Java实现最小二乘法线性拟合，传感与检测，单臂半桥全桥实验，江南大学自动化

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电桥特性曲线：

Java实现最小二乘法线性拟合及计算灵敏度、非线性误差的代码：

/**
 * @Author: Yeman
 * @Date: 2021-10-29-23:03
 * @Description:
 */
public class LeastSquares {
    public static void matching(double[] x, double[] y, double[] input) {
        double k = getK(x, y);
        double b = getB(x, y);
        System.out.println("线性回归系数k值：\t" + k + "\n" + "线性回归系数b值：\t" + b);
        double maxy = 0; //用来记录最大偏差
        //寻找最大偏差
        for (int i = 0; i < input.length; i++) {
            if (Math.abs(k * input[i] + b - y[i]) > maxy){
                maxy = Math.abs(k * input[i] + b - y[i]);
            }
        }
        System.out.println("最大偏差为：" + maxy);
        //求灵敏度
        double s = 0;
        double sum = 0;
        for (int i = 1; i < y.length; i++) {
            sum += y[i] - y[i-1];
        }
        s = sum / (y.length - 1) / 20;
        System.out.println("灵敏度为：" + s);
        //求线性误差
        System.out.println("非线性误差为：" + maxy/y[10]);
    }

    /*
     * 返回x的系数k 公式：k = ( n sum( xy ) - sum( x ) sum( y ) ) / ( n sum( x^2 ) - sum(x) ^ 2 )
     */
    public static double getK(double[] x, double[] y) {
        int n = x.length;
        return (double) ((n * pSum(x, y) - sum(x) * sum(y)) / (n * sqSum(x) - Math.pow(sum(x), 2)));
    }

    /*
     * 返回常量系数系数b 公式：b = sum( y ) / n - k * sum( x ) / n
     */
    public static double getB(double[] x, double[] y) {
        int n = x.length;
        double k = getK(x, y);
        return sum(y) / n - k * sum(x) / n;
    }

    /*
     * 求和
     */
    private static double sum(double[] ds) {
        double s = 0;
        for (double d : ds)
        {
            s = s + d;
        }
        return s;
    }

    /*
     * 求平方和
     */
    private static double sqSum(double[] ds) {
        double s = 0;
        for (double d : ds) {
            s = (double) (s + Math.pow(d, 2));
        }
        return s;
    }

    /*
     * 返回对应项相乘后的和
     */
    private static double pSum(double[] x, double[] y) {
        double s = 0;
        for (int i = 0; i < x.length; i++) {
            s = s + x[i] * y[i];
        }
        return s;
    }

    public static void main(String[] args) {
        double[] x = {0,20,40,60,80,100,120,140,160,180,200};
        double[] y1 = {0,4.1,8.1,12.2,17.1,21.7,25.8,29.9,34.1,37.8,43.3};
        double[] y2 = {0,7.5,15.1,22.9,30.7,38.6,46.3,54.2,62.0,69.9,77.8};
        double[] y3 = {0,15.0,31.3,47.0,62.6,78.3,93.8,109.6,125.5,141.2,157.3};
        double[] inputs = x;
        System.out.println("===单臂电桥：");
        matching(x, y1,inputs);
        System.out.println("======半桥：");
        matching(x, y2,inputs);
        System.out.println("======全桥：");
        matching(x, y3,inputs);
    }
}

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