Modal parameter based structural identification using input–output data: Minimal instrumentation and global identifiability issues

• Physical parameter identification with input–output measurements is investigated.
• Proposed method does not require any a priori mass/stiffness information.
• Mass normalized mode shape expansion procedure developed for shear-type systems.
• Input–output balance proposed to mass normalize measured mode shape components.
• Instrumentation set-ups proposed for experiment designs for unique identification.

It is of interest to the modal testing and structural health monitoring community to be able to identify the mass and stiffness parameters of a system from its vibration response measurements. On the other hand, incomplete instrumentation of the monitored system results in measured mode shapes which are incomplete and may lead to non-unique identification results. In this study, the problem of mass normalized mode shape expansion, and subsequent physical parameter identification, for shear-type structural systems with input–output measurements is investigated. While developing a mode shape expansion algorithm, the issue of global identifiability of the system is also addressed vis-à-vis instrumentation set-ups. Several possible minimal and near-minimal instrumentation set-ups which guarantee a unique estimation of the unmeasured mode shape components from the measured components are identified for various experimental designs. An input–output balance approach, applicable to any general structural model, is proposed to mass normalize the mode shape components observed at the instrumented degrees of freedom. Using the proposed mode shape expansion and the input–output balance procedures, along with the modal orthogonality relations, the mass and stiffness matrices of the system can be estimated. The advantage of the algorithm lies in its ability to obtain a reliably accurate identification using the minimal necessary instrumentation with no a priori mass or stiffness information. The performance of the proposed algorithm is finally discussed through numerical simulations of forced vibration experiments on a 7 degree of freedom shear-type system.