Oscillation is a significant indicator of performance degradation in industrial process control loops. Therefore, an effective oscillation monitoring mechanism is essential for ensuring the safe and stable operation of these processes. However, random noise and external disturbances are prevalent in process oscillation data, leading to a low signal-to-noise ratio (SNR), which severely affects the accuracy of oscillation detection and diagnosis. To address this, this paper proposes a novel denoising technique for industrial process data, combining complete ensemble empirical mode decomposition with adaptive noise ( CEEMDAN), detrended fluctuation analysis (DFA), and canonical correlation analysis (CCA). First, CEEMDAN is used to decompose the signal into a series of intrinsic mode functions (IMFs). Next, DFA is employed to classify the IMF components into information-dominated and noise-dominated categories. Then, CCA is applied to the noise-dominated IMF components to remove noise. Finally, the outputs of CCA are combined with the information-dominated IMF components to reconstruct the denoised oscillation signal. Simulation and experimental results using actual industrial oscillation data show that, compared to existing denoising techniques, this method achieves the lowest root mean squared relative error (RMSE) and the highest correlation in the denoised signals, demonstrating excellent denoising accuracy and robustness.