898 NONDESTRUCTIVE TESTING/Sonic velocities in regions in proximity to the structural constraint. Quite often, this sound radiation dominates over th...

133KB Sizes 7 Downloads 138 Views


velocities in regions in proximity to the structural constraint. Quite often, this sound radiation dominates over the sound radiated by the resonant corner and edge modes ± the point and line forces produce sound radiation at all frequencies and not only at resonant frequencies.

Nomenclature C E h pe pp v r s

damping coefficient Young's modulus thickness of plate external pressure acoustic radiation loading Poisson's ratio density radiation efficiency

See Plates 47, 48. See also: Boundary conditions; Eigenvalue analysis; Fluid/structure interaction; Forced response; Noise, Noise radiated from elementary sources; Plates; Wave propagation, Waves in an unbounded medium.

Further Reading Beranek LL (ed.) (1992) Noise and Vibration Control Engineering. New York: John Wiley. Berry A, Guyader J and Nicolas J (1990) A general

formulation for the sound radiation from rectangular, baffled plates with arbitrary boundary conditions. Journal of the Acoustical Society of America 88: 2792± 2802. Crocker MJ and Price AJ (1969) Sound transmission using statistical energy analysis. Journal of Sound and Vibration 9: 469±486. Fahy FJ (1985) Sound and Structural Vibration: Radiation, Transmission and Response. Academic Press. Junger MC and Feit D (1986) Sound, Structures and their Interaction. MIT Press. Keltie RF and Peng H (1987) The effects of modal coupling on the acoustic power radiation from panels. Journal of Vibration Acoustic. Stress and Reliability in Design, Transactions of ASME 109: 48±54 Maidanik G (1962) Response of ribbed panels to reverberant acoustic fields. Journal of the Acoustical Society of America 34: 809±826 Morse PM and Ingard KU (1986) Theoretical Acoustics. McGraw-Hill. Norton MP (1999) Fundamentals of Noise and Vibration Analysis for Engineers. Cambridge University Press. Pan J, Snyder SD, Hansen CH and Fuller CR (1992). Active control of farfield sound radiated by a rectangular panel ± a general analysis. Journal of the Acoustical Society of America 91: 2056±2066. Pierce AD (1981) Acoustics: An Introduction to its Physical Principles and Applications. McGraw-Hill. Skudrzyk EJ (1968) Simple and Complex Vibratory Systems. Pennsylvania State University Press. Wallace CE (1970) Radiation resistance of a rectangular panel. Journal of the Acoustical Society of America 51: 946±952.

NONDESTRUCTIVE TESTING Sonic S Doebling and C Farrar, Los Alamos National Laboratory, NM, USA Copyright # 2001 Academic Press doi:10.1006/rwvb.2001.0138

Introduction According to the American Society for Non-destructive Testing (ASNT), nondestructive testing (NDT) is defined as `the examination of an object with tech-

nology that does not affect the object's future usefulness'. Sonic NDT (SNDT) refers to the examination of the integrity of a structure using dynamic response methods where the velocities of the excitation and response signals are significantly below the speed at which sound travels through the materials that compose the object. Thus, the measures that are commonly used to describe a structure's vibration behavior are also frequently used in SNDT. Distinction should be made between local SNDT, used to inspect local sections of a structure for flaws, and global SNDT, used to inspect large sections of a structure for changes in mechanical properties. Global sonic nondestructive testing (GSNDT) is the focus of this article. Common synonyms for GSNDT in


recent literature include vibration-based damage identification (or damage detection) and structural health monitoring. Structural health monitoring is also used to describe the overall measurement and analysis process whereby GSNDT is used to monitor the integrity of a structure over either continuous or discrete time intervals. This article will explain the theoretical basis for GSNDT, provide an overview of the implementation process with discussion of major issues, and provide a historical context for the application of GSNDT.

Basis of Global Sonic Nondestructive Testing The basic philosophy of GSNDT is that the dynamic mechanical response of a structure is a function of the mechanical condition of the structure. Thus, observed changes in the dynamic response can be indicative of changes in mechanical condition. The basic approach of GSNDT is the comparison of measured vibration properties for the structure from two different measurement events to assess whether the structure has changed from its original configuration. First the structure is mechanically excited, using either an excitation that occurs in the normal operation of the structure (referred to as operating or ambient excitation) or an excitation that is introduced specifically for the purposes of identifying the dynamic response properties (referred to as forced excitation). Next, the structural response is measured using vibration instrumentation (typically accelerometers or strain gauges) and the data sets are digitized, transmitted, and stored electronically (see entry on Modal analysis, experimental, Measurement techniques). Features of these signals are then compared from experiments conducted at different times to assess whether damage has occurred. (Modal parameters have commonly been used, but more general types of parameters and measures have also been introduced.) Using GSNDT to assess the integrity of a structure allows the operator of the structure to follow a more cost-effective condition-based maintenance strategy (i.e., maintain the structure when necessary) rather than a time-based maintenance strategy (i.e., maintain the structure at a specific time interval no matter what condition it is in). The following example illustrates the ability to identify changes in structural condition from changes in measured vibration properties. Consider the two degrees-of-freedom (2-DOF) vibration oscillator shown in Figure 1. Using the methods of standard analytical modal analysis, the free equation of motion of the system can be written as:

m 0

0 m

x1 x2


2k ÿk

ÿk 2k

x1 x2


  0 0


Likewise, the modal frequencies, on , and mode shapes, Un can be written as: r   1 k U1 ˆ o1 ˆ m 1 r   1 3k U2 ˆ o2 ˆ m ÿ1


The reader will note from eqn [2] that the modal frequencies and mode shapes are functions of the mass and stiffness parameters of the system. Thus, by observing changes in these features (the modal frequencies and mode shapes), changes in the structural condition (mass and stiffness parameters) can be observed. Typically, it is assumed for practical applications that the types of damage of interest will primarily manifest as changes to the stiffness parameters while the mass parameters remain constant. Thus, for a given change in modal frequency and mode shape, information about changes to the structural stiffness parameters can be inferred.

Overview of Sonic NDT Process The process of implementing GSNDT involves four primary steps. Each of these steps is described in detail below: 1. Operational evaluation: definition of potential damage scenarios for the system and assessment of operating conditions 2. Data acquisition and cleansing: observation of the system over a length of time using periodically spaced measurements 3. Data transformation and feature extraction; selection of parameters of interest from the data 4. Feature comparison and statistical model building: analysis of the features to determine the current mechanical state of the system

Figure 1 Two-degrees-of-freedom system.

900 NONDESTRUCTIVE TESTING/Sonic Operational Evaluation

Data Acquisition and Cleansing

The first step in implementing GSNDT is operational evaluation. Operational evaluation refers to the assessment of the type of damage to be observed using GSNDT, the operational and environmental conditions under which GSNDT must be applied, the limitations which are present that will affect the GSNDT process, and the economic justification associated with GSNDT. The first step in defining the damage that will be detected using GSNDT is to assess what level of damage is to be considered. The five levels of damage (originally presented as four levels but later modified) are:

Sensor and excitation selection and placement The data acquisition phase of GSNDT involves selecting the types of sensors to be used, selecting the location where the sensors should be placed, determining the number of sensors to be used, and defining the data acquisition/storage/transmittal hardware. This process will be application-specific. Economic considerations will play a major role in making these decisions. Another consideration is how often the data should be collected. In some cases it may be adequate to collect data immediately before and at periodic intervals after a severe event. However, if fatigue crack growth is the failure mode of concern, it may be necessary to collect data almost continuously at relatively short time intervals. Because data can be measured under varying conditions, the ability to normalize the data becomes very important to the GSNDT process. One of the most common procedures is to normalize the measured responses by the measured inputs. When environmental or operating condition variability is an issue, the need can arise to normalize the data in some temporal fashion to facilitate the comparison of data measured at similar times of an environmental or operational cycle. Sources of variability in the data acquisition process and with the system being monitored need to be identified and minimized to the extent possible. In general, all sources of variability cannot be eliminated. Therefore, it is necessary to make the appropriate measurements such that these sources can be statistically quantified.

. Level 1: Existence of damage: simple binary indication that `something has changed' . Level 2: Location of damage: spatial location of damage to resolution allowed by the sensor set . Level 3: Type of damage: classification of damage into discrete typesets, usually from applicationspecific knowledge base . Level 4: Magnitude of damage: usually expressed as a percentage reduction in localized stiffness . Level 5: Prognosis of remaining useful life of structure: requires specific knowledge of the nature of the damage, damage propagation, future loading, and the level of damage tolerance possessed by the structure It is important to define precisely what type of damage is being sought and to select the appropriate instrumentation for that damage type. Typically it is desirable to preselect a relatively small candidate set of damage locations prior to applying the GSNDT techniques. Inclusion of too many candidate damage cases creates the danger of nonuniqueness, that is, the existence of more than one damage case that creates the same change in the measured features. Because many of the GSNDT techniques are essentially inverse modeling approaches, nonuniqueness is a major source of false-positive indications of damage. Another factor to be considered is whether or not examples of the undamaged and damaged structure are available for GSNDT. If examples of each type of damage are available, as in the case of most rotating machinery applications, then the identification of damage can be conducted in a supervised learning mode. If examples of each type of damage are not available, as in most civil engineering applications, then the identification of damage must be conducted in an unsupervised learning mode. The implication of the learning mode is explained under the section on feature comparison and statistical model building, below.

Data acquisition, processing, and storage Data acquisition for GSNDT involves scaling and antialias filtering the data, converting the data to digitized samples, and storing the samples in electronic form on a magnetic or optical medium. Transmission of the data is a significant issue, because many schemes for GSNDT of large structures such as bridges and buildings require large distances (1 km and greater) between the sensor and the storage medium. Historically, long cables have been used to bring the sensor signals back to a central location for scaling, filtering, digitization, and storage. This approach has significant drawbacks as a result of signal loss and noise in the cables as well as monitoring of cable integrity. Alternatives have been proposed that use wireless systems. Some wireless systems perform a local `clustering' of transducer signals via cables to a `local' data acquisition system. With several of these `local' systems across a large structure, the need to run cables along the entire structure is eliminated. Another approach is to make an integrated sensing, signal


conditioning, digitizing and storage unit, then deploy one such unit at each desired measurement point on the structure. A master unit at a centralized location queries each of the remote units via wireless connection to retrieve the data.

meters, in this case without much loss of information about the signal. Selection of the features to be identified is crucial to the GSNDT process. There are three basic characteristics of the features that must be considered:

Data cleansing and validation Data validation is the process of deciding whether or not the data are generally acceptable and suitable for use in GSNDT. Data cleansing is the process of selectively choosing data to accept for, or reject from, the feature selection process. Filtering is a type of data cleansing where one rejects data in certain frequency bands. The data validation and cleansing process is usually based on knowledge gained by individuals directly involved with the data acquisition. Judgment of individuals based on experience and consistency across channels and data sets are some of the criteria that are commonly used. Finally, it should be noted that the process of data acquisition and cleansing is not static, but involves feedback from the feature extraction and feature comparison steps.

1. Sensitivity: the feature must be relatively sensitive to the type of damage that was selected in the operational evaluation step. Also, the feature must be relatively insensitive to the measurement interference defined in the operational evaluation step. 2. Observability: the feature must be observable by the measurements defined in the data acquisition and cleansing step. In other words, the measurements obtained must contain information that the feature can be extracted from. 3. Dimensionality: it is desirable to minimize the length of the feature vector (defined as the dimensionality of the feature). In the example presented above, if the magnitudes of the individual data points had been the feature of interest, the feature vector would have dimension 1024 (or 1026 after including the starting point and spacing of the time axis). However, upon converting to the modal properties, the feature vector has dimension 3. Low dimensionality is crucial to ensuring that the multidimensional parameter spaces defined in the statistical model-building section below are well populated. (For example, in a multivariate Gaussian distribution, it is important to have low enough dimensionality such that the data set is adequate to populate the tails of the distribution.)

Data Transformation and Feature Extraction

Once the data have been acquired and validated, the process of condensing useful GSNDT information from the data begins. Usually the raw data time series are not directly indicative of changes in the structural properties. Thus, GSNDT requires the use of transforms and features to determine the state of the structure. A transform is a mathematical operation that is applied to the data to change the domain under which the data are viewed. A transform may include assumptions about the form of the data, but does not inherently add or remove information from the data. (Thus, for each transform there is also an inverse transform.) An example is the Fourier transform, which assumes that the data can be represented by superposed sinusoids, then computes the required coefficients for these sinusoids. The inverse Fourier transform returns the data back to the time domain without loss of information. Feature extraction is the process of extracting information from the data (or a transform of the data) such that the overall quantity of data is reduced. Thus, it is through feature extraction that the GSNDT analyst seeks to reduce the (usually very large) set of raw data to the few parameters that are of interest. Note that there is a tradeoff when extracting features as information is typically lost in the process. Take, for example, the harmonic sine wave shown in Figure 2. It is composed of 1024 data points. However, if it is noted that the signal is simply a sine wave of amplitude 2, frequency 4 Hz, and phase 0, the 1024 data points have been reduced to three para-

This so-called curse of dimensionality is demonstrated as shown in Figure 3. For a univariate (dimension 1) standard normal distribution, 90% of the data

Figure 2 Sine wave for example of feature extraction.


in the distributions falls between 71.6 and +1.6. However, for a 10-dimensional standard normal distribution, less than 1% of the data falls within a distance 1.6 from the origin. Thus, a tremendous amount of data is required to describe the features accurately with so many dimensions. Feature computation techniques can be defined as regressive or nonregressive. Regressive features are computed by curve-fitting (regression) of a parametric formula to the data or a transform of the data. Examples of regressive features are modal parameters, autoregressive moving average (ARMA) coefficients, and finite element model perturbations. Features computed directly from the data without the use of parametric curve-fitting are called nonregressive. Maximum/minimum values, root-meansquare values, and zero-crossing counts are examples of nonregressive features. In general, regressive features are more computationally intensive to extract, but are generally desirable because of the ability to incorporate an understanding of the underlying mechanics into the model. Modal parameters are commonly used features in GSNDT because the GSNDT field grew to a great extent out of the community that practices experimental modal analysis (see Modal analysis, experimental, Measurement techniques). Techniques for extracting modal parameters (and for defining the data acquisition necessary to do so) are well defined and both software and hardware are available commercially. Modal parameters are determined by regression of parameters to the frequency response function or its time domain equivalent, the impulse response function. Another issue to note is that some features are computed directly from the data or its transforms, whether by regression or not (such as modal parameters), whereas some features are themselves computed from other features. Perturbations to finite element model parameters based on regression to identified modal parameters are examples of `features of other features'.

Nonregressive features Nonregressive features are attractive for GSNDT because they can give insight about the state of the structure without the need for detailed computations or model assumptions. Examples of nonregressive features include simple mathematical functions of the time series, such as the maximum value and the root-mean-square value. Another commonly used nonregressive feature is the comparison of the error in the frequency response function or the coherence function between the undamaged and damaged data sets. Advanced nonlinear signal-processing techniques can also be used as nonregressive features for GSNDT. Examples include higher-order spectra, beat phenomena, time±frequency transforms, and wavelet transforms. In the rotating machinery industry, almost all GSNDT is performed using nonregressive features of the signal. Examples include the root-meansquare value of the response signal, increase of power spectral density magnitude at particular resonant frequencies, and the existence of harmonic resonances at multiples of the rotational speed. In applications where the damage can be distributed across a large spatial region (such as in civil infrastructure), nonregressive features are mainly useful for performing a quick check on the data. Detailed insight into the nature of the structural damage in such cases generally requires some sort of regression in order to bring knowledge of the underlying geometry and mechanics into the diagnosis process. In many GSNDT applications, it is acceptable to treat the measurement set as representing the response of a purely linear system. In other situations, it may not be acceptable to assume linearity, but it is often mathematically convenient to do so anyway. For some applications, assumption of linear structural response is simply not valid. This situation occurs when the materials that compose the structure are inherently nonlinear (such as polymers or foams), or when the damage itself introduces nonlinearity. In the latter case, features that detect the onset of nonlinearity are used to conduct level 1

Figure 3 Illustration of the `curse of dimensionality'. (A) 1-D: 10 bins; (B) 2-D: 100 bins; (C) 3-D: 1000 bins.


GSNDT. Changes in the coherence function and estimated probability density function can be used in this way. Regressive features By far the most commonly used regressive feature in GSNDT applications are modal parameters, specifically the modal frequency, modal damping ratio, and mode shape. Also, functions of these features are among the most commonly used features in GSNDT. While modal parameters are typically not the best features to use for GSNDT from a sensitivity standpoint, there is widespread belief in the community that they are useful indicators of damage. Their popularity is owed to the physical insight that they provide and the large number of commercial software packages that are available to compute them. Modal frequency is the most commonly used linear feature, followed by the mode shape and functions of the mode shape, such as mode shape curvature, bending strain energy, modal flexibility, and loaddependent Ritz vectors. Modal damping has been used for GSNDT, but due to a high level of experimental variability it tends not to be a very indicative feature. Finite element method updating (see Finite element methods), which was originally developed to tune linear finite element models to measured modal parameters, is also used to estimate changes in the finite element material and geometric parameters, which can be used as features in GSNDT. In the case of nonlinear response, general-purpose regression techniques include ARMA coefficients, polynomial fits, and the update of finite element method parameters using nonlinear data. Feature Comparison and Statistical Model Building

Once features have been extracted from the data, they are compared with features extracted from previous data sets to assess whether or not structural damage has occurred. In some cases, such as rotating machinery applications, examples of `undamaged' and `damaged' feature sets are available, and thus the GSNDT problem reduces to classification of the measured feature into the appropriate damage set. This situation is referred to as supervised comparison. The alternative, when only undamaged feature sets or damaged feature sets are available, is referred to as unsupervised learning. In unsupervised learning, it is not possible to make a set classification, but only a hypothesis about the likelihood that the new feature is a member of the existing feature set. Feature comparison techniques can be categorized as being either deterministic (i.e., features are considered to be absolute values that are measured exactly) or statistical

(i.e., features are considered to be samples from a random parent population). Most deterministic feature comparisons are simple error comparisons (either absolute error or normalized in some way). For features such as modal frequency, the error comparison can be done for each value in the feature vector. However, for features with spatial distribution such as mode shapes, comparison metrics that reduce the aggregate comparison to a set of scalar values is desirable. An example of such a metric for mode shapes is the modal assurance criterion (MAC). Using the results of the feature comparison to assess whether or not damage has occurred requires the definition of whether the damage identification will be unsupervised or supervised. In the case where examples of data from the damaged structure are not available, unsupervised methods must be used to detect clustering in the data and then look for outliers to the cluster to detect damage. Examples of clustering techniques include density estimation, expectation maximization, and k-means algorithms. In the case where examples of data from the damaged structure are available, supervised methods can be used to classify what damage case the current features most closely represent, or to use regression to assess the location and magnitude of damage. Examples of classification techniques include Fisher's discriminant, quadratic classification, and k-nearest neighbors. Regression techniques include linear, polynomial, and k-nearest neighbors. Neural networks can be utilized in both classification and regression techniques. The field of statistical process control also offers techniques for trending the data to track the onset of damage and predict future behavior. Consideration of variability An important issue in the comparison of features is the variability that is present in the features as a result of factors other than structural damage. These factors can include environmental effects (such as temperature, wind, humidity, etc.), operational interference (such as acoustic loads or extraneous vibration excitations), and electrical noise. Often these effects cannot be mitigated, but the quantification of the effects is nevertheless crucial to produce a credible GSNDT result. If the effect is cyclical, observation of the feature variability over one or more complete cycles of the effect can give an approximation of the perturbation in the feature value due to this effect. Including a measure of the effect in the feature vector (such as a measurement of temperature differential or automotive traffic flow) can be an effective technique for accounting for the source of variability.


An example of the effect of temperature-induced variability in features is shown in Figure 4. Pictured in this figure are measurements of the first modal frequency of a bridge structure taken over a 24-h period at 2-h intervals. Superimposed are measurements of temperature differential between the eastern and western edges of the bridge. Clearly indicated is a strong variability of this feature (first modal frequency) as a function of deck temperature differential. False-positive and false-negative indicators A key aspect of GSNDT is the elimination of false-positive and false-negative indicators from the damage diagnosis process. False-positive refers to the situation where damage is indicated when in fact none is present. False-negative refers to the situation where damage is not indicated, even though it is present. Although false-negative indicators pose the larger problem in terms of life safety, false-positive indicators are a significant issue in that they can irreparably damage the credibility of the GSNDT technique being applied or the engineer applying it. When developing or implementing a GSNDT technique on a set of data, it is important to compare two data sets from the undamaged structure under different experimental and environmental conditions to study false-positive indicators. It is also important to compare data sets from the undamaged structure and the damaged structure at various levels of damage to study falsenegative indicators and to define the threshold at which damage can be detected.

GSNDT History and Applications Early Work

It is the authors' speculation that damage or fault detection, as determined by changes in the dynamic properties or response of systems, has been practiced in a qualitative manner, using acoustic techniques, since modern human beings have used tools. More recently, this subject has received considerable attention in the technical literature and a brief summary of the developments in this technology over the last 30 years is presented below. Specific references are not cited. The development of vibration-based damage detection technology has been closely coupled with the evolution, miniaturization, and cost reductions of fast Fourier transform (FFT) analyzers and digital computing hardware. To date, the most successful application of vibration-based damage detection technology has been for monitoring rotating machinery. The rotating machinery application has taken an almost exclusively nonregressive approach to damage detection. The detection process is based strictly on pattern recognition applied to time histories or spectra generally measured at a single point on the housing of the machinery during normal operating conditions. Often this pattern recognition is only performed in a qualitative manner. Databases have been developed that allow specific types of damage to be identified from particular features of the vibration signature. For these systems the approximate location of the damage is generally known, making a single-channel

Figure 4 Example of feature variability as a function of temperature change.


FFT analyzer sufficient for most periodic monitoring activities. Typical damage that can be identified includes loose or damaged bearings, misaligned shafts, and chipped gear teeth. Today, commercial software integrated with measurement hardware is marketed to help the user systematically apply this technology to operating equipment. During the 1970s and 1980s the oil industry made considerable efforts to develop vibration-based damage detection methods for offshore platforms. This damage detection problem is fundamentally different from that of rotating machinery because the damage location is unknown and because the majority of the structure is not readily accessible for measurement. To circumvent these difficulties, a common methodology adopted by this industry was to simulate candidate damage scenarios with numerical models, examine the changes in resonant frequencies that were produced by these simulated changes, and correlate these changes with those measured on a platform. A number of very practical problems were encountered, including measurement difficulties caused by platform machine noise, instrumentation difficulties in hostile environments, changing mass caused by marine growth and varying fluid storage levels, temporal variability of foundation conditions, and the inability of wave motion to excite higher vibration modes. These issues prevented adaptation of this technology and efforts at further developing this technology for offshore platforms were largely abandoned in the early 1980s. Applications to Rotating Machinery

The rotating machinery application represents a mature technology where vibration-based damage detection has made the transition from a research topic to industry practice. Vibration-based damage detection for rotating machinery has been repeatedly applied with success to a variety of machinery elements such as roller bearings and gears. In the past, the greatest emphasis has been on the qualitative interpretation of vibration signatures both in the frequency and, to a lesser extent, in the time domain. Numerous summaries and reviews of this approach are available in textbook form, including detailed charts of machinery fault analysis. The approach taken has generally been to consider the detection of damage qualitatively on a fault-by-fault basis by examining acceleration signatures for the presence and growth of peaks in spectra at certain frequencies, such as multiples of shaft speed. A primary reason for this approach has been the inherent nonlinearity associated with damage in rotating machinery. Recently, more general approaches to damage detec-

tion in rotating machinery have been developed. These approaches utilize formal statistical methods to assess both the presence and level of damage on a statistical basis. Aerospace Applications

The aerospace community began to study the use of vibration-based damage detection during the late 1970s and early 1980s in conjunction with the development of the space shuttle. This work has continued, with current applications being investigated for the National Aeronautics and Space Administration's space station and reusable launch vehicle. The shuttle modal inspection system (SMIS) was developed to identify fatigue damage in components such as control surfaces, fuselage panels, and lifting surfaces. These areas were covered with a thermal protection system, making them inaccessible and, hence, impractical for conventional local nondestructive examination methods. This system has been successful in locating damaged components that are covered by the thermal protection system. All orbiter vehicles have been periodically subjected to SMIS testing since 1987. Space station applications have primarily driven the development of experimental/analytical damage identification methods. These approaches are based on correlating analytical models of the undamaged structure with measured modal properties from both the undamaged and damaged structure. Changes in stiffness indices as assessed from the two model updates are used to locate and quantify the damage. Since the mid-1990s, studies of damage identification for composite materials have been motivated by the development of composite fuel tank for a reusable launch vehicle. Civil Structure Applications

The civil engineering community has studied vibration-based damage assessment of bridge structures since the early 1980s. Modal properties and quantities derived from these properties, such as mode shape curvature and dynamic flexibility matrix indices, have been the primary features used to identify damage in bridge structures. Environmental and operating condition variability present significant challenges to the bridge-monitoring application. The physical size of the structure also presents many practical challenges for vibration-based damage assessment. Regulatory requirements in some eastern Asian countries, which mandate the companies that construct the bridges periodically to certify their structural health, are driving current research and commercial development of vibration-based bridge-monitoring systems.


Concluding Remarks The field of GSNDT, while composed of well-developed technologies such as dynamic sensing, digital signal processing, modal testing, experimental modal analysis, and statistical pattern recognition, is still in its infancy. Only in the field of rotating machinery inspection has GSNDT crossed the chasm between research and application. Open research issues still exist in the areas of operational evaluation, data acquisition and cleansing, data transformation and feature extraction, and feature comparison. Nevertheless, the potential economic and societal benefits of effective GSNDT are of significant enough magnitude that research continues so that these hurdles may be overcome. See also: Data acquisition; Modal analysis, experimental, Measurement techniques; Model updating and validating; Nondestructive testing, Ultrasonic; Rotating machinery, monitoring; Transform methods.

Further Reading Bishop CM (1995) Neural Networks for Pattern Recognition. Oxford: Oxford University Press. Braun S (1986) Mechanical Signature Analysis ± Theory and Applications. London: Academic Press. Craig RR Jr (1981) Structural Dynamics: An Introduction to Computer Methods. New York: John Wiley. Doebling SW, Farrar CR and Prime MB (1998) A summary review of vibration-based damage identification methods. The Shock and Vibration Digest 30: 91±105. Maia NMM and Silva JMM (eds) (1997) Theoretical and Experimental Modal Analysis. Taunton: Research Studies Press. Mitchell JS (1993) Introduction to Machinery Analysis and Monitoring. Tulsa, OK: PenWel Books. Natke HG and Czeslaw C (1997) Model-Aided Diagnosis of Mechanical Systems. Berlin: Springer-Verlag. Salawu OS (1997) detection of structural damage through changes in frequency ± a review. Engineering Structures 19: 718±723.

Ultrasonic L W Schmerr Jr, Iowa State University, Ames, IA, USA Copyright # 2001 Academic Press doi:10.1006/rwvb.2001.0139

High-frequency propagating sound waves are commonly used in industry as a means for nondestructively evaluating a component for flaws. Figure 1

shows the instrumentation of a typical ultrasonic flaw inspection setup. In such an inspection, a pulser generates very short repetitive pulses of electrical energy that are used to drive an ultrasonic transducer. A piezoelectric crystal in the transducer converts the electrical pulses into mechanical motion, producing an elastic wave which then propagates into the component and interacts with any flaws present. Waves scattered from the flaws can be received by another piezoelectric transducer and converted back to electrical signals. These received signals are amplified by the receiver section of the pulser/receiver, captured and displayed as a voltage vs time trace on a digital oscilloscope, and transferred to a computer for signal processing and data interpretation. An oscilloscope display of the flaw signals is one of the most common types of ultrasonic displays, called an A-Scan. A typical A-scan voltage vs time display is shown in Figure 2 for a pulse±echo setup where the same transducer is used as both a transmitter and receiver. In contrast, the two-transducer setup shown in Figure 1 is called a pitch±catch setup. In an A-scan display, one normally sees, in addition to the flaw signal(s), other responses from the geometry, such as the back surface reflection shown in Figure 2, and a large negative response at the beginning of the time trace, called the `main bang'. This main bang signal comes from some of the electrical energy generated while the pulser is firing leaking through into the receiving section. This signal produces a `dead zone' close to the transducer that is unusable for inspection purposes since other responses are buried in this large signal. In addition to the A-scan, there are two other commonly-used types of display in the nondestructive testing field. The B-scan, shown in Figure 3, uses a position sensor to measure the location (x-position) of the transducer as it moves along a linear scan path. When a signal is received from a flaw or a part of the geometry, the arrival time of this signal is used to generate a corresponding depth (z-position) from which the signal arose in the component being inspected. A response that is proportional to the amplitude of the signal received is then recorded on a computer display at these measured x- and z-positions. As the transducer moves, a complete cross-sectional display is then generated on the computer screen, as shown in Figure 3, producing in effect a side view of the interior of the component. Only a black and white B-scan image is shown in Figure 3 but in practice these images may be grayscale or color-coded. Another type of flaw response display used in nondestructive testing is called a C-scan. In this case, a transducer is mechanically moved in a twodimensional plane, typically in a raster-like scan as shown in Figure 4. Both the x- and y-coordinates of