### 1. Introduction

### 2. Finite Element Model Update

### 2.1 Optimization Parameter Selection

*E*

_{11}and

*E*

_{22}, and shear moduli,

*G*

_{12},

*G*

_{13}, and

*G*

_{23}, which are considered to significantly influence the mechanical properties of orthotropic plate materials, were selected as optimization parameters.

### 2.2 Finite Element Model Development

### 2.3 Finite Element Model Update

The optimization parameters are discretized and coded as bits to construct the first generation.

The modal analysis is conducted for each object that belongs to the first generation and the fitness assessment is conducted via derived natural frequencies.

The construction of the next generation is conducted until the required fitness is fulfilled or the maximum number of iterations is reached, via elitist model, selection phase, crossover phase, and mutation phase processes, as well as the fitness assessment process on the constructed next generation.

### 3. Discrete Genetic Algorithm

### 3.1 Optimization Parameter Discretization and Coding

*N*, the selected database is expressed as an array

_{ij}*L*composed of

_{ij}*N*

_{ij}_{,}

*(=log*

_{b}_{2}

*N*) number of bits (

_{ij}*N*

_{ij}_{,}

*-bit), as expressed in Eq. (1). where*

_{b}*k*-th bit value in the coded array of the optimization parameter. For example, when the optimization parameters,

*E*

_{11},

*E*

_{22},

*G*

_{12},

*G*

_{13}, and

*G*

_{23}becomes the

*k*-th bit value of the

*N*

_{ij}_{,}

*-bit array, respectively.*

_{b}### 3.2 Fitness Assessment

*J*is expressed by Eq. (4) and was defined by considering the weight of the relative squared error for each natural frequency of the modal test and finite element analysis results (Zahari et al. 2016). where

*W*, and

_{i}*n*represent the

*i*-th natural frequency derived from finite element analysis and modal test, weight for the -th natural frequency (“1” was applied as the weight in this study), and number of natural frequencies used in the optimization process, respectively. The natural frequency

### 3.3 Discrete Genetic Algorithm Development

#### 3.3.1 First generation construction

*N*populations that formulate the initial generation are generated as chromosome groups (

_{pop}*G*

_{1},

*G*

_{2}, ⋯

*G*

_{Npop}) with bit arrays. Each chromosome is randomly allocated with a bit value of “0” or “1.”

#### 3.3.2 Elitist model

#### 3.3.3 Selection phase

#### 3.3.4 Crossover phase

#### 3.3.5 Mutation phase

#### 3.3.6 Convergence check

### 4. Numerical Examples

### 4.1 Verification of the Finite Element Model Update Method

*E*

_{11}and

*E*

_{22}, and shear modulus,

*G*

_{12}, were selected as optimization parameters. Table 3 summarizes the ranges of material properties, as well as those of the discrete genetic algorithm parameters. The ranges were configured to include the material properties from Table 1. As a reference, 16 (4-bit) optimization parameter databases were configured for each parameter, and the moduli,

*G*

_{23}and

*G*

_{13}were fixed at 6.900E+09 N/m

^{2}. However, the number of individuals for each generation was set as 50, and the probabilities of crossover and mutation were set as 0.9 and 0.1, respectively. The convergence criteria were established by setting 1E-10 and 100 as the required cost and maximum number of iterations, respectively.

*J*converged to zero, and the material properties derived via the inverse method matched the material properties of Table 1 without displaying any error. This indicates that the material property inversion method implemented in this study was successfully executed.

### 4.2 Application to Cantilevered CFRP Beam

*E*

_{11}, and

*E*

_{22}, and shear moduli,

*G*

_{12},

*G*

_{13}, and

*G*

_{23}, were selected as optimization parameters. Table 4 summarizes the ranges of the material properties, as well as those of the discrete genetic algorithm parameters. As a reference, the number of discrete data for the elastic moduli,

*E*

_{11}and

*E*

_{22}, was set to 64 (6-bit) and 32 (5-bit), respectively, and the number of discrete data for the shear moduli was set to 8 (3-bit). However, the number of individuals for each generation was set to 40, and the probabilities of crossover and mutation were set to 0.9 and 0.1, respectively, same as that of the previous section. The convergence criteria were established by setting 1E-6 as the required cost and 50 as the maximum number of iterations.