<p>To cope with the difficulties of quantifying uncertainty precisely in practical engineering, this paper proposed a systematic data-based method for non-probabilistic convex modelling under dependent uncertainty variables. In this method, marginal intervals of uncertain variables were determined from data by the grey mathematics and the width factors of marginal intervals were defined. The correlation analysis technique was adopted to establish characteristic matrixes of convex models and to unify their modelling process. After that, the width factor of marginal interval was adaptively corrected and the precise convex models enclosing all data were established. Besides, to ensure the quality of data and the accuracy of convex modelling results, the grey judgment criterion and cluster analysis were used for preprocessing data. In the end, the effectiveness and superiority of the proposed method were illustrated in detail through three numerical examples and by corresponding comparisons with the competitive methods existed. Meanwhile, the applicability of the proposed method in engineering was demonstrated by biaxial tensile testing machine.</p>