Hybrid model based on K-means++ algorithm, optimal similar day approach, and long short-term memory neural network for short-term photovoltaic power prediction

Photovoltaic(PV) power generation is characterized by randomness and intermittency due to weather changes.Consequently, large-scale PV power connections to the grid can threaten the stable operation of the power system. An effective method to resolve this problem is to accurately predict PV power. In this study, an innovative short-term hybrid prediction model(i.e., HKSL) of PV power is established. The model combines K-means++, optimal similar day approach,and long short-term memory(LSTM) network. Historical power data and meteorological factors are utilized. This model searches for the best similar day based on the results of classifying weather types. Then, the data of similar day are inputted into the LSTM network to predict PV power. The validity of the hybrid model is verified based on the datasets from a PV power station in Shandong Province, China. Four evaluation indices, mean absolute error, root mean square error(RMSE),normalized RMSE, and mean absolute deviation, are employed to assess the performance of the HKSL model. The RMSE of the proposed model compared with those of Elman, LSTM, HSE(hybrid model combining similar day approach and Elman), HSL(hybrid model combining similar day approach and LSTM), and HKSE(hybrid model combining K-means++,similar day approach, and LSTM) decreases by 66.73%, 70.22%, 65.59%, 70.51%, and 18.40%, respectively. This proves the reliability and excellent performance of the proposed hybrid model in predicting power.

Application of fuzzy optimal selection of similar slopes to the evaluation of slope stability

The numerical calculation method is widely used in the evaluation of slope stability,but it cannot take the randomness and fuzziness into account that exist in rock and soil engineering objectively.The fuzzy optimization theory is thus introduced to the evaluation of slope stability by this paper and a method of fuzzy optimal selection of similar slopes is put forward to analyze slope stability.By comparing the relative membership degrees that the evaluated object sample of slope is similar to the source samples of which the stabilities are detected clearly,the source sample with the maximal relative membership degree will be chosen as the best similar one to the object sample,and the stability of the object sample can be evaluated by that of the best similar source sample.In the process many uncertain influential factors are considered and characteristics and knowledge of the source samples are obtained.The practical calculation indicates that it can achieve good results to evaluate slope stability by using this method.

One-Dimensional Optimal System and Similarity Reductions of Wu–Zhang Equation

The one-dimensional optimal system for the Lie symmetry group of the(2+1)-dimensional Wu–Zhan equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent symmetry reduction systems are presented in the form of table. It is noteworthy that a new Painlev integrable equation with constant coefficient is in the table besides the classic Boussinesq equation and the steady cas of the Wu–Zhang equation.