A key aspect of technical debt (TD) management is the ability to measure the amount of principal accumulated in a system. The current literature contains an array of approaches to estimate TD principal, however, only a few of them focus specifically on architectural TD, and none of these are fully automated, freely available, and thoroughly validated. Moreover, a recent study has shown that many of the current approaches suffer from certain shortcomings, such as relying on hand-picked thresholds. In this paper, we propose a novel approach to estimate architectural technical debt principal based on machine learning and architectural smells to address such shortcomings. Our approach can estimate the amount of technical debt principal generated by a single architectural smell instance. To do so, we adopt novel techniques from Information Retrieval to train a learning-to-rank machine learning model that estimates the severity of an architectural smell and ensure the transparency of the predictions. Then, for each instance, we statically analyse the source code to calculate the exact number of lines of code creating the smell. Finally, we combine these two values to calculate the technical debt principal. To validate the approach, we conducted a case study and interviewed 16 practitioners, from both open source and industry, and asked them about their opinions on the TD principal estimations for several smells detected in their projects. The results show that for 71% of instances, practitioners agreed that the estimations provided were representative of the effort necessary to refactor the smell.