Summary: In real-world engineering, uncertainty is ubiquitous within material properties, structural geometry, load conditions, and the like. These uncertainties have substantial impacts on the estimation of structural performance. Furthermore, information or datasets in real life commonly contain imperfections, e.g., noise, outliers, or missing data. To quantify these impacts induced by uncertainties on structural behaviours and reduce the effects of data imperfections simultaneously, a machine learning-aided stochastic analysis framework is proposed. A novel supervised machine learning technique, namely the Capped Extended Support Vector Regression (CX-SVR) technique, is developed to effectively suppress the effects of outliers and noise in datasets. Its inherent convexity in optimization and capped strategy theoretically supports the accuracy of CX-SVR, especially in handling datasets with imperfections. Once the effective surrogate model is established, subsequent analyses, like sampling-based methods, can circumvent the cumbersome physical model, which is potentially the nest of computational burden and errors in engineering applications. The high robustness of the proposed approach can be summarized in four main aspects: unrestrictive selection of the system inputs and their statistical information, ‘perfect’ or ‘imperfect’ data, enough statistical information (including statistical moments, probability density functions, and cumulative distribution functions) of the system outputs, and physical problems from various engineering fields.