## 1 Introduction
To accurately predict the optimum belt speed, [PERSON] et al. [29] established the relationships between the belt speed and material instantaneous flow rate. Still, the energy consumption mechanism of a belt conveyor has not been reported yet. Presently, optimal control is a well-accepted approach in energy optimization field [30; 31; 32]. Based on the practical engineering problem, [PERSON] [33] deduced a speed control strategy that considered the parameters of friction force, power consumption, number of bags per hour and the interval time between two adjacent bags to reduce the power consumption of the baggage transport system. Mathematically, the above coordination is usually formulated as a kind of optimization problem. Typically, an accurate energy model is one of the key optimization objectives of belt conveyor's energy optimization problem. Based on the International Organization for Standardization (ISO) 5048, an energy model of belt conveyors was proposed for calculation of the drive power [34]. Figure 1: The phenomena of unevenly distributed or intermittent bulk materials on the conveyor belt. Then, this model can be used as the optimization objective with other operation constraints to assess the optimal scheduling of conveyor belts in a coal power plant [35]. With the consideration of time-of-use (TOU) tariff, load shifting was achieved by operation efficiency optimization. In order to improve the practicability, a closed-loop model predictive control (MPC) methodology was proposed to deal with the disturbances arising from coal consumption forecasting and the feed rate [36]. Furthermore, [PERSON] and [PERSON] [37] took conveying systems and crushers as a whole for energy efficiency optimization and firstly investigated the energy models of belt conveyors and ring hammer crushers. It should be noted that to a large extent, the dynamic characteristics determine the working performance [38]. However, both energy improvement methods at equipment level and operational level did not consider the dynamic characteristics of a belt conveyor in transient operation. For example, detrimental vibrations may occur on the belt and conveyor structures when the material flow fluctuates. That is because the dynamic characteristics of a fabric conveyor belt is nonlinear and viscoelastic. When speed adjustment is not properly controlled on the belt, it will cause potential risks, such as belt slipping around pulley and belt tearing at the splicing area, especially when the speed changes dramatically [39]. Based on Deutsches Institut fur Normung (=German Industry Standard, DIN) 22101, [PERSON] [40] questioned the appropriateness of speed control for energy savings because the nonlinear and viscoelastic dynamic characteristics of the conveyor belts were not considered. The speed control strategy must fulfil the reliability and safety requirements of the belt conveyor system. [PERSON] et al. [41; 42; 43] proposed the Estimation-Calculation-Optimization (ECO) method to adjust the control parameters of the belt conveyor system after dynamic characteristics analysis. It could greatly improve the reliability of the speed control system of the belt conveyor. [PERSON] [44] provided a reliability assessment of a single motor drive on a belt conveyor station with a changeable structure of frequency converter power modules. Nevertheless, their approach did not consider actual non-uniform material distribution either. Furthermore, today's conveyor belts have been built with longer transmission distance, up to tens of kilometers. For such a long conveyor belt, complex characteristics will be always expected, such as nonlinear, hysteresis, creep, and relaxation. It becomes even more complicated due to the interactions of the belt and the bulk material. At present, a variety of theoretical and numerical methods have been developed to simulate the dynamic characteristics of this long belt [45; 46; 47]. The theoretical calculation of longitudinal belt characteristics only considers a uniform bulk material distribution.