Automatic Detection and Estimation of Amplitudes and Frequencies of Multiple Oscillations in Process Data

This paper presents a novel method for detection and estimation of multiple oscillation frequencies and amplitudes present in a time series. The method is based on the Fourier Series decomposition of the time series utilizing the principle of linear regression technique. First, the frequencies of oscillations are estimated and then their amplitudes are found. Statistical hypothesis tests are performed on the oscillation amplitudes to determine the number of significant frequencies present in a time series. A new oscillation index is defined which is bounded between 0 and 1 and signifies the strength of oscillation. The impact of oscillation on the variable or on the control loop is determined from a new index called, Relative Oscillation Amplitude in Percentage (ROAP). The proposed method is evaluated extensively using simulated examples and industrial data.