LITERATURE REVIEW
2.2. LITERATURE REVIEW
2.2.1. Placement of sensors in operation modal analysis
Any arbitrary sensor placement may not provide good modal information like modal frequency and modal damping for a set of target modes. Thus, there exists a great deal of interest to identify the sensor locations for extraction of better modal information for target single or multiple modes in OMA. Limitation of availability of sensors, which is a common issue for large structural systems, attracts more interests in this regard. Observability (Chen 1984) measure was considered by many authors for identification of better sensor locations.
Waldraff et al. (1998) considered maximization of minimum singular value of the observability grammian for sensor placement problem. Wilson and Guhe (2005) considered the minimization of condition number of the observability grammian. Similar work was implemented in structural system based on maximization of minimum eigen-value of observability grammian by Reynier and Abou-Kandil (1999). Hac and Liu (1993) considered the correlation between output-energy and observability grammian in the problem of control of flexible structure. Udwadia (1994) and Kirkegaard and Brincker (1994) evaluated sensor placement considering better information about identifying parameters based on the information and entropy theory. In these methods, the optimal sensor configuration is taken as the one that maximizes various norms (determinant or trace) of the Fisher information matrix (FIM) or its variants. In another approach based on information theory, Yuen et al.
(2001) and Papadimitriou (2004) selected optimal sensor configuration as the one that minimizes the information entropy which gives a direct measure of the uncertainty in the estimate of system parameters. Kammer (1990) developed an iterative technique (effective-
independence) to find sensor location based on determinant of FIM. Yao et al. (1992) employed GA (genetic algorithm) using determinant of FIM. In these works of Kammer (1990) and Yao et al. (1992), modal responses were considered as parameters of estimation with best possible information and FIM was found as function of only target mode shape vector matrix. A modal approach framework was presented for placement of actuator / sensor for the flexible structures by Gawronski and Lim (1996); Gawronski (1997); Gawronski (2004). This modal approach framework evaluates modal participation at individual degree of freedom (DOF). Modal participation is evaluated separately for the target modes and subsequently sensor locations are identified using these participation profiles. System norms (H2, H∞, Hankel) associated to a mode of system were considered in the problem of active control by Gawronski (2004). Placement issues were analysed in almost-balanced coordinate (Gawronski 1997) as well as balanced coordinate (Gawronski and Lim 1996). Heo et al.
(1997) proposed kinetic energy optimization technique (EOT) for sensor placement evaluation. Basic derivation of EOT has similarity with that of effective independence method. Papadopoulos and Garcia (1998) presented two methods for structural sensor placement. The first method selects the most linearly independent impulse responses at all candidate sensor locations and the second method iteratively removes sensors with lesser information contribution to FIM using principal component analysis. Pickrel (1999) presented sensor location methodology in test engineer's perspective with an example of a transport aeroplane. Cherng (2003) presented an approach based on the analytical formulation of singular value decomposition for a candidate-blocked Hankel matrix using signal subspace correlation techniques. Li et al. (2004) presented an easy to implement sensor placement technique for structural vibration measurement based on uniform design theory.
Meo and Zumpano (2005) carried out a comparative study among three groups of techniques as effective independence based techniques, kinetic energy based techniques and
variance method. They considered the Nottingham suspension bridge for comparisons and showed that effective independence based techniques perform better. Li et al. (2008) discussed an extension of MinMAC algorithm and carried out a comparative study with other techniques considering a bridge structure. It may be mentioned that works of Meo and Zumpano (2005); Li et al. (2008), regarding other techniques e.g. effective independence driving-point residue (EFI-DPR), eigenvalue vector product (EVP), non-optimal drive point (NODP), mode shape summation plot (MSSP), QR decomposition (QRD) as well as space domain sampling, are useful. Li et al. (2007) studied inherent relationship between two important sensor placement methods, modal kinetic energy (MKE) and effective independence (EI). Liu et al. (2008) attempted to overcome the difficulties of the GA and proposed the decimal two-dimension array coding method instead of binary coding method.
Li et al. (2009) presented a simple and fast computational algorithm for evaluation of Effective Independence (EI) technique for sensor location identification based on QR decomposition. Stephan (2012) presented an approach for identifying the most relevant sensor placement locations based on two criteria: observability of mode shapes and information shared by sensors. A novel approach was introduced for optimal sensor and/or actuator placement for structural health monitoring (SHM) applications in a Bayesian framework (Flynn and Todd 2010). Starting from a general formulation of Bayes risk Flynn and Todd derived a global optimality criterion within a detection theory framework.
Nestorovic and Trajkov (2013) considered the problem of optimal actuator and sensor placement for active large flexible structures. A placement optimization method was proposed based on balanced reduced models to overcome disadvantages arising from challenging numerical procedures related with high order structural models. It may be mentioned that many times sensor placement is carried out with reduced model retaining selected DOF as master nodes. A static reduction proposed by Guyan (1965) and System
equivalent reduction expansion process (SEREP) proposed by O’Callahan et al. (1989) are commonly considered for reduced model retaining only master nodes. Bonisoli et al. (2009) presented a master node selection criteria by means of applying SEREP approach with modal-geometrical selection criterion (MoGeSeC) methodology. Meo and Zumpano (2005) presented an example of master node selection for a bridge structure. Finally, a sensor placement methodology developed in the present work and same is proposed to be used in operational modal analysis (OMA) (Debnath et al. 2012). In this sensor placement methodology, modal contribution in output energy (MCOE) was proposed as a modal measure to evaluate modal participation. MCOE is evaluated using observability grammian for any types of response measurement (displacement, velocity or acceleration), when a system is released from any initial condition.
Major techniques for sensor placement as found in literature are: EI technique, kinetic energy approach based MKE technique and modal approach based technique. The modal approach provides more flexibility in the selection of sensor-location as compared to the other techniques. However, the existing modal measures (Hankel, H∞ and H2 norms) used by the modal approach require the knowledge of input-locations where excitations are provided.
It is indeed difficult to precisely identify the input-locations in case of output-only system identification or OMA. In view of this, existing modal measures don’t appear to be quite suitable for sensor placement in OMA based on the modal approach methodology. Therefore, there is a scope for further exploration of a new modal measure which is more suitable in OMA.