基于模糊非线性回归的煤炭发热量预测研究

Prediction research of calorific value of coal based on fuzzy nonlinear regression

针对经典线性回归模型无法反映变量间的非线性关系,不适宜预测有模糊数的煤炭发热量的问题,提出了一种基于三角模糊数的多元非线性回归的煤炭发热量预测模型。以我国新疆伊犁地区煤炭工业分析为建模数据和模型检验数据,将计算模糊中心值和模糊幅度值的问题转化为约束非线性优化问题,采用MATLAB优化工具箱求解。最后对比分析了模糊非线性回归、经典线性回归、BP(Back Propagation)神经网络及支持向量机回归4种模型对测试煤样发热量的预测结果。结果表明,模糊非线性回归模型的线性拟合优度值为0.9997,调整后的非线性拟合优度值为0.9838,均方误差为0.4473;测试煤样的平均相对误差为0.0203,80%的测试煤样模糊隶属度大于0.5。模糊非线性回归模型具有很高的精确度和可靠性,可用来预测预报煤炭发热量。

In order to cover the shortages of the classical linear regression model,which wasnt able to reflect the nonlinear relationship between variables and forecast the coal calorific value with fuzzy numbers accurately,a kind of multivariate nonlinear regression prediction model of coal calorific based on triangular fuzzy numbers was put forward.The proximate analysis of coal in Yili of Xinjiang was adopted as modeling data and model test data.The calculation of fuzzy center value and fuzzy amplitude value was converted to constrained nonlinear optimization,then the equation was solved with the MATLAB optimization toolbox.The predicting outcomes of calorific value of fuzzy nonlinear regression,traditional linear regression,BP neural network and SVR（ support vector regression） were compared.The results showed that,the figure of merit of fuzzy nonlinear regression model was 0.9997,after adjustment,it was 0.9838,the mean square error was 0.4473.The average relative error of coal samples was 0.0203,the fuzzy membership degree of 80% coal samples were above 0.5. Because of the high accuracy and reliability,the fuzzy nonlinear regression model could be used to predict the coal calorific value.