## 1 Introduction  
Power electronic systems are essential in fields like renewable energy, aerospace, and electric vehicles because they offer high efficiency and precise control [1, 2]. Despite their advantages, these systems often face reliability challenges in harsh environments. Among their critical components are power semiconductor devices, particularly insulated gate bipolar transistors (IGBTs), which are highly effective but also vulnerable to failure [3]. To enhance system reliability, it is crucial to understand how real-world stresses affect these components and to develop models that predict their lifespan. According to industry-focused surveys [4, 5], semiconductor switches and capacitors are the components in power converters most prone to failure. Random failures are primarily attributed to unexpected overloads and system transients. In contrast, long-term wear-out failures are predominantly caused by thermal stresses, mechanical vibrations, and humidity. In recent year,s several research works have been conducted to investigate the impact of thermal stresses on the lifespan of IGBTs. Reference [6] highlights the differences in power cycling test results between DC and switching modes, focusing on thermal stresses in IGBT power modules, particularly bond-wire contacts and interconnections. It was found that, under identical \(\Delta T_{j}\) conditions, the higher load current in DC mode induces greater thermal stress on bond wires compared to switching mode, resulting in slightly higher local \(\Delta T\) and reduced lifetime. A thermal fatigue feedback loop method has been suggested in [7] to assess the lifetime of an IGBT module, considering the cumulative impact of solder-layer fatigue. A three-dimensional (3D) finite element method (FEM) model is developed for the IGBT module, and, combined with accelerated aging experiments, it highlights the significance of the accumulated thermal resistance increase in thermal network modeling and lifetime evaluation. The Cauer thermal network is then enhanced to create the fatigue feedback loop model, incorporating the effects of solder-layer fatigue to better estimate the power module's lifetime. As mentioned, power cycling and thermal stress failure mechanisms have been thoroughly researched, while the impact of vibrational stress on IGBT modules is still not well-understood and warrants further exploration. Bridging this knowledge gap is essential for enhancing the design and performance of IGBT modules in practical applications. Vibrations, which can originate from diverse sources, may manifest as either random or harmonic. In addition, in real-world environments, vibrations typically exhibit a random nature [8]. In the aviation, wind turbines, and automotive industries, numerous products are subjected to vibrational conditions during operation. Among these environments, simple harmonic vibrations represent the most basic form, while random vibrations are the most prevalent [9]. Simple harmonic vibration represents the most fundamental type of vibration, as any periodic vibration can be constructed by combining multiple simple harmonic vibrations. In contrast, random vibration is the most intricate form, requiring probabilistic methods for analysis. Random vibration analysis, often referred to as power spectral density (PSD) analysis, is a spectral analysis technique grounded in probability and statistics. It converts time-history statistical samples into a power spectral density representation [8]. The main contributions of this paper are as follows:  
* Modal analysis was performed on the IGBT module to determine its natural frequencies. These identified frequencies were then compared with the vibration frequencies present within the wind turbine nacelle to evaluate potential resonance effects.