I. What is System Identification?

System identification is an active area in control engineering and electrical engineering. In system identification,
experimental measurements in terms of an input-output data stream of an unknown system
are used to model the system mathematically, as shown in the following illustration.

System identification has been applied widely in aerospace engineering, mechanical engineering and
structural engineering for active control, model validation and updating, conditional assessment,
health monitoring and damage detection.

The way that system identification works differs fundamentally from the commonly encountered
structural analysis and design situations. When analyzing or designing a structure, we work on
a forward problem which means that we obtain results (i.e., performance or design details of the structure)
based on an assumed or a pre-defined model of the structure and a known input (e.g., a loading).
Thus the appropriateness and accuracy of the structural model play a critical role in our routine analysis
and design, and they need validations for various reasons such as the following:

1) uncertainties in the quality of building materials and uncertainties occurred in construction procedures;

2) complexity of building responses in a nonlinear and inelastic range caused by either natural
(e.g., earthquakes) or man-made extreme events, and

3) deterioration and aging of building materials and building connections.

Applying system identification to structural engineering and engineering mechanics offers an effective means of
validating structural models and design assumptions and many other more. In the context of structural engineering,
here a system refers to a structure (e.g. a building or bridge) or a part of a structure. Inputs and outputs
are dynamic excitations (either force or base excitations) and structural responses, respectively, and they are
sampled at discrete time instances from real-world when they can be contaminated with unwanted
disturbances, i.e., noise.

In system identification, we work on inverse problems rather than forward problems. Theoretically there is a
daunting challenge of nonuniquenesss, which means there can be more than one solution which can fit
the input-output data equally well. Other major challenges and excitements in system identification may be
the following issues:

1) Mathematical descriptions of physical systems, the so-called fiction of a true system. This challenge refers to
the usefulness and correctness of the mathematical model structure adopted in the identification scheme;

2) Choice of parametric and nonparametric identifications. Here the former identification technique has
an advantage of being easily related to physical properties of the system to be modeled while the latter has
the superiority of  being adaptive and powerful interfacing with data;

3) Handling real-world uncertainties and complexities. This brings the need of applying probabilistic methods,
statistical measurements, and the demand for robust identification algorithms and data processing techniques. 

Identification of structural systems requires a deep understanding of structural dynamic response and
building material behavior. Therefore, structural engineers are the best to undertake the task when
equipped with the knowledge learned from other relevant disciplines. Related fields/areas to system identification
are: engineering mechanics, structural dynamics, structural control, random vibrations,
numerical methods, and signal processing.