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⛄ 内容介绍
文章阐述MATLAB的曲线拟合工具箱(Curve Fitting Toolbox)的交互式图形界面和程序调用两种方式的使用方法,并以某柴油发动机稳态工况下的试验数据绘制万有特性图为例,介绍利用曲线拟合工具箱进行曲面拟合的步骤和方法,并给出关键代码,探讨利用该工具箱改进拟合效果和绘图质量.对拟合结果的数理统计校验表明拟合结果完全符合要求,MATLAB的曲线拟合工具箱为发动机特性的曲面拟合提供更大的便利.
⛄ 部分代码
% Your digitized plot goes here. You can use e.g. Plot Digitizer or many
% other digitizers available on Matlab Central.
% Here the trench IGBT module SKM145GB066D from Semikron will serve as an
% example. Note that the thermal chain parameters are given explicitely for
% this particular module but this is not always the case. In fact, it's usually not
% the case. More on thermal modelling:
% http://www.plexim.com/download/documentation .
x_igbt_zth = [1.02e-05, 1.46e-05, 1.93e-05, 2.52e-05, 3.14e-05, 3.92e-05,...
5.03e-05, 6.71e-05, 8.89e-05, 0.0001185, 0.000159193, 0.000215443, 0.00029157,...
0.000403431, 0.000541969, 0.000722727, 0.000970911, 0.00132372, 0.00184512, 0.002553,...
0.00350648, 0.00514681, 0.00733474, 0.0112534, 0.01664, 0.0225198, 0.0332994, 0.0444054,...
0.0632823, 0.0831518, 0.104528, 0.135335, 0.171386, 0.206112, 0.272833, 0.361154,...
0.492388, 0.65661, 0.831518, 0.992647];
y_igbt_zth = [0.000438281, 0.000600275, 0.000779386, 0.00100595, 0.00123818, 0.00152402,...
0.00189824, 0.0024793, 0.0031811, 0.00408155, 0.0052994, 0.00675922, 0.00877605,...
0.0111273, 0.0141926, 0.0176776, 0.0216298, 0.026623, 0.0333577, 0.0410584,...
0.0487691, 0.0603848, 0.0747672, 0.0936806, 0.117378, 0.138597, 0.168579, 0.195541,...
0.228164, 0.252384, 0.271013, 0.28419, 0.292749, 0.299781, 0.30336, 0.30336,...
0.30336, 0.305166, 0.30336, 0.30336];
% rng('shuffle');
asur = 0; % 1 --> the asynchronous update rule; 0 --> the synchronous update rule
evaporation_constant = 1; % Static optimization problem (SOP)
swarm_size = 50;
init_position = 3; % note that parameters are coded using exponential function;
% the initial area covered by the swarm is then [0.001, 1000];
% this should work for most thermal models of
% semiconductor switches and heat sinks in power electronic systems. If the
% optimizer fails to identify your device, you should try setting
% init_position = 5 .
init_speed = 1;
diversity_limit = 0; % Static optimization problem (SOP)
velocity_clamping = 2;
num_of_iter = 10000; % don't worry -- it will take seconds to complete the task at hand
% Constricted PSO
correction_factor = 2.05;
Kappa=2/abs(2-2*correction_factor-sqrt((2*correction_factor)^2-8*correction_factor));
% The problem
num_of_D = 6; % 6 parameters of the Foster-type RC ladder network to be identified
% More declarations
swarm = zeros(swarm_size,4,num_of_D);
swarm_diversity = zeros(1,num_of_D);
swarm_dir = zeros(1,num_of_D);
%% Initial swarm position and velocity
for index=1:swarm_size,
swarm(index, 1, :) = init_position*(rand(num_of_D,1)-0.5)*2;
swarm(index, 2, :) = init_speed*(rand(num_of_D,1)-0.5)*2;
end
swarm(:, 4, 1) = 10e10; % initial best value --> some value out of practical limits
%% The swarm is turned on
for iter = 1 : num_of_iter,
for n = 1 : swarm_size,
r1 = 10^swarm(n, 1, 1); % resistances
r2 = 10^swarm(n, 1, 2);
r3 = 10^swarm(n, 1, 3);
c1 = 10^swarm(n, 1, 4); % capacitances
c2 = 10^swarm(n, 1, 5);
c3 = 10^swarm(n, 1, 6);
%% In this example the 3rd order Foster chain is used.
% Particles are rated here using sum of squared errors.
% Obviously you can define your own cost function.
fitness = 0;
for i = 1:numel(x_igbt_zth),
⛄ 运行结果
⛄ 参考文献
[1]黄兵锋, 解方喜, 傅佳宏. MATLAB曲线拟合工具箱在发动机特性拟合中的应用[J]. 湖北文理学院学报, 2014, 35(5):5.
