Identification and doing without it, V: A formal mathematical analysis for a case of mix-up of individuals, and of recovery from failure to attain identification

Identification, when sought, is not necessarily obtained. Operational guidance that is normatively acceptable may be necessary for such cases. We proceed to formalize and illustrate modes of exchanges of individual identity, and provide procedures of recovery strategies in specific prescriptions from an ancient body of law for such situations when, for given types of purposes, individuals of some relevant kind had become intermixed and were undistinguishable. Rules were devised, in a variety of domains, for coping with situations that occur if and when the goal of identification was frustrated. We propose or discuss mathematical representations of such recovery procedures.

Numerical and experimental studies of a substructural identification strategy

For structural health monitoring it is impractical to identify a large structure with complete measurement due to limited number of sensors and difficulty in field instrumentation. Furthermore, it is not desirable to identify a large number of unknown parameters in a full system because of numerical difficulty in convergence. A novel substructural strategy was presented for identification of stiffness matrices and damage assessment with incomplete measurement. The substructural approach was employed to identify large systems in a divide-and-conquer manner. In addition, the concept of model condensation was invoked to avoid the need for complete measurement, and the recovery process to obtain the full set of parameters was formulated. The efficiency of the proposed method is demonstrated numerically through multi-storey shear buildings subjected to random force. A fairly large structural system with 50 DOFs was identified with good results, taking into consideration the effects of noisy signals and the limited number of sensors. Two variations of the method were applied, depending on whether the sensor could be repositioned. The proposed strategy was further substantiated experimentally using an eight-storey steel plane frame model subjected to shaker and impulse hammer excitations. Both numerical and experimental results have shown that the proposed substructural strategy gave reasonably accurate identification in terms of locating and quantifying structural damage.