ABSTRACT

An optimal novel approach is proposed to estimate the transition probabilities associated with both homogeneous and non-homogeneous Markov chains. The approach applies an exhaustive optimisation technique to search for the optimal transition probabilities associated with minimal sum of squared errors (SSE), wherein the error defined as the difference between predicted and observed pavement condition ratings. Three state transitions are allowed in constructing the relevant transition probability matrix (TPM). In the homogenous chain, the approach yields one optimal TPM applicable to an analysis period of (n) years. Whereas, one distinct optimal TPM can be derived for each year if non-homogenous chain is deployed. A sequential iterative optimisation approach is proposed wherein the optimal TPM for a given year becomes the input for the subsequent year. Sample results are presented for two projects (A & B) with superior and inferior performances, respectively. The sample results indicate that the non-homogenous chain provided significant reduction in the SSE compared to the homogeneous one. However, the use of 10 condition states instead of 5 resulted in moderate reduction in the SSE considering both homogeneous and non-homogeneous Markov chains. Also, the results indicate that the use of three state transitions made significant impact when deploying 10 condition states instead of 5 especially in the case of inferior performance.

摘要

提出了一种最佳的新颖方法来估计与同构和非同构马尔可夫链相关的跃迁概率。该方法应用了详尽的优化技术来搜索与最小平方误差之和（SSE）相关的最佳过渡概率，其中误差定义为预测的路面状况等级与观察的路面状况等级之间的差。在构造相关的转移概率矩阵（TPM）时，允许进行三个状态转移。在同质链中，该方法可得出一个最佳TPM，适用于（n）年的分析时间。而如果部署了非同质链，则每年可以得出一个不同的最佳TPM。提出了一种顺序迭代优化方法，其中给定年份的最佳TPM成为下一年的输入。分别给出了两个表现优异和劣质的项目（A和B）的样本结果。样本结果表明，与同质链相比，非同质链显着降低了SSE。但是，使用10个状态而不是5个状态会同时考虑均质和非均质马尔可夫链，导致SSE的适度降低。同样，结果表明，在部署10个状态状态而不是5个状态状态时，使用三个状态转换会产生重大影响，尤其是在性能较差的情况下。样本结果表明，与同质链相比，非同质链显着降低了SSE。但是，使用10个状态而不是5个状态会同时考虑均质和非均质马尔可夫链，导致SSE的适度降低。而且，结果表明，在部署10个状态状态而不是5个状态状态时，使用三个状态转换会产生重大影响，尤其是在性能较差的情况下。样本结果表明，与同质链相比，非同质链显着降低了SSE。但是，使用10个状态而不是5个状态会同时考虑均质和非均质马尔可夫链，导致SSE的适度降低。而且，结果表明，在部署10个状态状态而不是5个状态状态时，使用三个状态转换会产生重大影响，尤其是在性能较差的情况下。