The Influence Factor Analysis of Symmetrical Half-Bridge Power Converter through Regression, Rough Set and GM(1,N) Model

Abstract

Analysis of power converter performance has tended to be engineering-oriented, focusing mainly on voltage stability, output power and efficiency improvement. However, there has been little discussion about the weight relations between these factors. In view of the previous inadequacy, this study employs regression, rough set and GM(1,N) to analyze the relations among the factors that affect the converter, with a symmetrical half-bridge power converter serving as an example. The four related affecting factors, including the current conversion ratio, voltage conversion ratio, power conversion ratio and output efficiency, are firstly analyzed and calculated. The respective relative relations between output efficiency and the other three factors are obtained. This research can be referred to by engineers in their design of symmetrical half-bridge power converters.

1. Introduction

Currently, two different models of power supply are available in the market, including linear power supply and switching power supply. Despite its simple circuit structure, high stability, small ripple, fast transient response, low electromagnetic interference and high reliability, linear power supply is associated with low efficiency and large size. A switching power supply is designed to compensate for the shortcomings of the linear power supply. Therefore, with technological advancements, the linear power supply has been gradually replaced by the switching power supply, which is widely used in 3C products. Despite switching power supply being credited with high conversion efficiency, light weight and a wide-range DC input, its circuit structure features a complex circuit and large electromagnetic interference. This study focuses on this phenomenon [1,2].

In this study, the symmetrical half-bridge power converter serves as a switching power supply. The symmetrical half-bridge power converter is different from push-pull single-ended driving or interleaved driving, which requires a double input voltage. It is widely used in converters whose power supply voltage is higher than the safety standard voltage value of the transistor.

Research on power converters has focused mainly on circuit design and practical development, including high-power two-way bridge power supplies [3]. A high-voltage switching resonant converter has been used to reduce switching loss in the system [4,5,6]. High-efficiency converters [7,8,9,10,11] and a reluctance motor drive system for the two-way voltage double front-end converter have been developed [12]. In battery charging applications [13,14,15,16], topology and design optimization were achieved in an optimized multiport DC/DC converter for transportation [17,18,19] and a PWM in a DC/DC converter [20,21]. Existing studies in the literature also include a passive RF-DC converter for energy harvesting at ultra-low input power at 868 MHz [22]; using extended Kalman filter observer technology to solve the fault problem in a DC/DC converter [23], as well as using a DC/DC converter for e-mobility charging [24]. Related to this study, the symmetrical half-bridge is related to high-power half-bridge converters [25,26,27]. However, little research deals with the integration of the three methods. This study, therefore, can be regarded as a pioneering study of converters [28].

The second section introduces the mathematics model employed, which includes regression analysis, the rough set method and the GM(1,N) model of grey system theory. Section 3 provides a field example of a symmetrical half-bridge power converter. Section 4 describes the complete calculation steps for the symmetrical half-bridge power converter. The final section draws conclusions from the results and puts forward suggestions for future research.

2. The Mathematical Model of Soft Computing

This section mainly describes the computing processes of regression analysis, rough set and grey GM(1,N) model. The procedure is described below.

2.1. Regression Analysis

Regression analysis is a method of statistically analyzing data. Its main purpose is to understand the relations between two or more variables and the direction and intensity of the correlation. It aims to establish a mathematical model to observe specific variables and predict the variables of interest. There are four steps in the calculation process [29,30].

1. List the equation

$$y_i(k)={\displaystyle \sum _{j=1}^N{a}_j{x}_j(k)}\hspace{1em}i=1,2,3,\cdots ,m,\hspace{1em}k=1,2,3,\cdots ,n$$

(1)

2. Expand Equation (1) to obtain

$$\begin{array}{l}{y}_1(1)=a_1{x}_1(1)+a_2{x}_2(1)+\cdots +a_N{x}_N(1)\\ y_2(2)=a_1{x}_1(2)+a_2{x}_2(2)+\cdots +a_N{x}_N(2)\\ y_3(3)=a_1{x}_1(3)+a_2{x}_2(3)+\cdots +a_N{x}_N(3)\\ \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \\ y_m(n)=a_1{x}_1(n)+a_2{x}_2(n)+\cdots +a_N{x}_N(n)\end{array}$$

(2)

3. Transfer Equation (2) into matrix form

$$\left[\begin{array}{c}{y}_1(1)\\ y_2(2)\\ ⋮\\ y_m(n)\end{array}\right]=\left[\begin{array}{cccc}{x}_1(1)& x_2(1)& \cdots & x_N(1)\\ x_1(2)& x_2(2)& \cdots & x_N(2)\\ ⋮& ⋮& \ddots & ⋮\\ x_1(n)& x_2(n)& \cdots & x_N(n)\end{array}\right]\left[\begin{array}{c}{a}_1\\ a_2\\ a_3\\ ⋮\\ a_N\end{array}\right]$$

(3)

4. Use $A={\left(X^{T}X\right)}^{-1}{X}^{T}Y$ to find the value of $a_N$, where

$$Y=\left[\begin{array}{c}{y}_1(1)\\ y_2(2)\\ ⋮\\ y_m(n)\end{array}\right],X=\left[\begin{array}{cccc}{x}_1(1)& x_2(1)& \cdots & x_N(1)\\ x_1(2)& x_2(2)& \cdots & x_N(2)\\ ⋮& ⋮& \ddots & ⋮\\ x_1(n)& x_2(n)& \cdots & x_N(n)\end{array}\right],A=\left[\begin{array}{c}{a}_1\\ a_2\\ a_3\\ ⋮\\ a_N\end{array}\right]$$

The value of $a_N$ is the weighting of $y_i$.

2.2. Rough Set Method

Rough set is used for classification. For the affecting factors in the system, the weighting of each affecting factor to the output of the system can be obtained.

The analysis steps of rough set are as follows [31]:

1. Information system (IS)

$$IS=(U,X)$$

(4)

where:

i.

$U=\{x_1,x_2,\cdots ,x_n\}$ is called the universal set;

ii.

$X=\{a_1,a_2,\cdots ,a_m\}$ is called the attribute set.

2. Information function

$$f_a:U\times X\to V_a$$

(5)

where:

i.

$U\times X$ is called the domain of universal set;

ii.

$V_a$ is called the range.

3. Discrete: based on Equation (6).

$$t=\frac{V_{\max .}-V_{\min .}}{k}$$

(6)

where:

i.

$V_{\max .}$ is the maximum value of the continuous attribute;

ii.

$V_{\min .}$ is the minimum value of the continuous attribute.

Through the discretization, one can obtain the attribute value

$$\{[d_0,d_1],[d_1,d_2],\cdots ,[d_{k-1},d_k]\}$$

(7)

where $d_0=V_{\min },d_k=V_{\max },d_{i-1}<d_i,\hspace{1em}i=1,2,3,\cdots ,k,i$ is the representative value of discrete normalization, and k is called the grade of discreteness.

4. Lower approximation and upper approximation

The lower approximation means that the attribute factor is completely determined to belong to U (intersection), while the upper approximation means that the attribute factor may belong to U (union).

5. Indiscernibility: For any $x_i$ and $x_j$, they are in the same category.

6. Positive, negative and boundary

$$po{s}_R(X)=\underset{\_}{R}(X),ne{g}_R(X)=U-\overline{R}(X),b{n}_R(A)=\underset{\_}{R}(A)-\overline{R}(A)$$

(8)

7. Dependents: The dependence of decision attribute D on conditional attribute C is

$${\gamma }_c\left(D\right)=\frac{\left|po{s}_c\left(D\right)\right|}{U}$$

(9)

where $po{s}_c(D)$ is the positive value of decision attribute D.

Under the conditional attribute C, the ratio of objects that can be completely classified into the whole number of objects in the set is calculated.

8. Significant: Indicates the importance of attributes in the decision-making system.

$${\sigma }_{\left(C,D\right)}\left(a\right)=\frac{{\gamma }_c\left(D\right)-{\gamma }_{c-\left\{a\right\}}\left(D\right)}{{\gamma }_c\left(D\right)}$$

(10)

where ${\gamma }_c(D)$ represents the degree of dependence between the decision attribute D and the condition attribute C, and calculates the importance of attribute a by using the change in value when a is removed from C.

2.3. GM(1,N) Model

As with rough set, the GM(1,N) model is used to find the weighting of each affecting factor to the output in the system. According to the definition of grey system theory, the grey differential equation of the model is [32]:

$$\frac{d{x}^{(1)}}{dt}+a{x}_1^{(1)}={\displaystyle \sum _{i=2}^N{b}_i{x}_i^{(1)}(k)}$$

(11)

where:

i.

$a$ and $b_i$ are coefficients;

ii.

$.x_1^{(1)}(k)$ is a standard sequence;

iii.

$x_i^{(1)}(k)$ are inspected sequences;

iv.

$x^{(1)}=\left({\displaystyle \sum _{k=1}^1{x}^{(0)}(k),{\displaystyle \sum _{k=1}^2{x}^{(0)}(k),\cdots ,{\displaystyle \sum _{k=1}^n{x}^{(0)}(k)}}}\right)$.

If in the sequence $x_i^{(0)}(k),\hspace{1em}i=1,2,3\cdots ,N$, $x_1^{(0)}(k)$ is the main behavior of the system, and $x_2^{(0)}(k),x_3^{(0)}(k),x_4^{(0)}(k),\dots \dots \dots x_N^{(0)}(k)$ are the factors that affect the main behavior, the analysis step is as follows:

1. Build up original sequence

$$\begin{array}{l}{x}_1^{(0)}=\{x_1^{(0)}(1),x_1^{(0)}(2),\cdots ,x_1^{(0)}(k)\}\\ x_2^{(0)}=\{x_2^{(0)}(1),x_2^{(0)}(2),\cdots ,x_2^{(0)}(k)\}\\ x_3^{(0)}=\{x_3^{(0)}(1),x_3^{(0)}(2),\cdots ,x_3^{(0)}(k)\}\hspace{1em}k=1,2,3,\dots n\\ \cdots \cdots \cdots \cdots \cdots \cdots \\ x_N^{(0)}=\{x_N^{(0)}(1),x_N^{(0)}(2),\cdots ,x_N^{(0)}(k)\}\end{array}$$

(12)

2. Build up AGO sequence

$$\begin{array}{l}{x}_1^{(1)}=\{x_1^{(1)}(1),x_1^{(1)}(2),\cdots ,x_1^{(1)}(k)\}\\ x_2^{(1)}=\{x_2^{(0)}(1),x_2^{(1)}(2),\cdots ,x_2^{(1)}(k)\}\\ x_3^{(1)}=\{x_3^{(1)}(1),x_3^{(1)}(2),\cdots ,x_3^{(1)}(k)\}\hspace{1em}k=1,2,3,\cdots ,n\\ \cdots \cdots \cdots \cdots \cdots \cdots \\ x_N^{(1)}=\{x_N^{(1)}(1),x_N^{(1)}(2),\cdots ,x_N^{(1)}(k)\}\end{array}$$

(13)

3. Transfer Equation (13) into a difference form

$$x_1^{(0)}(k)+a{z}_1^{(1)}(k)={\displaystyle \sum _{i=2}^N{b}_i{x}_i^{(1)}(k)}$$

(14)

where $z_1^{(1)}(k)=0.5x_1^{(1)}(k)+0.5x_1^{(1)}(k-1)\hspace{1em},k\ge 2$

4. Based on Equation (14), we substitute the AGO data, and we obtain

$$\begin{array}{l}{x}_1^{(0)}(2)+a{z}_1^{(1)}(2)=b_2{x}_2^{(1)}(2)+\cdots \cdots +b_N{x}_N^{(1)}(2)\\ x_1^{(0)}(3)+a{z}_1^{(1)}(3)=b_2{x}_2^{(1)}(3)+\cdots \cdots +b_N{x}_N^{(1)}(3)\\ \cdots \cdots \cdots \cdots \cdots \cdots \\ x_1^{(0)}(n)+a{z}_1^{(1)}(n)=b_2{x}_2^{(1)}(n)+\cdots \cdots +b_N{x}_N^{(1)}(n)\end{array}$$

(15)

Then, transfer Equation (15) into matrix form, as shown in Equation (16)

$$\left[\begin{array}{c}{x}_1^{(0)}(2)\\ x_1^{(0)}(3)\\ ⋮\\ x_1^{(0)}(n)\end{array}\right]=\left[\begin{array}{cccc}-z_1^{(1)}(2)& x_2^{(1)}(2)& \cdots & x_N^{(1)}(2)\\ -z_1^{(1)}(3)& x_2^{(1)}(3)& \cdots & x_N^{(1)}(3)\\ ⋮& \cdots & & \\ -z_1^{(1)}(n)& x_2^{(1)}(n)& \cdots & x_N^{(1)}(n)\end{array}\right]\left[\begin{array}{c}a\\ b_2\\ ⋮\\ b_N\end{array}\right]$$

(16)

According to the least squares method, by using $\widehat{a}={(B^{T}B)}^{-1}{B}^T{Y}_N$, we find the values where:$Y_N=\left[\begin{array}{c}{x}_1^{(0)}(2)\\ x_1^{(0)}(3)\\ ⋮\\ x_1^{(0)}(n)\end{array}\right]B=\left[\begin{array}{cccc}-z_1^{(1)}(2)& x_2^{(1)}(2)& \cdots & x_N^{(1)}(2)\\ -z_1^{(1)}(3)& x_2^{(1)}(3)& \cdots & x_N^{(1)}(3)\\ ⋮& \cdots & & \\ -z_1^{(1)}(n)& x_2^{(1)}(n)& \cdots & x_N^{(1)}(n)\end{array}\right]\widehat{a}=\left[\begin{array}{c}a\\ b_2\\ ⋮\\ b_N\end{array}\right]$.

3. Real Example and Verification

This paper first designs seven sets of parameter values, and then provides a sample of symmetrical half-bridge power converters. The relevant measurement values are obtained through conducting experiments. The three input factors, which are the internal parameters of the converter, include the current conversion ratio, voltage conversion ratio and power conversion ratio. The output factor refers to the efficiency of the converter. Soft computing is employed to analyze the weighting relationship among the input factors and output factor [33].

3.1. The Circuit of Symmetrical Half-Bridge Power Converter

The circuit of the symmetrical half-bridge power converter is shown in Figure 1.

The completed product, which is based on the circuit diagram in Figure 1, is shown in Figure 2.

3.2. The Experimental Data

The experimental values are shown in

Table 1. The experimental values of symmetrical half-bridge power converter.

Parameter	Ii (A)	Io (A)	Pi (W)	Vi (V)	Vo (V)	Po (W)	Duty Cycle (%)	Efficiency (%)
01	0.084	0.632	13.02	155.0	19.016	12	35	92.2
02	0.164	1.261	25.42	155.0	19.006	24	35	94.4
03	0.246	1.893	38.13	155.0	19.006	36	35	94.4
04	0.328	2.525	50.84	155.0	19.010	48	35	94.4
05	0.412	3.158	63.86	155.0	19.002	60	35	94.0
06	0.497	3.792	77.04	155.0	19.994	72	35	93.5
07	0.590	4.426	91.45	155.0	19.998	84	35	91.9

.

The data in Table 1 are the actual values of the overall measurement. In order to comply with the calculation of the mathematical model, they are converted into the ratios of various parameters, as shown in

Table 2. The rearrangement of data of Table 1.

No.	Io/Ii	Vo/Vi	Po/Pi	$*\mathbf{Efficiency}\left(\mathit{\eta }\right)$
01	7.523810	0.122684	0.944138	0.922
02	7.689024	0.122619	0.944138	0.944
03	7.695122	0.122619	0.944138	0.944
04	7.698171	0.122645	0.939555	0.944
05	7.665049	0.122594	0.934579	0.940
06	7.629779	0.128994	0.918535	0.935
07	7.501695	0.129019	0.921659	0.919

* Efficiency transfer to type of decimal point.

.

4. Calculation and Analysis

This section mainly explains the calculation process and results of three soft computing methods.

4.1. Regression Analysis

The analysis sequences are built based on the mathematics model.

Output efficiency: $y$ = (0.922, 0.944, 0.944, 0.944, 0.940, 0.935, 0.919)

The ratio of output current to input current (I_o/I_i):

$x_1$ = (7.523810, 7.689024, 7.695122, 7.698171, 7.665049, 7.629779, 7.501695)

The ratio of output voltage to input voltage (V_o/V_i):

$x_2$ = (0.122684, 0.122619, 0.122619, 0.122645, 0.122594, 0.128994, 0.129019)

The ratio of output power to input power (P_o/P_i):

$x_3$ = (0.944138, 0.944138, 0.944138, 0.939555, 0.934579, 0.918535, 0.921659)

Substitute into Equation (3) for weighting:

$$\left[\begin{array}{c}0.922\\ 0.944\\ 0.944\\ 0.944\\ 0.940\\ 0.935\\ 0.919\end{array}\right]=\left[\begin{array}{ccc}7.523810& 0.122684& 0.944138\\ 7.689024& 0.122619& 0.944138\\ 7.695122& 0.122619& 0.944138\\ 7.699171& 0.122646& 0.939555\\ 7.665049& 0.122594& 0.934579\\ 7.629779& 0.128994& 0.918535\\ 7.501695& 0.129019& 0.921659\end{array}\right]\left[\begin{array}{c}{a}_1\\ a_2\\ a_3\end{array}\right]$$

Use $A={(X^{T}X)}^{-1}{X}^{T}Y$ to find the values of $a_1~a_3$, where:

$$A=\left[\begin{array}{c}{a}_1\\ a_2\\ a_3\end{array}\right],X=\left[\begin{array}{ccc}7.523810& 0.122684& 0.944138\\ 7.689024& 0.122619& 0.944138\\ 7.695122& 0.122619& 0.944138\\ 7.699171& 0.122646& 0.939555\\ 7.665049& 0.122594& 0.934579\\ 7.629779& 0.128994& 0.918535\\ 7.501695& 0.129019& 0.921659\end{array}\right],Y=\left[\begin{array}{c}0.922\\ 0.944\\ 0.944\\ 0.944\\ 0.940\\ 0.935\\ 0.919\end{array}\right]$$

The final results are shown in

Table 3. The final results of regression analysis.

Parameter	$\frac{{\mathit{I}}_{\mathit{o}}}{{\mathit{I}}_{\mathit{i}}}$	$\frac{{\mathit{V}}_{\mathit{o}}}{{\mathit{V}}_{\mathit{i}}}$	$\frac{{\mathit{p}}_{\mathit{o}}}{{\mathit{p}}_{\mathit{i}}}$
Regression analysis	0.1265	−0.1437	−0.0123
Correlation	Positive correlation	Negative correlation	Negative correlation

.

Regression analysis shows that the actual circuit $\frac{I_o}{I_i}$ is positively correlated, while the other two are negatively correlated.

4.2. Rough Set Method

Rough set must firstly discretize the values. Accordingly, this paper discretizes the measured values into four grades.

Table 4. Discretization results of four grades.

Group/Parameter	$\frac{{\mathit{I}}_{\mathit{o}}}{{\mathit{I}}_{\mathit{i}}}$	$\frac{{\mathit{V}}_{\mathit{o}}}{{\mathit{V}}_{\mathit{i}}}$	$\frac{{\mathit{p}}_{\mathit{o}}}{{\mathit{p}}_{\mathit{i}}}$	$\mathbf{Efficiency}\left(\mathit{\eta }\right)$
01	1	1	4	1
02	4	1	4	4
03	4	1	4	4
04	4	1	4	4
05	4	1	3	4
06	3	4	1	3
07	1	4	1	1

shows the result.

Table 4 indicates the ratio of output current to input current as R₁, the ratio of output voltage to input voltage as R₂, the ratio of output power to input power as R₃ and efficiency as decision attribute D. Then_, the discrete data are converted into the rough set model to calculate the significance of each attribute factor.

1. Calculate the attribute set $\frac{U}{C}=\frac{U}{\{R_1,R_2,R_3\}}$={{$x_1\},\{x_2,x_3,x_4$},{$x_5$},{$x_6$},{$x_7$}}

2. Calculate the decision set $\frac{U}{D}=\left\{\right\{x_1,x_7\},\{x_2,x_3,x_4,x_5\},\{x_6\left\}\right\}=\{X_1,X_2,X_3\}$; hence, $po{s}_C(D)$ = {$\{x_1\},\{x_2\},\left\{x_3\right\},\{x_4\},\{x_5\left\}\right\}$, and substitute into Equation (9) to obtain ${\gamma }_c\left(D\right)=\frac{\left|po{s}_C\left(D\right)\right|}{\left|U\right|}=\frac{7}{7}=1$.

3. Analyze the conditional attributes of each factor

(1) Omit $R_1$

$$\begin{gathered} \frac{U}{C}=\frac{U}{\{R_2,R_3\}}=\left\{\right\{x_1,x_2,x_3,x_4\},\{x_5\},\{x_6,x_7\left\}\right\} \\ \frac{U}{D}=\left\{\right\{x_1,x_7\},\{x_2,x_3,x_4,x_5\},\{x_6\left\}\right\}=\{X_1,X_2,X_3\} \end{gathered}$$

Hence, $po{s}_C(D)$ = {$x_5$}, and substitute into Equation (9) to obtain ${\gamma }_c\left(D\right)=\frac{\left|po{s}_C\left(D\right)\right|}{\left|U\right|}=1$; then, substitute into Equation (10) to obtain ${\gamma }_{c-\left\{R_1\right\}}\left(D\right)=\frac{\left|po{s}_C\left(D\right)\right|}{\left|U\right|}=\frac{1}{7}$. Therefore, the significance of ${\sigma }_{\left(C,D\right)}(R_1)==\frac{1-\frac{1}{7}}{1}=\frac{6}{7}$.

(2) Omit $R_2$

$$\begin{gathered} \frac{U}{C}=\frac{U}{\{R_1,R_3\}}=\{\{x_1\},\{x_2,x_3,x_4,x_5\},\{x_6\},\{x_7\left\}\right\} \\ \frac{U}{D}=\left\{\right\{x_1,x_7\},\{x_2,x_3,x_4,x_5\},\{x_6\left\}\right\}=\{X_1,X_2,X_3\} \end{gathered}$$

Hence, $po{s}_C(D)$ = {{$x_1$},{$x_2$},{$x_3$},{$x_4$},{$x_5$},{$x_6$},{$x_7$}}, and substitute into Equation (9) to obtain ${\gamma }_c\left(D\right)=\frac{\left|po{s}_C\left(D\right)\right|}{\left|U\right|}=\frac{7}{7}=1$; then, substitute into Equation (10) to obtain ${\gamma }_{c-\left\{R_2\right\}}\left(D\right)=\frac{\left|po{s}_C\left(D\right)\right|}{\left|U\right|}$$=1$. Therefore, the significance of ${\sigma }_{\left(C,D\right)}(R_2)=\frac{1-1}{1}=0$.

(3) Omit $R_3$

$$\begin{gathered} \frac{U}{C}=\frac{U}{\{R_1,R_2\}}=\left\{\right\{x_1\},\{x_2,x_3,x_4,x_5\},\{x_6\},\{x_7\left\}\right\} \\ \frac{U}{D}=\{\{x_1,x_7\},\{x_2,x_3,x_4,x_5\},\{x_6\left\}\right\}=\{X_1,X_2,X_3\} \end{gathered}$$

Hence, $po{s}_C(D)$ = {{$x_1$},{$x_2$},{$x_3$},{$x_4$},{$x_5$},{$x_6$},{$x_7$}}, and substitute into Equation (9) to obtain ${\gamma }_c\left(D\right)=\frac{\left|po{s}_C\left(D\right)\right|}{\left|U\right|}=\frac{7}{7}=1$, and substitute into Equation (10) to obtain ${\gamma }_{c-\left\{R_3\right\}}\left(D\right)=\frac{\left|po{s}_C\left(D\right)\right|}{\left|U\right|}=1$; therefore, the significance of ${\sigma }_{\left(C,D\right)}(R_3)=\frac{1-1}{1}=0$.

The final results are shown in

Table 5. The final results of rough set under four grades.

Grade/Parameter	$\frac{{\mathit{I}}_{\mathit{o}}}{{\mathit{I}}_{\mathit{i}}}$	$\frac{{\mathit{V}}_{\mathit{o}}}{{\mathit{V}}_{\mathit{i}}}$	$\frac{{\mathit{p}}_{\mathit{o}}}{{\mathit{p}}_{\mathit{i}}}$
Four grade	0.8571	0	0
Rank	1	2	2

.

4.3. GM(1,N) Method

1. The analysis sequences are built based on the mathematical model.

Output efficiency:

$x_1^{(0)}$ = (0.922, 0.944, 0.944, 0.944, 0.940, 0.935, 0.919)

The ratio of output current to input current (I_o/I_i)

$x_2^{(0)}$ = (7.523810, 7.689024, 7.695122, 7.698171, 7.665049, 7.629779, 7.501695)

The ratio of output voltage to input voltage (V_o/V_i):

$x_3^{(0)}$ = (0.122684, 0.122619, 0.122619, 0.122645, 0.122594, 0.128994, 0.129019)

The ratio of output power to input power(P_o/P_i)

$x_4$ = (0.944138, 0.944138, 0.944138, 0.939555, 0.934579, 0.918535, 0.921659)

2. Build up AGO sequence

$x_1^{(0)}$ = (0.922, 1.866, 2.81, 3.754, 4.694, 5.629, 6.548)

$x_2^{(0)}$ = (7.5238, 15.2128, 22.908, 30.6061, 38.2712, 45.901, 53.4026)

$x_3^{(0)}$ = (0.1227, 0.2453, 0.3679, 0.4906, 0.6132, 0.7422, 0.8712)

$x_4^{(0)}$ = (0.9441, 1.8883, 2.8324, 3.772, 4.7065, 5.6251, 6.5467)

$z_1^{(1)}$ = (1.394, 2.338, 3.282, 4.224, 5.1615, 6.0885)

3. Substitute into Equation (16) to obtain the weighting

$$\left[\begin{array}{c}1.866\\ 2.81\\ 3.754\\ 4.694\\ 5.629\\ 6.548\end{array}\right]=\left[\begin{array}{cccc}-1/394& 15.2128& 0.2453& 1.8333\\ -2.338& 22.908& 0.3679& 2.8324\\ -3.282& 30.6031& 0.4906& 3.772\\ -4.224& 38.2172& 0.6132& 4.7065\\ -5.1615& 45.901& 0.7422& 5.6251\\ -6.0885& 53.4026& 0.8712& 6.5467\end{array}\right]\left[\begin{array}{c}a\\ b_2\\ b_3\\ b_4\end{array}\right]$$

Uses $\widehat{a}={(B^{T}B)}^{-1}{B}^T{Y}_N$ to find the values of weighting where: $Y_N=\left[\begin{array}{c}1.866\\ 2.81\\ 3.754\\ 4.694\\ 5.629\\ 6.548\end{array}\right],B=\left[\begin{array}{cccc}-1/394& 15.2128& 0.2453& 1.8333\\ -2.338& 22.908& 0.3679& 2.8324\\ -3.282& 30.6031& 0.4906& 3.772\\ -4.224& 38.2172& 0.6132& 4.7065\\ -5.1615& 45.901& 0.7422& 5.6251\\ -6.0885& 53.4026& 0.8712& 6.5467\end{array}\right],\widehat{a}=\left[\begin{array}{c}a\\ b_2\\ b_3\\ b_4\end{array}\right]$.

The final results are shown in

Table 6. The final results of GM(1,N) model.

Grade/Parameter	$\frac{{\mathit{I}}_{\mathit{o}}}{{\mathit{I}}_{\mathit{i}}}$	$\frac{{\mathit{V}}_{\mathit{o}}}{{\mathit{V}}_{\mathit{i}}}$	$\frac{{\mathit{p}}_{\mathit{o}}}{{\mathit{p}}_{\mathit{i}}}$
Weighting	0.2478	0.2141	0.0091
Rank	1	2	3

.

5. Conclusions

Research on power converters in the past has turned out good results in circuit design and product development. The integration of regression analysis, rough set analysis and GM(1,N) can be regarded as a pioneering research method. The paper first develops a practical sample. By employing regression analysis, rough set and the GM(1,N) model, this study finds that the current conversion ratio has the greatest impact on efficiency. This finding is consistent with the basic principle of the power converter, which is the characteristic of current amplification. The analysis method implemented in this study, therefore, is reasonable.

This study analyzes only one of the symmetrical half-bridge power converters. Soft computing for classification, according to this research, is applicable to electrical engineering. A forthcoming study is suggested to aim at other types of power converters on the one hand, and to combine other related mathematical models to increase the integrity of the overall analysis on the other.