Chirp Mode Research Articles

An Adaptive Chirp Mode Decomposition-Based Method for Modal Identification of Time-Varying Structures

Modal parameters are inherent characteristics of civil structures. Due to the effect of environmental factors and ambient loads, the physical and modal characteristics of a structure tend to change over time. Therefore, the effective identification of time-varying modal parameters has become an essential topic. In this study, an instantaneous modal identification method based on an adaptive chirp mode decomposition (ACMD) technique was proposed. The ACMD technique is highly adaptable and can accurately estimate the instantaneous frequencies of a structure. However, it is important to highlight that an initial frequency value must be selected beforehand in ACMD. If the initial frequency is set incorrectly, the resulting instantaneous frequencies may lack accuracy. To address the aforementioned problem, the Welch power spectrum was initially developed to extract a high-resolution time–frequency distribution from the measured signals. Subsequently, the time–frequency ridge was identified based on the maximum energy position in the time–frequency distribution plot, with the frequencies associated with the time–frequency ridge serving as the initial frequencies. Based on the initial frequencies, the measured signals with multiple degrees of freedom could be decomposed into individual time-varying components with a single degree of freedom. Following that, the instantaneous frequencies of each time-varying component could be calculated directly. Subsequently, a sliding window principal component analysis (PCA) method was introduced to derive instantaneous mode shapes. Finally, vibration data collected under various operational scenarios were used to validate the proposed method. The results demonstrated the effective identification of time-varying modal parameters in real-world civil structures, without missing modes.

Intelligent Fault Diagnosis Method for Constant Pressure Variable Pump Based on Mel-MobileViT Lightweight Network

The sound signals of hydraulic pumps contain abundant key information reflecting their internal mechanical states. In environments characterized by high temperatures or high-speed rotation, or where sensor deployment is challenging, acoustic sensors offer non-contact and flexible arrangement features. Therefore, this study aims to develop an intelligent fault diagnosis method for hydraulic pumps based on acoustic signals. Initially, the Adaptive Chirp Mode Decomposition (ACMD) method is employed to remove environmental noise from the acoustic signals, enhancing the feature signals. Subsequently, the Mel spectrum is extracted as the acoustic fingerprint features of various fault states of the hydraulic pump, and these features are used to train the MobileViT network, achieving accurate identification of the different fault modes. The results indicate that the proposed Mel-MobileViT model effectively identifies and classifies various faults in constant pressure variable pumps, outperforming other models. This study not only provides an efficient and reliable intelligent method for the fault diagnosis of critical industrial equipment such as hydraulic pumps, but also offers new perspectives on the application of deep learning in acoustic pattern analysis.

Research on ACMD-ICYCBD method for rolling bearing fault feature extraction

Aiming at the difficulty in obtaining the eigenfrequency of the vibration component of rolling bearing faults in a strong background noise environment and the problem of extraction efficiency, the adaptive chirp mode decomposition (ACMD) combined with Improved maximum second-order cyclostationary blind deconvolution (ICYCBD) fault feature extraction algorithm is proposed. Firstly, to improve the signal-to-noise ratio, the original signal is adaptively decomposed using the ACMD method, and the optimal components are selected based on the principle of maximizing the correlation gini coefficient index. Secondly, to improve the accuracy of parameter setting and extraction efficiency, an improved CYCBD method is proposed to estimate the cyclic frequency set of CYCBD using the proposed enhanced energy harmonic product spectrum (EEHPS) method for the optimal components, the envelope spectrum peak factor index is improved by proposing the envelope spectral period pulse factor (EPPF) index, and the filtering length of the CYCBD is selected adaptively using the step search to obtain the optimized filtered signal. Finally, the envelope spectrum analysis is carried out to extract the fault information accurately. The simulation signals and experimental data show that the method can quickly and accurately extract the fault characteristics of rolling bearings under strong background noise, and the comparison with other methods shows the effectiveness and superiority of the proposed method.

Fault diagnosis of railway freight car rolling bearings based on ACMD and improved MCKD

To address the issue of accurately extracting fault characteristic information of railway freight car bearings under noisy conditions, this paper proposes a fault diagnosis method based on Adaptive Chirp Mode Decomposition (ACMD) and an optimized Maximum Correlation Kurtosis Deconvolution (MCKD) using a Sparrow Search Algorithm Combining Sine-Cosine and Cauchy Mutation (SCSSA). Firstly, ACMD is used to decompose and reconstruct the original fault signal to obtain several Intrinsic Mode Functions (IMFs). Then, the IMFs are filtered according to the Gini coefficient indicator, with the IMF having the largest Gini coefficient selected as the optimal component. Secondly, the SCSSA is employed to iteratively optimize the filter length L, fault signal period T, and displacement parameter M in the MCKD algorithm, determining the optimal parameter combination for MCKD. This avoids the limitations of manual settings and enhances the accuracy of fault diagnosis. The optimized MCKD is then applied to the optimal component, and deconvolution is performed using maximum correlation kurtosis as the criterion to extract fault characteristic information through its envelope spectrum. To verify the effectiveness and generalizability of the proposed method, simulations, experimental signals from the Case Western Reserve University Bearing Center, and actual measured signals from railway freight car bearing 353130B are used to analyze inner ring faults. The experimental results demonstrate that the method can accurately extract fault characteristic information of railway freight car bearings under noise interference and identify the fault type.

Time-varying characteristics analysis of bridge under moving vehicle using a modified time-frequency method with limited sensors

Investigating the bridge dynamic characteristics under operational traffic load is critical for bridge health monitoring. As vehicles traverse the bridge, the bridge frequencies present time-varying characteristics owing to the effect of vehicle-bridge dynamic interaction. The recently introduced variational nonlinear chirp mode decomposition (VNCMD) demonstrates significant benefits in identifying structural instantaneous frequencies (IFs) from the measured responses. However, its practical application is limited by the requirement for artificially setting priori parameters (i.e., upper bound of noise level and number of modal components). In this study, a modified VNCMD (MVNCMD) is proposed to overcome this limitation and is employed to identify the IFs of the bridge under moving vehicle using single sensor data. First, by modifying the optimization function, the proposed MVNCMD adopts a novel algorithm framework that eliminates the necessity for presetting the upper bound of noise level. An autoregressive spectrum-based method is then introduced to preset the number of modal components. The proposed MVNCMD is evaluated using a synthetic non-stationary signal, demonstrating its effectiveness in identifying IFs and overcoming the limitations of the original VNCMD. Furthermore, the numerical simulation involving different parameter analysis and laboratory experiments of the coupled vehicle-bridge system are conducted to validate the effectiveness of the proposed method. It is to be shown that the proposed MVNCMD method is capable of identifying the IFs of the bridge under moving vehicle using single sensor data and outperforms other time-frequency methods in terms of identification accuracy, which provides a robust tool for analyzing the time-varying characteristics of the vehicle-bridge interaction system.

Joint extraction-based multivariate chirp mode decomposition and its application to fault diagnosis of rotating machinery under variable speed conditions

Vibration signals from rotating machinery during variable speed conditions exhibits non-stationary characteristics, posing a challenge for fault diagnosis. When a machine fails, the vibration signal of any component connected to the bearing carries valuable information about the equipment’s status. Processing multichannel variable speed signals at the same time avoids losing part of information and improves fault diagnosis. Therefore, this study put up a novel approach called joint extraction-based multivariate chirp mode decomposition (JMCMD) to analyze multichannel signals of rotating machinery with varying speeds. The approach comprises the joint extraction framework and the multichannel signal instantaneous frequency initialization (MSIFI). First, JMCMD employs a joint component extraction framework, which can precisely and simultaneously extract complicated characteristic components close to each other in multiple channels. Second, this study extends the parameterized demodulation (PD) technique to multiple channels to find the initialized instantaneous frequency of multichannel signals. Through the joint extraction strategy’s integration with MSIFI, JMCMD is capable of efficaciously extracting all significant characteristic components of multichannel signals. Additionally, the high-resolution time–frequency representation (TFR) constructed from JMCMD’s output can clearly reveal the time-varying fault characteristic frequency of the rotor-bearing system. Simulation analysis and actual cases demonstrate that the suggested approach is an effective way to identify fault feature components, making it highly applicable in signal decomposition and fault detection.

Multivariate iterative nonlinear chirp mode decomposition: principles and applications

Abstract The rotor-bearing system (RBS) of a hydroelectric unit includes multiple components such as the rotor, rotor shaft, coupling, turbine, and main shaft. There is a strong coupling relationship between the vibration signals of multiple bearing sections. At the same time, the vibration signal of the RBS contains rich frequency components, which can effectively reflect the operating state of the shaft system of the unit. Therefore, synchronous signal analysis across multiple rotor bearing sections is required to completely grasp the operating status of the unit. In this study, the Multivariate Iterative Nonlinear Chirp Mode Decomposition (MINCMD) is proposed to analyze signals on multiple sections simultaneously. MINCMD follows the step-by-step extraction idea of Adaptive Multivariate Chirp Mode Decomposition (AMCMD), but it adopts a new algorithm framework by modifying the objective function. Furthermore, AMCMD does not converge well without a good initial instantaneous frequency (IF). Therefore, a method based on parameterized demodulation (PD) is introduced in MINCMD to solve the multi-channel frequency initialization problem. The effectiveness of the proposed algorithm is verified through a simulation test and real data from hydroelectric units.

Transmission tower bolt-loosening time–frequency analysis and localization method considering time-varying characteristics

To address the issues of high concealment and difficult positioning of loose bolts in transmission towers, this paper proposes a new method for locating loose bolts in transmission towers. In this method, we divide the vibration response of the transmission tower into low-frequency signals of 2–25 Hz and high-frequency signals of 25–75 Hz. For the low-frequency signals, the single signal component is obtained by adaptive Chirp mode decomposition and uses the general demodulation transformation to deeply denoise the non-modal information. Since frequency characteristics themselves do not contain time information, considering the importance of time information for positioning, we propose a low-frequency time-varying frequency feature that preserves time characteristics based on synchronous wavelet transform and peak search. For the high-frequency signals, we use singular value decomposition to remove signal outliers caused by pulse excitation and eliminate forced vibrations through wavelet packet transform. Without altering its inherent characteristics, this method enables high-frequency time-domain signals to better represent the nonlinear characteristics of transmission towers. Furthermore, based on the powerful capabilities of Timesnet and Transformer in dealing with time series data, we propose a fault diagnosis model, which ultimately achieves the positioning of loose bolts in transmission towers. The bolt node model proves that this approach can better represent the loose bolt characteristics, and the transmission tower model verifies the effectiveness of this approach in locating loose bolts in transmission towers. Finally, bolt-loosening tests were conducted on a 110 kV transmission tower, and the accuracy of the positioning results reached 92.8%, demonstrating the effectiveness and efficiency of this method in practical positioning applications.

Real-time identification of time-varying cable force for cable-stayed bridges based on vibration monitoring

Time-varying cable-force identification is fundamental for assessing the fatigue damage of stay cables. This study proposes a novel method for real-time time-varying cable force identification. This method updates the cable vibration signals through the sliding window and employs adaptive chirp mode decomposition (ACMD) to identify the instantaneous frequencies of the cables. Finally, the cable forces were calculated based on the taut string theory. The novelty of this study lies in the introduction of ACMD to enhance the accuracy of cable-force identification, while adaptively determining the key parameters of ACMD based on the scale space peak picking (SSPP) algorithm. The effectiveness of this method was been verified through numerical models, with the results showing that the maximum relative error in cable-force identification was 0.87%. Furthermore, this method was successfully applied to a sea-crossing cable-stayed bridge, demonstrating its ability to assess cable force accurately.

Swarm Intelligence-Based Improved Adaptive Chirp Mode Decomposition Algorithm for Suppression of Ocular Artifacts from EEG Signal

Swarm Intelligence-Based Improved Adaptive Chirp Mode Decomposition Algorithm for Suppression of Ocular Artifacts from EEG Signal

A Hybrid LSTM Network for Long-Range Vehicle Trajectory Prediction Based on Adaptive Chirp Mode Decomposition

A Hybrid LSTM Network for Long-Range Vehicle Trajectory Prediction Based on Adaptive Chirp Mode Decomposition

Adaptive sparse estimation of nonlinear chirp signals using Laplace priors.

The identification of nonlinear chirp signals has attracted notable attention in the recent literature, including estimators such as the variational mode decomposition and the nonlinear chirp mode estimator. However, most presented methods fail to process signals with close frequency intervals or depend on user-determined parameters that are often non-trivial to select optimally. In this work, we propose a fully adaptive method, termed the adaptive nonlinear chirp mode estimation. The method decomposes a combined nonlinear chirp signal into its principal modes, accurately representing each mode's time-frequency representation simultaneously. Exploiting the sparsity of the instantaneous amplitudes, the proposed method can produce estimates that are smooth in the sense of being piecewise linear. Furthermore, we analyze the decomposition problem from a Bayesian perspective, using hierarchical Laplace priors to form an efficient implementation, allowing for a fully automatic parameter selection. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm is found to yield reliable estimates even when encountering signals with crossed modes. The method's practical potential is illustrated on a whale whistle signal.

Fault Diagnosis of Synchronous Generator Based on Adaptive Chirp Mode Decomposition Permutation Entropy and Deep Learning

Generators are subject to extreme environmental conditions that can cause critical areas to gradually break down, potentially leading to catastrophic failures. This paper proposes a hybrid method for generator fault diagnosis. Firstly, adaptive chirp mode decomposition (ACMD) is applied to decompose the vibration signal into five intrinsic mode function (IMF) components. Then, the permutation entropy (PE) of each IMF is calculated to construct the feature vector. The deep learning part of the proposed method uses convolutional neural network (CNN) as a classifier to recognize different faults. Finally, the visualization result using t-Distributed Stochastic Neighbor Embedding (t-SNE) is presented. The result of classification suggests that the method proposed in this paper realizes fault diagnosis with the accuracy of 98%, which has a higher recognition rate than other methods mentioned in this paper.

Study on the frequency modulation phenomenon in the rotor system with blade-casing rub-impact fault

In an aero-engine rotor system, a blade-casing rub-impact fault can lead to a frequency modulation phenomenon of the vibration signal. This paper discusses the extraction of the modulation information in the fault signal using the variational nonlinear chirp mode decomposition (VNCMD) method to detect early rub-impact faults. The regularities of frequency modulation are revealed in both the simulated and experimental blade-casing rubbing signals. According to the frequency modulation law, an empirical formula is summarized to judge the rub-impact fault type. Then, we propose an evaluation index to judge the fault severity based on the energy theory by using the advantage of the VNCMD method that can reconstruct the decomposed fault signal. Finally, the fault severity in the simulated and experimental signals with different parameters is compared. The results show the correctness and reliability of this evaluation index. The research in this paper provides a theoretical basis for the detection and judgment of the rubbing severity of blade-casing rub-impact faults.

Wind turbine gearbox fault diagnosis via adaptive IMFogram

Wind turbines usually operate in mountainous, offshore and other field environments. As the wind speed is constantly changing, the gearboxes of wind turbines operate under variable operating conditions, resulting in a non-stationery and time-varying signal characteristic. For existing time–frequency analysis (TFA) methods, they undergo low time–frequency energy concentration as well as noise interference during the fault feature extraction. IMFogram, a recently proposed time–frequency representation (TFR) method, calculates local frequency and amplitude information of signals based on fast iterative filtering (FIF). Moreover, it is able to remove uncertainty on the time–frequency plane, allowing a long enough time window to reduce the local boundary effects associated with the signal decomposition methods. Therefore, it has potential advantages for TFA. However, the actual performance of IMFogram calculation largely depends on the decomposition effect provided by FIF and the selection of model parameters. With the purpose of obtaining a more distinct and focused TFR of the wind turbine vibration signal, a novel TFA method, namely Adaptive IMFogram (AIMFogram), is proposed in this paper. Firstly, a range of intrinsic mode functions (IMFs) are gained after the decomposition of vibration signals using an improved variational nonlinear chirp mode decomposition, which is treated as the input to AIMFogram to solve the unsatisfied result by traditional FIF under strong noise. Secondly, Renyi entropy-based particle swarm optimization is conducted to perform adaptive parameter optimization of the AIMFogram. Later, using the optimal parameter, the proposed AIMFogram achieves a high-resolution TFR of complex multi-component vibration signals. To verify whether the proposed AIMFogram is effective or not, the method was successfully employed to the fault diagnosis of the rolling bearing in an experimental bench and the gearbox in a 850-kW wind turbine.

Variational generalized nonlinear mode decomposition: Algorithm and applications

Recently proposed variational signal decomposition methods like adaptive chirp mode decomposition (ACMD) and generalized dispersive mode decomposition (GDMD) have attracted much attention in various fields. However, these methods are difficult to simultaneously separate chirp components and dispersive components. This paper proposes a variational generalized nonlinear mode decomposition (VGNMD) framework to address this issue. The VGNMD first introduces an adaptive time–frequency fusion and clustering (ATFFC) scheme to improve noise robustness and resolution of time–frequency distribution (TFD) of signal in a noisy environment and to accurately obtain the TFD of each mode. Then, a mode-type discrimination criterion is established to categorize modes into chirp modes or dispersive modes based on their time–frequency (TF) ridges. Finally, with these TF ridges as initial instantaneous frequencies (IFs) or initial group delays (GDs), a variational optimization algorithm is applied to accurately reconstruct the modes and refine their IFs or GDs. Simulated examples and real-life applications to bat echolocation signal analysis and railway wheel/rail fault diagnosis are considered to show the effectiveness of the VGNMD. The results indicate that the proposed approach can accurately extract chirp modes and dispersive modes simultaneously, and is well-suitable for analyzing nonlinear signals with discontinuous TF patterns.

Automated Variational Nonlinear Chirp Mode Decomposition for Bearing Fault Diagnosis

The variational non-linear chirp mode decomposition (VNCMD) requires initialization of number of modes (NMs) and instantaneous frequency (IF). This paper proposes an automated method for NM selection and IF initialization which works on the scale-space representation based automated boundary detection in magnitude spectrum (MS). The proposed automated VNCMD (AVNCMD) method is applied for bearing fault detection in which the kurtosis based dominant mode selection method is recommended. The instantaneous amplitude (IA) and IF with spectral entropy are computed from the dominant mode. Features are given to feed forward neural network classifier. Methodology is investigated on two datasets for inner race, outer race, and ball race faults detection. The proposed method classifies inner race, outer race, and ball race bearing faults with 97.52% accuracy and classifies inner race and outer race bearing fault with 100% accuracy. Efficacy of the proposed method is compared with the existing methods to justify the superiority.

An adaptive VNCMD and its application for fault diagnosis of industrial sewing machines

Due to the non-linearity and non-stationarity of sound signals from complex transmission structure and frequent start-stop of industrial equipment, such as sewing machine, its incipient faults cannot be accurately identified with classical fault diagnosis methods. Therefore, a new fault diagnosis method with an adaptive variational nonlinear chirp mode decomposition (AVNCMD) is proposed. Firstly, a pre-processing step of convex optimization with generalized minimax-concave penalty function and spline-kernelled chirplet transform is applied to obtain the time–frequency distribution (TFD) with energy concentration, and a peak frequency extension method is proposed to adaptively search initial instantaneous frequencies of AVNCMD on the TFD; then the Pearson correlation coefficient is introduced as the termination condition of the adaptive signal decomposition. Secondly, multi-domain features are extracted from the decomposed nonlinear chirp modes, and an optimal features set is constructed by the feature preference method of an improved ReliefF. Finally, the fault classification is realized by the extreme learning machine, whose input weights and biases are optimized via the salp swarm algorithm. The AVNCMD is testified to be accurate in simulation with nonlinear amplitude modulation–frequency modulation signals and be effective in actual sound signals of industrial sewing machines on four different states. Through the detailed analysis of the measured sound signals in factory, the proposed fault diagnosis method can identify four states of the industrial sewing machines with an overall identification accuracy of 95.0%.

A novel variational nonlinear chirp mode decomposition-based critical brain-region investigation for automatic emotion recognition

The field of affective computing that deals with emotion recognition from physiological information, particularly electroencephalography (EEG), is becoming more and more important. Researchers have employed these signals to identify emotions, but the majority of them only distinguish a limited number of emotional states (e.g. happiness, fear, sadness, calmness, anger, etc.). This study outlines the proposed model for classifying nine emotional states from the DREAMER database into arousal, valence, and dominance dimensions using a discrete scale. To create it, we studied variational non-linear chirp mode decomposition (VNCMD) to decompose the EEG signals into five distinct modes. 11 entropy features were extracted from each mode. Then a comparative analysis of six popular machine learning-based classifiers was performed. The VNCMD's third mode with a rotational random forest classifier gave the best performance parameters for this application. This systematic analysis revealed that the best brain region, i.e., the anterior frontal area using only 2 channels, provided the highest accuracy and F1-score for arousal: 96.07% and 97.30%, valence: 94.49% and 95.58%, and dominance: 95.83% and 97.19% categories. Results, using the DREAMER dataset, show that our model can have the highest predictive ability with AUCs of 0.98, 0.98, and 0.97 for the arousal, valence, and dominance categories, respectively. The findings of this study demonstrate that the features, brain regions, and machine learning models commonly employed in emotion classification tasks may be used in more difficult tasks, like the prediction of precise values for arousal, valence, and dominance.

An Enhanced Adaptive Chirp Mode Decomposition for Instantaneous Frequency Identification of Time-Varying Structures

An Enhanced Adaptive Chirp Mode Decomposition for Instantaneous Frequency Identification of Time-Varying Structures