%% LED光谱合成与优化 - 修正版
% 中央民族大学数学建模竞赛 - 问题2解决方案
% 所有函数定义移至文件末尾
%% 初始化
clear; clc; close all;
% 定义波长范围 (380-781nm)
wavelengths = 380:1:781; % 402个波长点
% 五通道LED SPD (实际应从Excel导入)
% 这里使用模拟数据代替
blue = zeros(402,1);
green = zeros(402,1);
red = zeros(402,1);
ww = zeros(402,1);
cw = zeros(402,1);
% 创建模拟SPD数据 (高斯分布)
for i = 1:402
wl = wavelengths(i);
blue(i) = exp(-((wl-450)/20).^2);
green(i) = exp(-((wl-540)/25).^2);
red(i) = exp(-((wl-620)/15).^2);
ww(i) = exp(-((wl-580)/80).^2);
cw(i) = exp(-((wl-500)/100).^2);
end
% 归一化SPD
blue = blue / max(blue);
green = green / max(green);
red = red / max(red);
ww = ww / max(ww);
cw = cw / max(cw);
% 模拟CIE标准函数
cie_x = zeros(402,1);
cie_y = zeros(402,1);
cie_z = zeros(402,1);
mel_sens = zeros(402,1);
D65 = zeros(402,1);
for i = 1:402
wl = wavelengths(i);
cie_x(i) = exp(-((wl-600)/100).^2);
cie_y(i) = exp(-((wl-550)/100).^2);
cie_z(i) = exp(-((wl-450)/80).^2);
mel_sens(i) = exp(-((wl-480)/40).^2);
D65(i) = exp(-((wl-550)/150).^2);
end
%% 优化问题设置
% 边界条件 (权重在0-1之间)
lb = [0, 0, 0, 0, 0];
ub = [1, 1, 1, 1, 1];
% 优化选项
options = optimoptions('fmincon', 'Display', 'iter', ...
'Algorithm', 'sqp', 'MaxFunctionEvaluations', 10000);
% 初始权重
w0 = [0.2, 0.2, 0.2, 0.2, 0.2];
%% 求解日间照明模式 (最大化Rf)
% 调用优化器
[w_opt_day, fval_day] = fmincon(...
@(w) obj_func_day(w, blue, green, red, ww, cw, cie_x, cie_y, cie_z, D65), ...
w0, [], [], [], [], lb, ub, ...
@(w) constraints_day(w, blue, green, red, ww, cw, cie_x, cie_y, cie_z, D65), ...
options);
% 计算实际Rf值
spd_day = synthesize_spd(w_opt_day, blue, green, red, ww, cw);
[~, rf_day] = calculate_rf_rg(spd_day, D65);
rf_day = -fval_day;
%% 求解夜间助眠模式 (最小化mel-DER)
% 调用优化器
[w_opt_night, mel_der_night] = fmincon(...
@(w) obj_func_night(w, blue, green, red, ww, cw, mel_sens, D65), ...
w0, [], [], [], [], lb, ub, ...
@(w) constraints_night(w, blue, green, red, ww, cw, cie_x, cie_y, cie_z, D65), ...
options);
%% 结果计算与展示
% 计算日间模式所有参数
spd_day = synthesize_spd(w_opt_day, blue, green, red, ww, cw);
[X_day, Y_day, Z_day] = calculate_xyz(spd_day, cie_x, cie_y, cie_z);
[cct_day, duv_day] = calculate_cct_duv(X_day, Y_day, Z_day);
[rf_day, rg_day] = calculate_rf_rg(spd_day, D65);
mel_der_day = calculate_mel_der(spd_day, mel_sens, D65);
% 计算夜间模式所有参数
spd_night = synthesize_spd(w_opt_night, blue, green, red, ww, cw);
[X_night, Y_night, Z_night] = calculate_xyz(spd_night, cie_x, cie_y, cie_z);
[cct_night, duv_night] = calculate_cct_duv(X_night, Y_night, Z_night);
[rf_night, rg_night] = calculate_rf_rg(spd_night, D65);
mel_der_night = calculate_mel_der(spd_night, mel_sens, D65);
% 显示结果
fprintf('\n===== 日间照明模式最优解 =====\n');
fprintf('权重: 蓝光=%.4f, 绿光=%.4f, 红光=%.4f\n', w_opt_day(1), w_opt_day(2), w_opt_day(3));
fprintf(' 暖白光=%.4f, 冷白光=%.4f\n', w_opt_day(4), w_opt_day(5));
fprintf('CCT: %.0f K, Duv: %.4f\n', cct_day, duv_day);
fprintf('Rf: %.1f, Rg: %.1f\n', rf_day, rg_day);
fprintf('mel-DER: %.3f\n\n', mel_der_day);
fprintf('===== 夜间助眠模式最优解 =====\n');
fprintf('权重: 蓝光=%.4f, 绿光=%.4f, 红光=%.4f\n', w_opt_night(1), w_opt_night(2), w_opt_night(3));
fprintf(' 暖白光=%.4f, 冷白光=%.4f\n', w_opt_night(4), w_opt_night(5));
fprintf('CCT: %.0f K, Duv: %.4f\n', cct_night, duv_night);
fprintf('Rf: %.1f, Rg: %.1f\n', rf_night, rg_night);
fprintf('mel-DER: %.3f\n', mel_der_night);
%% 光谱可视化
figure('Position', [100, 100, 1200, 500]);
% 日间模式光谱
subplot(1, 2, 1);
plot(wavelengths, spd_day/max(spd_day), 'b', 'LineWidth', 2);
hold on;
plot(wavelengths, mel_sens/max(mel_sens), 'g--', 'LineWidth', 1.5);
title('日间照明模式光谱');
xlabel('波长 (nm)');
ylabel('归一化强度');
legend('合成光谱', '视黑素灵敏度', 'Location', 'northeast');
grid on;
xlim([380, 780]);
% 夜间模式光谱
subplot(1, 2, 2);
plot(wavelengths, spd_night/max(spd_night), 'r', 'LineWidth', 2);
hold on;
plot(wavelengths, mel_sens/max(mel_sens), 'g--', 'LineWidth', 1.5);
title('夜间助眠模式光谱');
xlabel('波长 (nm)');
ylabel('归一化强度');
legend('合成光谱', '视黑素灵敏度', 'Location', 'northeast');
grid on;
xlim([380, 780]);
%% 权重分布图
figure();
labels = {'蓝光', '绿光', '红光', '暖白光', '冷白光'};
subplot(1, 2, 1);
bar(w_opt_day);
set(gca, 'XTickLabel', labels);
title('日间模式权重分布');
ylabel('权重系数');
ylim([0, 1]);
subplot(1, 2, 2);
bar(w_opt_night);
set(gca, 'XTickLabel', labels);
title('夜间模式权重分布');
ylabel('权重系数');
ylim([0, 1]);
%% ==================== 函数定义区域 ====================
% 以下为所有函数定义,确保位于文件末尾
function spd = synthesize_spd(weights, blue, green, red, ww, cw)
% 合成五通道光谱
w_b = weights(1);
w_g = weights(2);
w_r = weights(3);
w_ww = weights(4);
w_cw = weights(5);
spd = w_b*blue + w_g*green + w_r*red + w_ww*ww + w_cw*cw;
end
function [X, Y, Z] = calculate_xyz(spd, cie_x, cie_y, cie_z)
% 计算CIE XYZ三刺激值
X = sum(spd .* cie_x);
Y = sum(spd .* cie_y);
Z = sum(spd .* cie_z);
end
function [cct, duv] = calculate_cct_duv(X, Y, Z)
% 计算相关色温(CCT)和Duv
% 转换到CIE 1960 UCS空间
u = 4*X / (X + 15*Y + 3*Z);
v = 6*Y / (X + 15*Y + 3*Z);
% 简化计算 - 实际应使用普朗克轨迹插值
% 这里使用近似公式
n = (X - 0.3320*Y - 0.0038*Z) / (0.0037*Y - 0.0011*Z);
cct = 437*n^3 + 3601*n^2 + 6861*n + 5517;
duv = sqrt((u - 0.2)^2 + (v - 0.3)^2); % 示例计算
end
function [rf, rg] = calculate_rf_rg(spd, ref_spd)
% 简化版显色指数计算
% 这里使用色差模拟
diff = mean(abs(spd - ref_spd));
rf = 90 - 15*diff; % Rf在75-95之间
rg = 95 - 10*diff; % Rg在85-105之间
end
function mel_der = calculate_mel_der(spd, mel_sens, D65)
% 计算褪黑素日光效率比
mel_flux = sum(spd .* mel_sens);
d65_mel = sum(D65 .* mel_sens);
mel_der = mel_flux / d65_mel;
end
function f = obj_func_day(weights, blue, green, red, ww, cw, cie_x, cie_y, cie_z, D65)
% 日间模式目标函数:最大化Rf
spd = synthesize_spd(weights, blue, green, red, ww, cw);
rf = calculate_rf_rg(spd, D65);
f = -rf; % 最大化Rf = 最小化 -Rf
end
function [c, ceq] = constraints_day(weights, blue, green, red, ww, cw, cie_x, cie_y, cie_z, D65)
% 日间模式约束条件
spd = synthesize_spd(weights, blue, green, red, ww, cw);
[X, Y, Z] = calculate_xyz(spd, cie_x, cie_y, cie_z);
[cct, ~] = calculate_cct_duv(X, Y, Z);
[rf, rg] = calculate_rf_rg(spd, D65);
% 约束条件:
% CCT在5500-6500K, Rg在95-105
c1 = 5500 - cct; % cct >= 5500
c2 = cct - 6500; % cct <= 6500
c3 = 95 - rg; % rg >= 95
c4 = rg - 105; % rg <= 105
ceq = []; % 无等式约束
c = [c1; c2; c3; c4]; % 非线性不等式约束 (需要c<=0)
end
function f = obj_func_night(weights, blue, green, red, ww, cw, mel_sens, D65)
% 夜间模式目标函数:最小化mel-DER
spd = synthesize_spd(weights, blue, green, red, ww, cw);
f = calculate_mel_der(spd, mel_sens, D65);
end
function [c, ceq] = constraints_night(weights, blue, green, red, ww, cw, cie_x, cie_y, cie_z, D65)
% 夜间模式约束条件
spd = synthesize_spd(weights, blue, green, red, ww, cw);
[X, Y, Z] = calculate_xyz(spd, cie_x, cie_y, cie_z);
[cct, ~] = calculate_cct_duv(X, Y, Z);
[rf, ~] = calculate_rf_rg(spd, D65);
% 约束条件:
% CCT在2500-3500K, Rf>=80
c1 = 2500 - cct; % cct >= 2500
c2 = cct - 3500; % cct <= 3500
c3 = 80 - rf; % rf >= 80
ceq = []; % 无等式约束
c = [c1; c2; c3]; % 非线性不等式约束 (需要c<=0)
end 上述代码哪些位置可以加入真实数据,请详细列举出来,并且给我加入真实数据的方法
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