李明瑧的学术空间

双线性弹塑性恢复力滞回曲线计算

%% 双线性恢复力模型
clear;clc;close all;
k0 = 20e6; Fy = 100e3; alpha = 0.05;
uy = Fy/k0; k1 = alpha*k0;

t = 0:0.01:10;
u = 0.02*sin(2*pi*0.5*t);
nt = length(u);

F = zeros(1,nt);
F(1) = 0; u_last = 0; F_last = 0;
state = 0;

for i=2:nt
    du = u(i) - u(i-1);
    if state == 0
        F_trial = F_last + k0*du;
        if F_trial > Fy
            state = 1; F(i) = Fy + k1*(u(i)-uy);
        elseif F_trial < -Fy
            state = -1; F(i) = -Fy + k1*(u(i)+uy);
        else F(i) = F_trial; end
    elseif state == 1
        if du < 0
            state = 0; F(i) = F_last + k0*du;
        else F(i) = F_last + k1*du; end
    else
        if du > 0
            state = 0; F(i) = F_last + k0*du;
        else F(i) = F_last + k1*du; end
    end
    u_last = u(i); F_last = F(i);
end

figure('Color','w');
plot(u,F,'b-','LineWidth',1.5);
xlabel('位移 u(m)'); ylabel('恢复力 F(N)');
title('双线性恢复力滞回曲线');
grid on; axis equal;

双线性模型+Newmark法+牛顿迭代弹塑性时程

%% 弹塑性时程分析
clear;clc;close all;
m = 100e3; k0=20e6; xi=0.05; Fy=80e3; alpha=0.05;
omega = sqrt(k0/m); c = 2*xi*m*omega;
gamma=0.5; beta=0.25; dt=0.02; t=0:dt:10; nt=length(t);

u=zeros(1,nt);v=zeros(1,nt);a=zeros(1,nt);
a(1)=0; Fs=0; state=0; u_last=0; Fs_last=0;
P = zeros(1,nt); P(10) = 120e3;

for i=1:nt-1
    u(i+1) = u(i);
    for iter=1:20
        du = u(i+1) - u_last;
        if state==0
            kt = k0; Fs_trial = Fs_last + kt*du;
            if Fs_trial>Fy
                state=1; Fs=Fy+alpha*k0*(u(i+1)-Fy/k0); kt=alpha*k0;
            elseif Fs_trial<-Fy
                state=-1; Fs=-Fy+alpha*k0*(u(i+1)+Fy/k0); kt=alpha*k0;
            else Fs=Fs_trial; end
        elseif state==1
            kt=alpha*k0;
            if du<0, state=0; kt=k0; Fs=Fs_last+kt*du;
            else Fs=Fs_last+kt*du; end
        else
            kt=alpha*k0;
            if du>0, state=0; kt=k0; Fs=Fs_last+kt*du;
            else Fs=Fs_last+kt*du; end
        end
        a(i+1) = 1/(beta*dt^2)*(u(i+1)-u(i)) - 1/(beta*dt)*v(i) - (1/(2*beta)-1)*a(i);
        v(i+1) = v(i) + dt*((1-gamma)*a(i)+gamma*a(i+1));
        R = P(i+1) - m*a(i+1) - c*v(i+1) - Fs;
        K_hat = kt + gamma/(beta*dt)*c + 1/(beta*dt^2)*m;
        du_iter = K_hat\R;
        u(i+1) = u(i+1) + du_iter;
        if norm(du_iter)<1e-8, break; end
    end
    u_last=u(i+1); Fs_last=Fs;
end

figure('Color','w');
plot(t,u,'b-','LineWidth',1);
xlabel('时间(s)');ylabel('位移(m)');
title('弹塑性时程分析位移时程');grid on;

多自由度体系地震响应计算通用函数

function [u, v, a] = newmark_beta(M, K, C, P, dt, beta, gamma)
% Newmark-β法求解结构动力响应
% 输入：M-质量矩阵 K-刚度矩阵 C-阻尼矩阵
%       P-荷载向量(nt*n列,每列对应一个时刻) dt-时间步长
%       beta, gamma-积分参数,默认beta=0.25,gamma=0.5(平均加速度法)
    if nargin<7, gamma=0.5; end
    if nargin<6, beta=0.25; end
    n = size(M,1);
    nt = size(P,2);
    u = zeros(n,nt); v = zeros(n,nt); a = zeros(n,nt);
    
    % 初始加速度
    a(:,1) = M\(P(:,1) - C*v(:,1) - K*u(:,1));
    
    % 有效刚度矩阵
    K_hat = K + gamma/(beta*dt)*C + 1/(beta*dt^2)*M;
    
    for i = 1:nt-1
        % 有效荷载
        P_hat = P(:,i+1) + M*(1/(beta*dt^2)*u(:,i) + 1/(beta*dt)*v(:,i) + (1/(2*beta)-1)*a(:,i)) ...
            + C*(gamma/(beta*dt)*u(:,i) + (gamma/beta-1)*v(:,i) + dt*(gamma/(2*beta)-1)*a(:,i));
        
        u(:,i+1) = K_hat\P_hat;
        a(:,i+1) = 1/(beta*dt^2)*(u(:,i+1)-u(:,i)) - 1/(beta*dt)*v(:,i) - (1/(2*beta)-1)*a(:,i);
        v(:,i+1) = v(:,i) + dt*((1-gamma)*a(:,i) + gamma*a(:,i+1));
    end
end

π平面上Mises与Tresca屈服面对比

% Mises屈服准则可视化
theta = linspace(0, 2*pi, 100);
sigma_s = 235;  % 屈服强度 MPa

% Mises圆（π平面）
r_mises = sqrt(2/3)*sigma_s*ones(size(theta));
x_mises = r_mises.*cos(theta);
y_mises = r_mises.*sin(theta);

% Tresca六边形
r_tresca = sigma_s./(sqrt(2)*cos(theta-pi/6 - pi/3*floor((theta-pi/6)/(pi/3))));
x_tresca = r_tresca.*cos(theta);
y_tresca = r_tresca.*sin(theta);

figure('Color','w'); hold on; axis equal;
plot(x_mises, y_mises, 'b-', 'LineWidth', 2);
plot(x_tresca, y_tresca, 'r--', 'LineWidth', 2);
xlabel('\sigma_1'''); ylabel('\sigma_2''');
legend('Mises屈服准则','Tresca屈服准则','Location','best');
title('π平面屈服面对比');
grid on;

基于sklearn的混凝土施工质量合格预测

import pandas as pd
import numpy as np
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report, roc_auc_score
from sklearn.preprocessing import StandardScaler

# 加载混凝土施工数据
# 特征：水泥用量、水灰比、坍落度、养护温度、养护时间等
data = pd.read_csv('concrete_quality.csv')
X = data.drop('quality_pass', axis=1)
y = data['quality_pass']  # 1=合格, 0=不合格

# 数据划分与标准化
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
scaler = StandardScaler()
X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

# 训练Logistic回归模型
model = LogisticRegression(random_state=42)
model.fit(X_train_scaled, y_train)

# 模型评估
y_pred = model.predict(X_test_scaled)
y_pred_proba = model.predict_proba(X_test_scaled)[:,1]
print(classification_report(y_test, y_pred))
print(f"AUC: {roc_auc_score(y_test, y_pred_proba):.4f}")

# 新样本预测
new_sample = scaler.transform([[380, 0.45, 160, 25, 28]])
quality_prob = model.predict_proba(new_sample)[0,1]
print(f"施工质量合格概率: {quality_prob:.2%}")

基于lifelines的生存分析工程应用

import pandas as pd
from lifelines import CoxPHFitter
import matplotlib.pyplot as plt

# 加载生存数据
# T-时间, E-事件(1=发生,0=删失), 其余为协变量
data = pd.read_csv('survival_data.csv')

# 拟合Cox模型
cph = CoxPHFitter()
cph.fit(data, duration_col='T', event_col='E')

# 输出结果
cph.print_summary()

# 绘制森林图
plt.figure(figsize=(8,6))
cph.plot()
plt.title('Cox模型风险比森林图')
plt.tight_layout()
plt.savefig('cox_forest.png', dpi=300)

# 预测生存曲线
cph.predict_survival_function(data.iloc[0:3]).plot()
plt.title('不同个体的生存曲线预测')
plt.ylabel('生存概率 S(t)')
plt.xlabel('时间')