## 4 Inverse Calculation for Acoustic Impedance of Ventilation Cloth  
The acoustic impedance of the ventilation cloth placed over vents is not easy to obtain, and, hence, has mostly been neglected in earlier research. Moreover, it may compromise the accuracy of the ECM circuit. In this study, an estimation of the acoustic impedance of the ventilation cloth was attempted. Due to the porous nature and thickness of the ventilation cloth, it was assumed that the contribution to acoustic impedance (\(Z_{ap}\)) was due to acoustic resistance (\(R_{ap}\)) only and the effect of acoustic mass (\(m_{ap}\)) was negligible. The PSO algorithm was used to set the SPL measurement curve as the target function, and the acoustic resistance of the ventilation cloth was obtained by inverse calculation. The PSO algorithm was proposed by [PERSON] and [PERSON] [36; 37] in 1995. It was originally conceived to imitate the movement of birds or fishes. The transmission behavior of natural swarms or flocks with a group of particles dropped in the search space has been reported [38]. The PSO optimization revolves around two primary component methodologies. It is understandable due to its ties to artificial life and bird flocking (swarming). It is also related to evolutionary computation and links both genetic algorithms and evolutionary programming. The PSO comprises a straightforward concept that can be executed in a few lines of computer code, requires only primitive mathematical operators, and is computationally inexpensive (in terms of memory requirement and speed). The implementation of PSO relies on two things, nearest-neighbor velocity matching and craziness. Random initialization of the population of birds is performed on a torus pixel grid with a position and X and Y velocities. At each iteration, for each bird, with other agent as its nearest neighbor, determinations are made and X and Y velocities are assigned to the bird in focus. This simple rule creates synchrony of movement. However, the flock quickly settles on a unanimous, unchanging direction. Therefore, a stochastic variable called craziness has been introduced. Each iteration adds some change to randomly chosen X and Y velocities. Such factors introduce enough variation into the system to provide an exciting and \"lifelike\" appearance to the simulation, while at the same time being wholly artificial. Thus, using the concept of information sharing in a biological society to provides opportunities for the particles in a group to communicate with each other and exchange information in the search for a more effective solution for finding the system optimization parameters. In recent years, PSO has been widely used in acoustics including automatic adjustment of off-the-shelf reverberation effects [39], comparison of optimization methods for compression driver design [40], optimization of micro-perforated sound absorber [41], and optimization of acoustic filters [42]. In this work, the parameter to be solved was treated as a particle swarm, and its initial position was \(x\). An objective function \(J(x,f)\) was defined to derive the best position \(x\_opt\) (best solution) of this particle swarm, as follows:  
\[J(x,f)=\sum_{f=20\text{Hz}}^{f=20\text{Hz}}(SPL_{m}(f)-SPL_{s}(x,f))^{2} \tag{8}\]  
The \(SPL_{m}\) is the measured sound pressure level, and \(SPL_{s}\) is the simulated sound pressure level (from the ECM model) of the microspeaker. When the objective function \(J(x,f)\) reached the minimum value during the optimization, the simulated SPL approaches the measured SPL. This indicates that the unknown parameter \(x\) in the objective function has converged to the optimal solution \(x\_opt\).