Seismic Damage Indices for Concrete Dams a Stateoftheart Review

Abstruse.

In structural applied science, damage detection in concrete gravity dams (CGDS) is a practical problem. Dam devastation can have severe financial consequences and may even lead to fatalities. Therefore, structural wellness monitoring in accelerate is crucial. In this regard, a well-known CGD, namely the Pino Flat Dam, has been chosen for the Finite Element Modeling. In this paper, harm is induced in the dam cervix through elasticity modulus reduction by xl % and eighty %. In addition, after applying Northridge earthquake, the acceleration in structure nodes for intact and damaged cases are recorded in vector formats. Using various methods, such every bit Discrete-time Fourier Transform (DTFT), Wavelet transform and Wiener transform, the differences between these two signals are investigated. The standard deviation (South.D.) of variations is chosen equally the performance metric and is practical to the signal amplitude betwixt intact and harm observations/signals. The reason why several signal processing algorithms are used is finding an approach which shows more than clearly the differences caused by the destruction. This is evaluated via S.D. values for dissimilar algorithms. The results confirm the superiority of DTFT over other given algorithms. DTFT has a negligible outperformance (approximately nada dB) with respect to the Wavelet transform in both the crest and the lower nodes of the dam. This rate for DTFT and Wavelet is 10dB higher than that of Wiener and 35 dB in comparison with the uncomplicated aamplitude difference. Moreover, the detection thresholds for the given methods are compared, and it is verified that the DTFT and Wavelet indicate the best performance.

Keywords: harm detection, concrete gravity dams, indicate processing, discrete-time Fourier transform, Wiener filter, Wavelet transform.

1. Introduction

Impairment in physical gravity dams is costly. This shortcoming is frequently due to ignoring the codes and regulations in the phase of designing and construction principles at the time of execution, the age of the dam or incorrect maintenance of the structure. In this study, it is attempted to observe damage in CGDs with recourse to the differences between the characteristics of the intact and damaged dams via point processing algorithms. In case minor faults are non detected in fourth dimension, they tin plow into major ones. Direct ascertainment cannot always be used for impairment detection in structures; therefore, other technics, such as signal processing, should be used. Signal processing algorithms are non frequently used in the analysis of concrete gravity dams.

To detect damage in structures, if the visible, direct observation can exist helpful. However, there are often limitations which brand the states examination these structures. These tests are divided into ii categories: subversive and non-destructive. The 2nd category is more acceptable due to the lack of damage [1]. For instance, by inserting some sensors on a span (without causing damage to the structure) and recording the structural response using signal processing techniques (such as the Wavelet Method) under an ambient vibration, the presence or absenteeism of damage in these structures can be realized [2].

So far, numerous researches using non-destructive techniques, such as indicate processing methods, take been studied, only the investigated structures mainly consist of unproblematic structural elements, such as frames, beams, and trusses which have much easier governing equations compared to the dams. The crusade of less attention in this issue tin can be related to complication in modeling and analysis and considering the interaction amidst different bodies as well as the high degree of freedom of the dams in comparison with other structures [three].

Cleary et al. have presented a non-mesh method for modeling of impairment in gravity dams nether earthquake loading. The proposed method, called Smoothed Particle Hydrodynamics (SPH), was implemented on the Koyna Dam under severe harmonic ground excitation. The results involve the formation and distribution of cracks which show a good agreement with the Finite Chemical element Method and experimental results. Moreover, they found that the amplitude and frequency of excitation hugely touch on the pattern of failure [4]. Alembagheri and Ghaemian studied the damage cess of a concrete arch dam (the Morrow Point Dam) through nonlinear Incremental Dynamic Assay (IDA), which includes the dam-foundation interaction. The conducted study introduces two damage indices based on Maximum Crest Displacement (DI_U) and Damage Energy Dissipation (DI_Eastward). They showed that the proposed harm indices could adequately assess the harm of the dam [five].

Among all engineering structures, dams are essential and strategic resources for any government. These constructions, like all other engineering structures, have always had the possibility of failure during their lifetime and this will intensify with increasing the operational life and environmental effects, such as earthquakes. For example, infinitesimal faults within the structure (similar modest cracks), if non diagnosed on time, might affect the whole body of the arrangement and it would lead to collapsing the structure, which might create a significant loss of property and man beings [6].

A fundamental problem in Structural Health Monitoring (SHM) involves performing impairment detection and isolation from a set of measured data. Typically, the number of sensors used to collect the required data is limited due to available funds, equipment, and accessibility [seven].

To observe the structural damage, initial investigations in harm detection used the changes in natural frequencies as one of the key properties of a dynamic system. Farrar et al. implemented the shifts in natural frequencies to identify the harm in an I-twoscore bridge and noted that shifts in the natural frequencies were non adequate for detecting the damage of small faults. Alternatively, every bit this research assumed, mode shapes (or their derivatives) could reveal the harm of a structural system [eight].

Lin investigated ambience modal identification based on non-stationary correlation technique in 2016. Overall, in this newspaper, it was recommended that if the ambient excitation is represented by a product model with a tiresome time-varying office, without whatever additional treatment of transforming the original non-stationary responses, these responses of the arrangement could be approximately treated equally a stationary random process. Then the non-stationary crosscorrelation functions of the structural response which are evaluated at arbitrary, fixed fourth dimension instants of structural responses are of the same mathematical course as those of the free vibration of a structure. From these non-stationary cantankerous-correlation functions, modal parameters of the original system tin can thus exist identified [nine].

In an article, Xuan Kong, Chun-Sheng Cai, and Jiexuan Hu investigated different levels for identification of vibration-based damage, which consisted of anticipation of the remaining useful lifetime of structures and conclusion-making for appropriate deportment. They offered a framework that contained several major parts, including the detection of harm occurrence via response-based methods, building reasonable structural models, selecting damage parameters and amalgam objective functions with sensitivity assay, adopting optimization techniques to solve the problem, predicting the remaining useful lifetime of structures, and making decisions for the next actions. For every office, the practical methods were reviewed, and the advantages and disadvantages were briefed for further recommendations [10].

In another paper by Giacomo Bernagozzi, Luca Landi, and Pier Paolo Diotallevi, some methods for vibration-based damage detection of ceremonious structures were used and compared, commencing with ambient vibration data. The results of the analyses were based on a dynamic identification of the modal parameters, which was carried out in output-merely conditions. The reviewed damage-sensitive features were the modal parameters, the modal flexibility matrix, and the damage-induced deflection. Due to unitary inspection loads of the identified construction, possible variations in these parameters could be adopted in order to discover, localize and quantify the harm. Furthermore, the efficacy of the various detected damage features was assessed, and the accuracy related to the identified modifications was defined through a comparison with those variations first assumed in the structural model [11].

F. Musafere, A. Sadhu, and K. Liu proposed a method with recourse to the framework of blind source separation (BSS) to detect damage time and severity. Other fourth dimension-frequency decompositions, such every bit Hilbert transform and time-varying machine-regressive modeling were investigated to enhance source separation adequacy of the BSS method [12].

Past a general review of the context above, it tin be seen that detecting structural damage is mainly investigated on unproblematic structural systems, like multi-story edifice frames, trusses, etc. In other words, due to their high degrees of liberty and complex geometry, physical gravity dams are rarely studied in the literature. Hence, the electric current written report aims to employ bespeak processing algorithms for identification of damages within this infrastructure. It seems that in that location are no similar studies in the field of reduction of the modulus elasticity in some elements and harm detection with signal processing algorithms such every bit DTFT, Wavelet, and Weiner.

The principal objective of this newspaper is detecting damage in concrete gravity dams using point processing algorithms. To do so, the acceleration amounts of different nodes along the dam summit have been measured for both the intact and damaged dams, and the related vectors take been recorded as intact and damaged observations respectively. The principal objective of this commodity is to notice a way to detect any damages in the dam efficiently. To evaluate the method used qualitatively, damage detection every bit an efficiency indicator take been taken into business relationship. It is worth mentioning that in many methods used in detection and interpretation theories, standard deviation parameter is used every bit a credited evaluation indicator [thirteen].

Every bit a simple arroyo, ane may calculate the differences in ascertainment domain for intact and damaged dams for each node and case of significant differences, find the dam damaged, but every bit this newspaper shows this approach has two conspicuous drawbacks. If nosotros take the lower nodes observations into account, we will see that in example of severe damage in the dam structure, there will exist lilliputian difference betwixt the intact and damaged dams, hardly indicating whatever damage. This is, of grade, due to the structural stability in the lower parts. On the other hand, if the extent of damage is negligible, this detection in the construction of the dams, using this simple approach, will give poor results.

Using more frequently used algorithms in signal processing areas, such as DTFT, Wavelet, and Wiener this paper shows that the presence of damage tin can exist detected much more accurately. In other words, the given algorithm has a college potential for detecting the difference in the given signals. The simulation results prove the aforementioned claim. They as well signal that using the DTFT approach which studies the input signal in the frequency domain, the deviation in the detection for both intact and damaged dams are much more apparent than the other approaches.

Moreover, the operation of the given approach regarding the sensitivity of the dams in instance of minor damages has been evaluated. To do so, in all the four algorithms, the detection threshold in the dam construction has been calculated and compared. Past detection threshold, the authors accept the minimum harm in the structure in mind which is detected past each algorithm. Equally the simulation results indicate, the DTFT arroyo has the best performance.

two. Proposed finite chemical element model

In this section, a well-known concrete gravity dam, i.east., the Pine Flat, shown in Fig. 1, is selected for the Finite Chemical element modeling of structures in ABAQUS. For simulating the mechanical behavior of the dam, a two-dimensional Finite Element model was developed in ABAQUS software. The programme was called due to its broad cloth and geometrical modeling capabilities.

Fig. i. A view of the CGD selected for modeling: the pine flat dam

The Pino Flat is a concrete gravity dam on the Kings River in the United states of america. The height of the dam is nearly 130 m. The dam's primary purpose is alluvion control, with irrigation, ability generation, and recreation secondary in importance [xiv].

Past neglecting the material nonlinearity effects and assuming the linear behavior, the mechanical properties of the mass physical, which are supposed to be the same in both static and dynamic cases, are given in Table ane.

Table i. Material properties of the pine apartment dam [xv]

Quantity	Unit	Pine flat
Density	kg/m3	2483
Modulus of elasticity	GPa	33.558
Poisson's ratio	–	0.255

Moreover, the post-obit assumptions have been fabricated in the modeling of dam-reservoir interaction:

• A rectangular shape is considered for the reservoir, with a length 3 times every bit the elevation of the dam (as recommended in [16]);

• The free-board in the lake is neglected in order to model the interaction between the dam and the reservoir easily; i.east., the h2o level is equal to the height of the dam;

• Dam-water interaction is modeled every bit a type tie, where the nodes are constrained together on the interface of the two media [16];

• The transmitting boundary condition is assigned to the reservoir'southward truncated far-end so that the pressure waves are non reflected in the reservoir [14];

• Cypher hydrodynamic pressure is assigned to the reservoir's costless surface, and there is no absorbing boundary status at the reservoir'south bottom [17];

• The Majority modulus of water; $K_w=$ 2.2 GPa;

• The density of water; ${\rho }_w=$ grand kg/m^three

In the modeling of the dam-foundation interaction, information technology is assumed that:

• In that location is a rigid foundation;

• At that place is no sliding along with the dam-foundation interface;

• The uplift pressure is non modeled in this study.

3. Damage scenario

Most of the damage sustained earthquakes often occur at the cervix of the dam. In the elements of the dam neck, as shown in the Fig. 2, harm occurs in the grade of elasticity modulus reduction past forty % and eighty %. The elasticity modulus is a quantity that measures the resistance of materials to existence deformed. To be more than precise, 0 % of devastation is categorized as intact, and any percentage of destruction is regarded as damaged.

Fig. 2. Destruction of elements in the dam neck

The Northridge earthquake tape (Fig. 3) is practical to the heel of the dam, and the acceleration of the intact and damaged structure is extracted in 26 nodes (Fig. four) in the upstream of the dam. It should be noted that dispatch is an essential dynamic parameter. Due to the abundance of data in this regard, some of the results have been selected and presented in the tables beneath.

Fig. iii. The acceleration record for the Northridge earthquake

Fig. 4. The numbering of the nodes in the upstream of the dam

four. Methodology

In this newspaper, signal processing algorithms have been implemented in MATLAB simulation environs. Furthermore, the required information related to 40 % and 80 % of devastation cases have been generated via ABAQUS.

four.1. Investigating the behavior of structure devastation in the time domain

To investigate the behavior of Pine Apartment dam-induced by the convulsion, on the Pine Flat Dam, diverse signal processing algorithms are used. Initially, the differences in acceleration after the earthquake are examined for unlike nodes of the structure (26 nodes). The results of 40 % destruction for the sample nodes are shown in Fig. 5.

Every bit information technology is seen in Fig. 5, the issue of devastation is more distinctive on higher nodes, especially as the changes on the crest of the dam are more than in comparison with those in the lower parts. The results for eighty % destruction for some sample nodes are shown in the following.

According to Fig. 5, in the instance of 80 % destruction, the issue on higher nodes is still more noticeable than the lower parts of the construction. Although differences of changes in fourth dimension for various nodes are obvious and, accordingly, the corporeality of destruction on different nodes could exist compared to one another in the scenarios in this newspaper, these changes may non be so remarkable for each selected scenario. Therefore, to perceive the severity of the above changes, the standard departure (square root) of the acceleration variations tin can be calculated and shown for the nodes of the structure. To do so, the standard deviations of the dispatch variations for different structure nodes (26 nodes) for destructions of 40 % and lxxx % are shown in Fig. 6.

Fig. 5. The amounts of acceleration difference before and after 40 % destruction on some sample nodes: a) node 1, b) node five, c) node half-dozen, d) node 26

a)

b)

c)

d)

Fig. 6. The amounts of acceleration deviation before and afterwards 80 % destruction on some sample nodes: a) node ane, b) node 5, c) node 6, d) node 26

a)

b)

c)

d)

Fig. vii. Standard deviations of acceleration variations for dissimilar structure nodes for 40 % and lxxx % destruction: a) 40 % destruction, b) 80 % destruction

a)

b)

4.2. Investigating destruction beliefs in the frequency domain via Fourier transform

Discrete-time Fourier transform for $X\left[n\right]$ detached-time signal is divers as [eighteen]:

(1)

$X\left(f\right)=\sum _{k=-\mathrm{\infty }}^{\mathrm{\infty }}x\left[n\right]\mathrm{due\; east}\mathrm{x}\mathrm{p}\left(-jk\mathrm{two}\pi f\right),$

where $n$ and $f$ announce the fourth dimension and frequency domain variables. The output function of the higher up equation is in the frequency domain and contains spectral features of $X\left[\mathrm{due\; north}\right]$ signal in the frequency domain [18]. A common approach for monitoring the changes in time in a procedure is to investigate the beliefs in the frequency domain. According to the Fourier theorem, each office with a express domain tin can be reconstructed as a linear combination of space sinusoidal components with different amplitudes, phases, and frequencies. If a function has quick changes in tithe me domain, its frequency spectrum will have sinusoidal components with high frequencies, the domain of which is proportionate with that of the main changes of the function in the fourth dimension domain. In this department, dam destruction past earthquake vibration in the frequency domain is investigated through Fourier transform. As an example, Fourier transform of fourth dimension observations for some sample nodes, with and without the destruction, is shown in Fig. eight.

Fig. 8. The results of Fourier transform on dam acceleration earlier and after 40 % destruction on some sample nodes

a) Node 1, damaged

b) Node 1, intact

c) Node v, damaged

d) Node 5, intact

eastward) Node 10, damaged

f) Node 10, intact

g) Node 20, damaged

h) Node 20, intact

In lower nodes, the difference betwixt the intact and damaged cases is less than that of college nodes (specially in the crest of the dam) signifying that the effect of the earthquake on the crest is more than contained of the devastation location. To investigate the differences between the intact and damaged states, differences of Fourier transform of observations before and after 40 % devastation are presented in Fig. ix.

Fig. 9. The amounts of acceleration difference before and later 40 % destruction on some sample nodes. a) node i, b) node 5, c) node ten, d) node twenty

a)

b)

c)

d)

In Fig. ten are presented the amounts of the standard deviation of acceleration differences for 26 nodes of the structure in the frequency domain for xl % and 80 % destruction.

Fig. 10. The standard difference of acceleration differences for 26 nodes of the construction in the frequency domain for 40 % and 80 % destruction: a) 40 % of destruction, b) fourscore % of destruction

a)

b)

The comparison of the two curves in Fig. 7 and Fig. 10, which represent standard deviations of 40 % and 80 % destructions in the frequency domain, clarifies that in each devastation case, the amounts of changes in the higher nodes of the structure are more than the lower ones. Furthermore, the severity of changes in 80 % destruction is more than 40 %, which was already expected. Besides, the differences are independent of the destruction center (nodes v and half dozen in this scenario), and in this structure, higher nodes confront more changes due to the shape of the structure.

four.three. Wavelet transform

An arbitrary function $f\left(t\right)$ tin can be characterized by a linear combination of a ready of independent basis vectors $\left({\psi }_k\right)$ every bit [19]:

(2)

$f\left(t\right)=\sum _{k=1}^{\mathrm{Northward}}{\alpha }_k{\psi }_k\left(t\right),$

where ${\alpha }_k$ is the $\mathrm{yard}$th coefficient of the linear combination; ${\psi }_{\mathrm{grand}}$ is the $m$th vector of the space footing and $\mathrm{Due\; north}$ is the space dimension. The continuous Wavelet transform tin be written as the inner product of the signal past a bones function every bit [20]:

(3)

$C\mathrm{Due\; west}{T}_x^{\psi }\left(\tau ,s\right)={\psi }_x^{\psi }\left(\tau ,\mathrm{south}\right)=<\mathrm{Ten}\left(T\right).{\psi }_{\tau ,s}\left(t\right)\ge .$

In this equation:

(4)

${\psi }_{\tau ,\mathrm{southward}}\left(t\right)=\frac{\mathrm{ane}}{\sqrt{\left|s\right|}}\psi \left(\frac{t-\tau }{s}\right),$

where $s$ is the scale parameter and $\tau$ is the transmission parameter. In the Wavelet transform, there is an inverse human relationship between the scale parameter and frequency $\left(s=1/f\right)$. Wavelet transform acts as a window and the signal is multiplied by the transform. In this transform, the width of the window changes parallel to the alterations of the frequency components, which is the virtually of import feature of the Wavelet transform. Wavelet transform is well-known in bespeak processing and is practical in processing characteristics, such as energy concentration in a part of the bespeak, discontinuity, sudden variations, etc. [21]. In most cases, Wavelet is implemented via a bank filter which consists of low-pass and high-pass filters.

After Wavelet decomposition, those coefficients with modest domains are mainly afflicted by noise, whereas more than significant coefficients have more information about the signal in comparison with noise. Therefore, the exchange of minor coefficients (smaller than a threshold amount) with zero and awarding of inverse Fourier transform crusade reconstruction of the input indicate with lower amounts of dissonance. Equally a result, the Wavelet transform leads to a reduction in noise (when it exists in the input data) [22].

4.three.one. Investigating destruction beliefs via wavelet transform

In the following effigy, the results of Wavelet transform application on the dam acceleration amounts before and after twoscore % devastation on some sample nodes are shown in Fig. 14.

Fig. 14. The results of the Wavelet transform application on the dam acceleration amount shown before and after forty% destruction on some sample nodes

a) Node one, damaged

b) Node ane, intact

c) Node v, damaged

d) Node 5, intact

e) Node 6, damaged

f) Node vi, intact

g) Node 26, damaged

h) Node 26, intact

In Fig. 15, the results of Wavelet transform application on the dam acceleration amounts are shown before and after eighty % destruction on some sample nodes.

In this process, the Wavelet transform can besides be obtained from the differences of the dam acceleration amounts before and later on the destruction, and its results tin can be investigated. The effect of this implementation for some sample nodes is shown in Fig. 16.

In Fig. 17, standard deviations of acceleration changes for different structure nodes for xl% and 80% destruction are shown in the field of the Wavelet transform.

Fig. 15. The results of the Wavelet transform application on the dam acceleration amount shown before and after 80% destruction on some sample nodes

a) Node one, damaged

b) Node one, intact

c) Node five, damaged

d) Node 5, intact

due east) Node 6, damaged

f) Node 6, intact

chiliad) Node 26, damaged

h) Node 26, intact

iv.four. Wiener filter

The human relationship between Wiener filter and $h\left[n\right]$ express impulse response with the length of $N$, the coefficients of which are non zip in 0 $\le n\le N-$ 1 is defined as the post-obit [18, 23]:

(5)

$\widehat{s}\left[\mathrm{due\; north}\right]=h\left[n\right]\otimes z\left[n\right]=\sum _{i=0}^{\mathrm{Due\; north}-1}h\left[i\right]z\left[n-i\right].$

In the above equation, the operator shows convolution. $z\left[n\right]$ is the variable of the new domain (later on transform).

Wiener filter is applied equally i, ii-dimensional or more to the input indicate. When the variance of the image is enormous, this filter relieves the signal fluctuations to some extent. Notwithstanding, in those areas of the input signals where the variance of changes is modest, Wiener filter relieves the betoken more. In comparison with linear filters, this method shows meliorate results and preserves the edges of changes which are located in the higher frequencies.

Wiener filter is also called the minimum of the root hateful square mistake. This is because the idea behind the Wiener filter is fulfilling a target function which is a function of the Mean Square Error (MSE).

In the Wiener filter process, Wiener transforms/filter can be obtained from the differences in dam acceleration amounts earlier and subsequently destruction, the results of which tin can exist investigated. The outcome of this implementation on some sample nodes can be seen in Fig. 18.

Fig. 16. The results of the wavelet transform application on the dam acceleration amounts before and after 40 % and eighty % destruction on some sample nodes

a) Node one, 80 % devastation

b) Node 1, xl % destruction

c) Node 5, 80 % destruction

d) Node five, 40 % destruction

e) Node 10, eighty % devastation

f) Node ten, 40 % devastation

g) Node 20, lxxx % devastation

h) Node 20, 40 % devastation

Fig. 17. Standard deviations of acceleration changes for different structure nodes for xl % and lxxx % devastation in the field of the Wavelet transform: a) 40 % of destruction, b) 80 % of devastation

a)

b)

Fig. eighteen. The results of the Wiener filter application on dam acceleration amounts before and later 40 % and eighty % destruction on some sample nodes

a) Node ane, 80 % destruction

b) Node 1, 40 % destruction

c) Node 5, 80 % devastation

d) Node v, 40 % destruction

east) Node 10, 80 % destruction

f) Node ten, 40 % destruction

g) Node 20, 80 % destruction

h) Node 20, 40 % destruction

The standard deviations of dispatch changes for unlike nodes of the structure in the field of Wiener transform for xl %, and lxxx % destruction are shown in Fig. 19.

It should be noted that all of the above transforms are linear and, every bit a result, the two operators of departure and transform can be moved, which will not bear on the results.

Fig. 19. Standard deviations of dispatch changes for dissimilar nodes of the structure in the field of Wiener transform for 40 % and 80 % devastation: a) 40 % of destruction, b) 80 % of destruction

a)

b)

5. Comparison of the efficiency of the suggested methods

In club to compare the efficiency of the presented methods in this paper, the standard deviations of unlike methods were initially reviewed. This quantity for 80 % of destruction is shown in Fig. 20.

Equally Fig. 20 show a transform of acceleration changes before and after the devastation on the construction, information technology is axiomatic that the methods providing more evident changes serve our purpose. Fig. xx illustrates that Fourier and Wavelet transform are better alternatives than Wiener transforms and the divergence of absolute value. Besides, the amounts of differences earlier and after application of devastation for each node in the Fourier transform is bigger than Wavelet. Information technology tin can be said that the Fourier transform is better than Wavelet and other methods in the detection of differences (destruction). In guild to present a more accurate comparison of the efficiency of dissimilar methods for the detection of the destruction in the dam, Fig. 21 shows the efficiency of each method.

Fig. twenty. The amounts of the standard deviations of acceleration changes for dissimilar nodes of the structure for 80 % devastation

a) DTFT of acceleration

b) Absolute of acceleration

c) Wiener of acceleration

d) Wavelet of acceleration

Fig. 21. The efficiency of the suggested methods for detection of destruction in the structure

The efficiency of the methods offered in this research for detection of destruction in the dam, based on the standard deviation of acceleration before and after destruction, is shown Fig. 21.

Amidst other approaches, the detection threshold is the i that best fits for devastation detection after the earthquake in both intact and damaged cases.

To extract the detection of each method, the devastation rate was gradually reduced and each time the dam acceleration amounts in different nodes (26 ones) were recorded and, post-obit that, the dam destruction detection curves were plotted. This process continued up to a point where the given algorithm was no longer able to detect the impairment.

For instance, Fig. 22 indicates the detection ability of the iv given methods for 5 % destruction.

Fig. 22. The efficiency of the proposed method based on a decibel (dB) for the detection of destruction in the dam

The curves of Fig. 22 accept been extracted via $\text{10}\mathrm{*}\mathrm{l}\mathrm{o}{\mathrm{g}}_{\mathrm{ten}}(.)$ an equation. According to the role curves of various methods based on decibel, the differences are negligible in the crest and lower nodes of the dam.

Equally it was seen, for small destructions (5 %), DTFT and Wavelet algorithms could easily detect the occurrence of destruction, though the Wiener algorithm had a weaker functioning. The range of differences in acceleration amounts or the absolute method could not discover the damage.

Fig. 23. A comparison of the detection threshold for the given methods regarding pocket-sized destructions detection

half dozen. Conclusions

In this newspaper, the beliefs of the intact and damaged dam after applying the earthquake was investigated via signal processing algorithms. The destruction in the Pino Apartment Dam was incurred by reduction of the elasticity module in some of the elements. To practise so, both fourth dimension and frequency domain algorithms were used. Later the awarding of the earthquake, the dispatch amounts of different nodes were recorded in the intact and damaged cases every bit ii signals with vector formats. In order to evaluate the difference between the signals, various indicate processing algorithms were applied to distinguish the differences betwixt the behavior of the intact and damaged structure at the time of the earthquake.

In this enquiry, Discrete-time Fourier Transform (DTFT), Wavelet transform, and Wiener transform were used to assess the dam in intact and damaged cases. To present a quantitative and precise analysis of the efficiency of each method, the standard divergence of the changes was considered, and its curves were plotted for the efficacy of different algorithms. According to the results obtained from the implementation of the mentioned approaches, it can exist claimed that DTFT had the nigh appropriate role, followed past Wavelet transform, which showed a shut efficiency to that of DTFT. This functional difference was exactly zero dB both in the crest and lower nodes of the dam. Also, the efficacy of DTFT and Wavelet was 10 dB better than that of Wiener transform and around 35 dB more than suitable than the time when the results of measurements are compared in a simple way and in the time domain. Signal processing algorithms draw the differences betwixt intact and damaged cases caused by the earthquake. Although the destruction occurred in the elements betwixt 5 and six nodes, as seen, dispatch amounts in different nodes vary, and these differences are apparent in the signal processing algorithms in this paper. Additionally, the detection threshold of the four mentioned methods was compared, and it was found that DTFT and Wavelet had a better function.

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Source: https://www.extrica.com/article/20202

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