Calibration and validation have long been a significant topic in traffic model development. In fact, when moving to dynamic traffic assignment (DTA) models, the need to dynamically update the demand and supply components creates a considerable burden on the existing calibration algorithms, often rendering them impractical. These calibration approaches are mostly restricted either due to non-linearity or increasing problem dimensionality. Simultaneous perturbation stochastic approximation (SPSA) has been proposed for the DTA model calibration, with encouraging results, for more than a decade. However, it often fails to converge reasonably with the increase in problem size and complexity. In this paper, we combine SPSA with principal components analysis (PCA) to form a new algorithm, we call, PC–SPSA. The PCA limits the search area of SPSA within the structural relationships captured from historical estimates in lower dimensions, reducing the problem size and complexity. We formulate the algorithm, demonstrate its operation, and explore its performance using an urban network of Vitoria, Spain. The practical issues that emerge from the scale of different variables and bounding their values are also analyzed through a sensitivity analysis using a non-linear synthetic function.

中文翻译：

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PC-SPSA：在 DTA 模型校准中使用降维来限制 SPSA 搜索噪声

长期以来，校准和验证一直是交通模型开发中的一个重要主题。事实上，当转向动态交通分配 (DTA) 模型时，动态更新需求和供应组件的需要给现有的校准算法带来了相当大的负担，常常使它们变得不切实际。由于非线性或增加问题维度，这些校准方法大多受到限制。十多年来，已为 DTA 模型校准提出了同时扰动随机近似 (SPSA)，并取得了令人鼓舞的结果。然而，随着问题规模和复杂性的增加，它往往无法合理收敛。在本文中，我们将 SPSA 与主成分分析 (PCA) 相结合，形成了一种新的算法，我们称之为 PC-SPSA。PCA 将 SPSA 的搜索范围限制在从较低维度的历史估计中捕获的结构关系内，从而减少问题的规模和复杂性。我们使用西班牙维多利亚的城市网络制定算法，演示其操作并探索其性能。还通过使用非线性合成函数的敏感性分析来分析因不同变量的规模和限制其值而产生的实际问题。