## 1 Introduction  
The electric wheel dump truck is the main carrying equipment in open pit mine. It has 300 tons of load capacity, and runs on uneven road surface for 24 working hours every day [1; 2; 3]. The frame is considered as one of pivotal bearing components, and thence its mechanical properties connected with strength and stiffness have significant influence on vehicle's safe operation [4]. In designing of frame structure, the mechanical parameters and geometrical features are considered as deterministic values. However, there is loading caused by manufacturing process. This influences parental material and creates measurement errors [5], so that the mechanical parameters of engineering frames appear different than nominal [6; 7]. Therefore, determination of the mechanical features of frame based on interval method is required. The blind number theory can characterize the uncertainties of multiple variables, and has simple operation rules and high credibility, which was extensively utilized in engineering fields including numerous uncertain information. [PERSON] et al. [8] presented a comprehensive evaluation model on groundwater resources carrying capacity with blind information. They showed a risk assessment model of surcharge about groundwater resources carrying capacity. Their conception was formulated by means of blind reliability theory. This theory was also applied to define the blind numbers of the parameters of environmental system according to the characteristics of several kinds of uncertainties coexisting in water environmental system [9]. The uncertain variables in time-dependent stochastic process of mechanical structure were expressed in blind number, and its time-dependent reliability calculation model based on blind number theory was established [10]. However, this theory was rarely used to estimate mechanical properties of engineering parts for obtaining the interval parameters. In fact, some difficult working conditions are not easy to be predicted during designing, so that the mechanical features of engineering structures can be insufficient. After determination of the interval values by means of the blind number theory, the redesigning of component at optimization rules is needed. For the uncertain optimization problem, there are usually three methodologies i.e., probabilistic analysis, fuzzy analysis and non-probabilistic interval analysis methods. In the first approach the uncertain mathematical characteristics are transformed into random variables. Their randomness could be characterized by probability distribution function [11; 12]. An optimization method for controller parameters of a gas turbine based on probabilistic robustness was presented and some uncertainties because of errors in measurement and manufacturing tolerances [11; 12]. The membership function is utilized to describe the uncertain parameters using fuzzy theory [13]. A unified method was developed for the uncertainty quantification of dis brake squeal for two fuzzy-interval cases, while the unified uncertain response was computed with the aid of the combination of level-cut strategy, Taylor series expansion, subinterval analysis and Monte Carlo simulation [14]. Both probability distribution function and membership function need a lot of data, however, the engineering problems have finite data [15]. The interval method could make up for the above shortcomings [16]. The reliability optimization design method for turbine disk strength base on interval uncertainty was developed, in which the uncertainty and reliability were represented with interval model and non-probabilistic reliability model [17]. The fatigue strength of the A-type frame was carried out by means of genetic algorithm taking into account uncertainties of the component in design and manufacture [18]. Nevertheless, these papers focus attention to single objective optimization problem, while the interval multi-objectives optimization problem is insufficiently presented.