## 3 Adaptation of Particle Swarm Optimization and the Proposed Weighted Control Algorithm  
Particle swarm optimization (PSO) is an iterative, population-based learning technique that is derived from the idea of swarm intelligence [26]. In PSO, a number of particles are dispersed randomly in a search space and each particle location is evaluated according to a specified fitness function. With each iteration of the algorithm, every particle moves to a new location in the search space based on its own history as well as on the behavior of other nearby particles. The overarching goal of the particle is to move closer to the optimum of the fitness function. To achieve this, each particle in the swarm tracks three vectors: \(\mathbf{x}\), which is the current position of the particle, \(\mathbf{v}\), which is its current velocity, and \(\mathbf{x_{b}}\), which is the previous best position of the particle. Each particle also interacts with neighboring particles and stores the best position found from all neighbors, \(g\), in order to leverage the benefits of the swarm. Each particle updates its three vectors every iteration through the equations:  
\[v_{i}(k+1)=\lambda v_{i}(k)+\rho_{1}\gamma_{1}(x_{b,i}(k)-x_{i}(k))+\rho_{2} \gamma_{2}(g(k)-x_{i}(k)), \tag{1}\]  
\[x_{i}(k+1)=x_{i}(k)+v_{i}(k+1), \tag{2}\]  
and  
\[\lambda=\lambda\times\tau, \tag{3}\]  
where \(i\) is the particle number, \(k\) is the iteration number, \(\rho_{1}\) and \(\rho_{2}\) are random numbers between 0 and 1, and \(\gamma_{1}\) and \(\gamma_{2}\) are the acceleration coefficients which are both assigned to be 2 as recommended in [26]. Equation (3) also includes an inertia weight, \(\lambda\), which affects the convergence and plays a role in balancing the desire of the particle to search locally versus globally [27]. An inertia damping constant, \(\tau\), is used to gradually modify this balance. \(\lambda\) is initially assigned to be 1 and is decreased using \(\tau\) equal to 0.99 [28], which results in a global search that gradually becomes more localized. At the end of each iteration, each position of the particle is evaluated according to a fitness function and the best position is updated if applicable. As will be discussed, the search space in this particular application has high dimensionality (\(x\in\mathbb{R}^{275x1}\)) and each element in the vector can assume a large range of values, from -1E8 to 1E8. As a result, it is easy for a particle to diverge from a localized optimal solution, resulting in an extremely large cost function. To alleviate this challenge, the algorithm was modified to include a homing mechanism for the particle. If the fitness function of the particle significantly exceeds the fitness found from the best position of all of the neighbors, the particle returns to its previously identified local best position. The particle also resets its velocity to zero to prevent it from quickly diverging again. This modified PSO algorithm is termed PSO-H. The algorithm is depicted in the block diagram shown in Figure 1.  
The PSO-H algorithm is used to optimize the necessary control parameters for executing a control algorithm that was originally proposed in [25]. At the core of this algorithm is a novel sensing paradigm that is based on the mechanisms employed by the mammalian cochlea, first implemented by [PERSON] for structural monitoring purposes [29; 30]. In this paradigm, the response of the structure is decomposed into its frequency components in real-time using a series of overlapping bandpass filters. As discussed in [11; 12], this bank of bandpass filters is optimized to fit the input signal by modifying the number of filters in the bank as well as their center frequency increments and passband frequency. The ability of this filter bank to decompose a signal into frequency components is attractive for the purposes of control, as it allows for instantaneous feature extraction, resulting in minimal signal processing at the actuation node.