Dynamic demand estimation on large scale networks using Principal Component Analysis: The case of non-existent or irrelevant historical estimates
Dynamic demand estimation on large scale networks using Principal Component Analysis: The case of non-existent or irrelevant historical estimates
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DOI：
10.1016/j.trc.2021.103504
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发表时间：
2022-03
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通讯作者：
Moeid Qurashi;Qingying Lu;Guido Cantelmo;C. Antoniou
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文献类型：
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作者：
Moeid Qurashi;Qingying Lu;Guido Cantelmo;C. Antoniou
由于涉及不确定性，非线性和维数，DTA模型的校准是复杂的，限制了传统校准方法的应用，特别是对于较大的网络。为此，主成分分析（PCA）正在慢慢建立自己作为新的艺术状态，因为它可以大大解决两个众所周知的挑战，即问题的维度和非线性。PCA应用程序将优化搜索空间限制在由正交主成分定义的较低维度空间中，并根据一组历史估计进行评估。在本文中，我们解决了基于PCA的校准技术的实际实施问题。具体来说，我们制定了一个数据同化框架，提出多个OD历史数据集生成方法，允许使用基于PC的算法的情况下，历史数据是不相关的或不可用的，通常是大规模的DTA模型的情况下。此外，我们提出了一个简化的问题公式，利用新的数据集生成框架的属性，并有助于更快，更有效的校准。该方法使用PC-SPSA算法实现，该算法将PCA与流行的同时扰动随机近似（SPSA）算法相结合，通常用于校准较小的网络。该方法进行了测试的大规模案例研究的慕尼黑大都市城市网络，令人鼓舞的校准结果。拟议的数据同化框架可以占空间，时间和日常的需求变化。不同的方法和组合进行了测试和比较。结果表明，为了避免过度拟合问题，应该使用所有这些相关性。此外，PCA和PC-SPSA的实现特性也使用不同的敏感性分析进行了探索，以评估使用PCA的代价和好处，即，简化SPSA超参数，历史数据集生成参数的作用和算法对不同目标需求波动的性能。分析表明，PC-SPSA的鲁棒性令人鼓舞的结果，并有助于建立简化的指导方针，实际上在大规模DTA模型上实施这样的PCA方法。
Calibrating DTA models is complex due to the involved indeterminacy, non-linearity, and dimensionality, restricting the application of conventional calibration approaches, especially for larger networks. For this, Principal Component Analysis (PCA) is slowly establishing itself as the new state of the art because it can greatly tackle two well known challenges—i.e. problem dimensionality and non-linearity. PCA application limits the optimization search space in a lower dimension space, defined by orthogonal Principal Components, evaluated upon a set of historical estimates. In this paper, we solve practical implementation problems for PCA-based calibration techniques. Specifically, we formulate a data-assimilation framework to propose multiple OD historical data-set generation methods which allows the use of PC-based algorithms in case the historical data is irrelevant or unavailable, often the case for large-scale DTA models. Furthermore, we propose a simplified problem formulation that leverages properties of the novel data-set generation framework and helps for faster and more efficient calibration. The methodology is implemented using the PC-SPSA algorithm, which combines PCA with the popular Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm, commonly used to calibrate smaller networks. The approach is tested on a large-scale case study of the Munich metropolitan urban network, with encouraging calibration results. The proposed data-assimilation framework can account for spatial, temporal, and day-to-day variations in the demand. Different methods and combinations are tested and compared. The results suggest that all these correlations should be used in order to avoid over-fitting issues. Furthermore, the implementation properties of PCA and PC-SPSA are also explored using different sensitivity analyses to assess the toll and benefits of using PCA i.e., ease in SPSA hyper-parameter, role of historical data-set generation parameters and the algorithm’s performance against different target demand fluctuations. The analysis shows encouraging results for PC-SPSA robustness and helps establishing simplified guidelines for implementing such PCA-methods practically on large-scale DTA models.