## 1 Introduction  
With the rapid development of electronic devices towards smaller sizes and lower power consumption, energy harvesting has become a realistic method to replace chemical batteries and provide power autonomy for wireless sensor networks [1]. Vibration energy, as a ubiquitous form of ambient energy, has attracted significant attention nowadays [2]. Piezoelectric [3], electromagnetic [4], electrostatic [5], and triboelectric [6] are the most prevalent modes of transduction mechanisms in this field. Among these conversion mechanisms, piezoelectric energy harvesting has been most extensively investigated because of its high efficiency, simple construction, high energy density, and lack of electromagnetic interference with the devices [7]. Much research has validated the aforementioned opinions. For instance, [PERSON] et al. [8] proposed the concept of optimized nonlinear energy harvesting for bridge structures. [PERSON] et al. [9] developed an enhanced piezoelectric wind vibration energy harvester that improved reliability, environmental adaptability, and power generation performance through the interaction between a cylindrical shell and a diamond baffle. [PERSON] et al. [10] proposed an energy harvester that contains an energy barrier, which converts energy from wind-induced vortex excitations into electrical energy using PVDF. Inspired by the flight mechanism of dipteran, [PERSON] et al. [11] proposed a novel bionic-dipteran energy harvester to collect ultralow-frequency vibration energy. [PERSON] et al. [12] systemic investigated the influence of frequency-up conversion effect on piezoelectric stack generators for high-performance energy harvesting. [PERSON] et al. [13] proposed a novel bistable piezoelectric energy harvester using easy to breakthrough potential well performance to increase output power. In order to improve the working efficiency of the energy harvester, many research studies have been conducted in this field. In summary, it involves three nonlinear technology methods: amplitude/frequency amplification technology, resonance tuning technology, and multi-stability technology. As for the amplitude amplification technology, the notable research work includes [PERSON] et al. [14], who introduced a novel energy harvester using a piezoelectric transducer to convert mechanical impact energy into electric energy. [PERSON] et al. [15] proposed a host-parasite vibration harvester that was designed to scavenge random low-frequency vibrations by incorporating bi-stability and frequency up-conversion. Using resonance tuning technology can enhance the performance of energy harvest by operating harvester at its resonance frequency. For example, [PERSON] et al. [16] presented a breakthrough in demonstrating ultra-wide bandwidth piezoelectric energy harvesters through the automatic resonance tuning phenomenon. [PERSON] et al. [17] systematically investigated a new proposed energy harvester that employs automatic resonance tuning technology to enhance energy harvesting efficiency. The implementation of these technologies has improved the efficiency of energy harvesters, but most of these designs have complex structures and high production costs, which to some extent limit the application of these technologies [18]. In order to address the aforementioned shortcomings, multi-stable energy acquisition technology has received increasing attention [19; 20; 21]. Among these technologies, bistable technology has been extensively studied due to its advantages such as simple structure, ease of describing mathematical models, and good energy capture effect [22; 23; 24]. In multi-stable power systems, the potential function of the system is divided into multiple potential energy wells by potential energy barriers, and the number of potential energy wells is the same as the number of stable states of the system [25; 26; 27]. Theoretical and experimental research results indicate that the shape of the potential energy well has a significant impact on the performance of the multi-stable collector.