## 1 Introduction  
Owing to their excellent mechanical properties, such as high specific strength, high specific stiffness and their potential for 'tailor-made' designs, advanced fiber-reinforced composite laminates are widely applied in the fields of aviation and aerospace, etc. Furthermore, the accurate prediction and evaluation on mechanical properties is very important and essential for structural responses, safety evaluation and the optimization design of composites. Here, as a kind of multiphase material, their mechanical performance parameters have some relationships with micro- and meso-structures [1, 2]. They may depend on fibers and matrix. As a result, many models are provided to study the effects of microstructures on many phenomena including mechanical performance quantification [3, 4, 5], damage evolution [6, 7] and failure prediction [8, 9], etc. However, it should be noted that micro- and meso-parameters in those models always show great dispersions or uncertainties owing to the inherent randomness of basic constituent materials including the fibers and matrix, and complicated multi-stage manufacturing processes [10, 11], such as the volume fractions of matrix and fibers, lack or excess amounts of resins in piles, voids and porosity of the matrix and inadequate bonding between the fibers and matrix [12, 13, 14, 15], etc. For example, a new method is proposed to generate random distributions of fibers in the transverse cross-section of fiber-reinforcedcomposites with a high fiber volume fraction for the sake of micro-mechanical analysis [10]. A probabilistic strength model is utilized for unidirectional composites with fibers in hexagonal arrays, where uncertainties in Young's modulus of fibers and matrix, fiber reference strength, fiber volume fraction and shear yield stress are taken into consideration [12]. In addition, a methodology is presented to evaluate the effects of microscopic manufacturing defects including fiber misalignment, waviness and volume fraction on mechanical performance [14]. An RVE-based micro-mechanical elastic damage model is presented to predict the effective elastic moduli in fiber-reinforced composites considering fiber size dependency [16]. In other words, uncertainties in composite materials can be built up from a constituent level (micro-scale), ply level (meso-scale) or a component level (macro-level) [17; 18; 19]. As a result, macro-mechanical parameters are also uncertain as functions of micro-mechanical parameters, and they have a significant influence on structural responses made from composite materials. Furthermore, how to carry out uncertainty quantification of macro-elastic mechanical parameters for composite laminates from a micro-scale perspective has become a valuable and important hot topic [20; 21; 22]. It will play an important role in the risk and reliability assessment of structures made up of composites, such as aircrafts, reusable launch vehicles and other high-risk applications. Generally speaking, the macro-elastic mechanical parameters of composite laminates can be predicted by theoretical analysis [23; 24] or measured by mechanical properties experiments [25; 26]. For example, a series-parallel mixture model is proposed to predict the overall property of particle-reinforced composites with more than two phases [27]. A micro-mechanics-based strength theory is addressed to estimate the ultimate strength of fiber-reinforced composites by [PERSON] [28]. On the basis of this study, a critical reliability evaluation of fiber-reinforced composite materials is carried out by taking good advantages of micro- and macro-mechanical analysis [29]. In addition, a method for the probabilistic failure analysis of laminated composite plates with random system parameters subjected to transverse loads is presented, where the statistics of the baseline random variables can be obtained from experiments [30].