# Ultrasonic Pulse-Echo Signals for Quantitative Assessment of Reinforced Concrete Anomalies
## 3 Formulation for Accurate Assessment of Void Defects  
Most ultrasonic measurements exhibit perplexity, as the results are subject to severe disturbances such as signal deviation, non-linearity, stochastic surface status, and mode conversion due to anisotropic and heterogeneous domains in the concrete. These are reflected in the UPE signal as spurious echoes and noise. The UPE testing data analysis contains ambient noise or signals corrupted by non-stationary acoustic noises, reducing the analysis efficiency. Denoising of the signals appears in several studies reported in the literature, many of which have certain limitations. Most studies relied on prior signal knowledge to enhance denoising, resulting in the loss of important data during filtering. Typical signal processing methods may not be effective in detecting fault features. However, combining various signal processing techniques can improve fault detection and analysis. To more accurately analyze the behavior of non-linear and non-stationary signals, many researchers have utilized empirical mode decomposition (EMD) to identify faults. EMD is capable of removing noise signals from non-linear and non-stationary signals. Research conducted [59, 60] highlighted that the EMD denoising method surpasses both median filtering and wavelet denoising in effectiveness. Nonetheless, when heavy noise is a factor, selecting the intrinsic mode function (IMF) in EMD can be difficult. The Hurst exponent is a valuable resource for detecting multifractality that may be disguised in non-linear and non-stationary signals. The Hurst analysis technique was employed to choose the appropriate IMF with the EMD method [61, 62]. This study presents a novel approach to removing noise from a UPE signal using data-driven analysis. The method involves breaking down the noisy signal into IMF components using EMD analysis, and then examining each IMF's Hurst exponent to determine which components require filtering. The filtered components are then reconstructed to eliminate the noise from the data. By utilizing the Hurst exponent to identify the threshold for maximum signal noise suppression, the method applies thresholding techniques to the IMFs for optimal noise removal. This method has proven more effective than traditional techniques, especially for low SN signals. A comprehensive understanding of IMF statistics in noise-only situations is essential in identifying the significance of a given mode. The estimation of the noise Hurst exponent is achieved using the aggregated variance method. This exponent is then utilized to evaluate the energies of IMFs within the noise model, a crucial step in determining the threshold of IMFs. Understanding the statistics of IMFs in noise-only scenarios can help determine the importance of a specific mode. Thus, the aggregated variance method is employed to  
Figure 3: Basic principles of the UPE device: (**a**) the first channel of transducers transmits signals that are subsequently received by other channels; (**b**) a transmitting and a receiving transducer produce an A-scan for void defection. Reproduced from [35], licensed under CC BY 4.0 (Deed—Attribution 4.0 International—Creative Commons). estimate the noise Hurst exponent, which is then applied to evaluate the IMF energies and establish the IMF threshold. Ultrasonic nondestructive testing can present challenges when it comes to detecting echoes caused by defects in backscattered signals due to backscattering and electronic noise. However, there is a solution in the form of the EMD algorithm. The EMD algorithm breaks down a non-linear and non-stationary signal into a series of zero-mean amplitude modulation and frequency modulation components. By doing so, it can accurately represent the observation's characteristic time scale. This means that a multi-component, non-linear, and non-stationary signal can be represented with precision using EMD within the context of ultrasonic theory.