### What is it about?

This paper presents a technique to construct a mathematical model of a dynamic system from measurements of its outputs over time. The dynamic system can be of any nature, provided it is or can be approximated as linear. It could be a structure (e.g., a bridge, building, a plane wing, etc.), a machine (e.g., a compressor, a turbine, a helicopter, etc.) a physiological system (e.g., the lungs , the cardiovascular system, etc.) or even a social or economical system. The main assumption behind this specific method that relies only on output measurement is that the system must be excited by a random input (more specifically, random and uncorrelated, i.e. white).

### Why is it important?

In many (engineering and non-engineering) applications, we deal with dynamic systems. Often it is of great benefit to have a mathematical model describing how the system responds to different inputs. For instance, a mathematical model allows us to predict how the system responds to input that we cannot or do not want to test on the real system. For the sake of an example, think of a bridge. We might not be able to generate strong wind, but we want to make sure the structure we designed does not dangerously oscillates to the strongest wind. And how about an earthquake? A mathematical model of our bridge helps us predict what kind of damage an earthquake might have caused. Additionally, estimating the mathematical model of a structure over and over again allows us to detect changes in the characteristics of the system itself. Think again of a bridge. If damage occurred, the model of the bridge changes. We detect the change and can raise an alarm, plan maintenance or take any other action needed to ensure the integrity of the bridge and of its users.

### Perspectives

The following have contributed to this page: Dr Francesco Vicario

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