Estimation of the FRF Through the Improved Local Bandwidth Selection in the Local Polynomial Method

Abstract

This paper presents a nonparametric method to measure an improved frequency response function (FRF) of a linear dynamic system excited by a random input. Recently, the local polynomial method (LPM) has been proposed as a technique to reduce the leakage errors on FRF measurements. The noise sensitivity of the LPM was similar to that of the classical windowing methods, while the leakage rejection is improved from an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ) to an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> ). This paper shows a methodology, to automatically tune the parameter of the LPM, viz., the local bandwidth that sets how many neighboring frequency lines are combined in a single-point estimate, to get lower noise sensitivity by increasing the smoothening of the original LPM, without any user interaction. The balance between noise reduction and bias error will be automatically retrieved.