CAJ | 학술논문

分形曲线的自仿射性及其工程应用是一个重要研究课题。标度指数是刻画自仿射分形曲线的特征值，Matsushita、Nikora、Sapozhnikov等分别根据方差、测度和对数关联积分提出标度指数的算法。本文分析了上述算法的不足，使用坐标和测度建立了一个新算法。本算法符合分形原理，可较好反映曲线的自仿射性和纵横方向的不同变化特征，计算过程简单明了，便于工程应用。最后，我们应用上述四种算法计算了中国下荆江河道的标度指数，揭示了河道的自仿射性和横向摆动特征，对河道整治工程具有重要参考意义。
분형곡선적자방사성급기공정응용시일개중요연구과제。표도지수시각화자방사분형곡선적특정치，Matsushita、Nikora、Sapozhnikov등분별근거방차、측도화대수관련적분제출표도지수적산법。본문분석료상술산법적불족，사용좌표화측도건립료일개신산법。본산법부합분형원리，가교호반영곡선적자방사성화종횡방향적불동변화특정，계산과정간단명료，편우공정응용。최후，아문응용상술사충산법계산료중국하형강하도적표도지수，게시료하도적자방사성화횡향파동특정，대하도정치공정구유중요삼고의의。
Self-affnity of fractal curves and its application are important research topics. The Scaling exponent is used to describe the eigenvalues of the self-affine fractal curve. Matsushita, Nikora and Sapozhnikov et al have proposed different algorithms of scaling exponent according to variance, measurement and logarithmic correlation integral, respectively. In this paper, we propose a new algorithm by analyzing the demerits of their methods. This new algorithm, based on the fractal theory, may better disclose the self-affinity and variable features of fractal curves in vertical and horizontal directions, and the calculating process is also simple and clear, which can be effectively applied to engineering. Moreover, the self-affine scaling exponent of Lower Jingjiang channel is simulated by the above four algorithms, so as to reveal the self-affinity and lateral oscillation features of waterway, which is of great value to channel improvement engineering.