## 3 Signal Processing and Artificial Intelligence for DT Development
### Signal Processing for DT Development  
Signal processing (SP) is a critical step in the design of a DT. This process is categorized into three types of analyses: time, frequency, and time-frequency analysis [77]. Time analysis involves extracting statistical indicators from signals, such as root mean square (RMS), kurtosis, and skewness, which provide essential insights into the signal's characteristics [78]. Frequency analysis, on the other hand, transforms the signal from the time domain to the frequency domain. Techniques like Fast Fourier Transform (FFT) and Power Spectral Density (PSD) are commonly employed in this context. Both time and frequency analyses are typically suited for stationary signals [79]. Meanwhile, for non-stationary signals, time-frequency analysis is preferred as it provides a combined perspective of temporal and frequency evolution. Techniques such as Wavelet Transform and Short-Time Fourier Transform (STFT) are widely used for this purpose [80]. These techniques are utilized in various ways to construct a DT for gearbox monitoring. [PERSON] et al. [22] employed the Discrete Wavelet Transform for feature extraction, followed by a step to select the most relevant features. This approach effectively distinguished between bearing faults in acquired signals and those generated by the DT. Similarly, [PERSON] et al. [81] applied frequency analysis to validate the DT of a helical gear, a crucial step to ensure the fidelity of the twin. A similarity criterion was subsequently used to adapt the model to real-world signals. [PERSON] et al. [82] refined the model to match experimental signals through feature matching, integrating both types of signals using Variational Mode Decomposition (VMD) after phase correlation. Envelope spectrum analysis was also applied to reduce noise and improve accuracy in diagnosing planetary gearboxes. [PERSON] et al. [83] utilized synchronous averaging for noise reduction, followed by a Discrete Fourier Transform. These steps allowed for the adaptation of virtual and real signals and the calculation of two feature indicators, CI1 and CI2, to estimate the severity of gear tooth cracks. [PERSON] et al. [84] used simple spectral analysis to detect fault frequencies and meshing frequencies. Meanwhile, [PERSON] et al. [70] applied Empirical Mode Decomposition (EMD) to select the most relevant mode based on energy entropy criteria, enabling signal denoising. Additionally, [PERSON] et al. [85] used Discrete Wavelet Transform for time-frequency feature extraction, ensuring the alignment of model-generated signals with real-world data. Further framework by [PERSON] et al. [86] employed lifting wavelets to extract features and adapt data distributions between the physical system and the DT. Similarly, [PERSON] et al. [87] conducted frequency decomposition for feature extraction to align the physical system's signals with those of its twin. [PERSON] et al. [23] utilized VMD to separate fault signatures from noise by calculating the highest correlation between meshing frequencies and decomposition modes. This noise was subsequently added to fault signatures to produce signals resembling real-world fault signals. [PERSON] et al. [88] aligned model data with experimental data using spectral analysis, as described by [PERSON] et al. [84]. Furthermore, [PERSON] et al. [89] adapted model signals to experimental data through Markov transfer, transforming signals into images based on SP and the extraction of temporal and frequency-based features. Lastly, [PERSON] et al. [90] extracted RMS from acoustic emission signals to monitor bearings. The RMS signal was then sampled and modeled using an autoregressive fuzzy Gauss-Laguerre approach, a method referred to as the \"smooth sliding DT\", which was used to classify the severity of bearing cracks. [PERSON] et al. [69] used a hash algorithm to represent the time-frequency data obtained from the real system and the DT.