## 1 Introduction  
Renewable energy represents the most promising avenue for mitigating the impact of climate change [1], serving as a viable alternative to traditional fossil fuel sources. Offshore currents, near-surface wind fields, and shallow rivers contain fluid energies that could potentially serve as renewable energy sources. However, owing to the dispersed and stochastic nature of these energies, achieving centralized and efficient harnessing poses a daunting challenge [2]. The development of effective methodologies and tools for energy harvesting has, thus far, remained elusive to researchers for an extended period of time [3]. In light of the low efficiency of conventional rotating turbines at low Reynolds numbers, [PERSON] [4] proposed a novel energy conversion paradigm that uses the coupling of heaving and pitching motions to harness flow energy. The oscillating foil stands out as a new energy utilization device [5] characterized by its simple structure, low oscillation speed, and low environmental demands. It is increasingly acknowledged as a technology with immense potential for development [6], gradually gaining traction in the commercial design, improvement, and adoption arena. Enhancing the energy harvesting efficiency of oscillating foils' performance by optimizing their motion parameters has been the subject of considerable interest. [PERSON] et al. [7] found that a sufficiently high pitching amplitude converted energy consumption into energy harvesting at a fixed frequency and amplitude. [PERSON] [8] conducted an inquiry into the efficacy of energy harvesting via oscillating foils, with an efficiency of 30% obtained by optimizing amplitude and frequency. [PERSON] and [PERSON] [9] enhanced aerodynamic characteristics by reducing the oscillating foils' pitching amplitude and effective angle of attack to avoid leading edge vortices, resulting in a higher thrust value. [PERSON] and [PERSON] [10; 11] employed NACA series airfoils to study oscillating foils and presented the energy harvesting efficiency-frequency-amplitude relationship. [PERSON] [12] studied foils' aerodynamic characteristics in water at \(Re=13\),800 and a 90\({}^{\circ}\) phase angle, identifying the highest energy harvesting efficiency to be between 0.10 and 0.26 at lower frequencies for lift production. [PERSON] [13] explored the spoiler flow stability and energy harvesting performance relationship and revealed that peak efficiency always appears between 0.10 and 0.15 frequencies as oscillation frequency decreases. [PERSON] reported a numerical effort in studying the performance of a sinusoidally oscillating hydrofoil at a high Reynolds number, addressing the limitation of existing research which has lower Reynolds numbers [14]. Researchers have unearthed that actively changing the shape of oscillating foils during flight, as seen in flying organisms such as birds or fish [15], can increase lift. Minor-scale deformation along the span and chord has been shown to enhance performance by [PERSON] [16]. [PERSON] [17] proposed a rippled foil contour with ripple and curvature, concluding that slender foils exhibit a superior energy harvesting capability. Based on this premise, [PERSON] and [PERSON] [18] discovered that spanwise bending has a smaller influence on power harvesting compared to chordwise bending. [PERSON] et al. [19] found that interplay between changes in shape and vortex shedding could improve energy harvesting performance, while [PERSON] [20] determined that local deformation near the trailing edge could boost lift and improve synchronization with heaving and pitching motions. [PERSON] [21] showed that foil deformation can enhance energy harvesting by studying the following three deformation modes: uniform deformation, leading edge deformation, and trailing edge deformation.