This paper proposes an experimental analysis on the convergence of evolutionary algorithms (EAs). The effect of introducing chaotic sequences instead of random ones during all the phases of the evolution process is investigated. The approach is based on the substitution of the random number generator (RNG) with chaotic sequences. Several numerical examples are reported in order to compare the performance of the EA using random and chaotic generators as regards to both the results and the convergence speed. The results obtained show that some chaotic sequences are always able to increase the value of some measured algorithm-performance indexes with respect to random sequences. Moreover, it is shown that EAs can be extremely sensitive to different RNGs. Some t-tests were performed to confirm the improvements introduced by the proposed strategy.

The design and application of Soft Sensors (SSs) in the process industry is a growing research field, which needs to mediate problems of model accuracy with data availability and computational complexity. Black-box machine learning (ML) methods are often used as an efficient tool to implement SSs. Many efforts are, however, required to properly select input variables, model class, model order and the needed hyperparameters. The aim of this work was to investigate the possibility to transfer the knowledge acquired in the design of a SS for a given process to a similar one. This has been approached as a transfer learning problem from a source to a target domain. The implementation of a transfer learning procedure allows to considerably reduce the computational time dedicated to the SS design procedure, leaving out many of the required phases. Two transfer learning methods have been proposed, evaluating their suitability to design SSs based on nonlinear dynamical models. Recurrent neural structures have been used to implement the SSs. In detail, recurrent neural networks and long short-term memory architectures have been compared in regard to their transferability. An industrial case of study has been considered, to evaluate the performance of the proposed procedures and the best compromise between SS performance and computational effort in transferring the model. The problem of labeled data scarcity in the target domain has been also discussed. The obtained results demonstrate the suitability of the proposed transfer learning methods in the design of nonlinear dynamical models for industrial systems.

This paper analyzes a number of strategies that are devoted to improving the generalization capabilities of neural-network-based soft sensors when only small data sets are available. The aim of this paper is to search for a strategy that is able to cope with the problem of scarcity of experimental data, which often arises in industrial applications. The strategies that are considered are based on the manipulation of experimental training data sets to increase their diversity either by injecting noise into the available data or by using the bootstrap resampling approach. A new method, which is based on an aggregation of neural models, trained on different training data sets, which are obtained by noise injection and bootstrap resampling, is proposed in this paper. The methods considered were compared in an industrial case study regarding the design of a backup soft sensor for a thermal cracking unit, working in a refinery in Sicily, Italy. The results of the case study show that all the methods considered produced an improvement in the estimation capability of the models. The best performance was obtained by using the method proposed by the authors.