## 1 Introduction  
A vibroacoustic analysis is an essential step in the design of aircraft, trains, cars, and industrial machines. It ensures the performance, quality, and safety of products and systems. Additionally, vibroacoustic analysis can be used to identify sources of noise and vibration in structures and systems. By comprehending the fundamental reasons for noise and vibrations, it is possible to develop efficient control strategies such as active noise cancelation to mitigate them. When developing modern aircraft designs, it is crucial to take into account the aircraft's noise and vibration features. Tiltrotor aircraft, known for their vertical take-off and landing capabilities, have gained popularity in both military and civilian applications. However, this distinctive configuration introduces novel challenges related to noise generation [1, 2, 3]. In recent years, some studies have proposed new methods or designs to reduce the structure-borne noise inside an aircraft or helicopter. For instance, [PERSON] et al. [4] proposed a novel periodic mono-material strut with geometrical discontinuity for the main gearbox of a helicopter that reduces the structure-borne noise inside the cabin. [PERSON] et al. [5] focused on the possibility-based design optimization (PBDO) method to optimize an electric vertical take-off and landing aircraft in the conceptual design phase. [PERSON] [6] considered the use of active trim panels for interior noise reduction instead of active fuselage structures (with actuators on fuselage panels or frames). In order to mitigate the interior noise of an aircraft, it is important to predict the interior noise properly. Over the past few years, numerous approaches such as statistical energy analysis (SEA) and advanced transfer path analysis (ATPA) have been developed to facilitate the characterization of the vibroacoustic behavior of structures and systems. The ATPA technique is used to identify the transmission paths of vibrations and noise in a system and to quantify the contributions of different components [7; 8]. ATPA involves measuring the vibration and noise levels at various points in a system and then using the theory of transfer matrices to determine the contributions of each path to the overall response [9]. In a network of interconnected nodes, a path between node \(i\) and node \(j\) is recognized if they are directly connected. In the context of a vibroacoustic system, these nodes represent subsystems, and signals (vibrations or acoustic pressure) are utilized to analyze and explore these paths. It is essential to differentiate between a path from \(i\) to \(j\) and a contribution from \(i\) to \(j\). A contribution indicates the signal amount reaching node \(j\) due to an excitation at node \(i\). This signal, however, can be transmitted through various paths from \(i\) to \(j\), irrespective of the direct connection between the two nodes. Thus, contributions describe inputs and outputs, while paths provide a description of the system's topology. The objective is consistently to characterize the response of every subsystem, which is quantified in terms of the acceleration of a vibrating component or the acoustic pressure within a specific area of concern, triggered by a distinct excitation. When considering the studied system as a black box containing \(n\) inputs and \(m\) outputs interconnected within, ATPA can forecast the individual contribution of each input to every output. It achieves this by decomposing the output signal into distinct contributions originating from each input signal. Additionally, ATPA can effectively analyze the interconnections between input and output signals within the black box, revealing the inherent structure of the mechanical system, including the paths through which signals propagate [3]. Consequently, when a comprehensive examination of the mechanical system is required, ATPA proves to be a valuable tool.