This multidisciplinary research presents a novel hybrid intelligent system to perform a multi-objective industrial parameter optimization process. The intelligent system is based on the application of evolutionary and neural computation in conjunction with identification systems, which makes it possible to optimize the implementation conditions in the manufacturing process of high precision parts, including finishing precision, while saving time, financial costs and/or energy. Empirical verification of the proposed hybrid intelligent system is performed in a real industrial domain, where a case study is defined and analyzed. The experiments are carried out based on real dental milling processes using a high precision machining centre with five axes, requiring high finishing precision of measures in micrometers with a large number of process factors to analyze. The results of the experiments which validate the performance of the proposed approach are presented in this study.

This multidisciplinary study presents the application of two well known soft computing methods – flexible neural trees, and evolutionary fuzzy rules – for the prediction of the error parameter between real dental milling time and forecast given by the dental milling machine. In this study a real data set obtained by a dynamic machining center with five axes simultaneously is analyzed to empirically test the novel system in order to optimize the time error.

This study presents a novel soft computing procedure based on the application of artificial neural networks, genetic algorithms and identification systems, which makes it possible to optimise the implementation conditions in the manufacturing process of high precision parts, including finishing precision, while saving both time and financial costs and/or energy. This novel intelligent procedure is based on the following phases. Firstly, a neural model extracts the internal structure and the relevant features of the data set representing the system. Secondly, the dynamic system performance of different variables is specifically modelled using a supervised neural model and identification techniques. This constitutes the model for the fitness function of the production process, using relevant features of the data set. Finally, a genetic algorithm is used to optimise the machine parameters from a non parametric fitness function. The proposed novel approach was tested under real dental milling processes using a high-precision machining centre with five axes, requiring high finishing precision of measures in micrometres with a large number of process factors to analyse. The results of the experiment, which validate the performance of the proposed approach, are presented in this study.

This multidisciplinary study presents the application of two soft computing methods utilizing the artificial evolution of symbolic structures – evolutionary fuzzy rules and flexible neural trees – for the prediction of dental milling time-error, i.e. the error between real dental milling time and forecast given by the dental milling machine. In this study a real data set obtained by a dynamic machining center with five axes simultaneously is analyzed to empirically test the novel system in order to optimize the time error.

This study presents a novel hybrid intelligent system which focuses on the optimisation of machine parameters for dental milling purposes based on the following phases. Firstly, an unsupervised neural model extracts the internal structure of a data set describing the model and also the relevant features of the data set which represents the system. Secondly, the dynamic system performance of different variables is specifically modelled using a supervised neural model and identification techniques from relevant features of the data set. This model constitutes the goal function of the production process. Finally, a genetic algorithm is used to optimise the machine parameters from a non parametric fitness function. The reliability of the proposed novel hybrid system is validated with a real industrial use case, based on the optimisation of a high-precision machining centre with five axes for dental milling purposes.

This study presents a novel hybrid intelligent system, which focuses on the optimisation of machine parameters for dental milling purposes. The basis of this approach is hybridizing two bio-inspired algorithms, as Neural Networks with Genetic Algorithms for choosing and modelling the feature subset that best descript the operation conditions. These operating conditions are given as parameters for a dental drill machine. The aim of this approach is twofold: a feature selection process is carried out while the modelling of the operating conditions is achieved. The reliability of the proposed novel hybrid system is validated with a real industrial use case, based on the optimisation of a high-precision machining centre with five axes for dental milling purposes.

A novel soft computing system to optimize a dental milling process is proposed. The model is based on the initial application of several statistical and projection methods as Principal Component Analysis and Cooperative Maximum Likelihood Hebbian Learning to analyze the structure of the data set and to identify the most relevant variables. Finally, a supervised neural model and identification techniques are applied, in order to model the process and optimize it. In this study a real data set obtained by a dynamic machining center with five axes simultaneously is analyzed to empirically test the novel system in order to optimize the time error.

A novel bio-inspired computational high-precision dental milling system is proposed in this interdisciplinar research. The system applies several bio-inspired models, based on unsupervised learning, that analyse and identify the most relevant features of high-precision dental-milling data sets and their internal structures. Finally, a supervised neural architecture and certain identification techniques are applied, in order to model and to optimize the high-precision process. This is done by empirically testing the model using a real data set taken from a dynamic high-precision machining centre with five axes.

We give two examples of trilinear forms defined on Hilbert spaces such that the first one is not nuclear but the series of its approximations numbers is convergent and the second one is not a Hilbert–Schmidt form but the series of the square of its approximation numbers is convergent.

We deal with multilinear forms t defined on Hilbert spaces and we investigate the relationships between nuclearity of t (respectively to be of Hilbert–Schmidt type) and summability properties of certain approximation numbers of t.

A bounded linear operatorT:X→Y(Banach spaces) is defined to be Tauberian provided whenever {xn}⊂Xis bounded and {T(xn)}⊂Yis weakly convergent, then {xn} has a weakly convergent subsequence. Hence, they appear as opposite to weakly compact operators. In 1991 a Tauberian operatorTbetween separable Banach spaces was found such that its second conjugateT** is not Tauberian. ThoughT** might not be Tauberian, in this paper we prove that it satisfies the following property whenXis separable: whenever {x*n*}⊂X** is bounded and {T**(x*n*)}⊂Y** is weakly convergent, then {x*n*} has aw*-convergent subsequence. Other properties ofT** are proved and the nonseparable case is also studied.