Shape Optimisation on Constrained Single-Chamber Muffler by Using GA Method and Mathematical Gradient Method

ACC accuracy desired in EPFM, IPFM, and FDM ! bit_n bit length ! sound speed (m/s) c0 ! D diameter (m) ! elite selection of elite (1 for yes and 0 for no) ! unmodified objective function F"X# ! f cyclic frequency ! cut-off frequency fc ! gen_no maximum number of generation ! the i-th inequality constraints gi"X# ! j imaginary unit ( ) ! !1 k wave number ( ) ! w /c0 length of the i-th segment of straight duct (m) Li ! mean flow Mach number at the i-th segment of Mi ! straight duct pc crossover ratio ! pressure; acoustic pressure at (Pa) Pi ! i pm mutation ratio ! popuSize number of population ! Q volume flow rate of venting gas (m/s) ! penalty parameter in EPFM rp ! penalty parameter in IPFM rp ! ! rt1 GA’s design parameter ( ) ! L1/L2 section area at (m) Si ! i STL sound transmission loss (dB) ! TT initial step size in EPFM, IPFM, and FDM ! maximum step size in EPFM, IPFM, and FDM Tmax ! acoustic particle velocity at (m/s) Ui ! i ww push-off factor in FDM ! initial starting point in EPFM, IPFM, and FDM X ! Y characteristic impedance ! air density (kg/m) !0 ! modified objective function " !