Patent Document ID: 8620631
Application ID: 13084429
Patent Status: 1

Claim One:
1. A computerized method of identifying Hammerstein models with known nonlinearity structures using particle swarm optimization, comprising the steps of: (a) generating M input-output data points from a Hammerstein system to be identified, the Hammerstein system having both linear and nonlinear parts, wherein M is a pre-defined integer and the Hammerstein system is defined by y â¡ ( k ) = B â¡ ( q - 1 ) A â¡ ( q - 1 ) â¢ x â¡ ( k ) + w â¡ ( k ) , where k is an integer, the Hammerstein system having an input u(k), y(k) representing the output of the Hammerstein system, w(k) representing measurement noise of the Hammerstein system, and q representing a set of parameters describing the nonlinear part, with q âˆ’1 being the unit delay operator, and B(q âˆ’1 ) being defined as B(q âˆ’1 )=b 0 +b 1 q âˆ’1 +. .. +b m q âˆ’m and A(q âˆ’1 ) being defined as A(q âˆ’1 )=1+a 1 q âˆ’1 +. .. +a n q âˆ’n , where m and n are integers and (m, n) represents the order of the linear part, and x(k) represents a non-measured intermediate variable which is the output of the nonlinear part, x(k) being given by x(k)=f(Î¸,u(k)), where f(Î¸,u(k)) is a function representing the nonlinear part and a 1 ,. .. , a n , b 0 ,. .. , b m and Î¸ are unknown parameters to be determined, wherein the generation of the M input-output data points is performed by a computer processor; (b) identifying the Hammerstein system by estimating the unknown parameters a 1 ,. .. , a n , b 0 ,. .. , b m and Î¸ from the input-output data, the estimation comprising the following steps (c) through (h) and being performed by the computer processor: (c) generating a set of random initial solutions for zeros and poles of the linear part and also for the sets of unknown parameters a 1 ,. .. , a n , b 0 ,. .. , b m and Î¸ of the nonlinear part within a pre-selected range; (d) evaluating a fitness function F for the set of random initial solutions, wherein the fitness function F is given by F = âˆ‘ k = 1 M â¢ ( y â¡ ( k ) - y ^ â¡ ( k ) ) 2 , where â¢ â¢ y ^ â¡ ( k ) = B ^ â¡ ( q - 1 ) A ^ â¡ ( q - 1 ) â¢ x ^ â¡ ( k ) , â¢ B ^ â¡ ( q - 1 ) = b ^ 0 + b ^ 1 â¢ q - 1 + â€¦ + b ^ m â¢ q - m , â¢ A ^ â¡ ( q - 1 ) = 1 + a ^ 1 â¢ q - 1 + â€¦ + a ^ n â¢ q - n , and x ^ â¡ ( k ) = c ^ 1 â¢ u â¡ ( k ) + c ^ 2 â¢ u 2 â¡ ( k ) + â€¦ + c ^ L â¢ u L â¡ ( k ) , L being an integer defined by representing the non-measured intermediate variable x(k) as x(k)=c 1 u(k)+c 2 u 2 (k)+. .. +c L u L (k), where c 1 , c 2 ,. .. , c L represent a further set of unknown parameters, and Ã¢ 1 ,. .. , Ã¢ n , {circumflex over (b)} 0 ,. .. , {circumflex over (b)} m , represent estimates of the unknown parameters a 1 ,. .. , a n , b 0 ,. .. , b m ; (e) minimizing the fitness function F to generate the estimated unknown parameters Ã¢ 1 ,. .. , Ã¢ n , {circumflex over (b)} 0 ,. .. , {circumflex over (b)} m and Î¸, (f) applying particle swarm optimization to the set of solutions by determining the most fit zeros and poles of the linear part calculated in step (d); (g) generating a new set of solutions composed of the most fit zeros and poles of the linear part and with the estimated parameters Ã¢ 1 ,. .. , Ã¢ n , {circumflex over (b)} 0 ,. .. , {circumflex over (b)} m and Î¸ generated in step (e); and (h) repeating steps (d) through (g) for a predetermined number of generations.