% ============== 主优化函数 ==============
function optimal_temperature_solution()
% ================== 主优化流程 ==================
% 1. 参数初始化
params = initialize_parameters();
% 2. 定义优化变量和约束边界
[lb, ub] = define_variable_bounds();
% 3. NSGA-III优化
[optimal_params, pareto_front] = nsga3_optimization(params, lb, ub);
% 4. 从Pareto前沿选择最佳解
[T_set, v] = select_best_solution(pareto_front);
% 5. 验证并可视化结果
[t, T, area, asymmetry, constraints] = verify_solution(T_set, v, params);
% 6. 输出最终结果
display_results(T_set, v, area, asymmetry, constraints, t, T);
% 7. 可视化Pareto前沿
visualize_pareto_front(pareto_front);
end
% ============== NSGA-III优化函数 ==============
function [optimal_params, pareto_front] = nsga3_optimization(params, lb, ub)
% 算法参数设置
pop_size = 100; % 种群大小
max_gen = 50; % 最大迭代次数
n_var = numel(lb); % 变量数量
% 初始化种群
population = initialize_population(lb, ub, pop_size);
% 评估初始种群
[objectives, feas_flags] = evaluate_population(population, params);
% NSGA-III主循环
pareto_front = [];
for gen = 1:max_gen
% 进化操作：选择、交叉、变异
offspring = evolve_population(population, lb, ub);
% 评估子代
[off_obj, off_feas] = evaluate_population(offspring, params);
% 合并种群
combined_pop = [population; offspring];
combined_obj = [objectives; off_obj];
combined_feas = [feas_flags; off_feas];
% 非支配排序
[fronts, ~] = non_dominated_sort(combined_obj, combined_feas);
% 环境选择
[population, objectives, feas_flags] = environmental_selection(...
combined_pop, combined_obj, combined_feas, fronts, pop_size);
% 保存当前Pareto前沿
pareto_front = [pareto_front; population(fronts{1}, :) objectives(fronts{1}, :)];
fprintf('第%d代: Pareto前沿解数=%d\n', gen, numel(fronts{1}));
end
optimal_params = population(1, :); % 返回第一前沿的第一个解
end
function population = initialize_population(lb, ub, pop_size)
% 使用拉丁超立方采样初始化种群
population = lhsdesign(pop_size, numel(lb)) .* (ub - lb) + lb;
end
function [objectives, feas_flags] = evaluate_population(population, params)
pop_size = size(population, 1);
objectives = zeros(pop_size, 2); % 两个目标：面积和不对称性
feas_flags = false(pop_size, 1); % 可行性标志
parfor i = 1:pop_size
T_set = population(i, 1:4);
v = population(i, 5);
try
% 模拟温度曲线
[t, T] = simulate_oven(T_set, v, params);
% 计算关键指标
metrics = compute_metrics(t, T);
% 检查制程界限约束
constraints_satisfied = check_constraints(metrics);
if constraints_satisfied
% 目标函数值
objectives(i, 1) = metrics.area; % 目标1: 最小化面积
objectives(i, 2) = metrics.asymmetry; % 目标2: 最小化不对称性
feas_flags(i) = true;
else
% 违反约束的惩罚
objectives(i, 1) = 1e10;
objectives(i, 2) = 1e10;
end
catch
% 模拟失败的惩罚
objectives(i, 1) = 1e10;
objectives(i, 2) = 1e10;
end
end
end
function offspring = evolve_population(population, lb, ub)
pop_size = size(population, 1);
n_var = size(population, 2);
offspring = zeros(pop_size, n_var);
% 锦标赛选择
tournament_size = 2;
for i = 1:pop_size
% 随机选择竞争者
competitors = randperm(pop_size, tournament_size);
% 选择最优的竞争者
[~, best_idx] = min(sum(population(competitors, :), 2));
selected(i) = competitors(best_idx);
end
% 模拟二进制交叉
pc = 0.9; % 交叉概率
eta_c = 20; % 分布指数
for i = 1:2:pop_size
if rand < pc
% 选择两个父代
p1 = population(selected(i), :);
p2 = population(selected(i+1), :);
% 交叉操作
[c1, c2] = sbx_crossover(p1, p2, lb, ub, eta_c);
offspring(i, :) = c1;
offspring(i+1, :) = c2;
else
offspring(i, :) = population(selected(i), :);
offspring(i+1, :) = population(selected(i+1), :);
end
end
% 多项式变异
pm = 1/n_var; % 变异概率
eta_m = 20; % 分布指数
for i = 1:pop_size
if rand < pm
offspring(i, :) = polynomial_mutation(offspring(i, :), lb, ub, eta_m);
end
end
end
function [c1, c2] = sbx_crossover(p1, p2, lb, ub, eta_c)
n_var = length(p1);
c1 = p1;
c2 = p2;
for j = 1:n_var
if rand < 0.5
% 确保不是相同值
if abs(p1(j) - p2(j)) > 1e-10
if p1(j) < p2(j)
y1 = p1(j);
y2 = p2(j);
else
y1 = p2(j);
y2 = p1(j);
end
yL = lb(j);
yU = ub(j);
rand_val = rand;
beta = 1.0 + (2.0 * (y1 - yL) / (y2 - y1));
alpha = 2.0 - beta^(-(eta_c+1.0));
beta_q = (rand_val <= (1.0/alpha)) ? ...
(rand_val * alpha)^(1.0/(eta_c+1.0)) : ...
(1.0/(2.0 - rand_val*alpha))^(1.0/(eta_c+1.0));
c1(j) = 0.5 * ((y1 + y2) - beta_q * (y2 - y1));
beta = 1.0 + (2.0 * (yU - y2) / (y2 - y1));
alpha = 2.0 - beta^(-(eta_c+1.0));
beta_q = (rand_val <= (1.0/alpha)) ...
(rand_val * alpha)^(1.0/(eta_c+1.0)) : ...
(1.0/(2.0 - rand_val*alpha))^(1.0/(eta_c+1.0));
c2(j) = 0.5 * ((y1 + y2) + beta_q * (y2 - y1));
% 边界处理
c1(j) = max(yL, min(yU, c1(j)));
c2(j) = max(yL, min(yU, c2(j)));
end
end
end
end
function mutated = polynomial_mutation(ind, lb, ub, eta_m)
n_var = length(ind);
mutated = ind;
for j = 1:n_var
if rand < (1/n_var)
y = ind(j);
yL = lb(j);
yU = ub(j);
delta1 = (y - yL) / (yU - yL);
delta2 = (yU - y) / (yU - yL);
rand_val = rand;
mut_pow = 1.0/(eta_m+1.0);
if rand_val <= 0.5
xy = 1.0 - delta1;
val = 2.0*rand_val + (1.0 - 2.0*rand_val) * xy^(eta_m+1.0);
deltaq = val^mut_pow - 1.0;
else
xy = 1.0 - delta2;
val = 2.0*(1.0 - rand_val) + 2.0*(rand_val - 0.5) * xy^(eta_m+1.0);
deltaq = 1.0 - val^mut_pow;
end
y = y + deltaq * (yU - yL);
mutated(j) = max(yL, min(yU, y));
end
end
end
function [fronts, rank] = non_dominated_sort(objectives, feas_flags)
pop_size = size(objectives, 1);
rank = inf(pop_size, 1);
dominated_count = zeros(pop_size, 1);
dominated_set = cell(pop_size, 1);
% 初始化
for i = 1:pop_size
for j = 1:pop_size
if i ~= j
% 可行性优先
if feas_flags(i) && ~feas_flags(j)
dominated = true;
elseif ~feas_flags(i) && feas_flags(j)
dominated = false;
else
% 双目标支配关系
dominated = all(objectives(i, :) <= objectives(j, :)) && ...
any(objectives(i, :) < objectives(j, :));
end
if dominated
dominated_set{i} = [dominated_set{i}, j];
dominated_count(j) = dominated_count(j) + 1;
end
end
end
end
% 寻找第一前沿
current_front = find(dominated_count == 0);
rank(current_front) = 1;
fronts = {current_front};
% 分层排序
k = 1;
while ~isempty(current_front)
next_front = [];
for i = 1:length(current_front)
p = current_front(i);
for j = dominated_set{p}
dominated_count(j) = dominated_count(j) - 1;
if dominated_count(j) == 0
rank(j) = k + 1;
next_front = [next_front, j];
end
end
end
k = k + 1;
current_front = next_front;
if ~isempty(next_front)
fronts{end+1} = next_front;
end
end
end
function [selected_pop, selected_obj, selected_feas] = environmental_selection(...
population, objectives, feas_flags, fronts, pop_size)
selected_pop = [];
selected_obj = [];
selected_feas = [];
current_front = 1;
% 逐步添加前沿直到达到或超过种群大小
while current_front <= length(fronts) && ...
size(selected_pop, 1) + length(fronts{current_front}) <= pop_size
% 添加整个前沿
front_indices = fronts{current_front};
selected_pop = [selected_pop; population(front_indices, :)];
selected_obj = [selected_obj; objectives(front_indices, :)];
selected_feas = [selected_feas; feas_flags(front_indices)];
current_front = current_front + 1;
end
% 如果还有空间，使用参考点选择
if size(selected_pop, 1) < pop_size
remaining = pop_size - size(selected_pop, 1);
last_front = fronts{current_front};
% 使用niching选择剩余个体
[selected, ~] = niche_selection(objectives(last_front, :), remaining);
selected_from_last = last_front(selected);
selected_pop = [selected_pop; population(selected_from_last, :)];
selected_obj = [selected_obj; objectives(selected_from_last, :)];
selected_feas = [selected_feas; feas_flags(selected_from_last)];
elseif size(selected_pop, 1) > pop_size
% 如果超过，截断最后一个前沿
selected_pop = selected_pop(1:pop_size, :);
selected_obj = selected_obj(1:pop_size, :);
selected_feas = selected_feas(1:pop_size);
end
end
function [selected_indices] = niche_selection(objectives, k)
% 简化版的niching选择
[N, M] = size(objectives);
selected_indices = [];
% 理想点
ideal_point = min(objectives);
% 归一化目标值
norm_obj = objectives - repmat(ideal_point, N, 1);
max_obj = max(norm_obj);
norm_obj = norm_obj ./ repmat(max_obj, N, 1);
% 创建参考点
p = 12; % 每个目标的划分数量
ref_points = generate_reference_points(M, p);
% 关联解到参考点
[association, ~] = associate_to_reference_points(norm_obj, ref_points);
% 选择解
selected_indices = [];
while length(selected_indices) < k
% 找到最少关联的参考点
counts = zeros(size(ref_points, 1), 1);
for i = 1:length(association)
if ~isempty(association{i})
counts(i) = length(association{i});
end
end
[~, min_idx] = min(counts);
if ~isempty(association{min_idx})
% 从该参考点的关联解中选择一个
candidates = association{min_idx};
[~, min_dist_idx] = min(vecnorm(norm_obj(candidates, :) - ref_points(min_idx, :), 2, 2));
selected = candidates(min_dist_idx);
selected_indices = [selected_indices; selected];
% 移除已选解
for i = 1:length(association)
if ~isempty(association{i})
association{i}(association{i} == selected) = [];
end
end
else
ref_points(min_idx, :) = [];
association(min_idx) = [];
end
end
end
function [T_set, v] = select_best_solution(pareto_front)
% 从Pareto前沿中选择面积最小的解
[~, min_idx] = min(pareto_front(:, 6)); % 第6列是面积
optimal_params = pareto_front(min_idx, 1:5);
T_set = optimal_params(1:4); % [预热区, 升温区, 回流区, 冷却区]
v = optimal_params(5); % 传送带速度
end
function visualize_pareto_front(pareto_front)
% 可视化Pareto前沿
figure('Position', [200, 200, 800, 600]);
% 提取目标和约束信息
areas = pareto_front(:, 6);
asymmetries = pareto_front(:, 7);
% 绘制Pareto前沿
scatter(areas, asymmetries, 50, 'filled');
xlabel('阴影面积 (°C·s)');
ylabel('不对称性 (s)');
title('Pareto前沿 (面积 vs 不对称性)');
grid on;
% 添加最优解标记
hold on;
[min_area, min_idx] = min(areas);
scatter(min_area, asymmetries(min_idx), 100, 'ro', 'LineWidth', 2);
text(min_area, asymmetries(min_idx), ' 面积最优解', 'FontSize', 12);
[min_asym, min_idx] = min(asymmetries);
scatter(areas(min_idx), min_asym, 100, 'go', 'LineWidth', 2);
text(areas(min_idx), min_asym, ' 对称性最优解', 'FontSize', 12);
legend('Pareto解', '面积最优解', '对称性最优解');
end
function params = initialize_parameters()
% 固定热物理参数
params = struct(...
'length', 4.355, ... % 炉子总长度 (m)
'boundaries', [0, 0.05, 0.30, 0.605, 1.665, 1.92, 2.07, 2.275, 2.425, 2.63, 2.78, 3.085, 3.235, 3.49, 3.64, 4.25, 4.355], ...
'initial_temp', 25, ... % 初始温度 (°C)
'thickness', 150e-6, ... % 焊接层厚度 (m)
'a', [8.42e-10, 8.42e-10, 8.42e-10, 8.42e-10, 8.42e-10, ...
8.07e-11, 1.55e-09, 1.22e-09, 1.22e-09, 1.14e-09], ...
'beta', [1.42e-06, 1.42e-06, 1.42e-06, 1.42e-06, 1.42e-06, ...
3.39e-06, 2.50e-06, 1.37e-06, 1.37e-06, 6.48e-07]...
);
end
function [lb, ub] = define_variable_bounds()
% 各温区温度范围约束 [预热区, 升温区, 回流区, 冷却区]
% 根据问题要求：温区1-5相同，8-9相同，10-11固定25°C
lb_temp = [165, 185, 225, 245]; % 温度下限 (°C)
ub_temp = [185, 205, 245, 265]; % 温度上限 (°C)
% 传送带速度范围约束 (cm/min)
lb_speed = 65; % 速度下限
ub_speed = 100; % 速度上限
% 组合所有边界
lb = [lb_temp, lb_speed];
ub = [ub_temp, ub_speed];
end
function metrics = compute_metrics(t, T)
% 初始化指标结构
metrics = struct();
% 1. 计算温度导数（斜率）
dTdt = gradient(T, t);
% 2. 找到超过217℃的区域
above_217 = T > 217;
if any(above_217)
start_idx = find(diff(above_217) > 0, 1) + 1;
end_idx = find(diff(above_217) < 0, 1, 'last');
if isempty(end_idx) || end_idx < start_idx
end_idx = length(T);
end
else
start_idx = 1;
end_idx = length(T);
end
% 3. 计算阴影面积
if start_idx < end_idx
area_segment = t(start_idx:end_idx);
temp_segment = T(start_idx:end_idx);
metrics.area = trapz(area_segment, temp_segment - 217);
else
metrics.area = 0;
end
% 4. 找到峰值温度
[metrics.peak_temp, peak_idx] = max(T);
metrics.peak_time = t(peak_idx);
% 5. 计算不对称性
if above_217(peak_idx) % 确保峰值在217℃以上
t_left = metrics.peak_time - t(start_idx);
t_right = t(end_idx) - metrics.peak_time;
metrics.asymmetry = abs(t_left - t_right);
else
metrics.asymmetry = 0;
end
% 6. 计算在150-190℃的时间（仅上升阶段）
rise_phase = (t <= metrics.peak_time);
in_range = (T >= 150) & (T <= 190) & rise_phase;
metrics.time_150_190 = trapz(t(in_range), ones(sum(in_range), 1));
% 7. 计算温度大于217℃的时间
metrics.time_above_217 = t(end_idx) - t(start_idx);
% 8. 计算斜率指标
metrics.max_rise_slope = max(dTdt(dTdt > 0));
metrics.min_fall_slope = min(dTdt(dTdt < 0));
end
function constraints_satisfied = check_constraints(metrics)
% 检查所有制程界限约束
constraints_satisfied = true;
% 1. 温度上升斜率约束
if metrics.max_rise_slope > 3
constraints_satisfied = false;
return;
end
% 2. 温度下降斜率约束
if metrics.min_fall_slope < -3
constraints_satisfied = false;
return;
end
% 3. 150-190℃时间约束
if metrics.time_150_190 < 60 || metrics.time_150_190 > 120
constraints_satisfied = false;
return;
end
% 4. 217℃以上时间约束
if metrics.time_above_217 < 40 || metrics.time_above_217 > 90
constraints_satisfied = false;
return;
end
% 5. 峰值温度约束
if metrics.peak_temp < 240 || metrics.peak_temp > 250
constraints_satisfied = false;
end
end
function [T_set, v] = extract_solution(optimal_params)
T_set = optimal_params(1:4); % [预热区, 升温区, 回流区, 冷却区]
v = optimal_params(5); % 传送带速度
end
function [t, T, area, asymmetry, constraints] = verify_solution(T_set, v, params)
% 分配温度到11个温区（根据问题要求）
zone_temps = [25, T_set(1), T_set(1), T_set(1), T_set(1), ... % 温区1-5: 预热区
T_set(2), T_set(3), T_set(3), T_set(4), 25]; % 温区6: 升温区, 7-8: 回流区, 9-10: 冷却区
% 运行完整模拟
[t, T] = simulate_oven(T_set, v, params);
% 计算所有指标
metrics = compute_metrics(t, T);
area = metrics.area;
asymmetry = metrics.asymmetry;
% 检查约束
constraints = struct();
constraints.rise_slope_ok = (metrics.max_rise_slope <= 3);
constraints.fall_slope_ok = (metrics.min_fall_slope >= -3);
constraints.time_150_190_ok = (metrics.time_150_190 >= 60) && (metrics.time_150_190 <= 120);
constraints.time_above_217_ok = (metrics.time_above_217 >= 40) && (metrics.time_above_217 <= 90);
constraints.peak_temp_ok = (metrics.peak_temp >= 240) && (metrics.peak_temp <= 250);
constraints.all_ok = constraints.rise_slope_ok && constraints.fall_slope_ok && ...
constraints.time_150_190_ok && constraints.time_above_217_ok && ...
constraints.peak_temp_ok;
end
function [t, T] = simulate_oven(T_set, v_cm_min, params)
% 单位转换
v = v_cm_min / 100 / 60; % cm/min -> m/s
total_time = params.length / v;
t = 0:0.5:ceil(total_time);
% 温度区配置（保持原有机理模型）
zone_temps = [25, T_set(1), T_set(1), T_set(1), T_set(1), ... % 温区1-5
T_set(2), T_set(3), T_set(3), T_set(4), 25]; % 温区6-10
% 创建温区配置
oven_config = struct(...
'temperatures', zone_temps, ...
'transition_zones', [...
struct('start', 1.92, 'end', 2.07, 'from', T_set(1), 'to', T_set(2)), ...
struct('start', 2.275, 'end', 2.425, 'from', T_set(2), 'to', T_set(3)), ...
struct('start', 2.63, 'end', 2.78, 'from', T_set(3), 'to', T_set(3)), ...
struct('start', 3.49, 'end', 3.64, 'from', T_set(3), 'to', T_set(4))]...
);
% 空间离散
xmesh = linspace(0, params.thickness, 30);
% 求解PDE（保持原模型）
sol = pdepe(0, @pdefun, @icfun, @bcfun, xmesh, t, [], params, oven_config, v);
% 中心点温度
T = sol(:, round(end/2));
end
% ============== 以下保持原PDE模型不变 ==============
function [c, f, s] = pdefun(x, t, u, dudx, params, oven_config, v)
y = v * t;
zone_idx = get_zone_index(y, params.boundaries);
a = params.a(zone_idx);
c = 1;
f = a * dudx;
s = 0;
end
function u0 = icfun(x, params, ~, ~)
u0 = params.initial_temp;
end
function [pl, ql, pr, qr] = bcfun(xl, ul, xr, ur, t, params, oven_config, v)
y = v * t;
zone_idx = get_zone_index(y, params.boundaries);
T_ext = get_oven_temperature(y, oven_config);
beta = params.beta(zone_idx);
pl = -beta * (ul - T_ext);
ql = 1;
pr = beta * (ur - T_ext);
qr = 1;
end
function zone_idx = get_zone_index(y, boundaries)
if y < boundaries(3)
zone_idx = 1; % 预热区
elseif y < boundaries(6)
zone_idx = 2; % 恒温区
elseif y < boundaries(8)
zone_idx = 3; % 升温区
elseif y < boundaries(14)
zone_idx = 4; % 回流区
else
zone_idx = 5; % 冷却区
end
end
function T_ext = get_oven_temperature(y, oven_config)
boundaries = [0, 0.05, 0.30, 0.605, 1.665, 1.92, 2.07, 2.275, 2.425, 2.63, 2.78, 3.085, 3.235, 3.49, 3.64, 4.25, 4.355];
temps = oven_config.temperatures;
% 检查过渡区
for i = 1:length(oven_config.transition_zones)
tz = oven_config.transition_zones(i);
if y >= tz.start && y < tz.end
T_ext = tz.from + (tz.to - tz.from) * (y - tz.start)/(tz.end - tz.start);
return;
end
end
% 恒定温区
if y < boundaries(3)
T_ext = temps(2);
elseif y < boundaries(6)
T_ext = temps(2);
elseif y < boundaries(8)
T_ext = temps(6);
elseif y < boundaries(10)
T_ext = temps(7);
elseif y < boundaries(14)
T_ext = temps(8);
else
T_ext = temps(10);
end
end
% ============== PDE模型结束 ==============
function display_results(T_set, v, area, asymmetry, constraints, t, T)
% 显示优化结果
fprintf('\n===== 最优炉温参数配置 =====\n');
fprintf('预热区温度: %.1f°C (温区1-5)\n', T_set(1));
fprintf('升温区温度: %.1f°C (温区6)\n', T_set(2));
fprintf('回流区温度: %.1f°C (温区7-8)\n', T_set(3));
fprintf('冷却区温度: %.1f°C (温区9)\n', T_set(4));
fprintf('传送带速度: %.1f cm/min\n', v);
fprintf('阴影面积: %.2f °C·s\n', area);
fprintf('不对称性: %.2f s\n', asymmetry);
% 显示约束状态
fprintf('\n===== 制程界限约束状态 =====\n');
fprintf('温度上升斜率: %s (%.2f ≤ 3°C/s)\n', ...
bool2str(constraints.rise_slope_ok), constraints.max_rise_slope);
fprintf('温度下降斜率: %s (%.2f ≥ -3°C/s)\n', ...
bool2str(constraints.fall_slope_ok), constraints.min_fall_slope);
fprintf('150-190℃时间: %s (%.1fs ∈ [60, 120]s)\n', ...
bool2str(constraints.time_150_190_ok), constraints.time_150_190);
fprintf('217℃以上时间: %s (%.1fs ∈ [40, 90]s)\n', ...
bool2str(constraints.time_above_217_ok), constraints.time_above_217);
fprintf('峰值温度: %s (%.1f°C ∈ [240, 250]°C)\n', ...
bool2str(constraints.peak_temp_ok), constraints.peak_temp);
fprintf('所有约束: %s\n', bool2str(constraints.all_ok));
% 绘制最终炉温曲线
plot_temperature_curve(t, T, area, asymmetry, T_set, v);
end
function str = bool2str(b)
if b
str = '✓ 满足';
else
str = '✗ 违反';
end
end
function plot_temperature_curve(t, T, area, asymmetry, T_set, v)
% 创建专业图表
figure('Position', [100, 100, 1200, 700]);
% 1. 主温度曲线
plot(t, T, 'b-', 'LineWidth', 2, 'DisplayName', '温度曲线');
hold on;
% 2. 标识关键温度线
yline(217, 'g--', 'LineWidth', 2, 'DisplayName', '217℃');
[peak_temp, peak_idx] = max(T);
yline(peak_temp, 'r--', 'LineWidth', 2, 'DisplayName', '峰值温度');
% 3. 标记阴影区域
above_217 = T > 217;
start_idx = find(diff(above_217) > 0, 1) + 1;
end_idx = find(diff(above_217) < 0, 1, 'last');
if ~isempty(start_idx) && ~isempty(end_idx) && start_idx < end_idx
fill([t(start_idx), t(start_idx:end_idx), t(end_idx)], ...
[217, T(start_idx:end_idx)', 217], 'm', ...
'FaceAlpha', 0.2, 'EdgeColor', 'none', 'DisplayName', '217℃以上区域');
end
% 4. 标记关键点
plot(t(peak_idx), peak_temp, 'ro', 'MarkerSize', 8, 'MarkerFaceColor', 'r', 'DisplayName', '峰值温度点');
text(t(peak_idx), peak_temp + 20, sprintf('峰值: %.1f°C', peak_temp), ...
'HorizontalAlignment', 'center', 'FontSize', 12, 'BackgroundColor', 'white');
% 5. 添加面积和不对称性标签
text(mean(t(start_idx:end_idx)), 230, sprintf('面积: %.2f °C·s\n不对称性: %.2f s', area, asymmetry), ...
'HorizontalAlignment', 'center', 'FontSize', 12, 'BackgroundColor', 'white');
% 6. 添加对称性示意图
if asymmetry > 0
plot([t(start_idx), t(peak_idx)], [225, 225], 'k-', 'LineWidth', 2);
plot([t(peak_idx), t(end_idx)], [225, 225], 'k-', 'LineWidth', 2);
text(mean([t(start_idx), t(peak_idx)]), 228, sprintf('t_L: %.1fs', t(peak_idx)-t(start_idx)), ...
'HorizontalAlignment', 'center', 'FontSize', 10);
text(mean([t(peak_idx), t(end_idx)]), 228, sprintf('t_R: %.1fs', t(end_idx)-t(peak_idx)), ...
'HorizontalAlignment', 'center', 'FontSize', 10);
end
% 7. 图形美化
title('最优炉温曲线 (面积最小化 + 对称性优化)', 'FontSize', 16);
xlabel('时间 (s)', 'FontSize', 14);
ylabel('温度 (°C)', 'FontSize', 14);
grid on;
set(gca, 'FontSize', 12);
legend('Location', 'northwest');
xlim([0, max(t)]);
ylim([0, max(T)*1.1]);
% 8. 添加数据框
data_text = {
sprintf('预热区温度: %.1f°C', T_set(1))
sprintf('升温区温度: %.1f°C', T_set(2))
sprintf('回流区温度: %.1f°C', T_set(3))
sprintf('冷却区温度: %.1f°C', T_set(4))
sprintf('传送带速度: %.1f cm/min', v)
sprintf('阴影面积: %.2f °C·s', area)
sprintf('不对称性: %.2f s', asymmetry)
};
annotation('textbox', [0.7, 0.15, 0.25, 0.18], 'String', data_text, ...
'FitBoxToText', 'on', 'BackgroundColor', 'white', 'FontSize', 10);
end修改代码中出错的部分
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本文介绍了如何在HTML中实现当Select元素的选择项发生变化时，如何将新的选择值传递出去的方法。一种方式是直接通过JavaScript函数处理，另一种则是利用表单（Form）来传输。
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