如何将scipy.optimize.minimize用于三个变量的函数？

Question

我试图优化这个功能：

def voce(strain, sigma_s, sigma_y, epsilon_0):
    stress = sigma_s - (sigma_s - sigma_y)*np.exp(-strain/epsilon_0)
    return stress

通过为sigma_s、sigma_y和epsilon_0找到最佳值。应变和应力应该是一维numpy阵列。

我试过：

initial_guess = [1, 1, 1]
result = minimize(voce, initial_guess)

但我得到了"ValueError:只能将大小为1的数组转换为Python标量“

我有点搞不懂怎么用这个

Answer 1

由scipy.optimize.minimize优化的函数应该返回一个标量值。请看这里。

也就是说，您可以实现一个for -循环，并为每个应变值求解应力.然后，你可以取压力值之和，并将其最小化。

在此之前，您需要首先按照以下方式重新构造您的语音功能：

import numpy as np

def voce(sigma_s, sigma_y, epsilon_0, strain):
    stress = sigma_s - (sigma_s - sigma_y)*np.exp(-strain/epsilon_0)
    return stress

现在，为了进行优化，引入一个新的函数，比如乐趣，您将传递sigma_s、sigma_y和epsilon_0以便最小化，strain (一维数组)作为您的语音函数的参数：

def fun(x, strain):

    sigma_s = x[0]
    sigma_y = x[1]
    epsilon_0 = x[2]

    stress = []
    sum = 0

    for i in strain:
        s = voce(sigma_s, sigma_y, epsilon_0, i)
        stress.append(s)

    sum = np.sum(stress)

    return sum

现在，按以下方式优化和打印结果：

from scipy.optimize import minimize

# strain = [x,y,z] <-- Assign your strain array here
initial_guess = [1, 1, 1]
res = minimize(fun, initial_guess, method="Nelder-Mead", args=(strain))
print(res)

此外，如果您想将声音方程与您的应力应变数据(意味着您已经从实验中测量到的应力值)进行拟合，您可以使用来自sklearn的均方误差将声音方程的结果(计算的应力)与实测的应力进行比较。为此，您可以将乐趣更改为：

from sklearn.metrics import mean_squared_error

def fun(x, measured_strain, measured_stress):

    sigma_s = x[0]
    sigma_y = x[1]
    epsilon_0 = x[2]

    calculated_stress = []
    error = 0

    for i in measured_strain:
        s = voce(sigma_s, sigma_y, epsilon_0, i)
        calculated_stress.append(s)

    error = mean_squared_error(measured_stress, calculated_stress)

    return error

其中measured_stress是一个一维数组.现在，按以下方式优化和打印结果：

from scipy.optimize import minimize

# measured_strain = [x,y,z] <-- Assign your measured strain array here
# measures_stress = [a,b,c] <-- Assign your measured stress array here
initial_guess = [1, 1, 1]
res = minimize(fun, initial_guess, method="Nelder-Mead",
               args=(measured_strain, measured_stress))
print(res)