Performance-Based Earthquake Engineering (PBEE) aims at designing structures that are able to satisfy multiple target performance levels at different ground motion intensities. The performance levels can be introduced into the overall design process through energy concepts. It is acknowledged that the design of structures protected by control systems such as base isolation or energy dissipation devices can be efficiently optimized by using an energy-based approach. The energy-based design approach incorporated within the probabilistic framework of the performance-based design is a promising design method. In its development, three important energy-based dissipation parameters are critically needed to evaluate, which are the ratio of hysteretic energy to input energy E_H/E_I, normalized cumulative damage η, as well as the equivalent number of cycles n_eq. Therefore, this study has taken a comprehensive investigation of these parameters for four hysteretic systems of structures with the vibration period of 0.05s–4s for 7 damping ratios, that is 0.02, 0.05, 0.1, 0.2, 0.3, 0.4 and 0.5, and 6 ductility factors, that is 2, 3, 4, 5, 6 and 8. Empirical formulas of predicting the mean values and standard deviations of the energy-based dissipation parameters are proposed as a function of vibration period, damping ratio, and ductility factors. The proposed predictive models can be easily and conveniently used to evaluate the energy-based dissipation parameters in a deterministic and probabilistic manner in the energy-based design in the framework of PBEE.

基于性能的地震工程（PBEE）旨在设计能够在不同的地面运动强度下满足多个目标性能水平的结构。可以通过能源概念将性能水平引入整个设计过程。公认的是，通过使用基于能量的方法，可以有效地优化受基础隔离或能量消散装置等控制系统保护的结构的设计。基于性能的设计的概率框架中包含的基于能量的设计方法是一种很有前途的设计方法。在其开发过程中，急需评估三个重要的基于能量的耗散参数，即滞后能量与输入能量之比E _H / E _I，归一化累积损伤η以及等效循环数n _eq。因此，本研究对七个阻尼比分别为0.02、0.05、0.1、0.2、0.3、0.4和0.5和6的振动周期为0.05s–4s的四个结构滞回系统的这些参数进行了全面研究。延性因子，即2、3、4、5、6和8。根据振动周期，阻尼比和延性因子，提出了基于能量的耗散参数的平均值和标准偏差预测的经验公式。所提出的预测模型可以在PBEE框架的基于能量的设计中轻松，方便地以确定性和概率的方式评估基于能量的耗散参数。