Background value is an important factor for the simulation precision and prediction accuracy of the grey system multivariate GM( 1 ,N) model. Usually, the traditional grey system multivariate GM( 1 ,N) model uses integral of trapezoidal method to calculate background value, unfortunately, in fact the error is large in practice. In order to improve the simulation precision and prediction accuracy, some papers published about how to build or improve the background value of grey system GM (1,1) model were studied, and based on approximation approach of numerical analysis, Newton-Cores Formula and Gauss-Legendre formula with higher precision were introduced to optimize the background. It showed that this method can improve the prediction accuracy effectively. Then, the optimized grey system multivariate GM( 1 ,N) model was applied to forecast traffic noise of the city. The average relative error of forecast data by the optimized grey system multivariate GM(1,7V) model deceased from original 2. 913% to 1. 108%. Application example showed that the simulation precision of optimized grey system multivariate GM(l,iV) model is higher than traditional grey system GM(1,1) model. The analysis and typical examples demonstrate the validity and applicability of the optimized method on simulation precision aspect. In addition, the rnoptimized method provides a new way to improve the prediction accuracy.%背景值是影响GM(1,N)模型模拟精度和预测精度的重要因素.传统灰色系统多因素GM (1,N)模型对背景值采用梯形法求积,误差较大.为了提高GM(1,N)模型的精度,基于数值分析中的逼近思想,采用数值积分中的Newton-Cores公式和Gauss-Legendre公式对背景值进行修正求积.理论分析表明该方法能够有效地提高模型的预测精度.然后将经过优化的GM(1,N)模型应用到城市道路交通噪声的预测上,模型预测值的平均误差从2.913％降低到了1.108％.应用实例表明优化后的GM(1,N)模型精度比原始GM(1,1)模型精度有较大提高,验证了该优化方法的实用性和有效性,且该方法为提高模型的预测精度提供了新的途径.
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