Fuzzy Cognitive Maps for Structural Damage Detection
Fuzzy cognitive map (FCM) is applied to the problem of structural damage detection. Structures are important parts of infrastructure and engineering systems and include buildings, bridges, aircraft, rockets, helicopters, wind turbines, gas turbines and nu
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Fuzzy Cognitive Maps for Structural Damage Detection Ranjan Ganguli
Abstract Fuzzy cognitive map (FCM) is applied to the problem of structural damage detection. Structures are important parts of infrastructure and engineering systems and include buildings, bridges, aircraft, rockets, helicopters, wind turbines, gas turbines and nuclear power plants, for example. Structural health monitoring (SHM) is the field which evaluates the condition of structures and locates, quantifies and suggests remedial action in case of damage. Damage is caused in structures due to loading, fatigue, fracture, environmental degradation, impact etc. In this chapter, the damage is modeled in a cantilever beam using the continuum damage and natural frequencies are used as damage indicators. Finite element analysis, which is a procedure for numerically solving partial differential equations, is used to solve the mathematical physics problem of finding the natural frequencies. The measurement deviations due to damage are fuzzified. Then they are mapped to a set of damage locations using FCM. An improvement in performance of the FCM is obtained using an unsupervised neural network approach based on Hebbian learning.
1 Introduction Structures such as bridges, buildings, nuclear power plants, aircraft, helicopters, turbines, vehicles etc. constitute a key component of modern engineering and economic infrastructure [6, 48]. However, such structures are susceptible to damage due to the environment and harsh operating conditions. Damage in structures can lead to degradation in performance and potential catastrophic failure. Therefore, a large amount of research has been expended on algorithms for accurate structural damage detection. These algorithms constitute the “brain” behind the so called structural health monitoring (SHM) systems which use measured sensor data to identify the presence, R. Ganguli(B) Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India e-mail: [email protected] E. I. Papageorgiou (ed.), Fuzzy Cognitive Maps for Applied Sciences and Engineering, Intelligent Systems Reference Library 54, DOI: 10.1007/978-3-642-39739-4_16, © Springer-Verlag Berlin Heidelberg 2014
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Damage location and size Pattern recognition
zi
zn
Data from undamaged structure
z5 zn-1
zi-1 z4
damage z1
z2
sensors z3
Fig. 1 Schematic of a structural health monitoring system
location and size of the damage in the structure. A schematic of a SHM system is shown in Fig. 1. A number of sensors are placed on the structure. The measurements obtained (z) are compared with the measurements of the undamaged structure (z 0 ) and the measurement deviations z = z − z 0 are calculated. These deviations are then given as inputs to a pattern recognition algorithm which calculates the damage location and size. Structural health monitoring involves the solution of pattern recognition problems involving noisy measured data and its relation to damage [46]. The presence of noise in the measurements can
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