2.
Table2: Identified frequency in different methods
• Figures of upon table will shown in follow slides.
Frequency(Hz)Method
1Fourier transformation(Fig7)
2.07Wavelet transformation(Fig8)
1.85Peak picking(Fig9)
2.051FDD(Fig10)

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Fig7:Fourier transformation of corroded structure

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Fig8:Wavelet transformation of corroded structure

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Fig9:Power spectrum density of corroded structure

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Fig10:Frequency Domain Decomposition output of corroded structure

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3. conclusion
• In this study, we tried to introduce 4 common structural system
identification methods, To be able to use any of these methods in
future research projects and adopting appropriate decision and
proper method. As was observed in this paper the frequency
parameter have decreased in corroded bridge structure, therefore,
These examinations and identifications can lead to damage and risk
reduction in critical structures.

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Thanks for your attention

Evaluation of Different System Identification Methods for Assessment of RC Structures in Aggressive Environments, Afshin KALANTARI

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