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In this paper we present a novel methodology, referenced as ORFEO (Ordinal classifier and Regressor Fusion for Estimating an Ordinal categorical target), to enhance the performance in ordinal classification problems for which the latent variable is observable. ORFEO is an artificial neural network model incorporating two outputs, one for ordinal classification, using the cumulative link model, and one for regression, using a linear model. Both outputs are simultaneously optimised considering a loss function that linearly combines both classification and regression losses. The main motivation behind developing the proposed approach is to enhance the performance of a standard ordinal classifier. This improvement is facilitated by considering the regression output, which allows the model to differentiate between patterns within the same category. The ORFEO model is applied to two problems in the field of marine and ocean engineering: short-term prediction of both significant wave height and flux of energy. Both problems are addressed considering four different coastal zones of the United States of America, using 13 datasets formed by buoys measurements and reanalysis data. A comprehensive comparison against 20 methodologies, including regression and nominal/ordinal classification approaches is performed, by using diverse nominal and ordinal performance metrics. Ranks achieved indicate that ORFEO outperforms all the compared methodologies in terms of all the performance measures, demonstrating the efficacy and robustness of the proposal. Finally, a statistical analysis is conducted, concluding that there are statistically significant differences across ordinal and nominal performance metrics in favour of the proposed ORFEO model. [ABSTRACT FROM AUTHOR]

Activation functions play an important role in deep learning models by introducing non-linearity to the output of a neuron, enabling the network to learn complex patterns and non-linear relationships in data and make predictions on more complex tasks. Deep learning models' most commonly used activation functions are Purelin, Sigmoid, Tansig, Rectified Linear Unit (ReLU), and Exponential Linear Unit (ELU), which exhibit limitations such as non-differentiability, vanishing gradients, and neuron inactivity with negative values. These functions are typically defined over a finite range, and their outputs are integers or real numbers. Using fractional calculus in designing activation functions for neural networks has shown promise in improving the performance of deep learning models in specific applications. These activation functions can capture more complex non-linearities than traditional integer-order activation functions, improving performance on tasks such as image classification and time series prediction. This paper focuses on deriving and testing linear and non-linear fractional-order forms of activation functions and their variants. The linear activation function includes Purelin. In contrast, the non-linear activation functions are Binary Step, Sigmoid, Tansig, ReLU, ELU, Gaussian Error Linear Unit (GELU), Hexpo, and their variants. Besides, the standard formula has been implemented and used in developing the fractional-order linear activation function. Furthermore, various expansion series, such as Euler and Maclaurin, have been used to design non-linear fractional-order activation functions and their variants. The single- and multi-layer fractional-order neural network models have been developed using the designed fractional-order activation functions. The simulation study uses developed fractional-order neural network models for predicting the Texas wind turbine systems' generated power. The performance of single and multi-layer fractional-order neural network models has been evaluated by changing the activation functions in the hidden layer while keeping the Purelin function constant at the output layer. Experiments on neural network models demonstrate that the designed fractional-order activation functions outperform traditional functions like Sigmoid, Tansig, ReLU, ELU, and their variants, effectively addressing limitations. • Activation functions are derived into fractional functions using fractional calculus. • The fractional neural network models have been made by adopting derived functions. • A Case study has been done on the Texas wind turbine with the models to predict the power. • The models' performance has been evaluated using the fractional functions. [ABSTRACT FROM AUTHOR]

Froth Flotation is one of the fundamental processes used in iron ore attainment. It involves various physical–chemical reactions, and its multivariate control is not trivial. Traditionally, plant operators get quality measurements from laboratory analysis of sampled material, which can take hours to be published. In this paper, we present alternatives that eliminate both the necessity to periodically sample material as well as the delay associated with laboratory analysis: a predictive machine learning model working as a soft sensor. Two different classes of models were developed, exploring both deep and shallow approaches of machine learning, with a deep neural network architecture constructed for the particular task at hand. All models yielded accurate predictions, with results favoring the deep neural network when a larger volume of data is available. [ABSTRACT FROM AUTHOR]

Multi-step time-series prediction is an essential supportive step for decision-makers in several industrial areas. Artificial intelligence techniques, which use a neural network component in various forms, have recently frequently been used to accomplish this step. However, the complexity of the neural network structure still stands up as a critical problem against prediction accuracy. In this paper, a method inspired by the proportional–integral–derivative (PID) control approach is investigated to enhance the performance of neural network models used for multi-step ahead prediction of periodic time-series information while maintaining a negligible impact on the complexity of the system. The PID-based method is applied to the predicted value at each time step to bring that value closer to the real value. The water demand forecasting problem is considered as a case study, where two deep neural network models from the literature are used to prove the effectiveness of the proposed boosting method. Furthermore, to prove the applicability of this PID-based booster to other types of periodic time-series prediction problems, it is applied to enhance the accuracy of a neural network model used for multi-step forecasting of hourly energy consumption. The comparison between the results of the original prediction models and the results after using the proposed technique demonstrates the superiority of the proposed method in terms of prediction accuracy and system complexity. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid intelligent tracking control approach is developed to address optimal tracking problems for a class of nonlinear discrete-time systems. The generalized value iteration algorithm is utilized to attain the admissible tracking control with off-line training, while the on-line near-optimal control method is established to enhance the control performance. It is emphasized that the value iteration performance is improved by introducing the acceleration factor. By collecting the input–output data of the unknown system plant, the model neural network is constructed to provide the partial derivative of the system state with respect to the control law as the approximate control matrix. A novel computational strategy is introduced to obtain the steady control of the reference trajectory. The critic and action neural networks are utilized to approximate the cost function and the tracking control, respectively. Considering approximation errors of neural networks, the stability analysis of the specific systems is provided via the Lyapunov approach. Finally, two numerical examples with industrial application backgrounds are involved for verifying the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]