probabilistic a pproach in a ssessing s tructural d amage...

Probabilistic approach in assessing structural damage using multistage artificial neural network using static and dynamic data

L. D. Goh1,2

, N. Bakhary1, A. A. Rahman

1, B. H. Ahmad

1

1 Faculty of Civil Engineering, Universiti Teknologi Malaysia,

81310 Johor Bahru, Malaysia.

e-mail: [email protected]

2 Faculty of Civil Engineering, Universiti Teknologi MARA,

13500 Permatang Pauh, Penang, Malaysia.

Abstract This paper addresses a probabilistic approach with consideration of uncertainties using a multistage

artificial neural network (ANN) in vibration-based damage detection. Because obtaining complete

measurement is a difficult task due to practical limitations, this paper also deals with a limited number of

measurements for damage detection by employing a multistage ANN to predict damage severity and

location. The multistage ANN consists of a two-stage ANN model. The first-stage ANN is to predict the

unmeasured structural responses based on the measured structural responses at the limited point

measurements while the second stage is for damage detection. The robustness of the proposed method is

demonstrated using the experimental static and dynamic data as the input parameters for the multistage

ANN. The results show that the proposed method is capable of considering random errors, thus providing

a reliable method for damage detection.

1 Introduction

An effective technique in assessing structural damage is vibration-based damage detection. The

underlying principle of the technique is that the occurrence of damage will cause a change in the physical

properties (mass, stiffness, damping) and dynamic properties (frequency response functions, natural

frequencies, damping ratios, and mode shapes) in a structure. Thus, by assessing the properties of a

structure, the damage information, such as location and the corresponding damage severity, can be

quantified. The advantages of this technique are that it is a nondestructive technique, and it does not

require knowing the damage location before assessing the structure, which is needed by local

nondestructive methods such as ultrasonic or acoustic techniques. Doebling et al. [1], Sohn et al. [2], and

Fan and Qiao [3] provide extensive overviews of vibration-based damage detection.

The effectiveness of techniques in vibration-based damage detection depends on the accuracy of the

structural model and the type of response data from the structures. The accuracy of the damage prediction

results is also highly dependent on the number of measurement points. Generally, the higher the number of

measurement points, the greater is the accuracy of the damage predictions. On the other hand, the effect of

uncertainties also leads to great shortcomings in assessing the actual condition of the examined structures.

Uncertainties associated with modelling and measurement data will cause false damage detection. To

ensure high accuracy in the damage assessment, uncertainty effects need to be addressed. This claim is

supported by the studies done by Yun and Bahng [4], Yun et al. [5], and Gonzalez-Perez and Valdes-

Gonzalez [6], whereby the authors imposed the noise injection method to consider uncertainties in

measurement data. Uncertainties always exist in damage identification procedures due to discretisation

errors, configuration errors, mechanical parameter errors, and measurement errors [7]. Techniques

introduced by various researchers to consider noise in measurement data include feedback control

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techniques [8], model reduction and expansion techniques [9, 10], model updating techniques [11, 12],

optimisation techniques [13], regularisation techniques [14], and artificial neural networks (ANN) [15–

17].

Other than the aforementioned techniques, a probabilistic approach makes researchers interested in

considering the effect of uncertainties on damage detection based on modal data. Zhang et al. [7] proposed

a probabilistic simultaneous identification method whereby the damage index and the damage probability

are derived from the statistical parameters of the physical parameters of undamaged and damaged

structures. Lam and Ng [18] employed a Bayesian probabilistic approach to compute the probability

density function (PDF) of the crack locations and their corresponding extents. A Bernoulli–Euler beam

was used to demonstrate the proposed approach. To incorporate measurement noise, a 3% white noise was

added to the calculated responses. Ng et al. [19] applied a two-stage probabilistic optimisation approach to

detect and characterise laminar damage in beam structures. The two-stage optimisation comprised

simulated annealing and a standard simplex search method. Jiang et al. [20] and Huang et al. [21] both

integrated two different techniques for damage detection using the response data contaminated with

uncertainties. Jiang et al. [20] combined a data fusion technique and probabilistic neural network models

to identify damage using measured response data, while Huang et al. [21] used the Bayesian model

updated with the extracted modal frequencies for identifying the global damage, and the damage index

method with the extracted mode shape for detecting local damage. Wang et al. [22] updated the dynamic

responses in both undamaged and damaged states and then compared the two probability distribution

characteristics in both models to obtain the probability of damage existence (PDE). The above methods

evidenced that the probability approach is capable of reducing the effect of uncertainties in damage

identification.

Hence, in this study, a probabilistic approach using a multistage ANN is proposed for structural damage

detection to predict the data at unmeasured points and to consider random errors resulting from modelling

and measurement errors. The input variables of the multistage ANN are the limited number of measured

responses while the output is the damage information. In this study, both dynamic data and static data are

used to demonstrate the applicability of the proposed method. The proposed probabilistic multistage ANN

consists of a two-stage model. The purpose of the first stage ANN is to predict the unmeasured structural

responses based on the measured structural responses from limited points. The combination of the

measured and predicted parameters from this first-stage ANN is then used as input into the second-stage

ANN to predict damage locations and severities. As uncertainties associated with modelling and

measurement errors have adverse effects on identification accuracy, in this approach, random errors are

introduced in the measured responses using the point estimate method introduced by Papadopoulos and

Garcia [23]. Thus, the output from the probabilistic multistage ANN is also statistical. The robustness of

the proposed method is demonstrated using the static and dynamic data from a laboratory-tested

prestressed concrete panel.

2 Probabilistic multistage ANN

This study applied feedforward backpropagation with one hidden-layer ANN model. The optimal number

of hidden neurons was determined through a trial and error process [24]. The tangent sigmoid transfer

function was applied in hidden layers while the linear transfer function was applied to the output layer.

The scaled conjugate gradient algorithm with an early stopping method was used in training to adjust the

weights and biases between the neurons in the network. The early stopping method was employed to

prevent an overfitting problem and poor generalisation during the training process [25]. The training data

were divided into three sets containing 70%, 20%, and 10% of the data, for training, validation, and testing

purposes respectively. The ANN models in this study were developed using the Neural Network Toolbox

that runs on the Matlab platform.

The schematic diagram of the probabilistic multistage ANN is shown in Figure 1. As mentioned earlier,

the first-stage ANN model (ANN1) is trained to relate the measured responses and the unmeasured

responses. The measured responses are divided in two: (i) modal data, which are frequencies and mode

shapes, and (ii) static displacements. These inputs are smeared with random noise by the mean of plus and

3778 PROCEEDINGS OF ISMA2014 INCLUDING USD2014

minus one standard deviation to both mode shapes and frequencies in the training data as proposed by

Papadopoulos and Garcia [23]. Errors () in both measured mode shapes and natural frequencies are

assumed to be normally distributed with zero means and specified variance. The noise is applied in terms

of the coefficient of variations. In this study, the uncertainties were taken as 3% for both mode shapes and

frequencies. Because there are two input variables employed for the multistage ANN, there are four main

functions in the ANN1 training. The outputs from the ANN1 are the unmeasured mode shape values from

the unmeasured measurement points.

Figure 1: Schematic diagram of the probabilistic multistage ANN model using dynamic data.

In the second-stage ANN (ANN2), the predicted mode shape values from ANN1 together with the input

variables of ANN1 (frequencies and measured mode shape values) are fed into the second-stage ANN.

The outputs of ANN2 are the Young’s modulus (E) values of each segment in the structure. Since the

input variables are in a statistical distribution, the outputs from the multistage ANN are also in a statistical

form. The statistical properties of E values are verified by the Monte Carlo simulation. The reliability of

the employed probability method in comparison with the Monte Carlo simulation in calculating the E

values has been demonstrated in Bakhary et al. [17]. After the probabilistic multistage ANNs have been

fully trained, each of the multistage ANN models is tested with testing data that are also smeared with

different combinations of plus and minus one standard deviation of random noise. The standard deviation

of E values of every segment is then calculated. Further details are provided in Goh et al. [26].

The two probability distributions of E values are compared for undamaged and damaged models to

compute the PDE value in each segment. In this study, the PDE values were used as an indicator of

damage existence. The higher the PDE value, the more severe is the damage. By setting the confidence

level at 95%, the lower bound of the undamaged model in the wth element is [E(Ew)-1.645σ(Ew)]. Thus by

referring to Figure 2, the PDE of any segment is defined as the shaded area in the figure, or:

) ) ∞)

= ∞

) (1)

where is the wth relative elemental stiffness for the undamaged model.

Figure 2: Schematic diagram of damage criterion PDE.

PDE

undamaged model

Lower bound = E(Ew) – 1.645 (Ew)

PDF undamaged

model

Measured mode

shapes values and

frequencies

Predicted mode shape

values at unmeasured points ANN1

ANN2

Location and

damage severities

STRUCTURAL HEALTH MONITORING 3779

Figure 3: Schematic diagram of the probabilistic multistage ANN model using static data.

In the application of the probabilistic multistage ANN in using the static data, all ANN parameters

employed in the network are similar to the parameters as utilised in the probabilistic multistage ANN

model, which uses the dynamic data. The input into the first-stage ANN was the limited measured

displacement data of the prestressed concrete panel. To consider uncertainties, the input data was smeared

with random errors of 3%. Because the model deals with only one variable as the input data, there are only

two training functions involved in the point estimate method, i.e.,

) and

), whereby

δ represents the static displacement. The output from the first-stage ANN is the predicted unmeasured

displacement data at the unmeasured point locations. For the second-stage ANN, the input is the

combination of the limited measured displacement data and the predicted unmeasured displacement data

from the first-stage ANN. The final outputs of the multistage ANN model are the E values of each

segment, which are used to calculate the PDE values. Figure 3 illustrates the schematic diagram of the

probabilistic multistage ANN model using the static data.

3 Experimental example

Experimental data of a prestressed concrete panel (Figure 4) were used to verify the proposed method. The

size of the prestressed concrete panel was 2.7 m 0.7 m 0.2 m. Four prestressing strands of 9.53 mm

each were embedded in the panel. The prestressing strands were placed at a 0.2 m distance from each

other with a 0.05 m concrete cover. The strands were made of seven low-relaxation, high-carbon steel

wires with a nominal steel area of 54.84 mm2. The strands were tensioned to approximately 71.61 kN,

which is 70% of the ultimate prestress force. The prestressing process was carried out using an external

hydraulic jack and cast with grade 50 concrete. The external strand anchors were released after the

concrete achieved the minimum designated strength of 35 N/mm2 at 7 days. The panel was supported at a

distance of 0.075 m from both ends.

A modal test was conducted on the prestressed concrete panel to obtain the intact data. To create damage

cases, six different static loads were applied in stages. The panel was loaded at 20 kN, 50 kN, 70 kN, 73

kN, 75 kN, and 79 kN. Figure 5 presents the loading configuration. Five linear variable differential

transformers were installed at the soffit of the prestressed concrete panel to record the displacement data

during each loading stage. Figure 6 presents the load-displacement responses of the prestressed concrete

panel at the midspan for all loading stages. At the end of each loading stage, a modal test was carried out

on the load-free panel.

Limited

measured

displacement

data

Predicted displacement data at

unmeasured points

ANN1

ANN2 E values


Figure 4: Prestressed concrete panel.

Figure 5: Loading configuration.

Figure 6: Load-displacement responses.

0

10

20

30

40

50

60

70

80

90

0 2 4 6 8 10 12

Lo

ad (

kN

)

Deflection (mm)

20 kN

50 kN

70 kN

73 kN

76 kN

79 kN

Load

1.0m

m 0.55m 1.0m 0.075m

m

0.075m

m


3.1 Finite element model

A finite element model of the prestressed concrete panel was prepared using the Structural Dynamic

Toolbox. The purpose of the numerical model is for data preparation to train the probabilistic multistage

ANN. The finite element model is modelled using the same geometrical and material properties as the

experimental model. The material properties of the prestressed concrete panel were elastic modulus of

3.6×1010

N/m2, density of 2456 kg/m

3, and Poisson’s ratio of 0.2. The material properties for prestressing

strands were elastic modulus of 2.0×1011

N/m2, density of 7385 kg/m

3, and Poisson’s ratio of 0.3. Four-

node quadrilateral Mindlin shell elements were applied for concrete in the numerical model. The

prestressing strands were idealised using pretension elements in SDT. The magnitude of the pretension

force applied in the strands was 71.61 kN. There were a total of 333 nodes and 432 elements in the finite

element model. For boundary conditions, all displacements were restrained along the global coordinate

axis at two simple supports at 0.075 m from both ends. The finite element model was divided into 10

segments for damage detection purposes, as depicted in Figure 7.

Figure 7: Segments on prestressed concrete panel model.

There is a total of 17 measurement points in the numerical model, which is considered the complete

measurement set as shown in Figure 8. In the application of the probabilistic multistage ANN using the

dynamic data, nine measurement data were measured at points 2, 4, 6, 8, 9, 10, 12, 14, and 16. The

remaining points 1, 3, 5, 7, 11, 13, 15, and 17 were considered the unmeasured points. Thus, the first-stage

ANN was used to predict the unmeasured data from the data obtained from the measured points. A total of

3,000 damage cases were generated from the finite element model for ANN training purposes. The

damages were imposed by reducing the E value at random segments.

Figure 8: Locations of the measurement points.

700 mm

225, 3@300, 2@225, 3@300, 225 = 2700 mm

700 mm

225, 6@150, 2@225, 6@150, 225 = 2700 mm

2 3 4 7 8 9 5 6 10 11 1 12 13 14 15 16 17

2 3 4 7 8 9 5 6 10 1


In the application of the probabilistic multistage ANN using the static data, there were five static

displacement data recorded for each loading stage. The measurement points were points 6, 8, 9, 10, and 12

(refer to Figure 8). These five static displacement data were considered as the input into the first-stage

ANN. Because the total of the measurement points in a complete measurement set was 17 points, the

remaining 12 points were considered unmeasured points, which were to be predicted by the first-stage

ANN. The static analysis was conducted using the similar finite element model of the prestressed concrete

panel. The static analysis was carried out for an applied load of 0 kN to 75 kN. A total of 6,400 training

data were prepared for ANN training purposes. Another probabilistic multistage ANN model was then

developed and trained based on the training data extracted from the finite element model of the prestressed

concrete panel.

3.2 Modal testing

Modal testing was performed on the intact prestressed concrete panel and at every loading stage in the

same way. The prestressed concrete panel was excited with an impact hammer (PCB Model 086D20) with

a black hard plastic tip (084A63) along the vertical. The sensitivity of the impact hammer was 0.23 mV/N,

and the measurement range was 22.24 kN pk. On the other hand, the acceleration responses of the panel

were measured using accelerometers (Kistler Model 8640A50) with a sensitivity of 100 mV/g. The

measurement range of the accelerometer was ±50 g. The accelerometers were installed by applying a thin

layer of petro wax between the bottom surface of the accelerometers and the concrete surface. Three tests

were performed at each measurement point, and an average was computed. The sampling frequency was

1,000 Hz. The frequency response function was calculated for all measured points, and the first four mode

shapes and the frequencies were analysed. Table 1 presents the frequencies computed from the finite

element model and the frequencies obtained from the modal tests on the panel for all the loading stages.

The frequencies from the finite element model and the experimental data show the existence of modelling

errors, which are due to the inaccuracy of material properties, nonideal boundary conditions, and nonlinear

structural properties. Thus, consideration of uncertainties in damage detection is essential to provide a

reliable output.

Damage state

Mode 1

(Hz)

Mode 2

(Hz)

Mode 3

(Hz)

Mode 4

(Hz)

Finite element 117.6 310.6 579.1 906.2

Intact panel 108.0 316.0 632 917

Loading stage of 20 kN 93.3 315.7 610.2 913

Loading stage of 50 kN 93.2 312.6 609 906.5



Loading stage of 75kN 89.3 292.6 580.2 882

Loading stage of 79 kN 68.9 253.1 568.9 855.5

Table 1: Natural frequencies obtained for intact and damaged states.


4 Results and discussion

The feasibility of the proposed method is demonstrated using the dynamic and static data as follows.

4.1 Probabilistic multistage ANN using dynamic data

This section presents the results of the probabilistic multistage ANN when applying the dynamic data to

predict the damage location and its corresponding damage severity. The results of the damage

identification are in the form of probability of damage existence (PDE) values. Table 2 presents the results

of the PDE values computed in all the damage states. Based on the loading configuration applied in this

study, bending failure is expected to take place. Thus, the PDE values in segments 5 and 6, which are

located at the midspan, are highlighted in the results to show the actual damaged segments.

Segments Loading Stage (kN)

20 50 70 73 75 79

1 0.5 1.1 0.2 5.6 10.3 5.1

2 2.8 10.3 0.8 0.1 3.0 0

3 6.0 0.4 0.1 4.9 2.5 0

4 6.9 16.5 0.5 7.0 15.6 19.3

5 24.9 26.4 39.8 47.1 75.3 74.4

6 29.0 39.2 43.3 57.7 74.2 80.8

7 1.2 13.3 11.5 0.5 3.8 0.1

8 0 5.2 5.6 0.6 1.3 13.4

9 9.8 0.3 11.5 4.4 1.3 0

10 0.9 1.0 1.8 12.7 9.3 1.5

Table 2: Results using the dynamic data.

Due to the loading configuration as described earlier, a flexure bending failure at the middle of the span of

the prestressed concrete panel is expected. From the table, it is observed that the PDE values are higher at

the actual damage segments 5 and 6 in all loading cases compared to other segments. This indicates that

the probabilistic multistage ANN is capable of detecting the location of the damage successfully. It is also

observed that the PDE values in the damaged segments increase as the damage severity increases. For

instance, the PDE value in segment 6 at the loading stage of 20 kN is 29.0%. The PDE value in segment 6

subsequently increased to 39.2% at the loading stage of 50 kN, 43.3% at the loading stage of 70 kN,

57.7% at the loading stage of 73 kN, 74.2% at the loading stage of 75 kN, and 80.8% at the loading stage

of 79 kN. A similar observation occurs with the PDE values in segment 5. The results correspond well

with the observation of crack propagation in the laboratory, where the cracks propagated farther when the

loads were increased.

Further observation of the PDE values obtained in segments 5 and 6 shows that the PDE values in these

two segments experienced a substantial increment after the loading stage of 73 kN. The PDE values

computed in segments 5 and 6 respectively are 75.3% and 74.2% at the loading stage of 75 kN, and 74.4%

and 80.8% at the loading stage of 79 kN. A substantial increment of the PDE values in the segments near

the middle span is due to the failure behaviour of the prestressed concrete panel under study. The first

crack was observed to occur near the midspan of the prestressed concrete panel at the loading stage of 73

kN. There was no crack observed in the first three loading stages in the beginning. The cracks in the

prestressed concrete panel propagated relatively quickly as the load increased after the loading stage of 73

kN since there was no reinforcement rebar other than the prestressed concrete strands to resist the applied


load. This explains why there were substantial increments of PDE values in the damaged segments after

the loading stage of 73 kN.

The effects of the structural nonlinearity and propagation error in the multistage ANN have caused some

of the segments to record a slightly high PDE value at the undamaged segments. For example, at the

loading stage of 50 kN, the PDE value in segment 4 was recorded as 16.5%. Another example is observed

in segment 4 of the loading stage of 79 kN where the PDE value computed was 19.3%. The nonlinearity

effect usually exists in the structural system identification, as explained in Kerschen et al. [27]. The

propagation error occurs due to the multiplication procedures involved during the computation of the

ANN. However, as compared to the deterministic approach, the probabilistic approach can partially

remove the effects of uncertainties on the damage detection results.

4.2 Probablistic multistage ANN using static data

This section further demonstrates the application of the probabilistic multistage ANN in using static data.

The static displacement data were obtained during the static test conducted in the laboratory on the

prestressed concrete panel. The aim of the extended study was to establish the robustness of the proposed

approach in applying both dynamic and static data to detect damage. The recorded static displacement data

from five points were utilised as the input into the multistage ANN. The multistage ANN predicted the

displacement data at the remaining 12 points before providing the outputs for the PDE computations.

Table 3 tabulates the results of the PDE values computed. The PDE values in segments 5 and 6 are

highlighted in the table to show the actual damaged segments.

Segment Load (kN)

21.4 31.7 41.5 51.5 56.5 61.8 66.3 71.5 73.8 75.3

1 0 0.4 0 0 0 0 0 0 0 0

2 0 2.2 0 0 0 0 0 3.2 0 0

3 0 13.8 15.0 0 0 0 0 0 0 0

4 0.1 8.1 8.2 0.1 0 0.5 15.2 49.6 100 97.8

5 12.1 12.8 10.6 11.6 10.6 26.4 79.5 52.8 100 100

6 10.5 11.5 11.4 9.2 55.7 58.4 99.9 90.1 100 100

7 0 8.3 11.4 9.2 1.7 2.2 69.9 99.9 100 100

8 4.3 1.4 0.4 0 0 0 0 0 0 0

9 0.5 8.9 8.7 4.6 1.3 2.9 0.1 0.5 0 0

10 0 8.8 6.7 2.6 0.8 2.2 0.0 1.5 0 0.4

Table 3: Results using the static displacement data.

From the results presented in the table, it is observed that when the load is low, the PDE values recorded at

the midspan are low. For example, the PDE values recorded at segments 5 and 6 for the first four loading

stages are below 14%. This shows that there is only minimal internal damage, which may have just started

to take place. As the loading increases, the PDE values are observed to increase in the damaged segments.

This indicates that the PDE values are consistent with the damage severities.

At the loading stage of 56.5 kN, there are substantial increments of PDE values at the damaged segments

near the midspan compared to the previous loading stages. The PDE value recorded in segment 6 is 55.7%

at the loading stage of 56.5 kN, while the PDE value recorded in the same segment for the loading stage of

51.5 kN is 9.2%. The substantial increase in the PDE value between these two stages may be due to the

possibility of the development of internal cracks in the prestressed concrete panel. The PDE values at the

damaged segments were observed to experience a gradual increment from the loading stage of 56.5 kN.


However, the PDE values recorded at both damaged segments 5 and 6 at the loading stage 71.5 kN show a

slight decrement compared to the PDE values recorded in the same segments of the preceding loading

stage of 66.3 kN. This may be due to the open and closed crack phenomenon. During the loading stage,

the cracks would be fully open above a zero load. The cracks can be closed at the crack tip for up to half

of the loading amplitude. This explains why the PDE values were reduced to 52.8% and 90.1% in

segments 5 and 6 respectively at the loading stage of 71.5 kN even though the loading increased.

Furthermore, the sizes of the cracks were observed to develop slightly wider and the crack length

propagated.

The PDE values were recorded at 100% at both damaged segments 5 and 6 at the loading stages of 73.8

kN and 75.3 kN. This affirms that the damage took place at the midspan of the prestressed concrete panel.

However, the PDE values of the neighbouring segments (segments 4 and 7) of the damaged segments at

the midspan (segments 5 and 6) provided by the multistage ANN were found to be relatively high. A

possible explanation for this is that the effect of nonlinearity caused the neighbouring segments of the

damaged segments to record relatively high PDE values.

The outcomes of the findings in this study prove that the proposed approach is not only feasible to apply

with dynamic data but also with the application of static displacement data. Hence, it is concluded that the

proposed method is a robust one to detect damage location and severity with the use of only a limited

number of measurement points. The accuracy of the results is not jeopardised even with the utilisation of a

limited number of measurement points.

5 Conclusion

This paper presented a probabilistic multistage ANN using a limited number of measurements with the

consideration of uncertainties. The feasibility of the proposed method was demonstrated using limited

measured static and dynamic data of a laboratory-tested prestressed concrete panel. The limited measured

static and dynamic data that were employed as the inputs into the probabilistic multistage ANN were

incorporated with 3% random noises. The results proved that the proposed probabilistic multistage ANN

is capable of identifying damage locations and provides a high probability of damage existence value in

the damaged structural segments when using either the static or dynamic data. This indicates that the

proposed method yields a reliable and robust approach to detecting structural damage, especially when

uncertainties are involved that resemble actual experimental conditions

Acknowledgements

Part of this study is funded by Exploratory Research Grant Scheme (ERGS), under VOT No.

R.J130000.7822.4L101, Universiti Teknologi Malaysia, and Ministry of Higher Education (MOHE)

Malaysia.

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