# MARIN – System Parameter Identification in Numerical Simulations #SWI2014

A common problem in numerical simulations is finding the correct parameter values of a mathematical model. A typical example from MARIN practice is the simulation of a ship manoeuvre, like a zig-zag or a turning circle (Figure 1), where the result is compared with the outcome of an experiment. The forces acting on the ship are calculated with a mathematical model which has a number of tuning parameters. The question then is: which parameter values give the best result?

For a single simulation (like a zig-zag or a turning circle) this boils down to solving an optimization problem as shown in Figure 2. The ‘behaviour’ of the experiment (physical or numerical) is determined by the function $$F$$, representing the real physics or the corresponding (complex) mathematical model, and the (input) control signal $$u$$. The behaviour of the simulation is determined by the function $$\widetilde{F}$$, representing the simpler mathematical model, and u. Various optimization techniques are available for the determination of the parameters $$p$$ which make the difference between the simulated realisation $$\widetilde{x}$$ and the experimental realisation $$x$$ minimal.

Figure 1: Zig-zag (left) and turning circle (right) manoeuvres

A more difficult problem is finding parameter values with a larger validity range, allowing for multiple simulations, such as a combination of a zig-zag and a turning circle or a complex manoeuvre in a harbour with waves and current. The broader question then is: Which basic control signals and which parameter values must be chosen for an optimal result for a class of realisations? Ideally, the optimization procedure has a component which ‘measures’ both the experimental behaviour and the simulated behaviour and which makes a comparison. The goal is to find optimal parameter values using a limited set of control signals.

Figure 2: Parameter identification scheme