给出文档中问题的MATLAB的验算点方法的代码

根据文档中的要求，以下是使用 MATLAB 实现 JC 法和优化法求解结构可靠度指标 β，并计算验算点坐标的示例代码。此外，还提供了蒙特卡洛法进行验证的方法（包括重要抽样）。

### JC 法和优化法求解可靠度指标 β 和验算点坐标

% 定义随机变量及其分布参数
distributions = struct();
distributions.Xi = makedist('ExtremeValue', 'mu', 0.01, 'sigma', 0.003);
distributions.A2 = makedist('Normal', 'mu', 0.30, 'sigma', 0.015);
distributions.X3 = makedist('Normal', 'mu', 480.0, 'sigma', 36/sqrt(1)); % 假设组号为1
distributions.X4 = makedist('Lognormal', 'mu', log(226e-6), 'sigma', 11.3e-6 / 226e-6);
distributions.X5 = makedist('Normal', 'mu', 0.5, 'sigma', 0.05);
distributions.X6 = makedist('Normal', 'mu', 0.12, 'sigma', 0.006);
distributions.X = makedist('Lognormal', 'mu', log(40.0), 'sigma', 6.0 / 40.0);
distributions.XH = makedist('Normal', 'mu', 0.8, 'sigma', 0.01 * 1); % 假设组号为1

% 功能函数
fun = @(u) distributions.Xi.icdf(normcdf(u(1))) + ...
      distributions.A2.icdf(normcdf(u(2))) + ...
      distributions.X3.icdf(normcdf(u(3))) + ...
      distributions.X4.icdf(normcdf(u(4))) + ...
      distributions.X5.icdf(normcdf(u(5))) + ...
      distributions.X6.icdf(normcdf(u(6))) + ...
      distributions.X.icdf(normcdf(u(7))) - ...
      distributions.XH.icdf(normcdf(u(8)));

% 初始猜测点
u0 = zeros(8, 1);

% 使用 fmincon 求解验算点
options = optimoptions('fmincon', 'Display', 'off');
[u_opt, ~] = fmincon(@(u) -fun(u), u0, [], [], [], [], -Inf*ones(8,1), Inf*ones(8,1), [], options);

% 计算可靠度指标 β
beta = norminv(fun(u_opt));

% 输出结果
disp(['验算点坐标: ', num2str(u_opt')])
disp(['可靠度指标 β: ', num2str(beta)])

### 蒙特卡洛法验证

% 蒙特卡洛模拟次数
N = 100000;

% 生成随机样本
Xi_samples = random(distributions.Xi, N, 1);
A2_samples = random(distributions.A2, N, 1);
X3_samples = random(distributions.X3, N, 1);
X4_samples = random(distributions.X4, N, 1);
X5_samples = random(distributions.X5, N, 1);
X6_samples = random(distributions.X6, N, 1);
X_samples = random(distributions.X, N, 1);
XH_samples = random(distributions.XH, N, 1);

% 计算功能函数值
g_values = Xi_samples + A2_samples + X3_samples + X4_samples + X5_samples + X6_samples + X_samples - XH_samples;

% 计算失效概率
Pf_mc = mean(g_values < 0);

% 计算可靠度指标 β
beta_mc = norminv(1 - Pf_mc);

% 输出结果
disp(['蒙特卡洛法失效概率 Pf: ', num2str(Pf_mc)])
disp(['蒙特卡洛法可靠度指标 β: ', num2str(beta_mc)])

% 重要抽样
% 假设重要性分布为均值平移后的正态分布
shift = -u_opt;
Xi_is = makedist('Normal', 'mu', 0.01 + shift(1), 'sigma', 0.003);
A2_is = makedist('Normal', 'mu', 0.30 + shift(2), 'sigma', 0.015);
X3_is = makedist('Normal', 'mu', 480.0 + shift(3), 'sigma', 36/sqrt(1));
X4_is = makedist('Lognormal', 'mu', log(226e-6) + shift(4), 'sigma', 11.3e-6 / 226e-6);
X5_is = makedist('Normal', 'mu', 0.5 + shift(5), 'sigma', 0.05);
X6_is = makedist('Normal', 'mu', 0.12 + shift(6), 'sigma', 0.006);
X_is = makedist('Lognormal', 'mu', log(40.0) + shift(7), 'sigma', 6.0 / 40.0);
XH_is = makedist('Normal', 'mu', 0.8 + shift(8), 'sigma', 0.01 * 1);

% 生成重要性抽样的样本
Xi_samples_is = random(Xi_is, N, 1);
A2_samples_is = random(A2_is, N, 1);
X3_samples_is = random(X3_is, N, 1);
X4_samples_is = random(X4_is, N, 1);
X5_samples_is = random(X5_is, N, 1);
X6_samples_is = random(X6_is, N, 1);
X_samples_is = random(X_is, N, 1);
XH_samples_is = random(XH_is, N, 1);

% 计算重要性权重
w = pdf(distributions.Xi, Xi_samples_is) .* ...
    pdf(distributions.A2, A2_samples_is) .* ...
    pdf(distributions.X3, X3_samples_is) .* ...
    pdf(distributions.X4, X4_samples_is) .* ...
    pdf(distributions.X5, X5_samples_is) .* ...
    pdf(distributions.X6, X6_samples_is) .* ...
    pdf(distributions.X, X_samples_is) .* ...
    pdf(distributions.XH, XH_samples_is) ./ ...
    (pdf(Xi_is, Xi_samples_is) .* ...
     pdf(A2_is, A2_samples_is) .* ...
     pdf(X3_is, X3_samples_is) .* ...
     pdf(X4_is, X4_samples_is) .* ...
     pdf(X5_is, X5_samples_is) .* ...
     pdf(X6_is, X6_samples_is) .* ...
     pdf(X_is, X_samples_is) .* ...
     pdf(XH_is, XH_samples_is));

% 计算功能函数值
g_values_is = Xi_samples_is + A2_samples_is + X3_samples_is + X4_samples_is + X5_samples_is + X6_samples_is + X_samples_is - XH_samples_is;

% 计算失效概率
Pf_is = sum(w .* (g_values_is < 0)) / sum(w);

% 计算可靠度指标 β
beta_is = norminv(1 - Pf_is);

% 输出结果
disp(['重要抽样法失效概率 Pf: ', num2str(Pf_is)])
disp(['重要抽样法可靠度指标 β: ', num2str(beta_is)])

以上代码实现了 JC 法和优化法求解结构可靠度指标 β 并计算验算点坐标，同时通过蒙特卡洛法和重要抽样法进行了验证。希望这些代码对你有帮助！