What Is Echolocation and How Does It Work

Echolocation

Echolocation allows these animals to practically "see" the objects of desire, say food or smaller targets to be preyed, or obstructions in their path of motion, by interpreting the reflected sound wave echoes.

From: Real-Time Data Acquisition in Human Physiology , 2021

Bio-inspired engineered sonar systems based on the understanding of bat echolocation

S. Kim , in Biomimetic Technologies, 2015

7.1 Introduction

Echolocation is an acoustical process which is used to locate and identify a target by sending sound pulses and receiving the echoes reflected back from the target. Echolocation is used by several mammals including dolphins, whales, and bats. The echolocation in bats has attracted large number of scientific researches due to their extraordinary abilities to fly in complete darkness and to use echolocation to capture their prey as well as to communicate between themselves by using self-generated bio-sonar signals. Since bat echolocation was first observed ( Griffin, 1958), their ability has attracted much interest not only from researchers looking at bat's biological and physiological characteristics but also from those in engineering who have been trying to learn from biological echolocating behavior and apply the principles to sonar engineering. Müller and Kuc (2007) have extensively reviewed bio-sonar-inspired technology motivated by echolocating animals. In their review, the importance of insights into various echolocating tasks solved by bats has been stressed as it potentially provides a wide range of methodologies for engineering of any technical sonar system. For example, binaural tracking sensors and rotational sensors have been motivated by the hearing mechanism of two ears and movement of external ears in bats (Barshan and Kuc, 1992; Kuc, 1996, 1997a,b, 2002; Carmena and Hallam, 2001; Carmena et al., 2001).

In this chapter, we will introduce an overview of bat echolocation and explore what is already known from previous research. Then we will investigate further what we can learn from bat bio-sonar to inspire engineers to develop more sophisticated sonar systems.

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Sparsity-Aware Learning: Algorithms and Applications

Sergios Theodoridis , in Machine Learning (Second Edition), 2020

Time-Frequency Analysis of Echolocation Signals Emitted by Bats

Bats use echolocation for navigation (flying around at night), for prey detection (small insects), and for prey approaching and catching; each bat adaptively changes the shape and frequency content of its calls in order to better serve the previous tasks. Echolocation is used in a similar way for sonars. Bats emit calls as they fly, and "listen" to the returning echoes in order to build up a sonic map of their surroundings. In this way, bats can infer the distance and the size of obstacles as well as of other flying creatures/insects. Moreover, all bats emit special types of calls, called social calls, which are used for socializing, flirting, and so on. The fundamental characteristics of the echolocation calls, for example, the frequency range and average time duration, differ from species to species because, thanks to evolution, bats have adapted their calls in order to become better suited to the environment in which a species operates.

Time-frequency analysis of echolocation calls provides information about the species (species identification) as well as the specific task and behavior of the bats in certain environments. Moreover, the bat biosonar system is studied in order for humans to learn more about nature and get inspired for subsequent advances in applications such as sonar navigation systems, radars, and medical ultrasonic devices.

Fig. 10.16 shows a case of a recorded echolocation signal from bats. Zooming at two different parts of the signal, we can observe that the frequency is changing with time. In Fig. 10.17, the DFT of the signal is shown, but there is not much information that can be drawn from it except that the signal is compressible in the frequency domain; most of the activity takes place within a short range of frequencies.

Figure 10.16. The recorded echolocation signal. The frequency of the signal is time-varying, which is indicated by focusing on two different parts of the signal.

Figure 10.17. Plot of the energy of the DFT transform coefficients, S _i . Observe that most of the frequency activity takes place within a short frequency range.

Our echolocation signal was a recording of total length $T=21.845\text{ms}$ [75]. Samples were taken at the sampling frequency $f_s=750$ kHz, which results in a total of l= 16,384 samples. Although the signal itself is not sparse in the time domain, we will take advantage of the fact that it is sparse in a transformed domain. We will assume that the signal is sparse in its expansion in terms of the Gabor dictionary.

Our goal in this example is to demonstrate that one does not really need all 16,384 samples to perform time-frequency analysis; all the processing can be carried out using a reduced number of observations, by exploiting the theory of compressed sensing. To form the observations vector, y , the number of observations was chosen to be $N=2048$ . This amounts to a reduction of eight times with respect to the number of available samples. The observations vector was formed as

$\mathit{y}=X\mathit{s},$

where X is an $N\times l$ sensing matrix comprising ±1 generated in a random way. This means that once we obtain y , we do not need to store the original samples anymore, leading to a savings in memory requirements. Ideally, one could have obtained the reduced number of observations by sampling directly the analog signal at sub-Nyquist rates, as has already been discussed at the end of Section 9.9. Another goal is to use both the analysis and synthesis models and demonstrate their difference.

Three different spectrograms were computed. Two of them, shown in Fig. 10.18B and C, correspond to the reconstructed signals obtained by the analysis (10.37) and the synthesis (9.37) formulations, respectively. In both cases, the NESTA algorithm was used and the $G_{(128,64)}$ frame was employed. Note that the latter dictionary is redundant by a factor of 2. The spectrograms are the result of plotting the time-frequency grid and coloring each node $(t,i)$ according to the energy $|\theta {|}^2$ of the coefficient associated with the respective atom in the Gabor dictionary. The full Gabor transform was applied to the reconstructed signals to obtain the spectrograms, in order to get better coverage of the time-frequency grid. The scale is logarithmic and the darker areas correspond to larger values. The spectrogram of the original signal obtained via the full Gabor transform is shown in Fig. 10.18D. It is evident that the analysis model resulted in a more clear spectrogram, which resembles the original one better. When the frame $G_{(64,32)}$ is employed, which is a highly redundant Gabor dictionary comprising 8l atoms, then the analysis model results in a recovered signal whose spectrogram is visually indistinguishable from the original one in Fig. 10.18D.

Figure 10.18. (A) Plot of the magnitude of the coefficients, sorted in decreasing order, in the expansion in terms of the G _(128,64) Gabor frame. The results correspond to the analysis and synthesis model formulations. The third curve corresponds to the case of analyzing the original vector signal directly, by projecting it on the dual frame. (B) The spectrogram from the analysis and (C) the spectrogram from the synthesis formulations. (D) The spectrogram corresponding to the G _(64,32) frame using the analysis formulation. For all cases, the number of observations used was one-eighth of the total number of signal samples. A, B, and C indicate different parts of the signal, as explained in the text.

Fig. 10.18A is the plot of the magnitude of the corresponding Gabor transform coefficients, sorted in decreasing values. The synthesis model provides a sparser representation in the sense that the coefficients decrease much faster. The third curve is the one that results if we multiply the dual frame matrix ${\tilde{G}}_{(128,64)}$ directly with the vector of the original signal samples, and it is shown for comparison reasons.

To conclude, the curious reader may wonder what these curves in Fig. 10.18D mean after all. The call denoted by (A) belongs to a Pipistrellus pipistrellus (!) and the call denoted by (B) is either a social call or belongs to a different species. The signal (C) is the return echo from the signal (A). The large spread in time of (C) indicates a highly reflective environment [75].

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Improved weighted thresholded histogram equalization algorithm for digital image contrast enhancement using the bat algorithm

M. Tuba , ... A. Arsic , in Bio-Inspired Computation and Applications in Image Processing, 2016

3 Bat algorithm

The BA is a metaheuristic algorithm based on swarm intelligence presented by Yang (2010) and later used to solve many different problems (Alihodzic and Tuba, 2014; Mirjalili et al., 2014; Luo et al., 2014 ). It has been inspired by the echolocation of bats with varying pulse rates of emission and loudness. All bats use natural sonar in order to navigate and hunt. The primary purpose of bat echolocation is to act as a signal system to sense distance. Bats move by using the time delay between emission and reflection from prey or obstacles. The echolocation behavior of bats can be formulated in such a way that it can be associated with the objective function to be optimized, and this makes it possible to design an optimization algorithm.

If some of the echolocation characteristics of bats are idealized, various bat-inspired algorithms can be developed (Yang, 2010). In order to transform echolocation behaviors of bats, Yang proposed three idealized rules:

1.

All bats use echolocation to sense distance, and they also "know" the difference between food/prey and background barriers in some unknown way.

2.

Bats fly randomly with velocity v _i at position x _i with a fixed frequency f _min, varying wavelength λ and loudness A ₀ to search for prey. They are able to automatically set the wavelength of their transmitted pulses and tune the rate of pulse emission r from [0,1], depending on the proximity of their target.

3.

Since the loudness of bats can vary in several ways, it is supposed that the loudness changes from a positive large value A ₀ to a minimum constant value A _min.

Based on these approximations and idealization, the basic steps of the BA can be described as shown next:

In the BA, an artificial bat has its location $x_i^t$ , velocity $v_i^t$ , frequency f _i  ∈ [f _min,f _max], loudness $A_i^t$ , and emission pulse rate $r_i^t$ , which are updated during the search process. Initialization of the bat population is performed randomly. Starting with an initial population of bats spread over the solution space, the algorithm proceeds in iterations. The new solutions $x_i^t$ are performed by moving virtual bats according to the following equations:

(4.1) $\begin{array}{l}{f}_i=f_{\text{min}}+\left(f_{\text{max}}-f_{\text{min}}\right)\cdot \beta ,\hfill \end{array}$

(4.2) $\begin{array}{l}{v}_i^t=v_i^{t-1}+\left(x^{*}-x_i^{t-1}\right)\cdot f_i,\hfill \end{array}$

(4.3) $\begin{array}{l}{x}_i^t=x_i^{t-1}+v_i^t,\hfill \end{array}$

where β is a random vector drawn from the closed interval [0,1] from a uniform distribution. Here x ^* is the current global best solution. These equations could guarantee the exploitability of the BA. Initially, each bat is randomly assigned a frequency, which is drawn uniformly from the interval [f _min,f _max]. A local search phase, which modifies the current best solution, is performed using a random walk:

(4.4) $\begin{array}{l}{x}_{\text{new}}=x^{*}+\varepsilon \cdot A^t,\hfill \end{array}$

where $A^t=〈A_i^t〉$ is the average loudness of all the bats at the time stept and ɛ from the interval [−1,1] is a random number. Pulse rate and loudness are responsible for controlling the local search. Therefore, the loudness A ⁱ and the rate r ⁱ of pulse emission have to be updated as the iterations proceed. As the loudness usually decreases once a bat has found its prey whereas the rate of pulse emission increases, the loudness can be chosen as any value of convenience. For simplicity, we can also use A ₀ = 1 and A _min = 0, whereA _min = 0 means that a bat has just found the prey. Mathematically, these characteristics are defined with the following equations:

(4.5) $\begin{array}{l}{A}_i^{t+1}=\alpha \cdot A_i^t,\hfill \end{array}$

(4.6) $\begin{array}{l}{r}_i^{t+1}=r_i^0\cdot \left(1-{\text{e}}^{-\gamma t}\right),\hfill \end{array}$

where α and γ are constants. In fact, α is similar to the cooling schedule in the simulated annealing algorithm (Kirkpatrick et al., 1983). For any 0 <α < 1 and γ > 0, we have

(4.7) $\begin{array}{l}{A}_i^{t+1}\to 0,r_i^t\to r_i^0,\text{as}t\to \infty ,\hfill \end{array}$

The choice of parameters requires some experimentations. For example, the initial loudness $A_i^0$ can typically be taken as 1, whereas the initial emission rate $r_i^0$ can be around zero or any value $r_0^i\in \left(\mathrm{0,1}\right]$ .

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Single-point wind forecasting methods based on ensemble modeling

Hui Liu , in Wind Forecasting in Railway Engineering, 2021

6.3.2.3.3 Bat algorithm

BA comes from the echolocation behavior of bats [ 15]. In the BA, to simulate the random search process of bats hunting prey and avoiding obstacles, the following idealized assumptions are made [16]:

(1)

All bats in the population use the echolocation method to perceive distance.

(2)

The flying speed $v_i$ of bat at position $x_i$ is random, and the bats have different frequencies $f_i\in \left[f_{\min },f_{max}\right]$ , impulse loudness $A_i$ , and impulse emission rate $r_i$ .

(3)

When a bat searches and captures prey, it will change its parameters and search for the optimal solution until the target stops or the termination condition is met.

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Swarm robotics – a case study: bat robotics

Andrés Iglesias , ... Patricia Suárez , in Nature-Inspired Computation and Swarm Intelligence, 2020

15.6.1 The bat algorithm

The idealization of the echolocation of microbats can be summarized as follows (see Yang (2010b) for details):

1.

Bats use echolocation to sense distance and distinguish between food, prey, and background barriers.

2.

Each virtual bat flies randomly with a velocity ${\mathbf{v}}_i$ at position (solution) ${\mathbf{x}}_i$ with a fixed frequency $f_{min}$ and varying wavelength λ and loudness $A_0$ to search for prey. As it searches and finds its prey, it changes wavelength (or frequency) of the emitted pulses and adjusts the rate of pulse emission r, depending on the proximity of the target.

3.

It is assumed that the loudness will vary from an (initially large and positive) value $A_0$ to a minimum constant value $A_{min}$ .

In order to apply the bat algorithm for optimization problems more efficiently, some additional assumptions are strongly advisable. In general, we assume that the frequency f evolves on a bounded interval $[f_{min},f_{max}]$ . This means that the wavelength λ is also bounded, because f and λ are related to each other by the fact that the product $\lambda \times f$ is constant. For practical reasons, it is also convenient that the largest wavelength is chosen such that it is comparable to the size of the domain of interest (the search space, for optimization problems). For simplicity, we can assume that $f_{min}=0$ , so $f\in [0,f_{max}]$ . The rate of pulse can simply be in the range $r\in [0,1]$ , where 0 means no pulses at all and 1 means the maximum rate of pulse emission. With these idealized rules, the basic pseudocode of the bat algorithm is shown in Algorithm 1.

Algorithm 1. Bat algorithm pseudocode.

Basically, the algorithm considers an initial population of $\mathcal{P}$ individuals (bats). Each bat, representing a potential solution of the optimization problem, has a location ${\mathbf{x}}_i$ and velocity ${\mathbf{v}}_i$ . The algorithm initializes these variables with random values within the search space. Then, the pulse frequency, pulse rate, and loudness are computed for each individual bat. Then, the swarm evolves in a discrete way over generations, like time instances until the maximum number of generations, ${\mathcal{G}}_{max}$ , is reached. For each generation g and each bat, new frequency, location and velocity are computed according to the following evolution equations:

(15.1) $f_i^g=f_{min}^g+\beta (f_{max}^g-f_{min}^g),$

(15.2) ${\mathbf{v}}_i^g={\mathbf{v}}_i^{g-1}+[{\mathbf{x}}_i^{g-1}-{\mathbf{x}}^{⁎}]f_i^g,$

(15.3) ${\mathbf{x}}_i^g={\mathbf{x}}_i^{g-1}+{\mathbf{v}}_i^g,$

where $\beta \in [0,1]$ follows the random uniform distribution and ${\mathbf{x}}^{⁎}$ represents the current global best location (solution), which is obtained through evaluation of the objective function at all bats and ranking of their fitness values. The superscript ${(.)}^g$ is used to denote the current generation g.

The best current solution and a local solution around it are probabilistically selected according to some given criteria. Then, search is intensified by a local random walk. For this local search, once a solution is selected among the current best solutions, it is perturbed locally through a random walk of the form

(15.4) ${\mathbf{x}}_{new}={\mathbf{x}}_{old}+ϵ{\mathcal{A}}^g,$

where ϵ is a random number with uniform distribution on the interval $[-1,1]$ and ${\mathcal{A}}^g=<{\mathcal{A}}_i^g>$ is the average loudness of all the bats at generation g.

If the new solution achieved is better than the previous best one, it is probabilistically accepted depending on the value of the loudness. In that case, the algorithm increases the pulse rate and decreases the loudness. This process is repeated for the given number of generations. In general, the loudness decreases once a bat finds its prey (in our analogy, once a new best solution is found), while the rate of pulse emission decreases. For simplicity, the following values are commonly used: ${\mathcal{A}}_0=1$ and ${\mathcal{A}}_{min}=0$ , assuming that the latter value means that a bat has found the prey and temporarily stops emitting any sound. The evolution rules for loudness and pulse rate are as follows:

(15.5) ${\mathcal{A}}_i^{g+1}=\alpha {\mathcal{A}}_i^g,$

(15.6) $r_i^{g+1}=r_i^0[1-exp(-\gamma g)],$

where α and γ are constants. Note that for any $0<\alpha <1$ and any $\gamma >0$ we have

(15.7) ${\mathcal{A}}_i^g\to 0,r_i^g\to r_i^0,\text{as}g\to \infty .$

In general, each bat should have different values for loudness and pulse emission rate, which can be computationally achieved by randomization. To this aim, we can take an initial loudness ${\mathcal{A}}_i^0\in (0,2)$ while the initial emission rate $r_i^0$ can be any value in the interval $[0,1]$ . Loudness and emission rates will be updated only if the new solutions are improved, an indication that the bats are moving towards the optimal solution. As a result, the bat algorithm applies a parameter tuning technique to control the dynamic behavior of a swarm of bats. Similarly, the balance between exploration and exploitation can be controlled by tuning algorithm-dependent parameters.

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Nature-inspired computation and swarm intelligence: a state-of-the-art overview

Xin-She Yang , Mehmet Karamanoglu , in Nature-Inspired Computation and Swarm Intelligence, 2020

1.3.7 Bat algorithm

The well-known echolocation of bats, especially microbats, is the main inspiration for BA, which was developed by Xin-She Yang in 2010 ( Yang, 2010). BA uses frequency tuning in a range from $f_{\min }$ to $f_{\max }$ , in combination with varying pulse emission rate r and loudness A (Altringham, 1996; Colin, 2000).

The position of a bat is used to represent a solution vector to an optimization problem, and a set of n solutions form the population. The iterative update of the position vectors is carried out by

(1.17) $f_i=f_{\min }+(f_{\max }-f_{\min })\beta ,$

(1.18) ${\mathit{v}}_i^t={\mathit{v}}_i^{t-1}+({\mathit{x}}_i^{t-1}-{\mathit{x}}_{⁎})f_i,$

(1.19) ${\mathit{x}}_i^t={\mathit{x}}_i^{t-1}+{\mathit{v}}_i^t\mathrm{\Delta }{\mathit{x}}_i^t,$

where ${\mathit{x}}_{⁎}$ is the best solution among the population and β is a random number in [0,1]. The time-discrete increment $\mathrm{\Delta }{\mathit{x}}_i^t=1$ can be used.

Though the actual echolocation and variations of pulse emission and loudness can be very complicated, we use a simple monotonic form for both r and A. We have

(1.20) $A_i^{t+1}=\alpha A_i^t,r_i^{t+1}=r_i^0(1-e^{-\gamma t}),$

where the parameters ( $0<\alpha <1$ and $\gamma >0$ ) control the variation properties.

Recent studies have suggested that BA can have a faster convergence rate with guarantees convergence within proper ranges of parameters (Chen et al., 2018). BA has been extended in different ways with many variants, including multiobjective BA (MOBA) and chaotic BA (Yang, 2011; Gandomi and Yang, 2014; Yang and He, 2013; Osaba et al., 2019). A new directional BA has also been developed by Chakri et al. (Chakri et al., 2017).

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Bat Algorithms

Xin-She Yang , in Nature-Inspired Optimization Algorithms (Second Edition), 2021

11.2 Bat Algorithms

If we idealize some of the echolocation characteristics of microbats, we can develop various bat-inspired algorithms or bat algorithms ( Yang, 2010). For simplicity, we now use the following approximate or idealized rules:

1.

All bats use echolocation to sense distance, and they also "know" the difference between food/prey and background barriers.

2.

Bats fly randomly with velocity ${\mathit{v}}_i$ at position ${\mathit{x}}_i$ . They can automatically adjust the frequency (or wavelength) of their emitted pulses and adjust the rate of pulse emission $r\in [0,1]$ , depending on the proximity of their target.

3.

Although the loudness can vary in many ways, we assume that the loudness varies from a large (positive) $A_0$ to a minimum value $A_{\min }$ .

Another obvious simplification is that no ray tracing is used in estimating the time delay and three dimensional topography. Though this might be a good feature for the application in computational geometry, we will not use this here, since it is more computationally extensive in multidimensional cases.

In addition to these simplified assumptions, we also use the following approximations for simplicity. In general, the frequency f in a range $[f_{\min },f_{\max }]$ corresponds to a range of wavelengths $[{\tilde{\lambda }}_{\min },{\tilde{\lambda }}_{\max }]$ . For example, a frequency range of [20 kHz, 500 kHz] corresponds to a range of wavelengths from 0.7 mm to 17 mm.

For a given problem, we can also use any wavelength for the ease of implementation. In the actual implementation, we can adjust the range by adjusting the frequencies (or wavelengths). The detectable range (or the largest wavelength) should be chosen such that it is comparable to the size of the domain of interest, and then toned down to smaller ranges. Furthermore, we do not necessarily have to use the wavelengths themselves at all. Instead, we can also vary the frequency while fixing the wavelength $\tilde{\lambda }$ . This is because $\tilde{\lambda }$ and f are related, since $\tilde{\lambda }f$ is constant. We use this latter approach in our implementation.

For simplicity, we can assume $f\in [0,f_{\max }]$ . We know that higher frequencies have short wavelengths and travel a shorter distance. For bats, the typical ranges are a few meters. The rate of pulse can simply be in the range of $[0,1]$ where 0 means no pulses at all and 1 means the maximum rate of pulse emission.

Based on the above approximations and idealized rules, the basic steps of BA can be summarized as the schematic pseudo code shown in Algorithm 11.1.

Algorithm 11.1. Bat algorithm.

11.2.1 Movement of Virtual Bats

In simulations, we have to use virtual bats. We have to define the rules of how their positions ${\mathit{x}}_i$ and velocities ${\mathit{v}}_i$ in a d-dimensional search space are updated. The new solutions ${\mathit{x}}_i^t$ and velocities ${\mathit{v}}_i^t$ at time step t are given by

(11.1) $f_i=f_{\min }+(f_{\max }-f_{\min })\beta ,$

(11.2) ${\mathit{v}}_i^{t+1}={\mathit{v}}_i^t+({\mathit{x}}_i^t-{\mathit{x}}_{⁎})f_i,$

(11.3) ${\mathit{x}}_i^{t+1}={\mathit{x}}_i^t+{\mathit{v}}_i^{t+1},$

where $\beta \in [0,1]$ is a random vector drawn from a uniform distribution. Here ${\mathit{x}}_{⁎}$ is the current global best location (solution) which is located after comparing all the solutions among all the n bats. Because the product ${\tilde{\lambda }}_i{f}_i$ is a constant, we can use $f_i$ (or ${\tilde{\lambda }}_i$ ) to adjust the velocity change while fixing the other factor ${\tilde{\lambda }}_i$ (or $f_i$ ), depending on the type of the problem of interest. In our implementation, we use $f_{\min }=0$ and $f_{\max }=O(1)$ , depending on the domain size of the problem of interest. Initially, each bat is randomly assigned a frequency that is drawn uniformly from $[f_{\min },f_{\max }]$ .

For the local search part, once a solution is selected among the current best solutions, a new solution for each bat is generated locally using random walk

(11.4) ${\mathit{x}}_{\mathrm{new}}={\mathit{x}}_{\mathrm{old}}+ϵA^{(t)},$

where $ϵ\in [-1,1]$ is a random number, while $A^{(t)}=\mathbb{E}(A_i^t)$ is the average loudness of all the bats at this time step. From the implementation point of view, it is better to provide a scaling parameter to control the step size. Therefore, we can rewrite the above equation as

(11.5) ${\mathit{x}}_{\mathrm{new}}={\mathit{x}}_{\mathrm{old}}+\sigma {ϵ}_t{A}^{(t)},$

where ${ϵ}_t$ is now drawn from a Gaussian normal distribution N $(0,1)$ , and σ is a scaling factor. In our demo implementation, we set $\sigma =0.1$ . Obviously, σ should be linked to the scalings of the design variables of an optimization problem under consideration.

The update of the velocities and positions of bats may have some similarity to the procedure in the standard particle swarm optimization, since $f_i$ essentially controls the pace and range of the movement of the swarming particles. However, BA can be more effective because it uses frequency tuning and parameter control to influence exploration and exploitation.

11.2.2 Loudness and Pulse Emission

In BA, the loudness $A_i$ and the rate $r_i$ of pulse emission have to be updated accordingly as the iterations proceed. Because the loudness usually decreases once a bat has found its prey, whereas the rate of pulse emission increases, the loudness can be chosen as any value of convenience. For simplicity, we can also use $A_0=1$ and $A_{\min }=0$ , assuming $A_{\min }=0$ means that a bat has just found the prey and temporarily stop emitting any sound. Now we have

(11.6) $A_i^{t+1}=\alpha A_i^t,r_i^{t+1}=r_i^0[1-\exp (-\gamma t)],$

where α and γ are constants. In fact, α is similar to the cooling factor of a cooling schedule in the simulated annealing discussed earlier in this book. For any $0<\alpha <1$ and $\gamma >0$ , we have

(11.7) $A_i^t\to 0,r_i^t\to r_i^0,\text{as}t\to \infty .$

We have used $\alpha =0.97$ and $\gamma =0.1$ in our simulations.

The choice of parameters requires some experimenting. Initially, each bat should have different values of loudness and pulse emission rate; this can be achieved by randomization. For example, the initial loudness $A_i^0$ can typically be taken as 1, whereas the initial emission rate $r_i^0$ can be around zero, or any value $r_i^0\in (0,1]$ if using (11.6). Their loudness and emission rates will be updated only if the new solutions are improved, which means that these bats are moving towards the optimal solution.

By analyzing the bat algorithm closely, we can see that BA can capture many characteristics of other algorithms. If we replace the variations of the frequency $f_i$ by a random parameter and setting $A_i=0$ and $r_i=1$ , BA essentially becomes the standard PSO. Similarly, if we do not use the velocities, we use fixed loudness and rate: $A_i$ and $r_i$ . For example, $A_i=r_i=0.7$ , this algorithm is virtually reduced to a simple harmony search (HS), as the frequency/wavelength change is essentially the pitch adjustment while the rate of pulse emission is similar to the harmonic acceptance rate (here with a twist) in the harmony search algorithm. In other words, HS and PSO can be considered as the special cases of BA. Therefore, it is no surprise that BA is efficient.

The current studies imply that the proposed new algorithm is potentially more powerful and thus should be investigated further in many applications of engineering and in solving industrial optimization problems.

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Ultrasonic cutting for surgical applications

M. Lucas , A. Mathieson , in Power Ultrasonics, 2015

23.1 Introduction: the origins of ultrasonic cutting for surgical devices

During Paul Langevin's development of an ultrasonic echolocation system during the late 1910s, it was observed that the ultrasound field emitted could induce pain in humans and even kill small fish that attempted to swim through it. These observations were the first to highlight the destructive capability of ultrasound when applied to living organisms and did not go unnoticed by an American, Robert Wood, who had worked with Langevin during 1917 ( Graff, 1977).

After returning to the United States, Wood's scientific interests lay away from ultrasound; however, after renewing an acquaintance with Alfred Loomis during the mid-1920s, the pair decided to investigate whether observations made during trials of the echolocation system offered further scope for research of interest to science and engineering.

Working from Loomis' independent research laboratory located at Tuxedo, New York, they investigated the influence and effect of high-power ultrasonics in a range of different topics, including pressure generated from acoustic radiation, the formation of emulsions and fogs, and the rate of chemical reactions; subsequently publishing their findings in 1927. They also observed the biological effects of high-power ultrasound on animal and plant cells and the fatal effect it could have on fish, frogs, and mice, although some experiments had a more fortunate outcome: "Mice are less sensitive, a 20-min exposure not resulting in death, and though at the end of the treatment the animal was barely able to move, the recovery was fairly rapid" (Wood and Loomis, 1927). Significantly, with respect to ultrasonic cutting and tissue dissection, Wood and Loomis reported that a vibrating glass rod cemented to a quartz transducer had the capability to cut or etch wood and glass, but when held between fingers and thumb it could induce blood blisters in the skin (Wood and Loomis, 1927).

From the late 1920s until the 1940s, much of the research in ultrasonics concentrated on sonar, ultrasonic nondestructive testing, and the effect of high-power ultrasound wave-fields in biological matter. The period between 1945 and 1955 saw the patenting (Balamuth, 1948, 1952) and commercialization of an ultrasonic impact grinder capable of machining hard and brittle materials such as tungsten carbide and glass (Cohan, 1951; Kelley, 1951). This device operated by impacting a vibrating tool against an abrasive slurry that gradually ground away the workpiece material. An innovative application of the ultrasonic grinding device by Balamuth and Catuna, reported in 1953, cut cavities in extracted teeth and introduced ultrasonics to dentistry and mineralized tissue cutting (Balamuth, 1963; Catuna, 1953). From these trials stemmed a miniaturized device designed for dentistry that operated on the same principles as its industrial counterpart. The ultrasonic dental unit, when compared to conventional mechanical or pneumatic-powered devices, promised several advantages: minimal tissue heating, reduced pressure applied to the operation site, and enhanced patient comfort (Balamuth, 1963; Catuna, 1953; Postle, 1958). Even though the ultrasonic dental device offered many benefits to both dentist and patient, it experienced only limited commercial success. A combination of factors contributed to this: the requirement for an abrasive paste that restricted the dentist's line of sight to the cutting site, the high cost of the device, and the eventual popularity of the competing technology, a high-speed miniature turbine handpiece, which had been developed during the same time frame (Cheery et al., 1974).

The limited commercial success of Balamuth and Catuna's dental device did slow the development of ultrasonic devices for a number of years, but by the early 1960s an ultrasonic device capable of cutting bone without the requirement of an abrasive paste had been used during bone-cutting trials (Mararow, 1960; McFall et al., 1961). Using an oscillatory motion to cut tissue directly was first filed for patent a few years earlier in 1955 by Vang (Vang, 1955). Vang's patent described a scalpel-like device that oscillated at frequencies between 6 and 12 kHz and claimed to be able to cut both hard and soft tissue. Two animal-based studies by Mararow (1960) and McFall et al. (1961) compared the performance of electric- and pneumatic-powered saws and burs to an ultrasonic scalpel device. Both studies reported that the ultrasonic device had benefits to the surgeon similar to those of the original impact grinder: enhanced precision and accuracy during cutting and a reduction in soft-tissue damage. However, the studies also commented on the limitations of the ultrasonic device. Mararow reported that material removal rate and healing rate were both slower in sites operated on using the ultrasonic device, with McFall et al. confirming the slower healing rate. It also was reported that the introduction of saline solution to the cutting process reduced healing time, and all sites healed satisfactorily by the end of the study's trial period. These observations led to a conclusion that ultrasonic devices may be preferable in surgical procedures requiring high precision and accuracy, provided a saline solution was used to minimize heating at the surgical site.

The first recorded human osteotomies conducted with an ultrasonic device were reported by Volkov in 1974 after completing 311 clinical procedures during 1969 (Volkov and Shepeleva, 1974). Volkov's device operated in a longitudinal mode at frequencies between 25 and 30   kHz and incorporated a detachable exponential-shaped horn with a "chisel-like" cutting tip. The geometry of the device permitted Volkov to complete the osteotomies through smaller incisions than were possible with conventional devices, hence minimizing soft-tissue damage and simplifying the surgical procedure. Volkov also noted that highly precise cuts and normal regeneration rates of repair in bone were achieved during and after surgery, respectively. Subsequently, studies by Horton and Aro, published during the 1970s and 1980s, also reported highly precise and accurate cuts using ultrasonic devices and reduction of trauma to surrounding tissue compared with conventional devices and instruments (Aro et al., 1982; Horton et al., 1975, 1981). These studies also commented on the benefit of applying saline solution to the cutting site to control tissue temperatures and again confirmed the limitation of a slow cutting rate. Horton and Aro additionally commented on other disadvantages: the device was difficult to operate because of its size and shape, there were problems with the device overheating, and it was necessary to control manually the optimal operating frequency. Nevertheless, similar to Volkov, Horton and Aro noted that bone cuts using the ultrasonic device healed normally.

Regardless of the limited adoption in cavity preparation during the 1950s and mineralized tissue cutting during the following decades, ultrasonic devices continued to be developed and were commercially successful for other clinical applications, such as the periodontal treatment of oral prophylaxis (Zinner, 1955) and endodontic treatments during root canal procedures (Suppipat, 1974). Ultrasonic scaling and endodontic devices offered similar advantages over conventional scaling instruments, including reduced damage to surrounding soft tissue and reduced procedure time, as well as improved patient acceptance. The development of thinner scaling tips (Trenter et al., 2002) and the introduction of biocidal agents coupled with specialized endodontic tips in root canal treatments (Martin, 1976) during the 1970s and 1980s facilitated the routine adoption of ultrasonic devices for periodontal and endodontic procedures (Walmsley et al., 1992).

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Bat algorithm–based automatic clustering method and its application in image processing

S. Nandy , P.P. Sarkar , in Bio-Inspired Computation and Applications in Image Processing, 2016

Abstract

The bat algorithm (BA) is inspired by the echolocation characteristics observed in microbats searching for prey. It is a nature-inspired optimization algorithm which has already proved its efficacy in various fields. In this chapter, the concept of the bat optimization algorithm is employed to design an automatic clustering method, and it is also applied to image segmentation. A new rule-based statistical hypothesis approach is adopted for merging similar clusters, which guides the optimization process to find an optimal number of clusters. The process of bat clustering is applied to the segmentation of five benchmark images. Experimental results on several standard benchmark datasets indicate that the proposed methods provide a possible way to partition linear and nonlinear benchmark datasets. The proposed method is compared with other standard algorithms over a nine-number artificial and real-life benchmark dataset. The experiment shows that the algorithm is faster and convergence is improved over of the method it is compared to.

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Analysis of Swarm Intelligence–Based Algorithms for Constrained Optimization

M.P. Saka , ... Ibrahim Aydogdu , in Swarm Intelligence and Bio-Inspired Computation, 2013

2.3.7 Bat Algorithm

BA is developed by Yang (2010) which simulates echolocation capability of micro bats. They use sonar called echolocation to detect prey, avoid obstacles, and locate their roosting crevices in the dark. Micro bats emit a very loud sound pulse and listen for the echo that bounces back from the surrounding objects. Their pulses vary in properties and can be correlated with their hunting strategies, depending on the species. They even use the time delay from the emission and detection of the echo, time difference between two ears, and loudness variations of the echoes to build up three-dimensional scenario of the surrounding. They can detect the distance and orientation of the target, type of prey, and even moving speed of the prey such as small insects. The echolocation characteristics of micro bats can be idealized as in the following ( Gandomi et al., 2012):

1.

All bats use echolocation to sense distance, and they also know the difference between food/prey and background barriers in some magical way.

2.

Bats randomly fly with velocity $v_i$ at position $x_i$ with a fixed frequency $f_{\min }$ , varying wavelength $\lambda$ , and loudness $A^0$ to search prey. They can automatically adjust the wavelength (or frequency) of their emitted pulses and adjust the rate of pulse emission $r\in [0,1]$ depending on the proximity of their target.

3.

Although the loudness can vary in many ways, it is assumed that the loudness varies from a large (positive) $A^0$ to a minimum $A_{\min }$ .

The steps of the algorithm are as follows (Yang, 2010):

1.

Initialize the bat population with position $x_i$ and velocity $v_i$ where each bat represents a candidate solution $x_i,i=1,\dots ,n$ to the optimization problem with m design variables $\left\{x\right\}={\{x_{1,}{x}_{2,}\dots ,x_m\}}^T$ and an objective function $f(x)$ . Initialize pulse rates $r_i$ and the loudness $A_i$ . Define pulse frequency $f_i$ at $x_i$ .

2.

Calculate the new solutions $x_i^t$ and velocities $v_i^t$ at time step t as

(2.30) $f_i=f_{\min }+(f_{\max }-f_{\min })\beta$

(2.31) $v_i^t=v_i^{t-1}+(x_i^{t-1}-x^{*})f_i$

(2.32) $x_i^t=x_i^{t-1}+v_i^t$

where β is a random vector taken from a uniform distribution in the range [0,1]. $x^{*}$ is the current global best location (solution) which is located after comparing all the solutions among all the n bats.

3.

If a randomly generated number rand>r _i , determine a solution among the best solutions.

4.

Generate a local solution around the selected best solution by a local random walk.

(2.33) $x_{\mathrm{new}}=x_{\mathrm{old}}+\epsilon A^t$

where the random number ε is drawn from [−1,1], while A ^t is the average loudness of all bats at this time step.

5.

If a randomly generated number rand>A _i and $f(x_i)<f(x^{*})$ accept new solutions, increase r _i , and reduce A _i :

(2.34) $A_i^{t+1}=\alpha A_i^t{r}_i^{t+1}=r_i^0[1-\exp (-\gamma t)]$

where $\alpha$ and $\gamma$ are constants. In fact $\alpha$ is similar to the cooling factor of a cooling schedule in the simulated annealing. For any $\alpha$ >0 and $\gamma$ <1, $A_i^t\to 0$ , $r_i^t\to r_i^0$ as $t\to \infty$ . In the simplest case, $\alpha$ can be taken equal to $\gamma$ .

6.

Rank the bats and find current best x ^* .

7.

Repeat steps 2–6 until termination criterion is satisfied which is usually taken as a predetermined maximum number of iterations.

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What Is Echolocation and How Does It Work

Source: https://www.sciencedirect.com/topics/engineering/echolocation

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