Robust Regression Analysis with LR-Type Fuzzy Input Variables and Fuzzy Output Variable

In this paper, we propose a fuzzy linear regression model with LR-type fuzzy input variables and fuzzy output variable, the fuzzy extent of which may be different. Then we give the iterative solution of the proposed model based on the Weighted Least Squares estimation procedure. Some properties of the estimates are proved. We also define suitable goodness of fit index and its adjusted version useful to evaluate the performances of the proposed model. Based on the Least Median Squares-Weighted Least Squares (LMS-WLS) estimation procedure, we give robust estimation steps for the proposed model. Compared with the well-known fuzzy Least Squares method, the effectiveness of our model on reducing the outliers influence is shown by using two examples.

Fuzzy identification of nonlinear dynamic system based on selection of important input variables

Input variables selection(IVS) is proved to be pivotal in nonlinear dynamic system modeling. In order to optimize the model of the nonlinear dynamic system, a fuzzy modeling method for determining the premise structure by selecting important inputs of the system is studied. Firstly, a simplified two stage fuzzy curves method is proposed, which is employed to sort all possible inputs by their relevance with outputs, select the important input variables of the system and identify the structure.Secondly, in order to reduce the complexity of the model, the standard fuzzy c-means clustering algorithm and the recursive least squares algorithm are used to identify the premise parameters and conclusion parameters, respectively. Then, the effectiveness of IVS is verified by two well-known issues. Finally, the proposed identification method is applied to a realistic variable load pneumatic system. The simulation experiments indi cate that the IVS method in this paper has a positive influence on the approximation performance of the Takagi-Sugeno(T-S) fuzzy modeling.

Application of a simplified ADM1 for full-scale anaerobic co-digestion of cattle slurry and grass silage:assessment of input variability

Mathematical modeling of anaerobic digestion is a powerful tool to predict gas yields and optimize the process.The Anaerobic Digestion Model No.1(ADM1)is a widely implemented model for this purpose.However,modeling full-scale biogas plants is challenging due to the extensive substrate and parameter characterization required.This study describes the modification of the ADM1 through a simplification of individual process phases,characteristic components and required parameters.Consequently,the ability of the simplified model to simulate the co-digestion of grass silage and cattle slurry was evaluated using data from a full-scale biogas plant.The impacts of substrate composition(crude carbohydrate,protein and lipid concentration)and variability of carbohydrate degradability on simulation results were assessed to identify the most influential parameters.Results indicated that the simplified version was able to depict biogas and biomethane production with average model efficiencies,according to the Nash-Sutcliffe efficiency(NSE)coefficient,of 0.70 and 0.67,respectively,and was comparable to the original ADM1(average model efficiencies of 0.71 and 0.63,respectively).The variability of crude carbohydrate,protein and lipid concentration did not significantly impact biogas and biomethane output for the data sets explored.In contrast,carbohydrate degradability seemed to explain much more of the variability in the biogas and methane production.Thus,the application of simplified models provides a reliable basis for the process simulation and optimization of full-scale agricultural biogas plants.

Attitude Control Considering Variable Input Saturation Limit for a Spacecraft Equipped with Flywheels

A new attitude controller is proposed for spacecraft whose actuator has variable input saturation limit. There are three identical flywheels orthogonally mounted on board. Each rotor is driven by a brushless DC motor （BLDCM）. Models of spacecraft attitude dynamics and flywheel rotor driving motor electromechanics are discussed in detail. The controller design is similar to saturation limit linear assignment. An auxiliary parameter and a boundary coefficient are imported into the controller to guaran- tee system stability and improve control performance. A time-varying and state-dependent flywheel output torque saturation limit model is established. Stability of the closed-loop control system and asymptotic convergence of system states are proved via Lyapunov methods and LaSalle invariance principle. Boundedness of the auxiliary parameter ensures that the control objective can be achieved, while the boundary parameter＇s value makes a balance between system control performance and flywheel utilization efficiency. Compared with existing controllers, the newly developed controller with variable torque saturation limit can bring smoother control and faster system response. Numerical simulations validate the effectiveness of the controller.