fuzzy logic expert system for automated damage detection...

FUZZY LOGIC EXPERT SYSTEM FOR AUTOMATEDDAMAGE DETECTION FROM CHANGES IN STRAIN

ENERGY MODE SHAPES

EDWARD S. SAZONOVa, POWSIRI KLINKHACHORNa, HOTA V.S. GANGARAOb and

UDAYA B. HALABEb,*

aLane Department of Computer Science and Electrical Engineering, West Virginia University,Morgantown, WV 26506, USA; bDepartment of Civil and Environmental Engineering, Constructed

Facilities Center, West Virginia University, Morgantown, WV 26506 USA

(Received 8 June 2001; In final form 25 September 2001)

In recent years, researchers have developed several methods for damage detection in structures employing strainenergy or curvature mode shapes. Experience shows that mode shape methods are highly sensitive to measurementnoise. Such sensitivity is a direct result of the second derivative applied to the displacement mode shapes, whichproduces curvature mode shapes. Calculation of strain energy mode shapes includes calculation of curvature as well.Consequently, the artifact false peaks (normally an indicator of damage) appear on the strain energy mode shapes,reducing accuracy of damage recognition. Combined with the intrinsic variance in damage peak shapes andamplitudes dependent upon magnitude and location of damage, the false peaks create a major problem for automateddetection of damage location. Most often, a highly qualified expert is required to analyze the data and to identify andlocate damage. In an attempt to replace the human expert with a computer, this paper describes a fuzzy logic expertsystem designed to mimic the human decision process. An expert system allows for easy encoding of expertknowledge as a set of rules. “Fuzziness” of the expert system allows better treatment of the uncertainties of theproblem and to simplify the expert system itself. The fuzzy expert system has been designed based on a finite element(FE) model of a simple beam and has provided reliable detection of damage for every tested damage scenario (100%recognition). The same system recognized damages with 100% accuracy, and no false positives or negatives on modeshapes acquired by impact testing and/or non-contact laser vibrometer techniques.

Keywords: Automated damage detection; Strain energy mode shapes; Curvature mode shapes; Fuzzy logic; Expertsystem

INTRODUCTION

Several non-destructive methods are being explored for structural damage detection based on

curvature mode shapes and strain energy mode shapes [1–9]. All these methods have

approximately the same damage detection procedure. For example, the procedure developed

at the Constructed Facilities Center, West Virginia University [3,4] is shown in Fig. 1. The

process of strain energy calculations is exemplified on the first mode of vibration, although

several modes are usually used. Dynamic data from experiments or finite element (FE)

ISSN 1058-9759 q 2002 Taylor & Francis Ltd

DOI: 10.1080/10589750290026556

*Corresponding author.

Nondestructive Testing and Evaluation, 2002 Vol. 18 (1), pp. 1–20

models of a structure provide initial data in the form of displacement mode shapes (DMS).

Strain energy mode shapes are computed from DMS through the application of the strain

energy formula (Fig. 1); the process includes calculation of the curvature mode shapes [3],

thus the strain energy mode shapes share all of the problems associated with the curvature

mode shapes. These problems are described further in this section.

Usually, strain energy mode shapes are computed for the structure with no damage

(baseline strain energy mode shapes or BSEMS) and for the structure under test, which may

have damage (test strain energy mode shapes or TSEMS). Then, the BSEMS are subtracted

from the TSEMS in order to obtain the so-called difference strain energy mode shapes

(DSEMS). The DSEMS indicate damage as changes in curvature at damaged locations,

observable as peaks on DSEMS. The strain energy method has a second derivative

(calculation of curvature) applied to the DMS in order to calculate both BSEMS and TSEMS.

Due to the nature of the second derivative, instrumentation and measurement noise is

significantly amplified on BSEMS and TSEMS and, consequently, on DSEMS. Visually,

such noise appears as peaks, which sometimes closely resemble damage peaks. The noise

problem stipulates the fact that DSEMS derived from several modes have to be considered

together in order to reject false peaks and to supply a reliable detection result. There are

several other problems (described in the section, “Building an Automated Damage Detection

System”) that significantly influence the complexity and quality of the damage detection

process. Routinely, a human expert is necessary to analyze mode shape information and

estimate damage location in a structure. Automated detection of damage using simple

FIGURE 1 Illustration of a damage detection method employing curvature calculations. First bending mode isshown.

E.S. SAZONOV et al.2

measures like magnitude of peaks (thresholding) proved less reliable, both in regard to noise

and multiple damage scenarios [10]. The purpose of this paper is to discuss an approach for

automated damage detection using strain energy mode shapes. Given DMS, the automated

system provides suspected damage locations as its output. This software system was

designed as a proof-of-a-principle using a FE model of a free–free beam. Given the

assumption that the behavior of the FE model very closely resembles the behavior of the real

beam and the fact that FE data do not have instrumentation and measurement noise present,

the FE model provides a valuable tool for studying damage peak behavior. The software

system was later successfully tested on experimental data acquired using impact testing and

non-contact scanning laser vibrometer.

INITIAL DATA

A FE model of an aluminum beam (the beam’s parameters are given in Fig. 2) was used as the

primary source of data during the design process. The FE data provided a noise-free

environment for testing and validation of the automated damage detection system. The model

is consistent with the aluminum beams that were later used in impact testing and laser

vibrometer experiments. Cracks were modeled by removing elements in the FE model;

removing a single element was equivalent to inflicting 12.5% reduction in the cross-section.

Each mode shape contained 61 scan points. About 30 different damage scenarios, including

different severity of single and multiple damages, provided the data set used during the

development process. The same 30 cases and about 50 additional cases provided the test set.

In addition to the FE model, the test set contained six experimental cases where data were

acquired by either impact testing (three cases) or laser vibrometry (three cases).

BUILDING AN AUTOMATED DAMAGE DETECTION SYSTEM

Automated damage detection requires establishing a group of parameters to be used for

distinguishing damage peaks from noise. Usually, peak magnitude information is used for

such separation; i.e. a threshold is set to separate damage and noise. Unfortunately, the

magnitude of information alone is not sufficient for reliable damage detection. A group of

related problems renders such an approach ineffective. These problems are as follows:

1. Random instrumentation and measurement noise may appear on DSEMS as peaks

resembling damage.

FIGURE 2 Finite element model of a beam.

FUZZY LOGIC FOR STRAIN DETECTION 3

2. Subtracting BSEMS from TSEMS may not completely cancel mode shape information

for undamaged locations. Incomplete cancellation of mode shape information is related

to the processes occurring in a damaged structure and may lead to the appearance of so-

called distortion peaks.

2.1. Both the amplitude of damage and distortion peaks depend on the severity of damage.

If a threshold is used for automated damage detection, the thresholding

algorithm should be able to set the threshold value adaptively to compensate

for this property.

2.2. Since neither damage location nor severity of damage is known a priori, it would be

difficult to develop a procedure for adaptive thresholding and, if used, such a

procedure would most probably introduce some additional error in the

interpretation of results for damage detection.

2.3. Amplitude of damage peaks also depends on damage location and order of the mode.

Observing a curvature mode shape, one can easily understand the reason for

this behavior. Curvature is related to the amount of bending energy at a

particular location [1,3]. There is no bending moment at the places where

strain energy is equal to zero. Therefore, a peak indicating damage either will

not appear at these locations or its amplitude will be very low. If damage is

located at such a place, amplitude of the peak might be much lower than the

amplitude of distortion or noise.

3. Damage peak shapes vary significantly depending on the peak’s location and noise

conditions.

4. Thresholding becomes further complicated if two or more damaged areas are present in

the structure. One of the closely spaced damages may completely mask another.

5. It is not always clear how to conduct the analysis across several modes. If a suspected

damage peak is found on some of the modes and is not found on the others, what

rules should be used to decide if it is an actual damage or not? Common sense rules

such as selecting the majority do not always work in situations like this. At the same

time, a human expert does not experience many of the problems associated with

thresholding.

An example, Fig. 3 shows the differences between the thresholding and the human

approach. The FE model simulates a rectangular aluminum beam that has two damaged

areas, the one at location 15 is equivalent to 25% depth cut, and another at location 20 is

equivalent to 12.5% depth cut. If thresholding at 50% of the maximum peak amplitude is

used for the detection of damage peaks, one could possibly find only one mode (mode 4) out

of the first five modes, where damage at location 20 can be detected. Thresholding with the

given threshold parameters does not detect this damage. Lowering the threshold could cause

the missing damage to appear on other mode shapes, but it would be difficult to establish a

procedure that could set the threshold at the optimal level. In addition, even if such a

procedure could be developed, it would not eliminate all the problems associated with the

thresholding. On the other hand, experience shows that a human expert easily detects this

type of damage.

A possible solution to this problem would be to create a system that has enough

“intelligence” to imitate the expert’s way of analyzing the mode shapes. One of the possible

implementations of such “intelligent” system is an expert system—a computer application

that allows explicit coding of the rules for making decisions. Expert knowledge may be

stored as a set of rules; the decision process analyzed and compared against the expert’s way


of thinking; the set of rules can be changed without redesigning the whole system [11]. These

features could provide a convenient way to solve the present problem.

Logical reasoning performed using fuzzy logic allows operations with the concept of

partial truth. A fuzzy variable can take values anywhere in the range from “absolutely false”

to “absolutely true”, therefore fuzzy logic represents a superset of the conventional “crisp”

logic. The notion of partial truth makes fuzzy logic a very good means to model the natural

uncertainty of language, and consequently, expert knowledge that can be expressed in natural

language. The apparatus of fuzzy logic has been accommodated to allow easy manipulation

with verbal descriptions of numeric variables [12]. A linguistic variable is “a variable whose

values are words or sentences in a natural or artificial language” [13]. Each linguistic variable

may be assigned one or more linguistic values, which are in turn connected to a numeric

FIGURE 3 DSEMS of a multiple damage case (locations 15 and 20, FE model).


value through the mechanism of membership functions. For example (Fig. 4), a reading from

a measuring device may be connected to a linguistic variable “width” through membership

functions “narrow”, “normal” and “wide”. For the sensor reading of 2.75 cm, the linguistic

variable width can be characterized as having 0.25 membership in the fuzzy set narrow, 0.75

membership in the fuzzy set normal and 0.0 membership in the fuzzy set wide. Fuzzy

reasoning is conducted by utilizing linguistic variables and fuzzy sets represented by their

membership functions in rules, usually having the form of expression “if . . . then . . .” For the

given example, a rule may be something like: “if beam’s width is narrow then maximum load

is low.”

An expert system that operates on a collection of fuzzy variables and rules, according to

the principles of fuzzy logic is a fuzzy expert system [14]. Reasoning about data in a fuzzy

manner has many advantages. For example, fuzzy logic has a natural way of dealing with

paradoxes, which are inherent to traditional logic; for instance, a peak may be classified both

as “damage” and as “false” at the same time without creating a contradiction [15]. Another

important feature is that fuzzy behavior is shown to produce good results, even in cases with

incompletely defined dependencies [16,17]. Finally, an important advantage of a fuzzy

system over a “classic” expert system is that a fuzzy system usually has significantly fewer

rules [18]. Thus, a fuzzy expert system should provide a convenient tool for creating an

automated damage detection system.

For this project, a custom fuzzy inference engine was designed and implemented in

JAVA programming language. The fuzzy engine allows evaluation of the fuzzy constructs

of arbitrary complexity expressed as text strings, that significantly simplifies human–

computer interface. For example, fuzzy rules in this paper can be directly parsed by the

fuzzy inference engine. Implementation of the fuzzy engine in JAVA allows cross-

platform portability and easy incorporation into Internet-based applications. Interested

readers can find a sample applet and the fuzzy engine source code at http://www.csee.

wvu.edu/~esazonov/.

Testing on classical fuzzy logic examples validated the performance of the fuzzy inference

engine. Validation of the fuzzy expert system performance was carried out by testing on the

mode shapes with known damage locations. Validation and design processes were closely

connected, each modification to the fuzzy expert system being exhaustively tested. The

linguistic variables and the rule base of the fuzzy expert system were compiled by

questioning three persons casually dealing with evaluation of strain energy shapes. Most

important characteristics (by the experts’ opinion) of the strain energy mode shapes such as

width, height, location of peaks, etc. were associated with appropriate linguistic variables.

The experts’ way of reasoning was encoded as several sets of fuzzy rules, each set

performing a logically separate part of the damage detection procedure. Fine tuning of the

rule base was performed by the expert evaluation of the fuzzy system’s reasoning: additional

rules were introduced for situations, where the system could not find an appropriate rule;

some rules were modified to eliminate undesirable effects. The final result is presented in the

subsequent sections of this paper.

FIGURE 4 An example of a fuzzy linguistic variable and membership functions.


DEFINING THE LINGUISTIC VARIABLES AND FUZZY RULES

Consider how a human expert approaches the problem of damage detection on strain energy

mode shapes:

. each mode shape is studied for the peaks present;

. a peak can “look like” or “not look like” a damage peak;

. for every “likely” peak, each mode shape in the set is studied for peaks at the same

location;

. perception of a peak as “likely or not” can either be further improved or worsened by

knowing such factors as magnitude of level of strain energy at a given location, peak

width and amplitude, presence of similarly located peaks on other modes, etc.;

. a decision is made based upon the assessment of peak characteristics and cross-mode

analysis.

The proposed fuzzy expert system simulates a human approach to search for the damage

location. Thresholding is eliminated completely. The automated system performs a damage

peak search in three stages as described below. These stages approximately correspond to

tasks normally performed by a human expert: estimation of parameters, evaluation of peaks

and matching peaks across modes.

Peak Analysis Stage

The first stage, “peak analysis”, aims at determining the metrics of every peak on the DSEMS

and preparing the data for fuzzy processing. Only peaks directed into the positive semiplane

(“upward”) are taken into consideration; due to the properties of the strain energy

computation, any peak directed into the negative semiplane (“downward”) can be classified

as false without further consideration. Parameters to be determined are illustrated in Fig. 5.

As a part of preprocessing, DSEMS are normalized so that the maximum positive amplitude

is equal to one. The normalization compensates for dependency on damage level and allows

simple fuzzy membership functions to be employed in the consequent stages. In order to

FIGURE 5 Parameters determined during the peak analysis stage.


locate peaks and determine their metrics, first derivative of DSEMS is computed and

analyzed for zero crossings. Any zero crossing from a positive to a negative value

indicates a peak of interest. Two metrics of magnitude are determined for each peak.

Metric Y1 is measured from the zero to the highest point of a peak. Metric Y2 is measured

from the base of a peak (i.e. at locations where the first derivative of the peak’s shape is

maximal for the left slope and minimal for the right slope) to its highest point. Besides Y1

and Y2, measurement of width is taken for each peak at its base. All these metrics along

with the peak’s location are stored for further processing. The average value of BSEMS

over the peak’s width is calculated and stored; this value is later used to characterize the

method’s sensitivity at that location. A flowchart for the peak analysis algorithm is given

in Fig. 6.

Peak Evaluation Stage

As the first step of the second stage (“peak evaluation”), all peaks found in the first stage

(peak analysis) are evaluated for likelihood to be a damage peak. This evaluation includes

consideration of the peak’s width, the values of metrics Y1 and Y2, and location and is

performed by applying fuzzy rules individually to each of the peaks. The main purpose of

this stage is to eliminate all peaks that do not satisfy the description of a damage peak and

establish a numerical measure of likelihood for all other peaks. The output of this stage is so-

called confidence mode shapes, where each peak has amplitude equal to the assigned

confidence. A flowchart of the algorithm for peak evaluation is given in Fig. 7. As in any

fuzzy system, linguistic variables and membership functions should be defined for every

parameter involved in decision-making. All membership functions for this fuzzy system

have been produced by empirical observation.

Membership functions were defined for the linguistic variables of width, metrics Y1 and Y2

of a peak, strain energy level for a given location and confidence (evaluation result). Graphs

of the membership functions for the peak evaluation stage are given in Fig. 8.

. Width has been defined as taking values of narrow, normal or wide. Experience shows

that for the given FE model, the normal width of a damage peak varies within 3–5 points

FIGURE. 6 Flowchart of the algorithm for the peak analysis stage.


FIGURE 8 Linguistic variables and membership functions for the peak evaluation stage.

FIGURE 7 Flowchart of the algorithm for the peak evaluation stage.


on location axis. Therefore, any peak narrower or wider than a given range does not

qualify to be a damage peak.

. Metric Y1 could be assigned as one of the following categories: “negative”, “low”,

“moderate” or “high”. Negative covers all peaks with the Y1 value below zero. Three

other categories cover three degrees of the metric’s values. The range of Y1 is between 0

and 1 due to normalization described in the section “Peak Analysis Stage”.

. Metric Y2 of a peak has been defined as “very low”, “low”, “moderate” or “high.” “Very

low” covers peaks with very low amplitudes that are not distinguishable from noise. All

other categories cover three degrees of the metric’s values. Unlike metric Y1, metric Y2 for

DSEMS may be greater than one because a peak’s base may lie below the zero axis (Fig.

5).

. Average value of BSEMS or “sensitivity” linguistic variable has four categories: “zero”, “

low”, “moderate”, and “high.” Parameters of a peak are compared against this value to

weigh the truthfulness of an evaluation. Zero sensitivity occurs at both ends of a beam due

to the properties of the numeric algorithm used to compute strain energy. This is a zone

where detection is impossible. Low, moderate and high represent three degrees of

sensitivity for a given location.

. The categories for the confidence of evaluation result are identified as: “reject”, “low”,

“moderate”, “high” and “very high.” The result of evaluation is a value between 0 and 1,

representing the system’s confidence whether this peak may or may not represent a

damage location. Reject is a category for peaks to be excluded from further consideration

because some of the peak’s properties do not fit a damage peak description. Four other

categories show different degrees of confidence.

Step two of the peak evaluation stage is performed by a rule-based fuzzy expert system.

Observation of damage peak behavior and expert knowledge served as the basis for

FIGURE 9 Rules for the peak evaluation stage (in notation used by the fuzzy engine).


producing evaluation rules. The rules reflect damage peak properties such as certain width

ranges, dependencies between values of metrics Y1 and Y2 and location. Rules used for

evaluation are illustrated in Fig. 9.

The given set of rules is invoked for every peak found during the peak analysis stage.

Results are stored for future use in the form of confidence mode shapes that will be processed

in the next stage.

Damage Search Stage

Stage three, “damage search stage”, takes the confidence mode shapes and performs a cross-

mode damage peak search. Each peak is compared to other peaks located approximately at

the same point in other modes (if such peaks exist), in addition to which, each mode is

evaluated for reliability. For example, if a given mode contains just one peak, the chances are

high that it is a damage peak. If a given mode contains 20 peaks, it is either a really bad

structure, which is not very likely, or a noisy mode where the damage peak is “masked” by

distortion and many false peaks are present. The reliability of such a mode should not be

high. Establishing reliability of a mode is a subjective matter that depends upon the utilized

data acquisition method (for example, impact testing generates more noise than laser

vibrometry) and an expected number of damaged areas. The corresponding linguistic

variables were produced based on experts’ “feeling” of mode shapes acquired by impact

testing with an expectation to see no more than two or three damages. The procedure for

cross-mode damage peak search is given in Fig. 10.

FIGURE 10 Procedure for the cross-mode damage peak search.


The output of this procedure is a single vector, carrying the “probability” of damage for

each location along the length. (The probability in this case is a fuzzy estimate rather than a

statistical term.) This vector identifies damage for every location. The search is performed by

employing several fuzzy evaluations. The following linguistic variables and membership

functions have been defined (Fig. 11):

. Mode reliability has been defined as “unreliable”, “low”, “moderate” and “high.” An

unreliable mode shape is a mode shape with no peaks. If a mode is unreliable, it should not

participate in decision-making. The other categories are three degrees of reliability.

. The number of peaks in a mode has categories identified as: “no peaks”, “low”,

“moderate” and “high.” These four categories depict the number of peaks in a mode shape

after peak evaluation.

. Distance between two points is used in judging the alignment of two peaks. The

categories have been set as “close” and “far.”

. Peak alignment has two categories, “aligned” and “not aligned”, which have been used for

evaluating whether two peaks are well aligned or not.

. Sensitivity has the following categories, identified as “very low”, “low”, “moderate” and

“high.” This linguistic variable has been redefined in comparison to the peak evaluation

stage.

FIGURE 11 Linguistic variables and membership functions for the damage search stage.


FIGURE 12 Rules for evaluating mode reliability (in notation used by the fuzzy engine).

FIGURE 13 Rules for evaluating peak alignment (in notation used by the fuzzy engine).

FIGURE 14 Rules for changing damage probability (in notation used by the fuzzy engine).


. Damage probability has been assigned categories of “decreased”, “decreased somewhat,”

“the same,” “increased somewhat” and “increased”. This linguistic variable represents a

decision after each peak-to-peak comparison. After all rules have been evaluated, this

variable is responsible for providing a decision to change damage probability for a given

location.

A damage peak search includes three separate fuzzy evaluations; each performed by its

own set of rules. Rules for evaluating mode reliability are given in Fig. 12. Rules for

evaluating peak alignment are given in Fig. 13. Left and right edge distances refer to the

distance between left and right edges of the two peaks, respectively. Using these left and right

edge distances rather than peak locations is more meaningful for peaks with different widths,

FIGURE 15 Results of the peak analysis stage.


which may or may not be symmetrical. Rules for changing damage probability are given in

Fig. 14.

After the fuzzy engine has evaluated every peak in every mode, so-called damage

probability vector contains information about detected damage. Negative values indicate

locations with false peaks due to the noise or distortion. Zero values indicate locations where

no damage-like peaks were present at all. Finally, the positive values indicate damage peaks.

TESTING AND RESULTS

Figures 15–21 show all stages of processing in which the damages from Fig. 3 are found.

Figure 15 contains peaks identified by the peak analysis stage. Figure 16 contains results of

the peak evaluation stage. Note that the number of peaks decreased due to elimination of

unlikely peaks and peak values changed according to the assigned confidence, through the

FIGURE 16 Results of the peak evaluation stage.


process described in the section “Peak Evaluation Stage”. Figure 17 contains a short

fragment of the rule evaluation diagnostics for the peak evaluation stage. This figure shows

rules fired for some peaks and evaluation results for those rules. Figure 18 shows results of

the damage search stage. Note that locations with the negative probability values have been

filled with zeros to provide an easy-to-read plot. Figure 19 shows fragments of the rule

evaluation diagnostics for this stage.

The fuzzy expert system detected both peaks with a good degree of confidence. Damage

probability value for the larger of the peaks was 0.96 while for the smaller of the peaks; it was

0.21 (1.0 is the maximum possible damage probability). Additionally, in order to make the

task more complex for the fuzzy damage detector, the detector was tested on data acquired by

impact testing on a real aluminum beam with the same geometric parameters (length and

cross-sectional dimensions) as the FE model. However, the locations of the damages were

different. DSEMS from the impact testing experiment are given in Fig. 20. Results of fuzzy

damage detection are given in Fig. 21 (all negative values are set to zero). They show that the

same system was able to tolerate significant amount of noise and distortion in the SEMS and

still provide accurate detection of structural damage. For example, the average signal-to-

noise ratio measured by comparing damage peak amplitude to the maximum noise peak

amplitude was 2.22, while the lowest value observed on a single mode shape was zero. The

average signal-to-noise ratio determined by comparing the number of damage and noise

peaks in a mode shape was 0.163 (6.1 false peaks per one damage peak, impact testing data).

FIGURE 17 A fragment of the peak evaluation diagnostic output.


The FE data provided a reliable base for teaching the system to distinguish between noise and

damage. Several other experiments using different damage scenarios provided by the FE

model (about 80 cases), impact testing (three cases) and non-contact laser vibrometer (three

cases) proved the reliability and robustness of the suggested approach [10]. For all of the test

cases, the system provided 100% detection of the damage without false positives, which is

equivalent to the expert performance on the same data set.

CONCLUSIONS

The results showed that the fuzzy expert system presented in this paper provided a reliable

and accurate outcome in recognition of different damage cases. Performance of this system

was superior to the performance of thresholding-based methods, especially in multiple

damage cases. In the example presented in this paper, the thresholding-based method was

able to detect only one of the two damaged areas, whereas the proposed fuzzy expert system

detected both of the damaged areas. Implementing the damage detection system as an expert

system allowed easy access to the decision process. Application of fuzzy logic allowed for

easy resolution of the uncertainties and contradictions within the set of rules and during

decision-making. Overall, the quality of damage detection was equal to an expert’s judgment,

thus accomplishing the set goals. A significant advantage of this system is its high noise

tolerance that was mainly achieved through utilization of the expert knowledge in the

problem domain of the strain energy mode shape analysis. When ordinary threshold-

ing/majority vote system treats all the peaks equally, without attempting to differentiate

FIGURE 18 Screenshot of the damage search stage.


between noise peaks and damage peaks, the fuzzy expert system takes into account whether a

peak is shaped like a damage peak, if peak’s parameters correspond to the peak’s location, if

the mode shape itself is reliable or highly contaminated by noise, etc. This “embedded

intelligence” makes all the difference in the damage detection results. The principles

employed here can be applied to building an expert system for automated detection of

structural damage in complex structures. Namely, employment of fuzzy logic within the

expert system framework with problem domain knowledge governing the damage detection

process would allow better coping with the complexity of strain energy mode shapes and

intricate behavior of damage peaks.

Future work in this area will be focused on making the system’s behavior adaptive. Such a

system would have self-learning capabilities and offer refinement of the rules and

membership functions during its operation. The basic expert knowledge in this case will be

adapted to operating conditions of the system.

Acknowledgments

The authors wish to acknowledge the financial support provided by the US Army (contract #

DAAE07-96-C-X226).

FIGURE 19 A fragment of the damage search stage diagnostic output.


FIGURE 20 DSEMS for damage at locations 38 and 47 (impact testing).

FIG. 21 Results of the automated damage detection (impact testing, damage at locations 38 and 47).


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