## 2 Non-Parameterized Time-Frequency Analysis
### Short-Time Fourier Transform
#### 2.1.3 Strength and Weakness  
* High-resolution and efficient computation
* Window effect and time-frequency trade-off  
First, STFT provides excellent time-frequency resolution, allowing signals to be represented in detail in both the time and frequency domains. This is particularly crucial for structural health monitoring, as the response signals of structures often exhibit non-stationary characteristics when subjected to external excitations or internal damages. Traditional Fourier transform methods are ineffective in processing such non-stationary signals, whereas STFT can accurately capture the temporal variations in signals, providing a solid basis for structural health assessment.  
Second, STFT is computationally efficient. Compared to other time-frequency analysis methods, STFT has relatively low complexity, enabling it to play a significant role in real-time applications. In structural health monitoring systems, real-time performance is a key indicator, as the timely and accurate detection of structural damages is vital for ensuring structural safety. The efficiency of STFT enables it to meet this requirement, providing strong support for real-time structural health monitoring.  
However, the short-time Fourier transform also has some limitations in signal processing within the field of structural health monitoring:  
One notable drawback is the window effect. The analysis results of STFT are highly dependent on the choice and length of the window function. In structural health monitoring, different window functions and lengths may lead to variations in time-frequency resolution, thereby affecting the accuracy of damage identification. Therefore, careful consideration is needed when selecting the window function and length to ensure consistent and accurate analysis results. Another key limitation is the inherent trade-off between time and frequency resolution. Due to the characteristics of the windowing process in STFT, it cannot achieve optimal resolution in both the time and frequency domains simultaneously. According to the Nyquist sampling theory, larger windows give higher frequency resolution but lower time resolution, and vice versa for shorter windows. In structural health monitoring, certain types of damage may exhibit rapidly changing characteristics, requiring time-frequency analysis methods to capture high-frequency components of signals within short periods. However, the performance of STFT in this aspect may be limited, leading to inaccurate identification of certain rapidly changing damage features.  
Furthermore, STFT struggles to accurately capture the time-frequency features of highly non-stationary signals, especially those with abrupt or transient components. In structural health monitoring, certain types of damage may cause abrupt or transient changes in signals, requiring time-frequency analysis methods to sensitively capture these changes. However, STFT may have deficiencies in this regard, leading to inaccurate identification of certain damage features.  
To address these limitations, STFT often needs to be combined with complementary methods, such as wavelet transforms or adaptive time-frequency techniques. These methods can compensate for the shortcomings of STFT in terms of time-frequency resolution and the capture of abrupt signals, improving its performance in complex signal analysis scenarios. Despite these challenges, STFT remains a fundamental and widely used time-frequency analysis tool. Owing to its advantages of simplicity, efficiency, and broad applicability, it plays a significant role in signal processing within the field of structural health monitoring.