Method for analyzing influence of impurities on magnetic performance of non-oriented silicon steel based on principal component regression analysis

1. A regression analysis based on the main ingredient of the inclusion impact on the magnetic performance of the non-oriented silicon steel analysis method, characterized in that the method comprises the following steps:

1.1 non-oriented silicon steel and statistics observed in the number of inclusions, obtain different number of impurities in the size of the statistical data interval;

1.2 standard reduction using standard deviation of the magnetic properties of the non-oriented silicon steel (iron loss P_1.5/50 and magnetic induction B₅₀) and statistical of impurities in standardized processing data, the various values to the same weight in operation analysis;

1.3 after the standardization of the inclusion statistical data dimensionality reduction processing: the a n a dependent variable are combined into n independent variable, the variance of conversion and variable and non-variable, m independent variable before choosing to replace the original n the role of the role of the relevant variables, wherein m < n;

1.4 all characteristic value in calculating the characteristic equation, and the cumulative contribution according to the characteristic value determining the quantity of the main ingredient, the composition of the main component then calculate the unit matrix and the orthogonal characteristic vector, to obtain main minute expression ;

1.5 the iron loss in a standardized respectively, magnetic induction value as variable, in order to draw the main is divided into a self-variable as regression analysis, the regression equation and the significance test for linear relationship, when the regression equation to a multicomponent, and its presence is not obvious since a variable, then the self-variable in the regression equation for significance test, until the respective sig obviously check value for the difference of the variable is lower than the given significance level α, α taking 0.05;

1.6 standard reduction the arithmetic inverse of a standard deviation of the linear regression equation on the original n is converted into a multi-component correlation variable of the linear equation;

1.7 obtained according to the above-mentioned method of plural linear equation from a quantitative analysis of the angle of non-oriented silicon steel with the magnetic section of the relationship between the size of the inclusions, non-oriented silicon steel distinguishing significant influence on the size of the magnetic inclusions interval.

2. Regression analysis based on the main ingredient inclusions of non-oriented silicon steel impact on the magnetic performance of the analysis method according to Claim 1, characterized in that the stated step 1.1 in the test sample is divided into rolling and longitudinal section of the viewing surface, said extracted inclusions > 1000 nm, 500-1000 nm, 200-500 nm, 100-200 nm range of the four dimensions.

3. Regression analysis based on the main ingredient inclusions of non-oriented silicon steel impact on the magnetic performance of the analysis method according to Claim 1, characterized in that the stated step 1.1 size in the > 1000 nm of random choice of impurities in 5000-10000 times to observe the field of view of, 100-1000nm the inclusions in 10000-20000 times under the field of view of the random statistical.

4. One of the main ingredients of the regression analysis on the basis of the influence of impurities in the magnetic performance of the non-oriented silicon steel according to Claim 1-3 analysis method, characterized in that the stated step 1.2 standard reduction in standard deviation of the data are as follows:

xi*=xi-x[!OverBar!]s---(1)

Wherein The data after the as standardized, x_i x i of the variable observed section of a, X the average value of the variable, the standard deviation s.

5. Regression analysis based on the main ingredient inclusions of non-oriented silicon steel impact on the magnetic performance of the analysis method according to Claim 4, characterized in that the stated step 1.4 the main components of the extracted in the number of satisfied by the condition that: each ingredient characteristic value is larger than 1 and their cumulative contribution of greater than 80%.

6. Regression analysis based on the main ingredient inclusions of non-oriented silicon steel impact on the magnetic performance of the analysis method according to Claim 5, characterized in that the stated step 1.4 units orthogonal feature vector calculated in the formula is as follows:

ti=ti1,ti2...,tipT=li/λi=li1,li2...,lipT/λi---(2)

The number of the main ingredient that wherein i, the number of variables that the p, l_i said main component vector, λ_i section i that the characteristic value of the main component. The principal component expression Z_i = t_i^T · [x₁^*, x₂^* …, x_p^*]^T.

7. Regression analysis based on the main ingredient inclusions of non-oriented silicon steel impact on the magnetic performance of the analysis method according to Claim 6, characterized in that the stated step 1.5 multivariate regression equation in assessing the significance of linear relations to realize F using statistic, of the parameter involved in the method for calculating the debts of variance statistics 1 in, table are N data in addition to the data of the standardized after;

Table 1 variance debts

Wherein S_return that the variables for the respective variables of the sum of the return of the linear regression, S_remaining that the sum of the residual difference, S_total that of the sum of total dispersion, The non-standard coefficient of the regression equation by a regression value is calculated, in other words y_ifitting value the return of the, For all the variable y_i the mean value, the statistics N the number of the sample.

The F_sig (p, N-p-1) =F, in other words when the sig less than 0.05 is, the difference is prominent, the use of the regression equation is linear is reliable, on the contrary, when the sig is greater than 0.05, the, difference does not significantly, then the test of the equation of the return of the linear relationship is not reliable, the regression equation need to continue to carry out for assessing the significance of the coefficient.

8. Regression analysis based on the main ingredient inclusions of non-oriented silicon steel impact on the magnetic performance of the analysis method according to Claim 7, characterized in that the stated step 1.5 in, when the multiple regression equation is not a variable in, required for assessing the significance of the respective variable, by eliminating redundant backlash law of the variable, eliminating corresponding to the largest value of the sig x_i, | t or struck off the | value corresponding to the signal reproduction, re-determines the corresponding regression equation, then the | value of sig value or | t test, until the sig value of less than 0.05 so far, but due to the relationship between the regression coefficient of correlation exists, when the several variables is not, cannot be removed at the same time together with these variables, can only be removed each time one of the most unobvious variables.

9. Regression analysis based on the main ingredient inclusions of non-oriented silicon steel impact on the magnetic performance of the analysis method according to Claim 8, characterized in that by comparing multiple linear regression equation obtained in the coefficient of the respective variable, inclusions from the quantitative analysis of the impact on the magnetic performance of the non-oriented silicon steel, visually distinguishing significant impact on the magnetic performance of the non-oriented silicon steel section size of inclusions.