Response surface methodology (RSM) has been widely recognized as an essential estimation tool in many robust design studies investigating the second-order polynomial functional relationship between the responses of interest and their associated input variables. However, there is scope for improvement in the flexibility of estimation models and the accuracy of their results. Although many NN-based estimations and optimization approaches have been reported in the literature, a closed functional form is not readily available. To address this limitation, a maximum-likelihood estimation approach for an NN-based response function estimation (NRFE) is used to obtain the functional forms of the process mean and standard deviation. While the estimation results of most existing NN-based approaches depend primarily on their transfer functions, this approach often requires a screening procedure for various transfer functions. In this study, the proposed NRFE identifies a new screening procedure to obtain the best transfer function in an NN structure using a desirability function family while determining its associated weight parameters. A statistical simulation was performed to evaluate the efficiency of the proposed NRFE method. In this particular simulation, the proposed NRFE method provided significantly better results than conventional RSM. Finally, a numerical example is used for validating the proposed method.

In robust design (RD) modeling, the response surface methodology (RSM) based on the least-squares method (LSM) is a useful statistical tool for estimating functional relationships between input factors and their associated output responses. Neural network (NN)-based models provide an alternative means of executing input-output functions without the assumptions necessary with LSM-based RSM. However, current NN-based estimation methods do not always provide suitable response functions. Thus, there is room for improvement in the realm of RD modeling. In this study, a new NN-based RD modeling procedure is proposed to obtain the process mean and standard deviation response functions. Second, RD modeling methods based on the feed-forward back-propagation neural network (FFNN), cascade-forward back-propagation neural network (CFNN), and radial basis function network (RBFN) are proposed. Third, two simulation studies are conducted using a given true function to verify the proposed three methods. Fourth, a case study is examined to illustrate the potential of the proposed approach. In conclusion, a comparative analysis of the three feed-forward NN structure-based modeling methods and conventional LSM-based RSM proposed in this study showed that the proposed methods were significantly lower in the expected quality loss (EQL) and various variability indicators.

Most of the existing statistical forecasting methods utilize the historical values of wind power to provide wind power generation prediction. However, several factors including wind speed, nacelle position, pitch angle, and ambient temperature can also be used to predict wind power generation. In this study, a wind farm including 6 turbines (capacity of 3.5 MW per turbine) with a height of 114 meters, 132-meter rotor diameter is considered. The time-series data is collected at 10-minute intervals from the SCADA system. One period from January 04th, 2021 to January 08th, 2021 measured from the wind turbine generator 06 is investigated. One period from January 01st, 2021 to January 31st, 2021 collected from the wind turbine generator 02 is investigated. Therefore, the primary objective of this paper is to propose a combined method for wind power generation forecasting. Firstly, response surface methodology is proposed as an alternative wind power forecasting method. This methodology can provide wind power prediction by considering the relationship between wind power and input factors. Secondly, the conventional statistical forecasting methods consisting of autoregressive integrated moving average and exponential smoothing methods are used to predict wind power time series. Thirdly, response surface methodology is combined with autoregressive integrated moving average or exponential smoothing methods in wind power forecasting. Finally, the two above periods are performed in order to demonstrate the efficiency of the combined methods in terms of mean absolute percent error and directional statistics in this study.

Electromagnetic forces generated by the short circuit current and leakage flux in low- and high-voltage windings of distribution transformers as well as amorphous core transformers will cause the translation, destruction, and explosion of the windings. Thus, the investigation of these forces plays a significant role for researchers and manufacturers. Many authors have recently used the finite element method to analyze electromagnetic forces. In this paper, an analytic model is first developed for magnetic vector potential formulations to compute the electromagnetic forces (i.e., axial and radial forces) acting on the low- and high-voltage windings of an amorphous core transformer. The finite element technique is then presented to validate the results obtained from the analytical model. The developed model is applied to an actual problem.

Over the last two decades, robust design (RD) has emerged as one of the best quality improvement tools in industry. Each step in the RD procedure plays an important role in acquiring the optimal combinations of control factors that minimize the bias and variability of a product/process. However, the premise of traditional optimization problems is based on the assumption that the relationships among the products/processes that reflect the estimated functions of input–output factors are well known. A number of recent studies have used neural networks (NNs) to discover such relationships without making any assumptions. The first purpose of this paper is to propose a new RD modeling approach that uses the optimal architecture of NN based on data obtained from the design of experiment (DoE) step of the RD process and the Akaike information criterion (AIC). The second purpose is to propose a principle of desirability functions (Dfs) for the feedback network in the NN structure. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed modeling method with both feedforward and feedback network structures in comparison to the least squares method (LSM) and the inverse problem-based (IP) response surface methodology (RSM). The results demonstrate the potential of the application of NNs to RD modeling.