基于分形理论的交通事故分析

以某市交通事故统计资料为例,首先采用功率谱分析方法论证了分形理论用于交通事故分析的可行性,计算结果表明在统计意义上,该市交通事故时间序列具有自仿射性。接着利用分形的自相似性与标度不变性将内区间的分形特性进行延拓,并由此构造了具有外推功能的分形插值算法,实现交通事故预测。该算法利用内区间的迭代函数系和吸引子由特定初始点进行搜索,通过迭代使得到的点集与吸引子的均方偏差最小,从而获得需要外推点的函数值作为预测值。最后对交通事故时间序列进行R/S分析,进一步验证了预测结果的合理性,结果表明该市未来几年交通事故仍有增长趋势,应继续加强交通管理。

Analysis of Traffic Accident Based on Fractal Theory

Taking statistic data of traffic accidents of a city as an example,the feasibility to analyze traffic accident using fractal theory was demonstrated firstly by power spectrum analysis.The calculation result shows that in the sense of statistics,time series of annual distribution of traffic accidents has certain self-affinity.Then the fractal property of inner interval was extended outwards by self-similarity and scale invariance of fractal,and on this basis a fractal extrapolation algorithm was proposed to realize the prediction of traffic accidents.By this algorithm the search was performed from a certain initial point by use of iterated function system and attractor of inner interval.When the mean square deviation between point set obtained by iteration and attractor become the minimum,the prediction value can be used as the function value of the point to be extrapolated.Finally,the R/S fractal analysis of time series of traffic accidents further shows that the forecasting value is reasonable.Case study results show that there will still be growth trend in the next few years and traffic management should be continued to strengthen.