Artificial neural networks with conformable transfer function for improving the performance in thermal and environmental processes.

This research proposes a novel transfer function based on the hyperbolic tangent and the Khalil conformable exponential function. The non-integer order transfer function offers a suitable neural network configuration because of its ability to adapt. Consequently, this function was introduced into neural network models for three experimental cases: estimating the annular Nusselt number correlation to a helical double-pipe evaporator, the volumetric mass transfer coefficient in an electrochemical reaction, and the thermal efficiency of a solar parabolic trough collector. We found the new transfer function parameters during the training step of the neural networks. Therefore, weights and biases depend on them. We assessed the models applied to the three cases using the determination coefficient, adjusted determination coefficient, and the slope-intercept test. In addition, the MSE for the training set and the whole database were computed to show that there is no overfitting problem. The best-assessed models showed a relationship of 99%, 97%, and 95% with the experimental data for the first, second, and third cases. This novel proposal made reducing the number of neurons in the hidden layer feasible. Therefore, we show a neural network with a conformable transfer function (ANN-CTF) that learns well enough with less available information from the experimental database during its training.

Artificial neural networks: a practical review of applications involving fractional calculus.

In this work, a bibliographic analysis on artificial neural networks (ANNs) using fractional calculus (FC) theory has been developed to summarize the main features and applications of the ANNs. ANN is a mathematical modeling tool used in several sciences and engineering fields. FC has been mainly applied on ANNs with three different objectives, such as systems stabilization, systems synchronization, and parameters training, using optimization algorithms. FC and some control strategies have been satisfactorily employed to attain the synchronization and stabilization of ANNs. To show this fact, in this manuscript are summarized, the architecture of the systems, the control strategies, and the fractional derivatives used in each research work, also, the achieved goals are presented. Regarding the parameters training using optimization algorithms issue, in this manuscript, the systems types, the fractional derivatives involved, and the optimization algorithm employed to train the ANN parameters are also presented. In most of the works found in the literature where ANNs and FC are involved, the authors focused on controlling the systems using synchronization and stabilization. Furthermore, recent applications of ANNs with FC in several fields such as medicine, cryptographic, image processing, robotic are reviewed in detail in this manuscript. Works with applications, such as chaos analysis, functions approximation, heat transfer process, periodicity, and dissipativity, also were included. Almost to the end of the paper, several future research topics arising on ANNs involved with FC are recommended to the researchers community. From the bibliographic review, we concluded that the Caputo derivative is the most utilized derivative for solving problems with ANNs because its initial values take the same form as the differential equations of integer-order.

Fitting of experimental data using a fractional Kalman-like observer.

In this paper, a fractional order Kalman filter (FOKF) is presented, this is based on a system expressed by fractional differential equations according to the Riemann-Liouville definition. In order to get the best fitting of the FOKF, the cuckoo search optimization algorithm (CS) was used. The purpose of using the CS algorithm is to optimize the order of the observer, the fractional Riccati equation and the FOKF tuning parameters. The Grünwald-Letnikov approximation was used to compute the numerical solution of the FOKF. To show the effectiveness of the proposed FOKF, four examples are presented, the brain activity, the cutaneous potential recordings of a pregnant woman, the earthquake acceleration, and the Chua's circuit response.