System identification is one of the most important research directions. It is a diverse field which can be employed in many different areas. One of them is the model-based fault diagnosis. Thus, the problems of system identification and fault diagnosis are closely related. Unfortunately, in both cases, the research is strongly oriented towards linear systems, while the problem of identification and fault diagnosis of non-linear dynamic systems still remains open. There are, of course, many more or less sophisticated approaches to this problem, although they are not as reliable and universal as those related to linear systems, and the choice of the method to be used depends on the application. The purpose of this paper is to provide a new system identification framework based on a genetic programming technique. Moreover, a fault diagnosis scheme for non-linear systems is proposed. In particular, a new fault detection observer is presented, and the Lyapunov approach is used to show that the proposed observer is convergent under certain conditions. It is also shown how to use the genetic programming technique to increase the convergence rate of the observer. The final part of this paper contains numerical examples concerning identification of chosen parts of the evaporation station at the Lublin Sugar Factory S.A., as well as state estimation and fault diagnosis of an induction motor.

This work is focused on the fact that the most probable distance of mutated points in multi-dimensional Gaussian and Cauchy mutations is not in a close neighborhood of the origin, but at a certain distance from it. In the case of the Gaussian mutation, this distance is proportional to the norm of the standard deviation vector and increases with the landscape dimension. This may cause a decrease in the sensitivity of the evolutionary algorithm to narrow peaks when the landscape dimension increases, but, simultaneously, it strengthens the exploration property of the algorithm. Moreover, the influence of the reference frame orientation on the effectiveness of the non-spherical multi-dimensional Cauchy mutation is analyzed using simulation experiments. Four multi-dimensional mutations (Gaussian, modified Gaussian, non-spherical and spherical Cauchy mutations) are applied to two classes of evolutionary algorithms based on real-valued representation, i.e. Galar's evolutionary search with soft selection and evolutionary programming. A comparative analysis is provided for convergence to the local optimum, sensitivity to narrow peaks, saddle crossing and symmetry problems.

This paper introduces a novel algorithm for the efficient verification of a Petri net-based concurrent control system. The proposed method is based on the computation of transition invariant coverage to detect possible errors in the modelled system. Transition invariants play a crucial role in ensuring the correctness and reliability of such systems; however, existing methods often struggle with high computational demand, especially in the case of large and complex systems. The proposed approach addresses this challenge by performing a fast polynomial-time analysis to identify uncovered transitions, thereby streamlining the verification process. The effectiveness and efficiency of the proposed technique is verified experimentally with a set of 386 test modules (benchmarks) and compared against two well-known established methods: the classical method proposed by Martínez–Silva (as a reference algorithm) and PIPE (Platform Independent Petri Net Editor) tool. The results of the experiments confirm high performance of the presented algorithm, which was able to compute results for all the tested cases. In contrast, both the reference algorithm as well as the PIPE tool failed to deliver results for all examined models within one hour. The proposed algorithm is especially useful in early design stages, offering system designers timely insights into potential issues.