Research on New Types of Suspension Vibration Reduction Systems (SVRSs) with Geometric Nonlinear Damping

Firstly, this paper puts forward two new types of suspension vibration reduction systems (SVRSs) with geometric nonlinear damping based on general SVRS (GSVRS), which only has geometric nonlinear stiffness. Secondly, it derives the motion differential equations for the two new types of SVRS, respectively, and discusses the similarities and differences among the two types and GSVRS through the comparison of motion differential equations. Then, it conducts dimensionless processing of the motion differential equations for the two new types of SVRS and carries out a comparative study on the vibration isolation performance of the two types of SVRS under impact excitation and random excitation, respectively. At last, it performs the optimal computation of the chosen new type of SVRS through the ergodic optimization method and studies the influence rule of SVRS parameters on vibration isolation performance so as to realize the optimization of vibration isolation performance.

Optimization of Energy Storage Operation Chart of Cascade Reservoirs with Multi-Year Regulating Reservoir

In view of the problems that have not been solved or studied in the previous studies of cascade Energy Storage Operation Chart (ESOC), based on a brief description of the composition, principle, drawing methods, and simulation methods of ESOC, the following innovative work has been done in this paper. Firstly, considering the inconsistency of inflow frequency of upstream and downstream watershed in selecting the typical dry years, a novel optimization model for selecting the overall inflow process considering the integrity of watershed was proposed, which aimed at minimizing the sum of squares of inflow frequency differences. Secondly, aiming at the influence of output coefficients (including number and values) on the results of ESOC, this paper proposed a new method to construct the initial solution of output coefficients and established an optimization model of output coefficients based on progressive optimality algorithms. Thirdly, to the optimization of ESOC with multi-year regulating reservoir, a discrete optimization model of drawdown level was constructed based on the idea of ergodic optimization. On these bases, taking the seven reservoirs in the Yalong River basin of China as an example, the typical dry years considering the inflow frequency inconsistency, the optimal output coefficients of ESOC and the optimal end-of-year drawdown level of a multi-year regulating reservoir (Lianghekou) were obtained, and compared with the previous research results, the ESOC optimized in this paper can increase the total power generation of the cascade system by 9% under the condition that the guaranteed rate did not change much. Furthermore, the difference of the optimal end-of-year drawdown levels between the cascade joint operation and single reservoir operation was discussed for the Lianghekou reservoir at the end of the case study. The obtained results were of great significance for guiding the actual operation of cascade reservoirs.

Support stability of maximizing measures for shifts of finite type

This paper establishes a fundamental difference between $\mathbb{Z}$ subshifts of finite type and $\mathbb{Z}^{2}$ subshifts of finite type in the context of ergodic optimization. Specifically, we consider a subshift of finite type $X$ as a subset of a full shift $F$ . We then introduce a natural penalty function $f$ , defined on $F$ , which is 0 if the local configuration near the origin is legal and $-1$ otherwise. We show that in the case of $\mathbb{Z}$ subshifts, for all sufficiently small perturbations, $g$ , of $f$ , the $g$ -maximizing invariant probability measures are supported on $X$ (that is, the set $X$ is stably maximized by $f$ ). However, in the two-dimensional case, we show that the well-known Robinson tiling fails to have this property: there exist arbitrarily small perturbations, $g$ , of $f$ for which the $g$ -maximizing invariant probability measures are supported on $F\setminus X$ .