Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off（PTO） system is a directly linear electric generator or a hydraulic motor...Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off（PTO） system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.展开更多
Grey prediction is vital in statistical prediction with wide applications.However,most grey prediction methods focus on annual predictions of the monotonic time series instead of the seasonal time series.The paper use...Grey prediction is vital in statistical prediction with wide applications.However,most grey prediction methods focus on annual predictions of the monotonic time series instead of the seasonal time series.The paper uses the extended model of the grey GM(1,1)model to predict the seasonal time series.Some improvements have been made in two aspects to improve the prediction accuracy of the model.1)We introduce seasonal multiple factors to transform the original time series,which improves the adaptability of the seasonal data to the model.The transformed series conforms to the law presented by the model.2)The seasonal data are in superimposed sine and cosine fluctuations with tendencies.Therefore,the paper extends the grey action quantity of the traditional GM(1,1)model.The newly extended grey model is called the GM(1,1,exp×sin,exp×cos)model,which is provided with the parameter optimization methods and time response equations.According to the proposed modeling method,we establish a GM(1,1,exp×sin,exp×cos)model for China's quarterly gross domestic product(GDP)with high accuracy.展开更多
The conventional grey GM(2,1)model built for the fast growing time sequence generally has big errors.To improve the modeling precision,the paper improves from the following two aspects:First,the paper transforms the a...The conventional grey GM(2,1)model built for the fast growing time sequence generally has big errors.To improve the modeling precision,the paper improves from the following two aspects:First,the paper transforms the accumulated generating sequence of original time sequence quantitatively to make the transformed time sequence have the better adaptability to the model;second,the paper extends the conventional grey GM(2,1)model’s structure to make the extended model meet the variation law of fast growing sequence better.The extended grey model is called the GM(2,1,Σexp(ct))model.The paper offers the parameter optimization method and the solving method of time response sequence of GM(2,1,Σexp(ct))model.Using the model and methods proposed,the paper builds the GM(2,1,Σexp(ct))models for the natural gas consumption of China and Chongqing City,China,respectively.Results show that the models built have high simulation precision and prediction precision.展开更多
The common models used for grey system predictions include the GM(1, 1), the GM(1, N),the GM(N, 1), and so on, but their whitening equations are all single ordinary differential equations.However, objects and factors ...The common models used for grey system predictions include the GM(1, 1), the GM(1, N),the GM(N, 1), and so on, but their whitening equations are all single ordinary differential equations.However, objects and factors generally form a whole through mutual restrictions and connections when the objective world is developing and changing continuously. In other words, variables affect each other. The relationship can’t be properly reflected by the single differential equation. Therefore, the paper proposes a novel simultaneous grey model. The paper gives a modeling method of simultaneous grey model SGM(1, 2) with 2 interactive variables. The example proves that the simultaneous grey model has high precision and improves the precision significantly compared with the conventional single grey model. The new method proposed enriches the grey modeling method system and has important significance for the in-depth study, popularization and application of grey models.展开更多
基金financially supported by the National Natural Science Foundation of China(Grant No.51239007)the Independent Research Project of State Key Laboratory of Ocean Engineering in Shanghai Jiao Tong University(Grant No.GKZD010023)
文摘Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off（PTO） system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.
基金Supported by National Natural Science Foundation of China (11401418)。
文摘Grey prediction is vital in statistical prediction with wide applications.However,most grey prediction methods focus on annual predictions of the monotonic time series instead of the seasonal time series.The paper uses the extended model of the grey GM(1,1)model to predict the seasonal time series.Some improvements have been made in two aspects to improve the prediction accuracy of the model.1)We introduce seasonal multiple factors to transform the original time series,which improves the adaptability of the seasonal data to the model.The transformed series conforms to the law presented by the model.2)The seasonal data are in superimposed sine and cosine fluctuations with tendencies.Therefore,the paper extends the grey action quantity of the traditional GM(1,1)model.The newly extended grey model is called the GM(1,1,exp×sin,exp×cos)model,which is provided with the parameter optimization methods and time response equations.According to the proposed modeling method,we establish a GM(1,1,exp×sin,exp×cos)model for China's quarterly gross domestic product(GDP)with high accuracy.
基金Supported by National Natural Science Foundation of China(11401418)。
文摘The conventional grey GM(2,1)model built for the fast growing time sequence generally has big errors.To improve the modeling precision,the paper improves from the following two aspects:First,the paper transforms the accumulated generating sequence of original time sequence quantitatively to make the transformed time sequence have the better adaptability to the model;second,the paper extends the conventional grey GM(2,1)model’s structure to make the extended model meet the variation law of fast growing sequence better.The extended grey model is called the GM(2,1,Σexp(ct))model.The paper offers the parameter optimization method and the solving method of time response sequence of GM(2,1,Σexp(ct))model.Using the model and methods proposed,the paper builds the GM(2,1,Σexp(ct))models for the natural gas consumption of China and Chongqing City,China,respectively.Results show that the models built have high simulation precision and prediction precision.
基金Supported by the National Natural Science Foundation of China (11401418)。
文摘The common models used for grey system predictions include the GM(1, 1), the GM(1, N),the GM(N, 1), and so on, but their whitening equations are all single ordinary differential equations.However, objects and factors generally form a whole through mutual restrictions and connections when the objective world is developing and changing continuously. In other words, variables affect each other. The relationship can’t be properly reflected by the single differential equation. Therefore, the paper proposes a novel simultaneous grey model. The paper gives a modeling method of simultaneous grey model SGM(1, 2) with 2 interactive variables. The example proves that the simultaneous grey model has high precision and improves the precision significantly compared with the conventional single grey model. The new method proposed enriches the grey modeling method system and has important significance for the in-depth study, popularization and application of grey models.
