Structural Health Monitoring - CiteSeerX

Structural Health Monitoring http://shm.sagepub.com

The Use of Vibration Data for Damage Detection in Bridges: A Comparison of System Identification and Pattern Recognition Approaches N. Haritos and J. S. Owen Structural Health Monitoring 2004; 3; 141 DOI: 10.1177/1475921704042698 The online version of this article can be found at: http://shm.sagepub.com/cgi/content/abstract/3/2/141

Published by: http://www.sagepublications.com

Additional services and information for Structural Health Monitoring can be found at: Email Alerts: http://shm.sagepub.com/cgi/alerts Subscriptions: http://shm.sagepub.com/subscriptions Reprints: http://www.sagepub.com/journalsReprints.nav Permissions: http://www.sagepub.com/journalsPermissions.nav

Downloaded from http://shm.sagepub.com at PENNSYLVANIA STATE UNIV on April 16, 2008 © 2004 SAGE Publications. All rights reserved. Not for commercial use or unauthorized distribution.

The Use of Vibration Data for Damage Detection in Bridges: A Comparison of System Identification and Pattern Recognition Approaches N. Haritos1, and J. S. Owen2 1

Department of Civil and Environmental Engineering, The University of Melbourne, Parkville, Victoria, 3010, Australia 2 School of Civil Engineering, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom This paper briefly outlines the rationale for structural health monitoring as an integral component of bridge management systems. Two different approaches, system identification and statistical pattern recognition, are summarised and applied in turn to vibration data collected from three scale modelreinforced concrete bridges. The results show that the system identification paradigm can successfully locate and quantify the damage to the decks when they are loaded to incipient collapse, especially when experience is used to determine the parameters to use in the finite element updating procedure. However, the study also demonstrated that this approach requires a large amount of high quality data, requirements that cannot always be met readily in the field. In contrast, although the statistical pattern recognition approach was not able to quantify or locate the damage, it was able to clearly indicate that damage had occurred from relatively few measurements. A comparison of the strengths and weaknesses of the two approaches suggests that they should be used in a complementary manner. The statistical pattern recognition approach can be employed as a simple, cost efficient way to indicate that damage has occurred. It can then trigger a more detailed investigation using system identification. Keywords

bridges finite elements structural health monitoring modal analysis artificial neural networks

1 Introduction Road Transport Authorities (RTAs) of countries throughout the world have the responsibility of maintaining the safe and efficient road networks that are important for a nation’s economic development. A key element of any road network is the bridge infrastructure. Also, bridge mainte-

nance is becoming an increasingly important issue in most developed countries. Limitations in the budgets available to RTAs for bridge maintenance, rehabilitation, and reconstruction programs necessitate implementing comprehensive Bridge Management Systems (BMSs) that can accurately prioritise this expenditure. This in turn requires that reliable condition assessment proce-

*Author to whom correspondence should be addressed.

Copyright ß 2004 Sage Publications, Vol 3(2): 0141–163 [1475-9217 (200406) 3:2;141–163; 10.1177/1475921704042698]

141


142

Structural Health Monitoring 3(2)

dures be implemented on bridges to feed into the BMSs. While periodic visual inspections provide a generally economical means of condition assessment, they tend to be subjective so that reported results can vary from operator to operator. Evidence gathered for an FHWA study on visual inspection [1] indicated significant variability in routine inspections and that a significant proportion of in-depth inspections do not reveal deficiencies beyond those that could be noted during a routine inspection. The latter point demonstrates a further problem with visual inspection, that any non-visible degradation of the bridge could remain undetected by visual inspection alone and the bridge could become compromised. Structural health monitoring (SHM) systems, based upon some form of bridge response measurements, can be used to alleviate some of the shortcomings of traditional visual inspection techniques. Ideally, the SHM system should be inexpensive, non-invasive and automated, so that subjective operator differences are avoided. In particular, neither the implementation nor operation of the system should involve closure of the bridge. Vibration data are ideally suited as the basis for such an SHM system; they are cheap to collect, give a picture of the global response from relatively few sensors, and they can be used to identify changes in stiffness associated with damage from changes in the modal parameters. A reduction in stiffness will lead to a reduction in natural frequency and a change in distribution of stiffness will lead to changes in mode shape. Recently, much research has been directed towards developing a robust SHM system based on the vibration data, principally in the fields of mechanical and aerospace engineering. Generally, a forced excitation is used to obtain the vibration data and hence the modal parameters, and these are then compared with computational models to predict the location and severity of damage. The application of these methods to civil engineering structures, and bridges in particular, has led to several studies on full-scale bridges e.g. [2,3], laboratory models e.g. [4–6] and computational simulations e.g. [7–9]. There are several detailed reviews of SHM methodology

for civil engineering and the growing literature in the field [10–12]. 1.1 System Identification Paradigm Traditionally, vibration data for SHM or damage detection have been processed according to a system identification paradigm, the aim being to obtain the modal characteristics and track changes. Early work by Cawley and Adams [13] proposed using sensitivity matrices to detect damage and this concept has since developed into the new discipline of model updating [14]. Here, Finite Element Analysis (FEA) models of the structure are modified by combining a sensitivity matrix, based on eigenvalues, eigenvectors and/or FRFs, with the differences between FEA predictions and experimental results. The application of this approach to damage detection is readily apparent; given an accurate FEA model of the undamaged structure, any subsequent updating using vibration data from a damaged structure will result in changes to the FE stiffness matrix that correspond to the damage. Parameters chosen for updating the FEA model of a reinforced concrete (RC) bridge would include effective flexural– torsional rigidities of the deck and boundary– stiffness conditions at supports. Although this approach would also be sensitive to changes in stiffness that arise due to other effects, such as thermal expansion, inference can be drawn from the location and severity of the stiffness change as to whether it is associated with damage. Much of the work considering system identification for SHM of bridges has been based on modal data and there has been some debate as to whether natural frequencies, mode shapes or curvature mode shapes are the best monitoring variables. For bridge testing, the measurement of reliable modal parameters is hindered by environmental factors [15], traffic, and even the shear size of the structure. Moreover, it is often necessary to rely on ambient excitation from traffic and wind to obtain the test data, instead of a forced excitation [16]. The difficulties in obtaining sufficiently robust and reliable modal estimates for bridges have led to more recent works considering alternative signal processing techniques for the damage detection problem, such


Haritos & Owen

Vibration Data for Damage Detection in Bridges

143

as wavelets and other time–frequency methods [17–19]. Some studies have also noted the inherent non-linear behaviour of damaged structures and have applied non-linear system identification techniques [20,21].

This paper will use data obtained from a series of tests performed on scale model bridges at the University of Melbourne to compare the system identification and statistical pattern recognition paradigms for SHM.

1.2 Statistical Pattern Recognition Paradigm

2

In light of these difficulties in obtaining sufficiently robust and reliable modal estimates, an alternative approach to SHM has been suggested based on making a statistical comparison between signals in order to distinguish between different structural conditions. This may involve grouping similar signals representing a given damage state – the classification problem – or identifying when signals change due to damage – the novelty detection problem. In both approaches the raw data are preprocessed to obtain a reduced data set, for example by fitting an auto-regressive (AR) model [22] or by using principal component analysis (PCA) [23] in either the time or frequency domains. Comparisons between the different data sets are then made using a distance measure, such as the Mahalanobis squared distance [24] and the results used to either group the data sets, classify, or detect changes. The classification or novelty detection can be performed simply by plotting the distance data against time, but the statistical pattern recognition approach is particularly suited to the use of artificial neural network (ANN) techniques [25,26].

2.1

Laboratory Tests on Flat Slab Bridges Description of Model Bridges

Three model RC flat slab bridges (40% scale model) were constructed and tested in the Francis Laboratory of the University of Melbourne. The models had variations in features common to a major class of such bridges built in the State of Victoria predominantly in the period from 1920 to 1940. The basic flat slab bridge configuration chosen for the test series consisted of five continuous spans corresponding to the prototype dimensions of 1.6 m for the cantilever end spans, 3.65 m for the first interior span, and 4.57 m for the central span (Figure 1(a)). The cross section variations for the three models, Models#1–#3, are illustrated in Figure 1(b). Models#1 and #2 possessed three pier columns at each pier-line (cast to form a column stub as can be seen in Figure 1(a)), while Model#3 possessed four such pier columns per pier-line. The model flat slab bridges simply rested on their truncated piers (column stubs) on top of a 360-mm deep steel beam running the full width of the deck at each pier-line. Model#1 7.4m

Model#2 6.7m 7.4m

Model#3 8.5m 0.25m 1.6m

Pier 1

3.65m

4.57m

Pier 2

3.65m

Pier 3 (a)

1.6m

9.2m

Pier 4 (b)

Figure 1 Schematic representation of model flat slab bridges (prototype dimensions): (a) plan and longitudinal; (b) transverse section.


144


Figure 2 Schematic of primary reinforcement layout and deck section capacity (1 m width).

Critical flexural region Figure 3

Critical region in bending moment diagram for collapse level load tests.

The primary reinforcement layout for this style of flat slab bridge is illustrated in Figure 2. A key feature of this layout is the ‘‘crank down’’ of selected top bars close to where the haunches meet the flat portions of the slab section on either side of the pier supports. This ‘‘crank down’’ leads to a significant reduction in negative moment capacity of the bridge slab in the central regions of internal spans (Figure 3). So these ‘‘crank down’’ locations become possible candidates for plastic hinge formation in the development of plastic collapse mechanisms for this style of flat slab bridge. 2.2 Static Tests The initial aim of the tests was to investigate the capacity of these bridges by applying static loads.

The sequence of static tests included a number of serviceability level load configurations and two configurations with concentrated axle loads at the cantilever tips (one for each end of the bridge) taken to incipient collapse levels. The critical region for flexural demand in the deck associated with the collapse level loading condition essentially straddles the first pier extending just beyond the reinforcement ‘‘crank down’’ locations on either side (see Figure 3). It is this region (at both ends of the bridge) that suffered the most damage in terms of flexural crack formation, and hence reduction in flexural rigidity, upon completion of the first stage of static testing. Following these initial tests, two of the models were repaired using Fibre-Reinforced Polymers (FRP) and re-tested statically using the same testing sequence.


Haritos & Owen


2.3 Dynamic Tests

damage to the hammer meant that the impact force could not be recorded for every test case. Measurements of the resultant vibration response of the deck were made using 15 accelerometers distributed across the deck slab. Both excitation (when possible) and response were captured and stored by the PC-based data acquisition system (DAS). The response record for each data channel consisted of 2048 data points sampled regularly over a 4-s period. The response records for two typical accelerometers, ‘‘L1’’ and ‘‘O’’, captured simultaneously, are depicted in Figure 4.

The opportunity arose to incorporate a series of dynamic tests on the flat slab bridge models during the static test program, to investigate the efficacy of dynamic response measurements in structural system identification (SSI) and damage detection. However, the tight time constraints on this program limited the extent of the dynamic testing to conditions before and after major static load increments. Testing was performed using an instrumented hammer to provide the excitation in the form of a staggered double blow, although

“L1”

1 0 -1

145

(m/s2)

2

“O”

0 -2 0

1

4

3

2

Time (s) Figure 4

Typical accelerometer response records (flat slab bridge model#1 – before static tests). BOTTOM

A9 A1

E8

BOTTOM

H9

A2

A3

D1

E5

G3

A4

A5

D2

E7

E6

D3

A6

A7

B7

E4

E3

B1

B2

B3

E1

E2

B4

B5

B6

F6

F5

C4

C5

C6

C7

F4

C1

C2

C3

F1

F2

D8

I9

G2

G1

I3

I2

I1

L3

L2

L1

G4

G6

I4

I5

J6

I7

L4

L5

G5

G7

G8

I8

J8

L8

L7

L6

H2

H1

J3

J2

J1

M3

M2

M1

H3

F7

J4

J5

J6

J7

M4

M5

D7

H4

H6

H7

K4

K5

K6

K7

M6

F3

H5

O

K3

K2

K1

M8

M7

N

K8

A8

B9

D4

C9

B8

C8 D5

E9

F8 D6

F9

M9

H8

G9

IMPACT

Fixed Positions

Roving Positions

Figure 5 Typical data capture grid (flat slab bridge model#1 – before static testing). Accelerometers are identified by letters (‘‘A’’ through ‘‘O’’), while test sequence is identified by a numeric suffix.


146


A typical measurement grid used for the dynamic tests is illustrated in Figure 5, which shows the measurement grid for Flat Slab Bridge Model#1. To achieve the required spatial resolution with only a limited number of sensors, the tests were carried out in stages, each having a sequence of between 40 and 50 hammer tests. Between sequences, two of the accelerometers (‘‘N’’ and ‘‘O’’) were retained at fixed locations, while the remainder were relocated to new positions on the measurement grid. Seven longitudinal grid lines (two edges, three pier-lines and two in between the pier-lines) and fourteen transverse grid lines (at half span for the cantilever ends and at one-third span for the internal spans) produced a total of 98 measurement positions on the grid.

3

Damage Detection Using System Identification Procedures

3.1 Experimental Modal Analysis Based Upon FRF Measurements Ewins [27] identifies a general class of frequency domain-based modal identification methods described as experimental modal analysis (EMA) testing techniques. These techniques require identification of the frequency response functions (FRFs) for each response measurement location on the measurement grid of the structure under test obtained from a controlled form of excitation (such as an impact device or some form of shaker). Estimates of the FRFs, h~jk ð!Þ, are obtained via: X ð!Þ h~jk ð!Þ ¼ j Fk ð!Þ

ð1Þ

where Xj ð!Þ and Fk ð!Þ are the Fourier Transforms of xj(t), the displacement response at point ‘‘j’’, and fk(t), the excitation force at position ‘‘k’’, respectively. ‘‘Ensemble averaging’’ of several realisations of h~jk ð!Þ obtained from repeat tests is normally required to reduce the effect of measurement ‘‘noise’’ for subsequent processing by suitable EMA algorithms. The EMA algo-

rithms seek to fit modal properties (mode shapes, natural frequencies and damping ratios) contained in the theoretical form of the FRF, hjk ð!Þ, given by: N X ’jn ’kn ’jn ’kn þ hjk ð!Þ ¼ ði! n Þ ði! n Þ n¼1

ð2Þ

in which ’jn and ’kn represent the jth and kth elements of the complex eigenvector for the nth mode shape of vibration and n is the complex eigenvalue for this mode, and the symbol ‘‘*’’ represents complex conjugation. Commercially available EMA packages normally exercise a two-stage fitting procedure to obtain estimates of the modal properties from the experimentally obtained FRFs. The complex eigenvalues, n, are first estimated followed by a linear least squares fitting procedure to establish the eigenvectors. The Direct Simultaneous Modal Analysis (DSMA) algorithm [28] is an alternative approach which has been found to exhibit superior performance over conventional methods. This uses a non-linear least squares fitting procedure described by: X

min fs , ’jn g ! ¼ ! min ... !max

X k

N X ~ hjk ð!Þ j¼1

2 !! M X ’jn ’kn ’jn ’kn þ ði! n Þ ði! n Þ n¼1

ð3Þ

where !min, !max represent the minimum and maximum values of circular frequency pertinent to the test results. 3.2 ‘‘Simplified’’ EMA A ‘‘Simplified’’ form of Experimental Modal Analysis (SEMA) can still be performed on a structure in the event that measurement data for response alone is available. This situation normally arises in practice when it is not possible to measure the excitation force, such as when ambient excitation is used on bridges. Here, the assumption is made that response measurements are dominated by ‘‘resonant’’ modes at their


Haritos & Owen


corresponding natural frequencies. This assumption is reasonable for those modes that are sufficiently ‘‘separated in frequency’’, but is violated by ‘‘closely-spaced’’ modes. The method is based on the relative response function, (RRF), defined by: Xq ð!Þ R~ qo ð!Þ ¼ Xo ð!Þ

ð4Þ

in which Xq(!) and Xo(!) are the Fourier transforms of the measured response records at locations ‘‘q’’ and ‘‘o’’ respectively, in which ‘‘o’’ is treated as the ‘‘reference’’ point. Now, Xq ð!Þ ¼

N X

hqk ð!ÞFk ð!Þ

ð5Þ

k¼1

where Fk(!) would correspond to the Fourier transform of the force trace at point ‘‘k’’ on the grid and hqk(!), is as described by Equation (2). Substituting Equation (5) into Equation (4), the RRF, Rqo(!i) (at a circular frequency ! corresponding to one of the natural frequencies !i), can be approximated to: Rqo ð$i Þ ¼

Xq ð$i Þ ’qi Xo ð$i Þ ’oi

ð6Þ

provided that the ‘‘separated modal frequency’’ assumption holds good for mode ‘‘i’’. Under these circumstances, the RRF reduces to the ratio of the modal amplitudes of mode ‘‘i’’. Modal frequencies can be ascertained from inspection of So(!), the autospectrum of response at the reference location. Locations in frequency of well-defined peaks in this spectrum correspond closely to natural frequencies of participating modes in the response. Model Parameters

Update

FEA Model

Predicted Modes

Dynamic Test (EMA/SEMA)

Observed Modes

147

While this simplified approach is capable of determining modal frequencies within the frequency resolution (¼ 1=T where T is the timelength-of-record) of the response measurement data and mode shapes to an accuracy dependent upon the number of ensemble averages, it cannot directly determine the level of damping in these modes. Under these circumstances, the Random Decrement (Randec) method can be applied to time domain traces of response measurements to obtain estimates of both the natural frequency and damping value associated with a chosen level of response [29].

3.3

Structural System Identification using FEA Model Updating

Finite Element Analysis model updating has developed rapidly in the past ten years and several systematic methodologies have been established to automatically update FE models. However, civil engineering structures are not best suited to these approaches because of their indeterminate nature and variable support conditions. Therefore a simplified manual approach (Figure 6) is often applied for structures like bridges. An FEA model of the structure under investigation is set up and initial values of parameters selected for model updating are then chosen. The FEA mesh is defined so that it constitutes a superset of the measurement grid adopted for performing dynamic response measurements. Engineering judgement is required to choose appropriate parameters for updating, and typically these would include the support conditions and the flexural and torsional stiffnesses of selected regions of the deck, for a RC bridge.

No Matching Criteria

Yes

OK

Figure 6 SSI procedure using FEA model updating.


148


A modal analysis is then performed on this first-cut FEA model to produce details of the mode shapes and corresponding natural frequencies of vibration. These modes are then compared with corresponding modes determined from an EMA (or SEMA) of the experimental response data. Criteria that can be used as a measure of how well the predicted modes match their observed counterparts would include how closely predicted modal frequencies correspond to the observed frequencies and how well correlated the corresponding associated mode shapes happen to be. The updating parameters selected earlier are then revised according to the correlation criteria, either systematically using sensitivity matrices or using engineering judgement. The process is then repeated until a satisfactory match is achieved and the resultant FEA model would then be considered ‘‘calibrated’’.

outlined in Figure 6 until satisfactory FEA model calibration was achieved. In the case of the damaged test condition, parameter chosen for the FEA model updating was simply the effective bending thickness of the plate element groups straddling the first pier-line from either end of the bridge. This included the haunched region of the deck and progressed for an additional line of elements past the crank-down location of the primary reinforcement, which is essentially the region identified in Figure 3 as the ‘‘critical flexural region’’ where significant cracking would be expected at incipient collapse. In this way the FEA updating procedure could be used to identify and quantify local damage in the bridge decks. Values of Young’s modulus established from investigation of the undamaged test condition were retained in the FEA models of the flat slab bridges in their damaged state.

3.4 Implementation of System Identification Methodology

4

The procedures outlined above were applied to the dynamic test data collected from all the three model flat slab bridges at selected stages of the static testing program that included the pre-test (undamaged) and post-test (damaged) condition states. FEA modelling was based on the STRAND6 [30] linear elastic modelling package using plate elements for the deck, locally thickened to model haunching, and offset beam elements for the kerb beams, where present. In the case of the undamaged test condition, parameters chosen for the FEA model updating in each model bridge configuration were the Young’s modulus of concrete for the deck (together with gross section properties) and the support condition at individual column stubs. Although all column stubs were treated as restrained vertically at their supports, the strategy for obtaining the horizontal support conditions for each pier-line allowed for two combinations: either the outer pair of column stubs were treated as horizontally fixed and the central columns free to slide in both horizontal directions, or vice versa. A systematic ‘‘trial and error’’ approach was then adopted that exercised the FEA model updating procedure

System Identification, Results from Flat Slab Models

4.1 Before Static Testing – Flat Slab Bridge Model#1 (undamaged) Figure 7 presents a comparison of a selection of modes from performance of the dynamic tests with those obtained from the FEA model updating procedure for Flat Slab Bridge Model#1 in the undamaged state. The FEA model adopted here was based upon symmetrical support conditions at the pier-column stubs. The first pier-line from each end allowed the internal column stubs to move in both horizontal directions whilst the external column stubs were fixed, whereas the opposite condition was introduced at the second pier-line from each end. A Young’s modulus value of 28 GPa, consistent with a concrete strength of 32 MPa, was required to achieve the close frequency match of the modes identified. Both SEMA and EMA (based upon the DSMA algorithm) were performed on the experimental data and the results for the selected modes are presented in Figure 7. These modes have been chosen to highlight some of the peculiarities of these two techniques when exercised in SSI studies. Both natural frequencies and mode


Haritos & Owen

DSMA


SEMA

66.0 Hz

FEA

65.3 Hz

66.0 Hz Mode#3

83.6 Hz

Mode#5

Mode#2

83.5 Hz Mode#4

88.7 Hz

Mode#2

Mode#1

Mode#1

149

85.9 Hz Mode#3

Mode#6

89.2 Hz

88.5 Hz

Mode#8

Mode#6 Mode#4

113.9 Hz

Mode#9 115.1 Hz

115.2 Hz

115.1 Hz Mode#10

120.3 Hz

Figure 7 Comparison of a selection of experimentally estimated modes with FEA (flat slab model#1 – undamaged).

shapes were used to compare measured and predicted vibration modes, comparisons between mode shapes being made using the modal assurance criterion (MAC). The results presented for the first mode for both DSMA and SEMA are highly correlated with the FEA model results (MAC > 0.95 with closely matched natural frequency estimates). Results for the next pair of modes presented show distinct differences, although the natural frequency estimates are within 5% of each other. Whereas the DSMA algorithm has been able to distinguish these modes clearly (MAC > 0.92 for

the separate modes), the SEMA analysis produced ‘‘quasi-modes’’ that appear as different realisations of a weighted superposition of the two true modes. Consequently MAC values for the SEMA results show significant correlation with both the FEA modes, which is dependent on modal participation. For the SEMA ‘‘quasimode’’ representation at 88.5 Hz, the dominant contribution comes from the torsional mode and this is reflected in the significantly higher MAC value with the FEA mode at 89.2 Hz (mode#6) compared with the flexural mode at 85.9 Hz (mode#5).


150


The next pair of modes presented shows similar features to the earlier pair, except that modal frequencies are now more closely spaced. Again the DSMA algorithm has successfully decoupled these modes, whilst SEMA suggests only one mode in this region – a ‘‘quasi-mode’’ that, again, appears as a weighted superposition of both the true modes. It is clear that SEMA has limitations compared with traditional EMA in SSI applications. However, if a sufficient number of separated modes are present in the data analysed and/or close scrutiny is exercised in the interpretation of ‘‘quasi-modes’’, the SEMA technique can still be valuable to the performance of SSI through the FEA model updating.

EMA

55.8 Hz

FEA Mode#2

Mode#5

90.5 Hz

90.7 Hz

Mode#6

79.1 Hz Mode#6

Mode#7

123.0 Hz

Mode#2

55.8 Hz

56.0 Hz Mode#6

123.3 Hz

Mode#14

120.2 Hz Mode#8

Mode#9

Figure 8

Figure 8 presents a comparison of a selection of experimental modes with those obtained from the FEA model updating after damage had been introduced to Flat Slab Bridge Model#1. The set was chosen on the basis that ‘‘separated modes’’ only from the SEMA analysis were to be depicted (MAC > 0.95 between FEA and SEMA). The FEA model was modified using the procedure outlined in Section 3.4 and Figure 6, resulting in a 30-mm reduction in effective plate bending thickness for all elements in the ‘‘critical flexural region’’ straddling the first pier from either end of the slab. This resulted in a sliding reduction in bending–torsional stiffness over the haunched region of approximately 50–65%. The match in natural frequency and mode shape between the experimental modes and the

SEMA Mode#2

159.8 Hz

4.2 After Static Testing – Flat Slab Bridge Model#1 (Damaged)

160.0 Hz

Mode#16

130.5 Hz

Comparison of a selection of experimentally estimated modes with FEA (flat slab model#1 – damaged).


Haritos & Owen


updated FEA model, as presented in Figure 8, is considered to be acceptable, given the limitations of the modelling strategy adopted. However, the torsional and plate-like modes in the test results appear to be ‘‘stiffer’’ (exhibit a significantly higher modal frequency) than their corresponding FEA model predictions. This would imply that the cracking pattern in the damaged region of the slab is more effective in reducing bending stiffness and less effective in reducing torsional stiffness in the actual slab. This agrees with the predominantly transverse cracking pattern observed on the deck. An FEA modelling strategy in which the damaged region of the slab is modelled using a uniform reduction in plate bending thickness cannot distinguish between non-commensurate bending and torsional stiffness effects, resulting in the differences observed in the modal ‘‘match’’. Comparing modes presented in Figure 8 with those in Figure 7, it is clear that the effect of

extensive cracking in the ‘‘critical flexural region’’ of the slab has lead to a substantial reduction in modal frequencies of similar modes. In addition, the localised region of damage has modified the shape of these modes, as a result of the increased local flexibility in this region. Further, the sequence, or ordering of the modes, can also change and new or different modes may be observed, especially higher up the modal sequence. 4.3

Results for Flat Slab Bridge Model#2

Figure 9 presents a comparison of a selection of experimental modes with those obtained from the FEA model updating procedure for Flat Slab Bridge Model#2, before and after damage was introduced. The results presented were chosen on the basis that only reasonably ‘‘separated modes’’

Before Damage SEMA

151

After Damage FEA

FEA

SEMA

71.0 Hz

71.4 Hz

59.3 Hz

59.7 Hz

96.3 Hz

95.4 Hz

93.0 Hz

87.7 Hz

99.0 Hz

101.4 Hz

72.3 Hz

86.7 Hz

140.5 Hz

127.2 Hz

123.5 Hz

112.8 Hz

Figure 9 Comparison of a selection of experimentally estimated modes with FEA (flat slab model#2 – undamaged and damaged).


152


from the SEMA analysis were to be considered, with MAC > 0.8 between SEMA and FEA modal predictions. EMA was not performed in either test state since the impact force was not measured. Modes with largely similar features between undamaged and damaged test states have been chosen in the comparison. The FEA model was based on that of Flat Slab Bridge Model#1 modified to include the presence of kerb beams running the length of the bridge. In updating the FEA model for the case of the damaged condition for this bridge model, the stiffness of the kerb beams was reduced by 50%

along the length of the ‘‘critical flexural region’’, while the plate bending thickness of the elements in the slab portion of this deck region was reduced by 30 mm. As was the case for Flat Slab Model#1, the resultant modal match between SEMA and FEA results for both test states is considered to be acceptable. Again, it is observed in Figure 9 that extensive cracking in the ‘‘critical flexural region’’ of the slab has lead to a substantial reduction in modal frequencies of similar modes. It has also modified the shape of these modes, as a direct consequence of the increased local flexibility in this region.

Before Damage SEMA

After Damage FEA

FEA

SEMA

65.3 Hz

65.6 Hz

50.5 Hz

49.9 Hz

75.5 Hz

77.9 Hz

61.0 Hz

66.1 Hz

83.8 Hz

85.8 Hz

75.5 Hz

69.5 Hz

121.3 Hz

115.3 Hz

101.5 Hz

115.1 Hz

169.5 Hz

147.2 Hz

140.8 Hz

134 Hz

Figure 10 Comparison of a selection of experimentally estimated modes with FEA (flat slab model#3 – undamaged and damaged).


Haritos & Owen

4.4


Results for Flat Slab Bridge Model#3

Figure 10 presents a comparison of a selection of experimental modes with those obtained from the FEA model updating procedure for Flat Slab Bridge Model#3. Where possible, modes with largely similar features between undamaged and damaged test states have been chosen in the comparison. The FEA model updating strategy for the slab and kerb beams largely paralleled that adopted for Flat Slab Bridge Model#2, except for one significant difference; more extensive damage over the ‘‘critical flexural region’’ associated with the Pier#1 end of the bridge, as a result of the static loading, resulted in significant asymmetry of the ‘‘softening’’ in this model bridge. The stiffness of the kerb beams running the length of the ‘‘critical flexural region’’ over Pier#1 was reduced by 60%, while the plate bending thickness of the elements in the slab portion of the deck region was reduced by 35 mm at this end. Kerb beam and slab thickness reductions in the ‘‘critical flexural region’’ associated with the opposite end of the bridge over Pier#4 remained at 50% and 30 mm, respectively. Again, the resultant modal match between SEMA and FEA results for the two test states, using this revised modelling strategy, is considered to be acceptable. The effects of the increased local flexibility in the cracked region over Pier#1, compared to that over Pier#4, can be observed in the details of the mode shapes of the FEA predicted modes for the damaged test state. This is especially noticeable in the first two modes and the last mode presented for the damaged test state in Figure 10, where the asymmetry in the mode shapes, reflecting the asymmetry in the softening effect of the induced damage, is clearly evident.

worked well in theory and under laboratory conditions, implementing the system in the field has proved more difficult. This is due to a range of issues including the difficulty of obtaining reliable, robust data from the field, the influence of changes in ambient conditions and the time to perform the EMA. In light of this, several authors have proposed using a different approach to process the dynamic data and to apply the techniques of statistical pattern recognition. In this approach, rather than identifying changes in the structural system directly from the vibration data, the aim is simply to detect that damage has occurred. This is achieved either by comparing the vibration data with data from known damage states, the classification problem, or by looking for changes in the statistics of the vibration data with time, the novelty detection problem. Although these two problems can be approached using slightly different techniques, they are essentially both examples of pattern recognition. Both the classification and novelty detection approaches were applied to the flat slab bridges considered in this study. In each case, although the techniques can be used on either time domain or frequency domain data, the RRFs were used, primarily because the double hammer impact did not result in exactly time synchronous data. 5.2

Implementation of Classification using Artificial Neural Networks

For the classification approach, the general method of Zang and Imregun [31] was followed and the RRF data were first reduced using PCA [32,33]. Essentially each RRF is treated as an n-dimensional vector, which can then be expressed in terms of a series of ortho-normal vectors obtained from the eigenvectors of the covariance matrix, ½:

5 Damage Detection Using Pattern Recognition Techniques ½ ¼

5.1 Pattern Recognition Methodology As noted in the introduction, although the system identification approach to damage detection has

153

XN i¼1

!T Ri ð!Þ R ð!Þ Sð!Þ ! Ri ð!Þ R ð!Þ Sð!Þ


ð7Þ

154


where R ð!Þ is the of the N available mean RRF vectors and Sð!Þ is their standard devia tion. If the eigenvectors of ½ are given by j , then the corresponding principal components zij for a given RRF Ri ð!Þ are given by: T Ri ð!Þ R ð!Þ zij ¼ j

ð8Þ

The number of principal components used is data dependent, though it is typical to use as few as possible so that the feature vector has the least number of components. The number chosen is usually determined by considering the error in reconstructing the RRFs from the calculated principal component values. The error when using the first j principal components is given by: PN

i¼jþ1

Ej ¼ PN

i¼1

i

i

ð9Þ

where i is the ith eigenvalue of the covariance matrix. For this study, adequate reconstruction was obtained using the first 10 principal components and these were used as the basis for a reduced data set. The resulting 10-component feature vectors were then used as the input to an ANN with 10 input nodes, and 10 nodes in the hidden layer. For Model#1, there were four nodes in the output layer, corresponding to the four damage conditions, undamaged, damaged, repaired and final load. For Models#2 and #3, there were just two nodes in the output layer, corresponding to the damaged and undamaged conditions. Each node in the hidden and output layers had a sigmoid activation function and the networks were trained by back propagation using a subset of the available data. A separate ANN was trained for each of the model decks, recognising the structural differences between them. 5.3 Implementation of Novelty Detection Approach For the novelty detection approach the mean value of the RRF data for the undamaged state were found for each of the decks. Then, the differences between the measured RRFs and the

mean were estimated for both the undamaged and damaged states, and the differences were compared. Two different techniques were used to determine the differences. The first, the Cosh spectral distance [34], considers all of the RRF data and the difference between a sample defines RRF, Rð!Þ , and the mean RRF, R ð!Þ , as: " XN R !j R !j 1 log C R, R ¼ j¼1 R !j 2N R !j # R !j R !j þ log 2 R !j R !j

ð10Þ

For the second, the Mahalanobis squared distance [35], only the reduced feature vectors from the PCA were used. The Mahalanobis squared distance is defined by: r2 ¼ fx mgT ½1 fx mg

ð11Þ

where fxg is the vector being compared, fmg the mean vector and ½ the covariance matrix of all the feature vectors for the undamaged state.

6

Pattern Recognition, Results for Flat Slab Bridge Decks

6.1 Principal Component Analysis Figure 11 shows the error in the RRF reconstruction for each of the three model bridges tested and shows that using the first 10 principal components is sufficient to replicate over 90% of the variability in the RRFs. Figure 12 compares typical original and reconstructed RRFs and shows acceptable agreement for most of the key features. The variation of principal component values with damage levels is illustrated in Figure 13, which shows a plot of the first five values for each record for each of the bridge decks considered. These results show that there are changes in at least one of the principal component values for each deck when damage is first introduced. These changes are clearly discernible against the background variation and are therefore significant


Haritos & Owen


155

0.6

Cumulative Error

0.5 0.4 Deck 1 Deck 2 Deck 3

0.3 0.2 0.1 0 0

10

20

30

40

50

Number of Principal Components Used

Figure 11

Reconstruction error for RRF for the three slabs.

when considering their use for SHM. For Model#1, there is only a small subsequent change in principal component value when the deck was repaired, but there is a more significant change when the final damage state is reached. This suggests that repair did not make a significant contribution to the overall stiffness. For Model#2, there are some clear variations in principal component value at points away from the addition of damage (e.g. after records 311 and 551). These correspond to changes in experimental set up and indicate the potential sensitivity to other changes besides damage. For Model#3, the change is most marked for the first principal component, which becomes much larger after damage, whereas there is a small decrease in the other values. When the first and second principal component values are plotted against each other for each deck (Figure 14), it is clear that the data from the different damage states form clusters. These clusters are generally distinct, meaning that it should be possible to readily distinguish between decks in different damage states. However, it can again be seen that the clusters for the damaged and repaired states for Model#1 are very close together confirming the observations from Figure 13.

6.2

Artificial Neural Networks

The effectiveness of the ANNs to distinguish between data in different damage classes can be illustrated by drawing up a confusion matrix that shows the number of correctly and incorrectly classified data points according to the damage states considered. In a confusion matrix the row headings represent the true classification, the column headings the classification predicted by the ANN and the contents of each cell the number of data records that share that combination of predicted and true classifications. Therefore, the diagonal terms represent the number of data sets that are correctly classified and the off-diagonal terms the number of data sets for which the ANN was confused and incorrectly classified the data. The confusion matrices for the three model slabs are shown in Tables 1–3, and these show that the ANNs are very successful at classifying the data. This is only to be expected when Figure 14 is considered, as it is clear that most of the data can be readily separated on two principal components alone. 6.3

Novelty Detection

The variations of Cosh spectral distance and Mahalanobis squared distance with record number for each of the model bridges considered are


156

Structural Health Monitoring 3(2) 1000

Model#1 Relative Response Ratio

100 10 1

Original Reconstructed

0.1 0.01 0.001 0.0001 40

60

80

100

120

140

160

180

Frequency (Hz) 10

Relative Response Ratio

Model#2

1 Original Reconstructed 0.1

0.01 40

60

80

100

120

140

160

180

Frequency (Hz) 10

Relative Response Ratio

Model#3

1 Original Reconstructed 0.1

0.01 40

60

80

100

120

140

160

180

Frequency (Hz)

Figure 12

Comparison of original and reconstructed RRFs for each of the model bridges.

shown in Figures 15 and 16, respectively. These figures show similar results to Figures 13 and 14 in that there are clear changes in both measures when damage is introduced. Again the results for Model#2 show that the measures are sensitive to other changes as well as damage. An interesting point to note is that the Cosh spectral distance

(Figure 15) is unable to distinguish between the damaged and repaired data for Model#1, which concurs with the PCA. However, using the Mahalanobis distance (Figure 16), the damaged and repaired data can be distinguished, though it is not possible to differentiate the repaired data from the final damage state. This suggests that


Haritos & Owen


157

50

Model#1 Principal Component Value

40 30 20

PC 1 PC 2 PC 3 PC 4 PC 5

10 0 -10 -20 -30 -40 0

50

100 Record Number

150

200

50


40 30 20 PC 1 PC 2 PC 3 PC 4 PC 5

10 0 -10 -20 -30 -40 -50 0

100

200

300

400

500

600

Record Number 60


50 40 30 PC PC PC PC PC

20 10 0

1 2 3 4 5

-10 -20 -30 -40 0

20

40

60 80 Record Number

100

120

Figure 13 Variation of principal component values with damage state: Model#1 (records 1–74 undamaged, 75–115 damaged, 116–156 repaired, 157–195 final), Model#2 (records 1–467 undamaged, 468–551 damaged), Model#3 (records 1–70 undamaged, 71–112 damaged).

using both distance measures might provide a more sensitive measure. Of course, this gives a somewhat misleading impression of the ease of discriminating between damaged and undamaged bridge stock because

only the extreme cases have been considered; in practice novelty detection would not be performed in this way, as there would be many more intermediate readings taken. However, the results do show that there are significant


158

Structural Health Monitoring 3(2) 15

Model#1 Principal Component

10 5 0 -5

Undamaged Damaged Repaired Final

-10 -15 -20 -25 -30 -35 -40 -10

0

10 20 30 Principal Component 1

40

50

50

Model#2

40 Principal Component

30 20 10 Undamaged Damaged

0 -10 -20 -30 -40 -50 -50

-40

-30

-20

-10 0 10 20 Principal Component 1

30

40

50

60

Model#3

Principal Component

50 40 30

Undamaged Damaged

20 10 0 -10 -10

Figure 14

0

10 20 30 Principal Component 1

40

50

Plots of principal component 1 against principal component 2.

Table 1 Confusion matrix for model#1 (classes 1–4 undamaged, damaged, repaired and final load, respectively).

Training Data

Class Class Class Class

1 2 3 4

Test Data

Class 1

Class 2

Class 3

Class 4

Class 1

Class 2

Class 3

Class 4

50 0 0 0

0 26 0 0

0 0 26 0

0 0 0 24

24 0 0 0

0 15 0 0

0 0 15 0

0 0 0 14


Haritos & Owen


Table 3 Confusion matrix for model#3 (class 1 undamaged, class 2 damaged).

Table 2 Confusion matrix for model#2 (class 1 undamaged, class 2 damaged).

Training Data Class 2

Class 1

Class 2

90 0

0 70

377 1

1 228

Class 2

Class 1

Class 2

45 0

0 26

25 0

0 16

Class 1 Class 2

3.5 COSH Spectral Distance

3 2.5 Undamaged Damaged Repaired Final

2 1.5 1 0.5 0 -0.5 0

50

100

150

200

Record Number 1.2

Model#2

COSH Spectral Distance

1

0.8 Undamaged Damaged

0.6

0.4

0.2

0 0

100

200

300

400

500

600

Record Number 0.7

Model#3

0.6 0.5 0.4 Undamaged Damaged

0.3 0.2 0.1 0 -0 .1 0

20

40

60

80

Test Data

Class 1

4

Model#1

COSH Spectral Distance

Class 1 Class 2

Training Data

Test Data

Class 1

159

100

120

Record Number

Figure 15 Variation of COSH spectral distance with record number.


160

Structural Health Monitoring 3(2) 1.0E+06 Mahalabonis Squared Distance

Model#1

1.0E+05 1.0E+04 Undamaged Damaged Repaired Final

1.0E+03 1.0E+02 1.0E+01 1.0E+00 0

50

100

150

200

Record Number 1.0E+04 Mahalabonis Squared Distance

Model#2

1.0E+03

Undamaged Damaged

1.0E+02

1.0E+01

1.0E+00 0

100

200

300

400

500

600

Record Number 1.0E+05 Mahalabonis Squared Distance

Model#3

1.0E+04

1.0E+03 Undamaged Damaged 1.0E+02

1.0E+01

1.0E+00 0

20

40

60 80 Record Number

100

120

Figure 16 Variation of Mahalanobis squared distance with record number.

differences between the vibration data for undamaged and damaged bridges, and that these differences can be detected using these techniques. These data can then be used to set thresholds for triggering more detailed investigations that take into account the natural variability of the data, as seen in the spread of results for the undamaged cases.

7

Discussion

The results of the work presented in this paper have shown that vibration data can be used to identify damage within model RC bridge decks using a range of different techniques. Both the system identification and statistical pattern recognition paradigms have been applied to a style of


Haritos & Owen


cantilever flat slab bridge that has been proving troublesome to the Road Authority in the state of Victoria, where over 200 such bridges in excess of 50 years old are located on the declared road network. Both methods have been shown to be feasible for detecting changes in stiffness associated with damage in these structures. However, although the work has focused on a particular generic bridge type, the methods have a wider applicability provided appropriate baseline calibrations can be carried out. However, the aim of this paper was not to show what can be done but to make comparisons between the various techniques. The first point to note is that the system identification paradigm provides a much more detailed picture of the damage state of the bridge. Whereas the pattern recognition approaches used here have only been able to discern whether or not the bridges were damaged, the system identification paradigm was able to determine the likely location of the damage and even assess its severity. Often, attempts to use a system identification paradigm have failed for civil engineering structures because of their complexity and the uncertainties about foundations and boundary conditions. These problems have often made it difficult if not impossible to reliably apply the systematic model updating techniques developed in other engineering disciplines. However, the FE modelling approach can be simplified by carefully selecting the updating parameters based on a prior understanding of how the structure is likely to behave and where damage is likely to occur. This approach has been used successfully in this paper and by other researchers and the result is a simpler and more reliable methodology. Despite the success of this updating exercise, some problems still remain. Although estimates of natural frequency could have been obtained from relatively few, well-placed sensors updating based on natural frequencies alone was not adequate to characterise local damage. Better results were obtained by including mode shape information, but many more measurement locations were needed to adequately identify the mode shapes. Furthermore, the EMA and SEMA

161

curve fitting routines were still time consuming and required significant operator input. Both these factors detract from the system identification approach to damage detection, especially if it is intended for SHM, where instrumentation is to be installed and left on a bridge for some considerable period of time. In contrast, the pattern recognition studies have shown that it is possible to identify distinct changes in the vibration data associated with damage from just one or two strategically placed sensors. The processing of the data is very quick, and can easily be done in real time, making it ideal for use within a remote SHM system. Furthermore, because the system is able to ‘‘learn’’, it should be possible to refine and retrain the classification system throughout the life of the monitoring program. An important point that is often made against using vibration data for damage detection on bridges is the difficulty of obtaining good quality, consistent FRF data that can be used as the basis for either the system identification or pattern recognition paradigms. However, the work done in this study has shown that useful results can be obtained even when RRF data are used based only upon measurements of the structural response. This is especially important given the complications caused by ambient excitation in modal surveys of bridges. Finally, this paper has set about comparing these two techniques as if they are alternative methods. Perhaps a more constructive approach to bridge health monitoring and damage detection is to use the strengths of each in a complementary combined system. In such an approach, an initial detailed modal survey would be carried out to establish a calibrated model of the undamaged system. This survey could then be repeated at regular intervals – say every five years, while in the meantime a reduced sensor set would be mounted on the bridge to monitor its response continuously. A pattern recognition approach would then be used to detect significant changes in this data, which would then trigger a more detailed investigation, including another thorough modal survey to determine the nature and location of the damage.


162

8


Conclusions

Both the system identification and pattern recognition techniques have been successfully applied to detect damage in model RC bridges using their vibration signatures. The system identification approach provides more detailed information on the location and severity of damage. However, it requires more measurement points and the systematic updating of FEA models is not straightforward for civil engineering structures. The use of prior knowledge to inform the model updating process does improve its effectiveness. The pattern recognition approach provides less information about the location and severity of damage, but requires less input data and is less sensitive to signal noise. In this study, pattern recognition techniques were successfully used to classify bridge models according to their damage state and to detect changes in vibration signatures. Finally, the two approaches are seen to be strongly complementary and a strategy for bridge SHM has been proposed that exploits the benefits of both the methods.

References 1. Moore, M., Phares, B., Graybeal B., Rolander D. and Washer, G. (2001). Reliability of visual inspection for highway bridges Volume I: Final Report FHWARD-01-020. 2. Peeters, B. and De Roeck G. (2001). One-year monitoring of the Z24-Bridge: environmental effects versus damage events. Earthquake Engng Struct. Dyn., 30, 149–171. 3. Farrar, C.R., Cornwell, P.J., Doebling, S.W., Prime, M.B., et al. (2000). Structural health monitoring studies of the Alamosa Canyon and I-40 Bridges, Los Alamos National Laboratory Report LA-13635-MS. 4. Ren, W-X. and De Roeck, G. (2002). Structural damage identification using modal data. II: test verification. Journal of Structural Engineering, 128(1), 96–104. 5. Jang, J-H., Yeo, I., Shin, S. and Chang, S-P. (2002). Experimental investigation of system identification based damage assessment on structures. Journal of Structural Engineering, 128(5), 673–1682. 6. Pearson, S.R., Owen, J.S. and Choo, B.S. (2001). The use of vibration signatures to detect flexural cracking in

reinforced concrete bridge decks. Key Engineering Materials, 204–205, 17–26. 7. Ren, W-X. and De Roeck, G. (2002). Structural damage identification using modal data. I: simulation verification. Journal of Structural Engineering, 128(1), 87–95. 8. Kim, J-T., Ryu, Y-S., Cho, H-M. and Stubbs N. (2003). Damage identification in beam-type structures: frequency based method vs mode-shape-based method. Engineering Structures, 25(1), 57–67. 9. Vestroni, F. and Capecchi, D. (2000). Damage detection in beam structures based on frequency measurements. Journal of Engineering Mechanics, 126(7), 761–768. 10. Doebling, S.W., Farrar, C.R., Prime, M.B. and Shevitz, D.W. (1998). A review of damage identification methods that examine changes in dynamic properties. Shock Vibration Digest, 30, 91–105. 11. Farrar, C.R., Doeblı´ ng, S.W. and Nix, D.A. (2001). Vibration-based structural damage identification. Phil. Trans. R. Soc. Lond. A, 359, 131–149. 12. Salawu, O.S. (1997). Detection of structural damage through changes in frequency: a review. Engineering Structures, 19(9), 718–723. 13. Cawley, P. and Adams, R.D. (1979). The location of defects in structures from measurements of natural frequencies. J. of Strain Analysis, 14, 49–57. 14. Mottershead, J.E. and Friswell, M.I. (1993). Model updating in structural dynamics: a survey. Journal of Sound and Vibration, 167(2), 347–375. 15. Sohn, H., Dzwonczyk, M., Straser, E.G., Kiremidjian, A.S., Law, K. and Meng, T. (1999). An experimental study of temperature effect on modal parameters of the Alamosa Canyon bridge. Earthquake Engng. Struct. Dyn., 28, 879–897. 16. Farrar, C.R. and James III, G.H. (1997). System identification from ambient vibration measurements on a bridge. Journal of Sound and Vibration, 205(1), 1–18. 17. Sun, Z. and Chang, C.C. (2002). Structural damage assessment based on wavelet packet transform. Journal of Structural Engineering, 128(10), 1354–1361. 18. Hou, Z., Noori, M. and St Amand, R. (2000). Waveletbased approach for structural damage detection. Journal of Engineering Mechanics, 126(7 ), 677–683. 19. Owen, J.S., Eccles B.J., Choo B.S. and Woodings, M.A. (2001). The application of auto-regressive time series modelling for the time-frequency analysis of Civil Engineering structures. Engineering Structures, 23(5), 521–536. 20. Van den Abeele, K. and De Visscher, J. (2000). Damage assessment in reinforced concrete using spectral and temporal non-linear vibration techniques. Cement and Concrete Research, 30, 1453–1464. 21. Owen, J.S., Tan, C.M. and Choo, B.S. (2002). Empirical model of the non-linear vibration of cracked


Haritos & Owen


reinforced concrete beams. Proceedings of the First European Workshop on Structural Health Monitoring, (pp. 195–202). Paris.

29.

22. Sohn, H., Farrar, C.R., Hunter, N.F. and Worden, K. (2001). Structural health monitoring using statistical pattern recognition techniques. Journal of Dynamic Systems, Measurement, and Control, 123(4), 706–711. 23. Sohn, H., Czarnecki, J.A. and Farrar, C.R. (2000). Structural health monitoring using statistical process control. Journal of Structural Engineering, 126(11): 1356–1363. 24. Worden, K., Manson, G. and Fieller, N.R.J. (2000). Damage detection using outlier analysis. Journal of Sound and Vibration, 229(3), 647–667. 25. Wu, X., Ghaboussi, J. and Garrett, J.H. (1992). Use of neural network in detection of structural damage. Computers and Structures, 42, 649–659. 26. Worden, K. (1997). Structural fault detection using a novelty measure. Journal of Sound and Vibration, 201(3), 85–101. 27. Ewins, D.J. (1985). Modal Testing: Theory and Practice, New York: John Wiley. 28. Chalko, T., Gershkovich, V. and Haritos, N. (1996). The Direct simultaneous modal approximation method.

30.

31.

32. 33. 34.

35.

163

In: Proc. IMAC XIV – 14th Intl. Modal Analysis Conf., (pp. 1130–1136), Dearbourn, Michigan, SEM. Cole, H.A. (1973). On-line failure detection and damping measurement of aerospace structures by random decrement signatures. NASA Contractor Report (NASA CR-2205), National Aeronautics and Space Administration, Washington. STRAND6.1 - Finite Analysis Package, Reference Guide, GþD Computing Pty. Ltd., Ultimo NSW Australia 2007, 1995. Zang, C. and Imregun, M. (2001). Structural damage detection using artificial neural networks and measured FRF data reduced via principal component projection. Journal of Sound and Vibration, 242(5), 813–827. Joliffe, I.T. (1986). Principal Component Analysis. New York: Springer-Verlag. Bishop, C.M. (1995). Neural Networks for Pattern Recognition. Oxford University Press. Trendafilova, I. (2001). Pattern recognition methods for damage diagnosis in structures from vibration measurements. Key Engineering Materials, 204–205, 85–94. Mahalanobis, P.C. (1936). On the generalized distance in statistics. In: Proc. Natl. Institute of Science of India, 12, 49–55.
