計算Modelica中的平均值和標準偏差

Question

計算Modelica中連續信號的平均值（平均值）和標準差（StdDev）的最佳方法是什麼？均值和StdDev應該計算固定的時間T;即從t-T到t。

Answer 1

下面是該問題的分立解決方案。它在Modelica中被編碼爲一個塊，具有1個連續輸入和2個連續輸出信號。使用Modelica內置函數樣本完成離散化：

block MeanStdDevDiscr 
"Determines the mean value and standard deviation of a signal for a fixed time interval T." 
    extends Modelica.Blocks.Interfaces.BlockIcon; 
    import SI = Modelica.SIunits; 

    parameter SI.Time T = 0.1 
    "Time interval used for calculating mean value and standard deviation"; 
    parameter Integer n = 10 "number of increments in T"; 

    Modelica.Blocks.Interfaces.RealInput u "signal input" 
    annotation (Placement(transformation(extent={{-140,-20},{-100,20}}))); 
    Modelica.Blocks.Interfaces.RealOutput[2] y 
    "y[1] = average value; y[2] = standard deviation" 
    annotation (Placement(transformation(extent={{100,-10},{120,10}}))); 

protected 
    parameter SI.Time dt = T/n "Precision of monitor"; 
    Real[n] uArray; 

initial equation 
    uArray = ones(n)*u; 

equation 
    when sample(0, dt) then 
    uArray[1] = u; 
    for j in 2:n loop 
     uArray[j] = pre(uArray[j-1]); 
    end for; 
    end when; 
    y[1] = sum(uArray)/n; // mean value 
    y[2] = sqrt(sum((uArray .- y[1]).^2)/n); // standard deviation 

    annotation (Diagram(graphics)); 
end MeanStdDevDiscr;