In Equations (4) and (5), the crossover probability will be reduced to preserve excellent chromosomes; on the contrary it will be added to evolutionary excellent chromosomes. And then, the mutation probability will be reduced to preserve excellent chromosomes; on the contrary it will increase the diversity of the population and avoid to falling into local optimum [18] . The overall structure of method 1 of ARGA can be described as follows.

A. Encoding: The parameters of the BLDC motor and induction motor are composed by real-coded values.

B. Initialization: A collection of individuals is referred to as a population. A population size of 100 is used to generate final segmentation boundaries.

C. Fitness function: The fitness function is adopted as follows.

where n is the total number of sampling point, and are the rotation speeds by using the identified and assigned parameters in Equations (14) and (15), respectively.

D. Selection: In this stage, the expected time of an individual being selected for recombination is proportional to its fitness value relative to the rest of the population. This operation is to achieve a mating pool with the fittest individuals selected according to a probabilistic rule that allows these individuals to be mated into new populations. The selection is carried out by using the roulette wheel method.

E. Crossover and Mutation: The crossover is the breeding of two parents to produce a single child, who has features from both parents and thus may be better or worse than either parent according to the objective function. The primary purpose of mutation is to introduce variation and help bring back some essential genetic traits, and also to avoid the premature convergence of entire feasible space caused by some super chromosomes [19] .

To reduce the premature convergence and improve convergence rate of the SRGA, the adaptive probabilities of crossover and mutation are presented in the ARGA. The probabilities of crossover and mutation are respectively given as follows.

where, and are the maximum, minimum and average individual fitness, respectively, and are crossover and mutation of probabilities, respectively and are coefficient factors. In this paper, , and [20] are taken.

From Equations (2) and (3), it is known that the adaptive and vary with fitness functions. The and increase when the population tends to get stuck at a local optimum and decrease when the population is scattered in the solution space.

The GAs have been extensively used in different domains as a type of robust optimization method. However, the GA to demonstrate a more serious question is a premature convergence problem, less capable local optimization, the late slow convergence and can’t guarantee convergence to the global optimal solution and so on. In recent years, many researches [21] [22] try to improve genetic algorithms, such as improving the encoding scheme, fitness function, genetic operator design. For this reason, the ARGA is proposed with the crossover probability and mutation probability as follows.

where, is the best individual fitness, is the better individual fitness in every group, is the average fitness, and f is every individual fitness in current generation. The means fixed maximal cross proba-

bility; means fixed minimum crossover probability; and are fixed maximal and mutation probabilities, respectively. In this paper, , , , and [23] [24] are taken.

As a result, the adaptive and are able to provide the optimum and targets at a certain solution. The improved chromosome crossover and mutation operators ensure the convergence of the GA more than the diversity of population [25] [26] .

An important problem in usage of the RGA is premature convergence, and the searching process may trap in a local optimum before the global optimum is found. This section employs an ARGA which adjusts mutation probability dynamically based on average square deviation (ASD) of population fitness value, which shows the population diversity to solve the premature problem. From compared analysis, it is shown the proposed ARGA efficiently avoid the premature problem [27] . Premature convergence can also be blamed in [28] by avoiding the loss of critical alleles due to selection and the schemata disruption due to crossover.

The selection operation reduces the diversity of population, the crossover operation does not decrease the diversity of population, and the mutation operation can advance the diversity. Mainly, all these issues produce two effects, the lack of diversity in the population and a disproportionate exploitation or exploration relationship, cause the premature problem [29] . When the ASD becomes smaller or less, it shows that many individuals are becoming as the same, so the mutation probability should be increased to advance the diversity of population for getting global optimal solutions.

A. Selection operator: The selection is carried out using the roulette wheel method in this paper.

B. Crossover operator: The crossover operation does not decrease the diversity of population, and the crossover probability is fixed.

C. Mutation operator: This section employs an adaptive method to adjust mutation probability dynamically based on the ASD value. When the ASD decreasing, mutation probability will be increased to advance the population diversity. The relationship between mutation probability and ASD is given as follows.

where is the maximum individual fitness, is mutation probability originally, and is the ASD of population in the generation, and is described as:

where is the fitness value of the individual of the generation, is the average fitness of the generation, and is the number of population.

In this section, a new GA with two species is proposed for the ARGA. The dual-specie GA composes of two sub-populations that constitute of same size individuals. The sub-populations have different characteristics, such as crossover probability and mutation operator. In one sub-population, the parents with higher similarity are cross with higher probability, and mutate with general mutation operator. In the other sub-population, the parents with smaller similarity are cross with higher probability and mutate with big mutation probability. Therefore, the new algorithm can obtain good exploitation and exploration ability [30] .

Multi-population GA [31] - [33] is an extension of traditional single population GA by dividing a population into several isolated sub-populations, within which the evolution proceeds and individuals are allowed to migrate from one sub-population to another [34] , and the flow chart is shown as follows (Figure 1).

For the dual-population GA, one has the following operators:

A. Selection operator: The proposed algorithm establishes two separate sub-populations by random initialization, and then carries on evolution inside single sub-population and migration between two sub-populations. Here, the roulette selection is employed.

B. Crossover operator: The crossover probability is correlated with parents’ similarity. The similarity between two individuals is defined as:

where and are two individuals, is the distance between and, and are the maximum and minimum individual fitness values, respectively, and are the fitness values of and, respectively.

The crossover1 emphasized local search ability, and crossover probability is positive correlated with the parents’ similarity; the crossover2 emphasized global search ability, and crossover probability is negative correlated with the parents’ similarity. It defines:

C. Mutation operator: Mutation1 is the normal mutation which proceeds with constant probability. Mutation 2 needs to have ability to robustly explore the solution space and to escape from local peak. The probability

of mutation 2 is adaptive mutation probability, and the probability value is considerably large and correlate with and the diversity of two sub-populations. The is defined as:

where and are the maximal fitness values; and are the average fitness values of population 1 and population 2, respectively.

In experimental results, three different input voltages are given to the BLDC motor for system’s identification. From numerical simulations, the method1 of ARGA, which not only accurately search for parameters, but also has small generation number inquick convergence, is the best method to identify parameters, and is also applied to the experimental system.

In order to compare experimental results, three different input voltages are employed by hand. The input voltages are ascendant before 1.5 sec and the stable after 1.5 sec, and shown in Figure 5(a) with steady-state voltages: 10.6 V, 11.5 V and 12 V. The rotation speeds for various voltage are comparing in Figure 5(b), where the

curves of the experimental and identified speeds are compared. In Figure 5(b), the identified rotation speeds are approximate with the experimental rotation speeds. The error percentages of rotation speeds are very small when the voltages are stable. The identified and experimental parameters are very approximate. The speed errors of the identified speeds with respect to the experimental ones are shown in Figure 5(c). For the BLDC motor system, the fitness values with respect to total number of generations is shown in Figure 5(d) and all the fitness values converge near the 650^th generation.

The feasible domains and identified parameters by method1 of ARGA are shown in Table 3. For the three different input voltages, the identified parameters are little different, and the rotation speeds are analogous as show in Figure 5(b). It is noted that the wide feasible domains may affect the identified values of system parameters, and their settings need numerical experience for rapid convergence. It is concluded that the identified parameters will be better if the feasible domains are smaller.

The input voltages are given to the induction motor for system’s identification in experimental results. From numerical simulations, the method 1 of ARGA, which not only accurately search for parameters but also has small generation number in quick convergence, is the best method to identify parameters, and is also applied to the experimental identification.

In order to obtain experimental results, , , , , and are taken in Equations (26) and (27) as the input AC voltages and shown in Figure 7(a). It is

seen the rotation speeds of the induction motor obtained from LabVIEW are low before 10 sec, and the induction is unstable during this interval. Therefore, the identification is performed after 10 sec when the system is stable. Figure 7(b) compares the curves of the experimental and identified rotation speeds. It is seen that the identified rotation speeds are close to the experimental ones. The comparisons of the identified speeds by the SRGA and ARGA with respect to the experimental ones are shown in Figure 7(c). It is seen that the error per-

centages are very small, and the errors of the ARGA are smaller than the SRGA. The fitness value with respect to total number of generations is shown in Figure 7(d). The SRGA converges near the 200^th generation. It is seen that the ARGA has faster convergence near the 50^th generation and higher fitness value.

In order to validate the identified parameters by the SRGA and ARGA in Equation (16), the input voltage as an exponential function in experiments is taken as follows:

where and V = 95, 150, 210 V, respectively. The input voltages are shown in Figure 8(a). Substituting (28) into (25), the input electrical voltages are obtained, and then substituting the electrical

voltages into (16), the rotation speeds are obtained. The rotation speeds for these three voltages are shown in Figures 8(b)-(d), respectively.

The electric currents can also be obtained from (16), and the input electrical current can be obtained by in Equation (19), and shown in Figures 9(a)-(c) for different voltages. It is seen that the electric currents by the SRGA and ARGA are similar, and the ARGA are better than SRGA.

The feasible domains and the identified parameters between the SRGA and method 1 of ARGA are compared in Table 4. It is seen the identified parameters are similar in experiments. However, the fitness value of the ARGA

is bigger than the SRGA, and it means the ARGA parameters are more accurate and correct. For the convergence in generations, the ARGA converges at the 53thgeneration, and is faster than the SRGA.