## 1 Introduction
They should be small enough to fulfill linear characteristic conditions and wide enough to allow for model identification. Thus, there is a need to acquire a large number of trials, where different amplitudes and sampling periods of pseudo-random input data are generated and output signal values are recorded. Moreover, all plant modes should be stimulated to get a reliable linear model. The majority of vessels are modeled using time-domain input-output data sets. There are two main methods to obtain a system response for the pseudo-random inputs. Data are obtained from real-time trials or on the basis of nonlinear ship dynamic simulators. The first method seems to be better because we identify real objects, not its mathematical model. However, it is really time-consuming and is a demanding task to obtain the necessary number of samples for the whole identification process. There is also a risk of external disturbances (wind, waves, and currents), which affect outputs. Even when tests are carried out in windless conditions, it is hard to stimulate all plant modes without passing ships into circulation. By having an available non-linear mathematical model,it is possible to simulate these trails, verify them during rapid prototyping, and obtain undisturbed input-output data sets. Although, identification is exposed to numerical errors, such as including some parts of the mathematical dependencies, instead of the actual ship dynamics. The family of the obtained models has significant parametric uncertainties, and individual coefficient values are identified with large standard deviations. In this paper, a regularization technique and model verification based on real-time ship trials is proposed to minimize drawbacks of model identification based on simulation results. Regularization is a technique presented above and used during the identification procedure. It defines and takes into consideration model flexibility constants. Furthermore, regularization reduces model parametric uncertainties [18]. The higher the model order, the higher its flexibility. However, this leads to the increase in all parameter estimates of variance errors. Regularization leads to better control over parameters' standard deviations and model matching. The main difficulty is to determine values of the bias error and variance coefficients. Their values define the Mean Square Error (MSE) of the estimated model parameters. [PERSON] in [18] proposes to use cross-validation, where bias error and variance are determined empirically. It is a time-consuming process where initial guesses may be not optimal ones. The second method to determine these coefficients is Marginalized Maximum Likelihood [18], where the regularization matrix should be parameterized empirically, and the likelihood function for their particular values should be written by hand. This method's accuracy also depends on the personal experience and particular likelihood functions. The obtained parameter values, also in this case, may not be optimal. There is a large group of heuristic algorithms that may be successfully used for optimization. Beyond them are, e.g., particle swarm optimization (PSO) and gravitational search algorithm (GSA). PSO may be used for multidimensional problems, and it ensures good convergence [19]. PSO and GSA algorithms, in their conventional form, are dedicated to finding the local minimum. Multilayered GSA proposed in [20] is dedicated to solving real-world problems. It has a better search performance, but its hierarchical structure is quite complicated, and the optimization procedure needs more computational power than when the genetic algorithm is used. Thus, it was proposed to use the conventional genetic algorithm. The genetic algorithm (GA) is a part of the evolutionary algorithms group, which was developed to find approximate optimization of problem solutions. It simulates the heritage mechanism occurring in nature to find the global minimum in a short time period [21]. It is commonly applied in plant identification for the future control system.