Structural damage diagnosis using high resolution images

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  • Structural damage diagnosis using high resolution images

    Gongkang Fua,*, Adil G. Moosab

    aDepartment of Civil and Environmental Engineering, Wayne State University, Detroit, MI 48202, USAbDiversied Computer Engineering and Development, Clawson, MI 48017, USA

    Abstract

    Structural damage diagnosis is a critical element for structural safety monitoring. This paper presents anew approach to diagnosing structural damage using high-resolution images by CCD camera. For mini-mum eort of instrumentation, this approach oers an unprecedentedly large amount of spatially intensivedata to be used for diagnosis. A probabilistic data processing procedure is presented here for diagnosingstructural condition. The proposed method is applied in the laboratory for a bridge model using a highresolution CCD camera for data acquisition. Results show that this method can clearly identify both theexistence and the location of all the structural damages used. The smallest of them introduced a 3% loss tothe structures stiness. # 2002 Published by Elsevier Science Ltd.

    Keywords: Damage diagnosis; High-resolution images; Image processing; Probabilistic diagnosis

    1. Introduction

    Many civil structures need periodic examination for proper operation and/or for maximizinglife span. Such monitoring is now practiced mainly through general visual inspection, followed bylocal in-depth examination when needed. These two steps are referred to as global and localdiagnosis, respectively. A typical application of this type of monitoring is to bridge structures inthe transportation infrastructure system.Global diagnosis for large structures is often labor intensive, costly, and possibly subjective.

    Signicant research eort has been made to develop physical testing techniques to improve, sup-plement, and/or even replace visual inspection. While nondestructive testing techniques for localdiagnosis for bridges have been noticeably advanced [1], techniques for global diagnosis have notreached a stage of routine application [2].The main reasons for this current state of the art can be summarized as follows: (1) previously

    proposed nondestructive testing methods for globally diagnosing bridges have been overwhelmingly

    0167-4730/02/$ - see front matter # 2002 Published by Elsevier Science Ltd.PI I : S0167-4730(02 )00004-8

    Structural Safety 23 (2001) 281295

    www.elsevier.com/locate/strusafe

    * Corresponding author. Fax: +1-313-577-3881.

    E-mail address: gfu@ce.eng.wayne.edu (G. Fu).

  • based on dynamic modal testing using accelerometers [3]. These sensors can perform measure-ment at a limited number of points on the structure. Covering a large area using many accel-erometers could be very expensive, and no techniques are available for eective diagnosis usingmeasurements from only a few points [4]. (2) The eectiveness of using modal testing to diagnose(including locating) small damage needs to be established and quantied. This is becausemeasurement data inevitably contain noise. This noise makes it dicult to identify the signal,especially when local and small damages are concerned. (3) Some approaches proposed to alsoinclude numerical modeling as a dominant or complementary tool (e.g., nite element modeling).Such modeling can also be costly for a large number of bridges in a transportation network. Inaddition, it remains unknown whether numerical modeling can realistically cover the incon-sistency between the nominally specied and the as-built conditions. Examples of such incon-sistencies include real concrete strengths being dierent from the specied values, non-structuralmembers adding structural stiness, etc.This paper presents a new approach to global diagnosis using high resolution images, which can

    be provided by a charge coupled device (CCD or CCD camera). A typical CCD is shown in Fig. 1,which has a sensor to receive light signals to process to digital images. The sensor here has anarray of 2048 by 2048 sub-sensors referred to as pixels. CCD has the following advantages inacquiring needed data for damage diagnosis for structural safety monitoring: (1) no sensors needto be attached to the structure, which signicantly reduces instrumentation costs including that

    Fig. 1. Apogee AP10 CCD with 50 mm lens.

    282 G. Fu, A.G. Moosa / Structural Safety 23 (2001) 281295

  • for interrupted normal operation of the structure. (2) A large number of points on the structurecan be covered for which measurement data are to be obtained. This oers an unprecedentedamount of spatially intensive data for enhancing diagnosis resolution and eectiveness. (3) Theprices for CCD have become very aordable and are expected to be more so in near future, dueto rapid advancements in the computer and electronics industry. Note also that, depending onoperation costs, the camera may be kept stationary at the site or brought to the site wheneverneeded.This paper rst presents the concept of using spatially intensive data for global diagnosis. It is

    followed by a discussion on measuring displacement using CCD images. Then laboratoryexperiments are presented for illustrating the proposed approach.

    2. Probabilistic advancing cross-diagnosis (PAC) method

    Due to the large amount of data that can possibly be made available, the proposed method usesa probabilistic framework for diagnosis including multiple structural signatures. In addition, ithas a strategy of focusing on neighborhoods of dierent size on the structure to advance theresolution of diagnosis. The details of this proposed method are discussed here.Assume that a number of, say H, sets of repeated measurement data are made available for the

    intact state of the structure to be monitored, denoted as [B]1L to [B]HL standing for the before state:

    B 1L B1L1 ; B1L2 ; B1L3 ; B1L4 ; . . . ; B1LJ

    . . . . . .B HL BHL1 ; BHL2 ; BHL3 ; BHL4 ; . . . ; BHLJ

    1

    The square brackets [ ] with a bolded letter inside are used here to indicate a matrix consistingof several vectors denoted by the bolded letters without brackets. Each vector BhLj (h=1, 2, . . .,H, j=1, 2,. . ., J) contains M data elements from a pre-selected data grid covering the interestedportion of the structure (possibly the entire structure). Accordingly, each of [B]1L to [B]HL con-sists of J vectors representing the replicates, i.e., J is the number of measurement replicates.Superscript L indicates the feature (i.e., a physical quantity) that is referred to. These featuresshould be inherent to the structure, responsive to structural damage, and otherwise invariant. Forexample, the following features are used in the experiments discussed below: D=displacement,S=slope, C=curvature, and C2=curvature squared. When the load on the structure remainsunchanged (e.g., the self-weight), these features are considered to be the structures inherentproperties. Note that other features can also be included if warranted. The HJ replicates in Eq.(1) are needed to deal with possible noise always present in measured data. Further, assume that anew measurement data set [A]L is made available for a structural state (an after state) to bediagnosed:

    A L AL1 ; AL2 ; AL3 ; AL4 ; . . . ; ALJ 2

    For the purpose of damage diagnosis, when a local area of the structure is focused, not neces-sarily all M data points are needed at the same time. Say, only N (4M) points are used, which

    G. Fu, A.G. Moosa / Structural Safety 23 (2001) 281295 283

  • are from a neighborhood on the structure. Note that N can be changed to focus on other neigh-borhoods of dierent geometric size and/or location. This neighborhood is referred to as N-neighborhood hereafter. As a typical situation, consider an N-neighborhood data set taken as asubset of the entire data set dened in Eqs. (1) and (2), denoted as [B]hL,N (h=1,2,. . .,H) and[A]L,N:

    B 1L;N B1L;N1 ; B1L;N2 ; B1L;N3 ; B1L;N4 ; . . . ; B1L;NJ

    . . . . . .

    B HL;N BHL;N1 ; BHL;N2 ; BHL;N3 ; BHL;N4 ; . . . ; BHL;NJ 3

    A L;N AL;N1 ; AL;N2 ; AL;N3 ; AL;N4 ; . . . ; AL;NJ 4

    This typical subset of data is used to diagnose the N-neighborhoods structural condition, asdiscussed below.

    2.1. Correlation coecient

    Correlation coecient (CC) is used here to indicate how much two vectors are alike to eachother. It is dened as the normalized dot product of the two data vectors X and Y from the sameN data points:

    CCXY XY i1;:::;NXiYi

    j1;:::;NX2j

    1=2

    k1;:::;NY2k 1=2 5

    where Xi and Yi are the data elements of the two vectors: (X1, X2, X3, . . ., XN)=X and (Y1, Y2,Y3, . . ., YN)=Y. CC for the N-neighborhood is calculated referring to a reference vector B

    L,Navg as

    follows:

    CCIL;NBi BIL;Ni BL;Navg ; :::::;CCHL;NBi BHL;Ni BL;NavgCCL;NAk AL;Nk BL;Navg i; k 1; 2; . . . ; J 6

    BL;Navg i1;2;...;JB1L;Ni j1;2;:::;JB2L;Nj . . .k1;2;...;JBHL;Nk

    = HJ 7

    These CC values range from 1 to +1 according to the denition in Eq. (5). For the prob-abilistic analyses discussed below, it is desirable that CC be converted through the Fisher transfer[5] to the following variables r. As a result, they range from negative to positive innity, and arecloser to being normally distributed:

    284 G. Fu, A.G. Moosa / Structural Safety 23 (2001) 281295

  • r1L;NBi 0:5Ln 1 CC1L;NBi

    = 1 CC1L;NBi

    ; . . . . . . rHL;NBi 0:5Ln 1 CCHL;NBi

    = 1 CCHL;NBi

    rL;NAk 0:5Ln 1 CCL;NAk

    = 1 CCL;NAk

    i; k 1; 2; :::; J 8

    These data elements are re-organized as vectors, to be used below for diagnosing changes due tostructural damage:

    r1L;NB r1L;NB1 ; r1L;NB2 ; r1L;NB3 ; :::::::::; r1L;NBJ

    ::::::

    rHL;NB rH;NB1 ; rHL;NB2 ; rHL;NB3 ; :::::::::; rHL;NBJ

    rL;NA rL;NA1 ; rL;NA2 ; rL;NA3 ; ::::::::; rL;NAJ

    9

    These H+1 r vectors contain information on how much alike between the reference vector BL,Navgand each vector in BhL,Ni and A

    L,Nk (h=1, 2, ,..., H; i, k=1, 2, ...,J).

    2.2. Probabilistic damage indicator

    For each feature (e.g., D, S, C, or C2 in the application experiments presented below), a like-lihood ratio (LR) for structural damage is dened as follows:

    LRL;N LFAL;N;B1L;N&:::&BHL;N h1;:::;HLFBhl;N;B1L;N&:::&BHL;N

    =H 10

    where

    LFAL;N;B1L;N&:::&BHL;N LnPrL;NA

    ;r1L;NB

    &:::&rHL;NB

    Pr1L;NB

    &:::&rHL;NB

    ;rL;NA

    LFB1L;N;B1L;N&:::&BHL;N LnPr1L;NB

    ;r1L;NB

    &:::&rHL;NB

    Pr1L;NB

    &:::&rHL;NB

    ;r1L;NB

    ::::::LFBHL;N;B1L;N&:::&BHL;N LnPrHL;N

    B;r1L;NB

    &:::&rHL;NB

    Pr1L;NB

    &:::&rHL;NB

    ;rHL;NB

    :11

    Pr1, r2 in Eq. (11) is the probability that one data set r1 belongs to the other data sets (r2s)probability density function, dened as:

    Pr1;r2 maxr1min r2

    f2 r dr

    maxr1 the maximum element in data set r1minr1 the minimum element in data set r1 12

    f2(r) Is the probability density for data set r2. It can be assumed to be a normal distribution,unless another distribution is deemed to be more appropriate. The statistical parameters such asthe mean and standard deviation for f2(r) can be estimated using data set r2. Note that r1 and r2 in

    G. Fu, A.G. Moosa / Structural Safety 23 (2001) 281295 285

  • Eq. (12) are interchangeable. LRL,N in Eq. (10) indicates the likelihood that [A]L,N belongs to the

    population or family of [B]1L,N to [B]HL,N for feature L. It is expected to be low for a damagestate represented by [A]L,N because the mean values of the measured quantities will change (fromthose of [B]1L,N to [B]HL,N), to say the least. The negative term in Eq. (10) represents a benchmarkfor comparison, accounting for noise in the baseline data [B]1L,N to [B]HL,N. When [A]L,N is closeto or belongs to the [B]hL,N (h=1,2,. . .,H) population, LRL,N is close to zero, indicating extremelylow probability of damage. Accordingly, lower LRL,N values indicate higher likelihood ofdamage.

    2.3. Cross diagnosis using multiple features

    These likelihood factors in Eq. (10) for all the features are combined here into a comprehensivelikelihood factor (CLF) as follows to be used as a single index for easy and reliable cross diag-nosis:

    Comprehensive likelihood factor CLFN LwL LRL;N 13

    LwL 1; wL > 0 14

    CLFN is a weighed likelihood factor using all the features, indicating the likelihood of struc-tural damage. A lower CLFN indicates higher likelihood of damage for the data point repre-senting the N-neighborhood. wL Is the weight for feature L. It should be higher when thesensitivity of that feature to the damage of concern is higher. In other words, more sensitive fea-tures (e.g., slope and curvature as opposed to displacement) should have higher weights. Notethat this sensitivity is aected by the dependence between the feature and the damage, and is alsoinuenced by the data noise because noise makes it dicult to identify a signal. Note also thatthis approach is intended to be applicable when dierent features L are used.For a selected N, CLFN in Eq. (13) serves as a damage indicator for a physical point on the

    structure representing the N-neighborhood. Thus, CLFN plotted for all the N-neighborhoodsover the entire data grid is referred to here as a condition map of the structure. These conditionmaps for dierent N should be easy to understand for engineers performing the diagnosis. Someexamples of condition map are shown in Figs. 69 where low CLF values indicate the damagelocations. The experiments leading to these results are discussed later in detail.Also note that when N is large to cover a large area, CLFN may become insensitive to local

    damage. It is because only a local area may be aected by the damage and shows abnormalbehavior. CC calculation using Eqs. (5) and (6) has an averaging or diluting eect over theN-neighborhood. With N varying from a large to a small value, the resolution of diagnosis isincreased because the diluting eect becomes lower. When N becomes small enough (forexample N=2) the focus will be on the damages immediate vicinity. Note that when N=1, theCC calculation in Eq. (6) will not be needed, then the before and after data in Eqs. (3) and(4) will be directly compared in Eq. (10) for diagnosis. Namely, BhL,1i and A

    L,1k (h=1, 2, . . .,H; i,

    k=1, 2, . . ., J) in Eqs. (3) and (4) each reduces from a vector to a scalar (a data element). As aresult, Eq. (9) will be:

    286 G. Fu, A.G. Moosa / Structural Safety 23 (2001) 281295

  • Fig. 2. (a) A steel I-beam W615 imaged using CCD. (Area at midspan enlarged in Fig. 2b.) (b) Close view of mid-span section of I-beam in Fig. 2a. (One-pixel column of beam edge digitized in Fig. 2c.) (c) Intensity distribution invertical direction at an edge point in Fig. 2b. (Circled points=digitized intensity from image; solid curve=6th orderpolynomial tting).

    G. Fu, A.G. Moosa / Structural Safety 23 (2001) 281295 287

  • r1L;1B B1L;11 ;B1L;12 ;BIL;13 ; ::::::;B1L;1J

    :::::::rHL;1B BHL;11 ;BHL;12 ;BHL;13 ; ::::::;BHL;1J

    rL;1A AL;11 ;AL;12 ;AL;13 ; ::::::;AL;1J

    15

    Note again that the vectors in the parentheses are understood as scalars as explained. With thisunderstanding, the rest of data processing from Eq. (10) to (14) remains unchanged.

    Fig. 3. Data grid and simulated damage cases (stiness change severity given in Table 1).

    Table 1Testing program for damage diagnosis

    Test ID Description of damage introduceda Stiness loss (%)

    DC1 1 cm long cut to bottom ange (12 cm...

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