Signal processing is the key component of SHM. The objective of signal processing is to extract features from the sensed data in order to determine whether the structure is damaged or not, as well as to determine damage type, its location and quantify the severity of the damage for further prognosis. Feature extraction based on signal processing is the most challenging aspect of SHM because of the complex processes involved in the structural response to dynamic loading. Signal processing algorithms for SHM must deal with the source of the signal, which is often noisy and complex, and detect features of interest. Many signal processing techniques have been used in vibration-based SHM research. The biggest challenge in realization of health monitoring of large real-life structures is automated detection of damage out of the huge amount of very noisy data collected from dozens of sensors on a daily, weekly, and monthly basis. The new methodologies for on-line SHM should handle noisy data effectively, and be accurate and efficient computationally.
Real world signals are often corrupted by noise which needs be removed before any further analysis or processing step. To solve this problem, several contributions based on di erent approaches have been proposed. Several approaches for signal denoising have been proposed. This includes approaches such as dictionary learning [1], empirical mode decomposition [2], singular and higher order singular values decomposition [3], [4] or canonical polyadic decomposition [5]. Particularly wavelet-based methods are considered as an essential tool for multi-resolution and time-frequency analysis [6]. They often provide relevant features to monitor industrial systems with time signals [7], [8], or can bu used for data augmentation [9]. The wavelet shrinkage operation that was theoretically investigated in [10] is still considered as one of the most powerful tools to perform signal denoising in many fields.
However, signals captured by flexible and wearable sensors are vulnerable to interference from various noise and artifacts, including power line interference, electrode contact noise, baseline wander or shift, motion artifacts, electromyographic noise, instrumentation noise, and electrosurgical noise. Therefore, pre-processing or noise filtering is essential before accurately examining cardiac signal features [9–13], as it directly impacts the sensing system’s performance.
To perform wavelet denoising, several hyperparameters need to be set. The parameters include the threshold used for wavelet shrinkage, the thresholding function and the wavelet family considered for the decomposition. Several heuristics have been proposed to address threshold selection [13], such as the universal threshold [10], Stein’s unbiased risk estimation or the Bayesian shrink method [14]. However, the selection of the wavelet family and the correct heuristics require specialized knowledge to remain robust to the complexity of the real data.
Currently, a range of noise removal techniques are available to suppress noise and artifacts in ECG signals, including digital filtering, adaptive noise reduction, wavelet transform, empirical mode decomposition, neural network-based methods, and hybrid methods [14–21]. Among these, wavelet transform stands out as one of the best denoising methods for non-stationary biomedical signals, widely used in image, sound, video, and mechanical processing fields [22–24]. In recent years, various wavelet transform methods have been developed to enhance the denoising of cardiac signals. Some of these methods involve improved wavelet transforms [25–29], such as Spcshrink of discrete wavelet transform (DWT), stationary wavelet transform (SWT), stationary wavelet packet transform (SWPT), dual-tree complex wavelet transform (DTCWT), double density complex (DDC) DWT, and stationary bionic wavelet transform (SBWT). Others combine wavelet transforms with conventional methods [30–34], such as modified median filter, ensemble empirical mode decomposition (EEMD), local means filter, variational modal decomposition in addition to wavelet transform. Furthermore, some methods integrate wavelet transform with artificial intelligent (AI) [35–40], such as deep belief network fusion extreme learning machine (DBN-ELM), machine learning, deep learning. Certain approaches combine multiple methods mentioned above. The combination with wavelet transform and other methods is executed in two ways: first, by conducting traditional and/or AI processing followed by wavelet filtering, or vice versa; second, by enhance the accuracy of the wavelet thresholding using traditional and/or AI methods.
Strain signals are often a noisy mixture of electrical signals generated from the activities of several different sources from ……. The main issues in the processing of strain signals are the denoising, separation and identification of the signals from different sources.
Most health monitoring systems are centered on measuring strains, accelerations, displacements, or a combination of these items. While acceleration measurements are suited for monitoring global behavior of structural systems, strain measurements provide a unique understanding of local behavior of the system. Recent research has focused on the use of specific types of strain sensors to not only evaluate their effectiveness in the field but also to examine their efficacy for detecting damage in a SHM application and their use continues to be studied.
Noise and distortion fundamentally constrain the measurement accuracy in signal processing and control systems, as well as decision accuracy in pattern recognition [1]. Digital signal processing algorithms can be categorized into four broad categories: transform-based signal processing, model-based signal processing, Bayesian statistical signal processing and neural networks [1]. The objective of a transform is to represent a signal or system through a combination of elementary signals (e.g., sinusoids, eigenvectors, or wavelets) that facilitate straightforward analysis, interpretation, and manipulation. Transform-based signal processing techniques encompass methods such as the Fourier transform, Laplace transform, z-transform, and wavelet transforms. Model-based methods employ a parametric model to describe the signal generation process, capturing predictable structures and expected patterns. These models facilitate forecasting future signal values based on past trajectories. However, they are sensitive to deviations from the signal class defined by the model. Bayesian inference theory offers a generalized framework for the statistical processing of random signals. In pattern recognition or signal estimation from noisy observations, Bayesian methods integrate the evidence from the observations with prior knowledge about the signal distributions and associated parameter distributions. Neural networks consist of relatively simple, non-linear, adaptive processing units organized to mimic the signal transmission and processing characteristics of biological neurons. These networks feature multiple layers of parallel processing elements connected through a hierarchically structured network. The connection weights are trained to memorize patterns and execute signal processing functions, such as prediction or classification. Neural networks excel in non-linear partitioning of signal spaces and in feature extraction and pattern recognition. In some hybrid systems, neural networks complement Bayesian inference methods for enhanced pattern recognition. Noises superposed upon the useful strain signal, may lead to unreliable structural condition assessment or prediction. Consequently, denoising becomes a crucial issue in an efficient SHM of civil structures. Numerous investigations have been carried out to implement the task of vibration signal denoising in frequency, time, and time-frequency. In the time domain, the synchronous averaging method, is one of the typical and powerful techniques to extract periodic signal components from a compound signal. The main application limitation of the time domain methods is that the effectiveness of denoising may dramatically diminish in a non-stationary noisy context. The widely used Kalman filtering is also an earlier proposed time domain denoising algorithm. The main application limitation of Kalman filtering is that the system model needs to be given manually, and the filtering effect will be degraded with an inaccurate system model. This method is suitable for the situation where the input signal is relatively stationary or the kinematics model of the test system is known.
The classical frequency domain methods, such as low-pass filters, high-pass filters, band-pass filters, can remove noise depending on the frequency bands between the vibration signal and noise. Consequently, noise in the same frequency band as the signal cannot be filtered by denoising methods. In addition, this approach may easily lead to greater signal distortion such as broadening narrow peaks.
Strain signals are of non-linear and non-stationary characteristics. Many effective methods have been developed to solve this problem. Time-frequency domain methods, which are primarily based on the wavelet transform (WT) and time-frequency analysis (TFA), can take both time and frequency information into account so that the noise in the time–frequency plane can be eradicated. Empirical mode decomposition (EMD) [2] is a recursive method for processing non-linear and non-stationary signals. Some novel EMD-based denoising techniques inspired by wavelet threshold have been developed. However, the EMD algorithm is susceptible to mode mixing, easily producing oscillations of different scales in one mode, or similar-scale oscillations in different modes [3, 4]. Aiming at the disadvantages of EMD, the improved ensemble EMD (EEMD) and complete ensemble EMD (CEEMD) methods can suppress the mode mixing effectively. But both require multiple iteration calculations, which reduce the denoising efficiency. In contrast to EMD, variational mode decomposition (VMD) proposed in 2014 can adaptively decompose any signal into a group of band-limited intrinsic mode functions (BLIMFs). Related studies have shown that VMD is superior to EMD in terms of tone detection, separation and denoising [5], but there still exists a problem of EMD-like endpoint effects in decomposition. In addition, singular value decomposition (SVD) algorithm, with good stability and invariance, is an effective approach to eliminate random noise and can retain important mutation information of the signals. SVD is regarded as a non-linear filter which suppresses the noise with different distributions greatly. However, it is usually influenced by the noise. The effectiveness of SVD denoising is not satisfied when the noise is heavy.
At present, one of its major drawbacks is that there are no mature and complete methods to select effective singular values. Throughout all the denoising methods suitable for non-linear and non-stationary signals, wavelet filtering which is a more efficient multi-resolution denoising approach. Its fundamental principle is that a threshold rule is applied to shrink the wavelet coefficients, and then the denoised signal is reconstructed by inverse wavelet transform from these shrunken wavelet coefficients [6].
As an effective tool for describing the non-stationary signal, wavelet transform (WT) [20] has already shown its tremendous power in mechanical equipment condition monitoring and fault diagnosis because of its property on multi-resolution analysis, which is in favor of identifying weak fault feature from noisy signals. And the denoising performance and efficiency rely on the reasonable selection of mother wavelet, decomposition level and threshold. The discrete wavelet transform (DWT) is constructed by the selected wavelet basis function and its corresponding scaling function, and can be implemented by a pair of low-pass and band-pass filters. The signals decomposed with DWT can avoid redundant information generated by CWT decomposition.
In traditional fault diagnosis, WT has been widely used for fault feature extraction and extensively studied for performance improvement. With the emergence of data-driven intelligent fault diagnosis, especially deep learning techniques, WT has attracted renewed attention for its ability of adding interpretability into the intelligent diagnosis models.
Comparatively, WT decomposes the signal into constituent wavelet coefficients in the time-scale domain and possesses many distinct merits, such as multi-resolution analysis (MRA) and fast calculation speed. In recent decades, WT has been constantly developed and applied to various fields of engineering.
Wavelet shrinkage denoising becomes a very popular technology for noise reduction in image and time series applications. Wavelet shrinkage denoising is a topic of interest in reduction noise, which is developed principally by Donoho and Johnstone, who called these approaches as WaveShrink [5]. It has two issues worth studying, how to define a good threshold operator and how to choose the threshold value for the noise coefficients. Some WaveShrinks are worth mentioning, such as Donoho and Johnstone introduced a denoising approach using soft and hard shrinkage with the universal threshold, which refers to VisuShrink [5]. They also introduced RiskShrink with minimax threshold [2], [5], [7] and SUREShrink with SURE (Stein’s Unbiased Risk Estimate) threshold [8], [9]. In a real application, researchers found that the universal threshold performs well in high noise intensity, while the SURE threshold works better in low noise intensity [6]. Various threshold operators have been proposed in the past decades [3]–[18]. The threshold operators provide the non-linearity for wavelet coefficients in the transform domain. The mechanism makes wavelet shrinkage denoising different from those denoising methods that are entirely linear.
Recently, the development of deep network architectures makes deep learning methods widely applied for denoising in various fields [7]. Deep learning-driven denoising techniques [8-10], such as autoencoders, artificial neural networks (ANN), recurrent neural networks (RNN), convolutional neural networks (CNN), can model the non-linear relationships between noise and the clean signal by pre-training whereby the redundant information in the new input signal can be filtered accurately. Compared with conventional denoising methods, deep learning-based denoising approaches can be expected to avoid complicated manual setting parameters and handle different tasks without many modifications. 深度学习方法的问题
Strain sensors are usually low-cost and densely distributed on a monitored structure. After long-term operation, there are various noises. Large data volume and real-time structural condition assessment especially requires high computational efficiency.
The crucial matter of each denoising process lies in removing most of the unwanted noise, without losing the useful part of the signal containing the true monitoring information. The essence of each denoising process is to effectively eliminate the majority of unwanted noise while preserving the useful information.
Several signal denoising techniques have been proposed in the literature, some of which are currently in development. Band-pass filter is the most basic and traditional way to remove noises. It uses cut-off frequencies which allow to remove all the frequency contents greater or lower than a certain frequency value, respectively. Moving average filters, as well as Gaussian filters, can be considered as typical examples belonging to such a category. However, while filters may be effective when noise occupies a distinct frequency band separate from the signal, they often fail when noise shares a similar frequency spectrum with the target signal. In such cases, significant portions of the useful signal can be inadvertently removed, rendering the filtering approach ineffective. This limitation also represents a major drawback of employing Fourier Transform for denoising purposes. However, in practical scenarios, noise distribution is sometimes non-uniform, necessitating the application of localized denoising techniques. A further powerful methodology for separating noise out of corrupted data involves the application of a discrete wavelet transform (DWT). In particular, in Dohono [11], a first DWT based approach for denoising one-dimensional signals was provided. Afterwards, Chang et al. [12] introduced an innovative adaptive Wavelet thresholding for image denoising and compression, called BaeyShrink method. Denoising algorithms built on discrete wavelet transform decomposes signals into different frequency resolution levels. Thresholding is then applied to higher frequency components which generally correspond to noise to eliminate this one. Furthermore, the use of singular value decomposition (SVD) for denoising purposes has also attracted considerable interest. Finally, a possible alternative approach in enhancing the quality of noise-affected signals may concern the application of a Kalman filter (KF). Studies on acceleration signals Ravizza1 et al. [13] investigated the effectiveness of DWT and SVD in denoising acceleration signal. 土木SHM中的信号去噪研究，加速度数据去噪，principal component方法[14]，深多学习方法，如[9]。 数值模拟的信号或小桥信号，简单。 Although there has been a lot of progress in the general area of signal denoising, noise removal remains a very challenging problem in real-world communication systems. Denoising algorithms are typically are chosen based on the type of image, as a specific algorithm may work for a given noise but not for another one. hence the importance of careful selection and tuning of denoising algorithms。
噪声特点 方法原理和优缺点 DWT去噪研究，小波基的选择[15]、分解层数的确定[16]。 本研究基于SWT对土木SHM信号进行滤波，根据信号特点，采用带通滤波、阈值去噪和空域滤波方法，对信号进行清洗和分解。