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The purpose of this paper is to propose a new linear-nonlinear data preprocessing-based hybrid model to achieve a more accurate result at a lower cost for wind power forecasting. For this purpose, a decomposed based series-parallel hybrid model (PKF-ARIMA-FMLP) is proposed which can model linear/nonlinear and certain/uncertain patterns in underlying data simultaneously.

To design the proposed model at first, underlying data are divided into two categories of linear and nonlinear patterns by the proposed Kalman filter (PKF) technique. Then, the linear patterns are modeled by the linear-fuzzy nonlinear series (LLFN) hybrid models to detect linearity/nonlinearity and certainty/uncertainty in underlying data simultaneously. This step is also repeated for nonlinear decomposed patterns. Therefore, the nonlinear patterns are modeled by the linear-fuzzy nonlinear series (NLFN) hybrid models. Finally, the weight of each component (e.g. KF, LLFN and NLFN) is calculated by the least square algorithm, and then the results are combined in a parallel structure. Then the linear and nonlinear patterns are modeled with the lowest cost and the highest accuracy.

The effectiveness and predictive capability of the proposed model are examined and compared with its components, based models, single models, series component combination based hybrid models, parallel component combination based hybrid models and decomposed-based single model. Numerical results show that the proposed linear-nonlinear data preprocessing-based hybrid models have been able to improve the performance of single, hybrid and single decomposed based prediction methods by approximately 66.29%, 52.10% and 38.13% for predicting wind power time series in the test data, respectively.

The combination of single linear and nonlinear models has expanded due to the theory of the existence of linear and nonlinear patterns simultaneously in real-world data. The main idea of the linear and nonlinear hybridization method is to combine the benefits of these models to identify the linear and nonlinear patterns in the data in series, parallel or series-parallel based models by reducing the limitations of the single model that leads to higher accuracy, more comprehensiveness and less risky predictions. Although the literature shows that the combination of linear and nonlinear models can improve the prediction results by detecting most of the linear and nonlinear patterns in underlying data, the investigation of linear and nonlinear patterns before entering linear and nonlinear models can improve the performance, which in no paper this separation of patterns into two classes of linear and nonlinear is considered. So by this new data preprocessing based method, the modeling error can be reduced and higher accuracy can be achieved at a lower cost.

Non-alcoholic fatty liver disease (NAFLD) is the most common liver disease which has become a public health concern, whose growing prevalence has been reported as around 33.9% in Iran. As oxidative stress plays a crucial role in the pathogenesis of NAFLD, antioxidant compounds such as quercetin could ameliorate the side effect of oxidative stress. The aim of the current study was to assess the effect of quercetin on lipid profile, liver enzymes and inflammatory indices in NAFLD patients.

In a randomized, double-blind, placebo-controlled trial conducted as a pilot study, 90 patients with NAFLD were supplemented with either a quercetin or a placebo capsule twice daily (500 mg) for 12 weeks. Both groups were advised to follow an energy-balanced diet with physical activity recommendations. Blood sample was obtained for laboratory parameters at baseline and the end of week 12.

At the end of the follow-up, quercetin group had significantly greater reduction in anthropometric parameters, cholesterol (−15 ± (−41, 0.00) in Q group versus −1± (−8, 2) in control group, p = 0.004), TG (−56.7 ± 22.7) in Q group versus −13.4 ± 27.7 in control group, p = 0.04), and tumor necrosis factor-α (TNF-α) (−49.5 ± (−99, 21) in Q group versus −5 ± (−21, 0.30) in the control group, p < 0.0001) compared to the control group. However, changes in fatty liver grade, liver enzymes, as well as high density lipoprotein-cholesterol and high-sensitivity C-reactive protein were not significantly different between the two groups.

To the best of the authors’ knowledge, this was the first study which assessed the effect of quercetin supplementation on liver enzymes, lipid profile and inflammatory indices of NAFLD patients as a double-blind placebo-controlled pilot study.