**7. Appendix I**

### **A. The depth of penetration of a shear wave (δ)**

The depth of penetration of a shear wave (δ) in a Newtonian medium is given by the equation shown below:

$$\mathcal{S}\_n = \frac{1}{\left(-o\mathbb{I}\_n \left(\frac{\rho\_m^2}{C\_m^2 + \left(o\mathbb{I}\_n \eta\_m\right)^2}\right)^{1/4}\right) \text{Sim}\left(-\frac{1}{2} \left(\arctan\left(o\mathbb{I}\_n \frac{\eta\_m}{C\_m}\right)\right)\right)}\tag{2}$$

ρm = density of medium (kg/m3),

ηm = viscosity of medium (kg/m.s),

Cm = stiffness of medium (N/m2),

ω = angular frequency (rad/s) and

n = harmonic number

### **B. Basic terminologies of a genetic algorithm**

*Individual:* A solution to the problem is called an individual.

*Population:* The total number of solutions is called population.

*Chromosome:* Each individual has a number of chromosomes that represent each parameter (i.e. variables to be determined) of the problem.

*Genes:* Each chromosome contains a fixed number of genes, the number of genes per chromosome determine the resolution of the total solution. The number of genes per chromosome is mostly determined by the broadness of the range in which each chromosome lies.

*Fitness:* Every individual has to be weighed according to its fitness. The individual fitness value determines its survival and breeding probability. A higher fitness individual has higher probability of survival.

### **C. Mason's transmission line model**

As seen in fig. 11, the biological process consist of a piezoelectric layer (MTSM sensor) and a non-piezoelectric biological layer. In this model, each layer of load can be represented as a T-network of impedances.

Fig. 11. Mason model representation of non-piezoelectric layers loaded on piezoelectric plate
