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Representation learning (RL) has gained increasingly considerable attention in intelligent fault diagnosis due to its great capability of automatically learning useful features. Most existing studies focus on developing various variants about RL through modifying loss function of original versions, whereas it is a challenging task. Using the promising sparse filtering as the basic module, this paper presents a simple and effective RL method called multi-scale and multi-pooling sparse filtering (MSMPSF). Instead of modifying loss function of sparse filtering, we simply introduce two fusion mechanisms into sparse filtering, i.e., multi-scale fusion and multi-pooling fusion. In detail, the former aims to learn different local features from the collected signals under multiple scales. The latter tries to fuse various local features using multiple poolings. With these two mechanisms, MSMPSF is capable of capturing complementary fault information hidden in raw signals of several scales and obtaining richly informative feature representations, hence it can perform better. The proposed method is evaluated through experiments on three datasets about gear and bearing. Extensive comparison results confirm that both of two mechanisms facilitate a significant improvement on diagnosis performance. Furthermore, our method receives very reliable and competitive results in terms of diagnosis accuracy and stability in comparison with existing related works.

In most practical applications of fault diagnosis methods, two problems will inevitably arise. First, limited by the monitored object itself and its environment, accelerators are difficult to install. Second, industrial applications lack data with fault labels, which limits the use of data-driven-based methods. To solve these problems, a current signal-based adaptive semisupervised framework (C-ASSF) is proposed. In C-ASSF, the Wasserstein generative adversarial network with gradient penalty (WGAN-GP) is adopted to extract recognizable features from only normal current signals. Subsequently, since WGAN-GP pays too much attention to body signals and ignores the changes caused by faults, the line spectrum feature extraction (LSFE) technique is utilized to remove the main frequency component of the current signal specifically. Finally, an index indicating the degree of deviation from the normal distribution is introduced to identify external bearing faults in drivetrains. Two groups of different experimental data sets are applied to verify the performance of C-ASSF. The results show that C-ASSF is superior to existing methods, such as self-organizing map (SOM) and stack autoencoder (SAE), and can not only identify faults in drivetrains but also identify different fault classes.

Playing a vital role in the safe operation of equipment, intelligent fault detection has been extensively applied in mechanical systems. However, the complicated mapping of signal symptoms and multicomponent failure modes under sharp speed variation makes it hard. The classification error is large due to insufficient samples in the fault condition. Aiming at these problems, a novel multitask redundant lifting adversarial network (MRLAN) is proposed. First, inspired by redundant second-generation wavelet transform, a reconstruction network is established to generate high-quality time–frequency representation of vibration signal, thus eliminating speed fluctuations and expanding training samples. The reconstruction network consists of transposed convolution layer, resume update layer, resume predict layer, and merge layer. Then, multitask category discriminator, which forms dual discriminator together with distance discriminator, is constructed to separate the features of multiple components, thereby realizing multiple tasks (multicomponent fault location and single-component health assessment). Finally, the model is alternately optimized through adversarial process between the generation network and the double discriminators. The proposed method is validated by two cases and other methods are also established to show its superiority. The results show satisfactory performance of MRLAN in multicomponent fault diagnosis under sharp speed fluctuation and little training data.

The synchrosqueezing transform (SST) and its ameliorated methods can enhance the energy concentration of the vibration signals in time-frequency domain, but it does not show enough effect for the weak feature extraction. Besides, many large-scale rotating machines such as aerospace engines and gas engines often work under complex vibrations, and this increases the difficulty for health monitoring based on vibration signals. This article presents a time-frequency analysis (TFA) named bilateral second-order SST (BFSST2). It can sharpen the instantaneous frequencies (IFs) like second-order SST (FSST2), and more importantly, it can extract the weak features such as amplitude-modulation frequency-modulation IFs and small-amplitude time-varying IFs which are easily ignored on time-frequency plane. To achieve the aforementioned target, the IFs are first obtained by employing FSST2, and then a bilateral function representing a novel negative-positive TFA is structured by combining the hyperbolic tangent function, exponential function, and sign function together. After that the large-amplitude IFs are transformed into small-negative amplitude ones by the product with the bilateral function, and this can not only enhance the original weak feature but also avoid its confusion with the transformed small-negative amplitude ones. The proposed BFSST2 is validated by a numerical simulation. At last, two case studies are given to illustrate its effectiveness in aerospace engine vibration monitoring.

Fault identification for bearings of special electromechanical equipment is significant to avoid catastrophic accidents. However, spectral aliasing and nonstationarity resulted from variable speed condition make this task difficult. In this paper, a modified self-organizing maps (SOM) based on nonlinear neural weight updating way is proposed to solve the problem of bearing fault severity identification in variable speed condition. Firstly, a multi-domain features extraction method based on angular re-sampling technique is introduced. Then considering the nonlinear relationship between fault severity and fault features, the traditional Euclidian distance of SOM is substituted with the geodesic distance when update the neural weight and select the best-matching cell, which can improve the nonlinear identification ability of proposed method. Finally, two cases are performed and the results show that the method can identify bearing fault with different severities effectively and have practical significance when considering both accuracy and time cost compared with other methods.

This paper proposes a pattern recognition method for the fault diagnosis of machinery based on an enhanced trace ratio linear discriminant analysis (ETR-LDA) algorithm. It is an extension of TR-LDA that pursues to maximize the between-class distance and minimize the within-class distance. Since TR-LDA focuses on the total between-class distance and ignores the attention to local features, it may lead to deficiencies in the classification of specific patterns/classes, which is defined as short board in this paper. To cope with this limitation, the proposed ETR-LDA makes a reconsideration of the relationship between the total between-class distance and the global separability. More specifically, a new objective function is derived in ETR-LDA by taking the smallest between-class distance into account. The optimal solution of this objective function is proved to improve the smallest between-class distance with no change to the convergence and the global optimality of the algorithm, and the separability of different classes is increased eventually. Both synthetic data and hard disk drive wearing experimental data are employed to verify the efficiency of the proposed method. The results show that ETR-LDA is able to distinguish those fault categories and outperform TR-LDA and other dimensionality reduction methods.

It has been challenging to correctly separate sources from their mixtures with large noise and unknown source number in underdetermined cases. To address this problem, a novel underdetermined blind source separation (UBSS) method is proposed using synchrosqueezing transform (SST) and improved density peaks clustering (DPC). First, SST is employed to reassign time-frequency (TF) coefficients of short time Fourier transform (STFT) of mixed signals from their original position to the center of gravity along frequency direction, contributing to sparser TF representation than STFT. Second, a single source point (SSP) identification method is proposed by directly searching the identical normalized TF vectors, which considers linear representation relations among TF vectors and therefore can identify SSPs more accurately in noisy cases. Third, DPC is improved to automatically identify source number, with which the mixing matrix can be estimated. After that, sources are finally recovered using l1-norm decomposition method. The effectiveness of the proposed method is validated with some numerical studies and experimental studies. The results show that the proposed method can estimate source number correctly, and recover sources accurately even in noisy cases.

To accurately estimate source signals from their post-nonlinear mixtures, a post-nonlinear blind source separation (PNLBSS) method with kurtosis constraints is proposed based on augmented Lagrangian particle swarm optimization (PSO). First, an improved contrast function is presented by combining mutual information of the separated signals and kurtosis ranges of source signals. Second, an augmented Lagrangian multiplier method is used to convert PNLBSS into an unconstrained pseudo-objective optimization problem. Then, improved PSO is applied to update the parameters in complex nonlinear spaces. Finally, numerical case studies and experimental case studies are provided to evaluate the performance of the proposed method. By adding the kurtosis ranges constraints, the estimation accuracy of source signals could be improved, which would benefit vibration and acoustic monitoring and control.

Tacholess order tracking (TLOT) is a promising tool for mechanical fault diagnosis in speed variation conditions without a tachometer. However, TLOT is still a challenging task due to the inaccurately acquired instantaneous phase of shaft and noise corrupted resample signal in angle domain. Therefore, an improved TLOT technique is proposed in this paper to deal with those limitations for mechanical fault feature extraction. In this method, the modified numerical integration (MNI) algorithm is proposed to estimate the instantaneous phase by integrating instantaneous frequency (IF), which is estimated by a time-frequency representation (TFR) approach. During the MNI, Romberg integration is investigated and performed to improve the estimated accuracy of instantaneous phase. Subsequently, a flexible synchronous average (FSA) algorithm based on Chirp-Z transform in angle domain is further employed to reduce noise interference for the resampled signal. The effectiveness and efficiency of the improved TLOT technology is verified by both simulations and experiments. Analysis results show that the proposed method has an outstanding performance for the mechanical fault diagnosis in the condition of speed fluctuation.

This paper presents an intelligent combustion fault diagnosis approach for V-type marine diesel engines with uneven firing intervals based on the instantaneous crankshaft speed (ICS). First, experimental ICSs of a 16-cylinder marine diesel engine under normal and different degrees of fault conditions are investigated to obtain the most sensitive fault features. A new polar representation method named cyclic-polar-map (CPM) is proposed to effectively demonstrate the fault features. The quantitative radii of the CPM are used to indicate the location and degree of fault. Then, a support vector machine (SVM)-based intelligent fault diagnosis system is developed for automatically detecting the combustion faults with the features extracted from the proposed CPM and the frequency analysis of ICS. In addition, for the SVM training set is not always available in practice, a dynamic model of the crankshaft system is developed to simulate different fault patterns. Finally, the efficiency of the proposed intelligent diagnosis approach is validated by experimental data. The results show that the proposed SVM-based intelligent diagnosis system using both CPM features and frequency domain features of the ICS can obtain good accuracies under different fault degrees at various speed and load conditions.

Remaining useful life (RUL) is a critical metric in prognostics and health management (PHM) because it reflects the future health status and fault progression of products. Most RUL estimation methods are based on degradation data. In practice, due to changing degradation mechanisms during products’ whole life cycle, the degradation data may consist of two or more distinct phases, and the time points of these mechanisms switching are usually nondeterministic. This property makes RUL estimation a difficult task. To solve this problem, this paper proposes a switchable state-space degradation model to characterize degradation paths with nondeterministic switching manner dynamically. To update the model parameters by newly available data, a novel statistical procedure based on Rao-Blackwellized filter/smoother and an expectation maximization algorithm is derived. To improve the robustness and efficiency of the RUL prediction, a semianalytic prediction model is developed, which can avoid significant fluctuation in RUL estimation. The developed methodologies can automatically track different degradation phases and adaptively update parameters related to prior distributions. Two real products degradation cases are used to verify our methodologies.

This paper proposes a vibration modeling method for a rotating blade with breathing cracks, considering the coupling of the centrifugal effects, the breathing effects and the crack effects. Firstly, considering the combined effects of the centrifugal stress and the bending stress, a crack breathing model for the rotating blade is proposed. Since the crack surface cannot provide the spanwise centrifugal tensile stress, an additional bending moment will be generated at the crack surface in the rotating state. Therefore, an additional bending moment caused by the centrifugal stress is then constructed. In addition, due to the discontinuity of the crack cross section, the additional stiffness caused by the centrifugal effects of the cracked blade will be smaller than that of the normal blade. Therefore, a correction coefficient of the centrifugal stiffness is built. Furthermore, based on the Lagrange equation and the assumed modal method, the vibration equation of the rotating blade with a breathing crack is established (RBC model), and a strategy is constructed for solving this vibration equation. Finally, taking the finite element model (FEM) as a reference, the vibration responses of the RBC model, the open crack model (OC) and the bilinear crack model (BC) are compared. The necessity of the RBC model is illustrated, and the accuracy of the RBC model is verified. The RBC model is a computationally efficient alternative to the finite element analysis for the rotating cracked blade. It can provide an important tool for the vibration modeling and the vibration analysis of the rotating shaft-disk-blade system with cracked blades.

Tacho-less order tracking (TLOT) is an effective technique to address the surveillance and diagnosis of mechanical fault on speed variation conditions without tachometers. Nevertheless, fault diagnosis with sharp speed fluctuations is still a challenging task, since the accurate instantaneous frequency (IF) cannot be obtained from the acquired condition signals. In this work, a modified TLOT method based on nonlinear compensating demodulation transform (NCDT) is proposed for fault diagnostics in extreme condition monitoring of machinery. During NCDT, the demodulation functions based on opposite cubic polynomial are investigated and performed to improve IF estimation. Then, a regression filter (RF) is employed to extract the interested harmonic component according to the estimated IF and instantaneous bandwidth for signal resampling. Finally, order spectrum analysis is used to analyze the resampled signal for mechanical fault diagnosis. Simulations, experiments and industrial cases are given to verify the effectiveness and efficiency of the proposed method. The results are as effective as those obtained by tacho-based method under sharp speed fluctuation.

The mechanically guided assembly that relies on the compressive buckling of strategically patterned 2D thin films represents a robust route to complex 3D mesostructures in advanced materials and even functional micro-devices. Based on this approach, formation of complex 3D configurations with suspended curvy features or hierarchical geometries remains a challenge. In this paper, we incorporate the prestrained shape memory polymer in the 2D precursor design to enable local rolling deformations after the mechanical assembly through compressive buckling. A theoretical model captures quantitatively the effect of key design parameters on local rolling deformations. The combination of precisely controlled global buckling and local rolling expands substantially the range of accessible 3D configurations. The combined experimental and theoretical studies over a dozen of examples demonstrate the utility of the proposed strategy in achieving complex reprogrammable 3D mesostructures.

With the increasing distance and time of voyage, condition monitoring and fault diagnosis of shipborne antenna play a crucial role in ship communication for navigation safety. However, it is still a challenging task to identify the hidden shipborne antenna fault from practical sensor-dependent vibration signals since the vibration features are always multi-modulated and submersed by heavy noise. Therefore, autonomous variational mode decomposition (AVMD) based on Independence-oriented Variational Mode Decomposition (IOVMD) and the Largest Lyapunov Exponent (LLE) criterion is proposed in this paper. First, the signal is decomposed into Intrinsic Mode Functions (IMFs) by IOVMD. Second, LLE of modes is calculated to measure fault information degree and then modes without fault features are eliminated. The combination rule is also defined and modes are combined orderly to enhance the fault feature expression. Then, an index structured by Kurtosis and LLE of combined signals is calculated and the combined signal is selected for demodulation. Finally, the combined signal is analyzed for fault identification by Hilbert Demodulation. A simulation and two cases show the effectiveness and superiority of the proposed method.

The key challenge of intelligent fault diagnosis is to develop features that can distinguish different categories. Because of the unique properties of mechanical data, predetermined features based on prior knowledge are usually used as inputs for fault classification. However, proper selection of features often requires expertise knowledge and becomes more difficult and time consuming when volume of data increases. In this paper, a novel deep learning network (LiftingNet) is proposed to learn features adaptively from raw mechanical data without prior knowledge. Inspired by convolutional neural network and second generation wavelet transform, the LiftingNet is constructed to classify mechanical data even though inputs contain considerable noise and randomness. The LiftingNet consists of split layer, predict layer, update layer, pooling layer, and full-connection layer. Different kernel sizes are allowed in convolutional layers to improve learning ability. As a multilayer neural network, deep features are learned from shallow ones to represent complex structures in raw data. Feasibility and effectiveness of the LiftingNet is validated by two motor bearing datasets. Results show that the proposed method could achieve layerwise feature learning and successfully classify mechanical data even with different rotating speed and under the influence of random noise.

Transverse breathing cracks are a primary damage mode in rotor systems and seriously influence the safety and reliability of equipment operation. The vibration characteristics exhibited by cracked rotors when passing through critical speeds serve as important evidence in the diagnosis of cracks, and a breathing mechanism model without weight dominance is needed to study these resonant characteristics. In this work, a restoring force modified model is proposed for studying the breathing mechanism of cracked Jeffcott rotors without weight dominance. Furthermore, a novel phase waterfall plot method that can identify frequency components with weak amplitudes is proposed to analyze the vibration response characteristics of cracked Jeffcott rotors. Numerical and experimental studies indicate that the phase waterfall plots effectively recognize the weak characteristic frequencies of cracked rotors. This study can also provide references for the crack monitoring of rotor systems.

Rolling contact fatigue is the main failure mechanism of tapered roller bearings. This study investigated the fatigue mechanism of rollers in a tapered roller bearing that failed in a run-to-failure test. Roller microstructure and crack morphology were investigated through scanning electron microscopy. A microhardness test was performed to investigate the strain hardening of the roller material induced by rolling contact fatigue. Results showed that microcavities and holes are important influential factors of crack initiation and propagation. Crack propagation angle affects crack morphology and propagation mode. Material strain hardening accelerates crack growth. Furthermore, roller misalignment causes uneven hardenability and severe damage to roller ends.

Fault characteristic frequency extraction is an important means for the fault diagnosis of rotating machineries. Traditional signal processing methods commonly use the amplitude information of signals to detect damages. However, when the amplitudes of characteristic frequencies are weak, the recognition effects of traditional methods may be unsatisfactory. Therefore, this paper proposes the phase-based enhanced phase waterfall plot (EPWP) method and frequency equal ratio line (FERL) method for identifying weak harmonics. Taking a cracked rotor as an example, the characteristic frequency detection performances of the EPWP and FERL methods are compared with that of the traditional signal processing methods namely fast Fourier transform, short-time Fourier transform, discrete wavelet transform, continuous wavelet transform, ensemble empirical mode decomposition, and Hilbert–Huang transform. Research results demonstrate that the effects of EPWP and FERL for the recognitions of weak harmonics which are contained in steady signals and transient signals are better than that of the traditional signal processing methods. The accurate identification of weak characteristic frequencies in the vibration signals can provide an important reference for damage detections and improve the diagnostic accuracy.

Effective condition monitoring of diesel engine can ensure the reliability of large-power machines and prevent catastrophic consequences. Cylinder pressure is capable of reflecting the whole combustion process of diesel engine, and hence can help to identify the malfunctions of the diesel engine during operation. In this paper, a graphic pattern feature-mapping method is proposed for graphic pattern feature recognition in data-driven condition monitoring. The graphic feature extraction and recognition are linked by labeled feature-mapping. It is used for identifying the running condition of the diesel engine via analyzing the cylinder pressure signal of the diesel engine. The different types of the malfunctions which are caused by different parts of the diesel engine such as induction system, valve actuating mechanism, fuel system, fuel injection system, etc. can be identified just by cylinder pressure signal. The bench experiment of a large-power diesel engine is performed to validate this graphic pattern recognition method. The results show that it has good accuracy on multi-malfunction identification and classification when the engine operates at one speed and one load.

Unbalance is an inevitable issue in rotating machineries due to the manufacturing tolerances, the assembly errors, the damage in rotating components, etc. The effects of unbalance on the nonlinear dynamics of cracked rotors are investigated in this paper. In order to overcome the assumption of weight dominance, 3D finite element models are employed to discretize the rotor and several contact pairs are defined on the cracked surfaces to simulate the intermittent breathing behavior of crack. Then, the complex free interface component mode synthesis method (CMS) is employed to reduce the model’s order and to increase the computational efficiency. Finally, the obtained models are used to study the effects of concentrated and distributed unbalances on the nonlinear dynamic response of cracked rotors. The results show that the unbalance can significantly affect the breathing mechanism of crack and consequently dramatically change the rotor’s dynamic behaviors. Moreover, the different levels and orientations of unbalance lead to obviously different results. Besides, the responses of rotors with two asymmetric distributed unbalance are similar to those of rotors with a single concentrated unbalance though the rotors are overall balanced.

The nonlinearity in complex equipment, such as turbofan engine and electric motor, is a substantial factor. The nature of complex equipment deterioration refers to a nonlinear deterioration process. An unsupervised feature extraction method based on greedy kernel principal components analysis (GKPCA) is proposed for nonlinear deterioration process under multi dimensional no-label signals. The 21 signals of turbofan engine and 6 signals of electric motor are analyzed using the method, respectively. The results show that: taking the first component as deterioration feature of complex equipment in system-level is appropriate; the more exact deterioration features with better performance in monotonicity, robustness and computation speed, are identified from GKPCA-PC1, thus the features can be used for online monitoring and warning of complex equipment; the unsupervised feature extraction method considering nonlinearity is more effective and efficiency for deterioration level identification and health management such as adding lubricant grease at optical time to prevent Over-alarm. The results verify the effectiveness and efficiency of the method in dealing with nonlinearity in deterioration feature extraction of complex equipment. Through the study, it reveals that considering the substantial nonlinearity in complex equipment is important for extracting more exact deterioration feature under multi dimensional no-label signals.

Both the model-based and data-driven techniques for fault detection have their merits and drawbacks. The fault detection systems are usually laid out separately with the health monitoring systems in practice. In this paper, the well-established observer-based residual generator is formulated to construct multiple evaluation functions which are employed as the classification features of the support vector machine (SVM) for fault detection. It can be regarded as a tentative approach to combine the model-based and data-driven methods to enhance the fault detection performance. The standard SVM is modified for fault detection to achieve the quantitative tradeoff between false alarm rate and fault detection rate. In Addition, this paper also provides a unified framework for fault detection and health monitoring based on the SVM. Simulations on the ship propulsion system show the effectiveness of the proposed method.

To reveal the mechanism of head-disk interface wear behaviors, this paper proposed a novel transformation on slider's vibration signals, which was derived to having a strong correlation with the slider wear. Based on the modal analysis, the high-frequency component was regarded as the air bearing mode while the low-frequency corresponds to the structure (suspension related) mode. Both structure and air bearing mode dissipated energies were extracted and the correlation analysis between the energy and wear volume verified the proportional relationship. Finally, regression analysis was employed to establish the linear model for wear and energy. This paper helps understand the wear mechanisms of slider from the interface dynamics response's view, and then provides a novel quantitative analysis approach for slider wear identification.

Complex equipment deterioration refers to a nonlinear multistate deterioration process, where the deterioration curve may not follow a typical shape such as exponential or linear function. A general solution is presented to nonlinear multistate deterioration modeling for deterioration level assessment and remaining useful life prognostics under no-label lifetime data including multi signals. In the solution, a three layer nonlinear multistate deterioration model of complex equipment is established based on hyper-parameter optimization. Hyper-parameter I and M, which determine the first two layers, are optimized by the proposed unsupervised extraction method based on greedy kernel principal components analysis and the improved Mann–Kendall criterion, respectively. As a determinant of the third layer, hyper-parameter N is optimized by the improved Bayesian information criterion to obtain optimized model, when parameters have been estimated under each alternative model structure at different N. The no-label lifetime dataset of turbofan engines are adopted for case study, and more accurate deterioration level and remaining useful life are obtained. The results verify the effectiveness of the presented solution. The study indicates that: nonlinearity makes an important effect on multistate deterioration modeling through hyper-parameters; the solution deals with nonlinearity in a systematic manner by hyper-parameter optimization of three layers.

The gearbox of a wind turbine (WT) has dominant failure rates and highest downtime loss among all WT subsystems. Thus, gearbox health assessment for maintenance cost reduction is of paramount importance. The concurrence of multiple faults in gearbox components is a common phenomenon due to fault induction mechanism. This problem should be considered before planning to replace the components of the WT gearbox. Therefore, the key fault patterns should be reliably identified from noisy observation data for the development of an effective maintenance strategy. However, most of the existing studies focusing on multiple fault diagnosis always suffer from inappropriate division of fault information in order to satisfy various rigorous decomposition principles or statistical assumptions, such as the smooth envelope principle of ensemble empirical mode decomposition and the mutual independence assumption of independent component analysis. Thus, this paper presents a joint subspace learning-based multiple fault detection (JSL-MFD) technique to construct different subspaces adaptively for different fault patterns. Its main advantage is its capability to learn multiple fault subspaces directly from the observation signal itself. It can also sparsely concentrate the feature information into a few dominant subspace coefficients. Furthermore, it can eliminate noise by simply performing coefficient shrinkage operations. Consequently, multiple fault patterns are reliably identified by utilizing the maximum fault information criterion. The superiority of JSL-MFD in multiple fault separation and detection is comprehensively investigated and verified by the analysis of a data set of a 750 kW WT gearbox. Results show that JSL-MFD is superior to a state-of-the-art technique in detecting hidden fault patterns and enhancing detection accuracy.

In this paper, a wavelet-based periodic group-sparse signal denoising approach is proposed for detecting faults in rotary machines. The proposed approach exploits group sparsity in the wavelet domain. For this purpose, a periodicity-induced overlapping group shrinkage technique is utilized to threshold the wavelet coefficients. The wavelet coefficients are obtained by using the tunable Q-factor wavelet transform to decompose the measured vibration signals. The proposed approach is constrained to promote sparsity more strongly than convex regularization for estimating periodic group-sparse signals in noise, while avoiding nonconvex optimization. In addition, this maximally sparse convex approach has the advantage of preserving the oscillatory behavior of the useful fault features. A simulated signal is formulated to verify the performance of the proposed approach in periodic feature extraction. The detection performance of the proposed approach is compared with that of the comparative methods via root mean square error values. Finally, the proposed approach is applied to fault diagnosis of both experimental cases and engineering application. The processed results demonstrate that the proposed feature extraction technique can effectively detect the fault features from heavy background noise.

The ‘Test, Analyze and Fix’ process is widely applied to improve the reliability of a repairable system. In this process, dynamic reliability assessment for the system has been paid a great deal of attention. Due to instrument malfunctions, staff omissions and imperfect inspection strategies, field reliability data are often subject to interval censoring, making dynamic reliability assessment become a difficult task. Most traditional methods assume this kind of data as multiple normal distributed variables or the missing mechanism as missing at random, which may cause a large bias in parameter estimation. This paper proposes a novel method to evaluate and predict the dynamic reliability of a repairable system subject to interval-censored problem. First, a multiple imputation strategy based on the assumption that the reliability growth trend follows a nonhomogeneous Poisson process is developed to derive the distributions of missing data. Second, a new order statistic model that can transfer the dependent variables into independent variables is developed to simplify the imputation procedure. The unknown parameters of the model are iteratively inferred by the Monte Carlo expectation maximization (MCEM) algorithm. Finally, to verify the effectiveness of the proposed method, a simulation and a real case study for gas pipeline compressor system are implemented.

As one of most critical component of high-speed locomotive, wheel set bearing fault identification has attracted an increasing attention in recent years. However, non-stationary vibration signal with modulation phenomenon and heavy background noise make it difficult to excavate the hidden weak fault feature. Variational Mode Decomposition (VMD), which can decompose the non-stationary signal into couple Intrinsic Mode Functions adaptively and non-recursively, brings a feasible tool. However, heavy background noise seriously affects setting of mode number, which may lead to information loss or over decomposition problem. In this paper, an independence-oriented VMD method via correlation analysis is proposed to adaptively extract weak and compound fault feature of wheel set bearing. To overcome the information loss problem, the appropriate mode number is determined by the criterion of approximate complete reconstruction. Then the similar modes are combined according to the similarity of their envelopes to solve the over decomposition problem. Finally, three applications to wheel set bearing fault of high speed locomotive verify the effectiveness of the proposed method compared with original VMD, EMD and EEMD methods.

It is significant to perform condition monitoring and fault diagnosis on rolling mills in steel-making plant to ensure economic benefit. However, timely fault identification of key parts in a complicated industrial system under operating condition is still a challenging task since acquired condition signals are usually multi-modulated and inevitably mixed with strong noise. Therefore, a new data-driven mono-component identification method is proposed in this paper for diagnostic purpose. First, the modified nonlocal means algorithm (NLmeans) is proposed to reduce noise in vibration signals without destroying its original Fourier spectrum structure. During the modified NLmeans, two modifications are investigated and performed to improve denoising effect. Then, the modified empirical wavelet transform (MEWT) is applied on the de-noised signal to adaptively extract empirical mono-component modes. Finally, the modes are analyzed for mechanical fault identification based on Hilbert transform. The results show that the proposed data-driven method owns superior performance during system operation compared with the MEWT method.

Mechanically guided three-dimensional (3D) assembly based on the controlled buckling of pre-designed 2D thin-film precursors provides deterministic routes to complex 3D mesostructures in diverse functional materials, with access to a broad range of material types and length scales. Existing mechanics studies on this topic mainly focus on the forward problem that aims at predicting the configurations of assembled 3D structures, especially ribbon-shaped structures, given the configuration of initial 2D precursor and loading magnitude. The inverse design problem that maps the target 3D structure onto an unknown 2D precursor in the context of a prescribed loading method is essential for practical applications, but remains a challenge. This paper proposes a systematic optimization method to solve the inverse design of ribbon-type 3D geometries assembled through the buckling-guided approach. In addition to the torsional angle of the cross section, this method introduces the non-uniform width distribution of the initial ribbon structure and the loading mode as additional design variables, which can significantly enhance the optimization accuracy for reproducing the desired 3D centroid line of the target ribbon. Extension of this method allows the inverse design of entire 3D ribbon configurations with specific geometries, taking into account both the centroid line and the torsion for the cross section. Computational and experimental studies over a variety of elaborate examples, encompassing both the single-ribbon and ribbon-framework structures, demonstrate the effectiveness and applicability of the developed method.

At present, the axis orbit (whirling) and the instantaneous angular speed (spinning) are important symptoms in the condition monitoring of rotor systems. However, because of the lack of research of the transient characteristics of axis orbit within a whirl cycle, the axis orbit cannot reflect the instantaneous characteristics of the rotation during one whirling cycle like the instantaneous angular speed. Therefore, in this paper, a new concept of instantaneous whirling speed of axis orbit within a whirling cycle is proposed and defined. In addition, the transient characteristics of instantaneous whirling speed are studied. Meanwhile, the response mechanisms are qualitative analyzed through the study of the work of the additional stiffness excitation and the conversion relationship between the kinetic energy and the potential energy. Then, the minimum of the relative instantaneous whirling speed (RWS) is proposed as a potential monitoring index for crack severity. The instantaneous whirling speed is a new attribute of axis orbit and a new perspective for the vibration analysis of cracked rotors. The addition of this new attribute significantly increases the effect of axis orbit for distinguishing normal and cracked rotors. The new analysis perspective and the new diagnosis index are potential supplements for crack diagnosis.

State-of-health (SOH) is an important index indicating the batterys energy storage performance and health condition. However, the volume of SOH is highly dependent on the batterys initial capacity rather than the current capacity. Consequently, it is intractable to infer the SOH of batteries with missing data. In this paper, we propose a dynamic Peukerts law-based battery SOH estimation method. The dynamic Peukerts law correlates capacity loss with Peukerts coefficient, and eliminates the degradation inconsistency and is applicable for the same type of battery. Since the Peukerts coefficient can be calculated by multi-discharging test, the SOH is able to be estimated directly, and therefore, the limitation of data missing is overcome.

To identify the major vibration and radiation noise, a source contribution quantitative estimation method is proposed based on underdetermined blind source separation. First, the single source points (SSPs) are identified by directly searching the identical normalized time-frequency vectors of mixed signals, which can improve the efficiency and accuracy in identifying SSPs. Then, the mixing matrix is obtained by hierarchical clustering, and source signals can also be recovered by the least square method. Second, the optimal combination coefficients between source signals and mixed signals can be calculated based on minimum redundant error energy. Therefore, mixed signals can be optimally linearly combined by source signals via the coefficients. Third, the energy elimination method is used to quantitatively estimate source contributions. Finally, the effectiveness of the proposed method is verified via numerical case studies and experiments with a cylindrical structure, and the results show that source signals can be effectively recovered, and source contributions can be quantitatively estimated by the proposed method.

This paper addresses the problem of extracting periodic oscillatory features in vibration signals for detecting faults in rotating machinery. To extract the feature, we propose an approach in the short-time Fourier transform (STFT) domain where the periodic oscillatory feature manifests itself as a relatively sparse grid. To estimate the sparse grid, we formulate an optimization problem using customized binary weights in the regularizer, where the weights are formulated to promote periodicity. In order to solve the proposed optimization problem, we develop an algorithm called augmented Lagrangian majorization–minimization algorithm, which combines the split augmented Lagrangian shrinkage algorithm (SALSA) with majorization–minimization (MM), and is guaranteed to converge for both convex and non-convex formulation. As examples, the proposed approach is applied to simulated data, and used as a tool for diagnosing faults in bearings and gearboxes for real data, and compared to some state-of-the-art methods. The results show that the proposed approach can effectively detect and extract the periodical oscillatory features.

Compound-fault diagnosis of mechanical equipment is still challenging at present because of its complexity, multiplicity and non-stationarity. In this work, an adaptive redundant multiwavelet packet (ARMP) method is proposed for the compound-fault diagnosis. Multiwavelet transform has two or more base functions and many excellent properties, making it suitable for detecting all the features of compound-fault simultaneously. However, on the other hand, the fixed basis function used in multiwavelet transform may decrease the accuracy of fault extraction; what’s more, the multi-resolution analysis of multiwavelet transform in low frequency band may also leave out the useful features. Thus, the minimum sum of normalized multifractal entropy is adopted as the optimization criteria for the proposed ARMP method, while the relative energy ratio of the characteristic frequency is utilized as an effective way in automatically selecting the sensitive frequency bands. Then, The ARMP technique combined with Hilbert transform demodulation analysis is then applied to detect the compound-fault of bevel gearbox and planetary gearbox. The results verify that the proposed method can effectively identify and detect the compound-fault of mechanical equipment.

Prognostics of the remaining useful life (RUL) has emerged as a critical technique for ensuring the safety, availability, and efficiency of a complex system. To gain a better prognostic result, degradation information is quite useful because it can reflect the health status of a system. However, due to the lack of accurate information about the plants’ degradation, the prognostic model is usually not well established. To solve this problem, this paper proposes a two-stage strategy that is in the context of data-driven modeling to predict the future health status of a bearing, where the degradation information was estimated by calculating the deviation of multiple statistics of vibration signals of a bearing from a known healthy state. Then, a prediction stage based on an enhanced Kalman filter and an expectation–maximization algorithm were used to estimate the RUL of the bearing adaptively. To verify the effectiveness of the proposed approach, a real-bearing degradation problem was implemented.

Due to the multi-modulation feature in most of the vibration signals, the extraction of embedded fault information from condition monitoring data for mechanical fault diagnosis still is not a relaxed task. Despite the reported achievements, Wavelet transform follows the dyadic partition scheme and would not allow a data-driven frequency partition. And then Empirical Wavelet Transform (EWT) is used to extract inherent modulation information by decomposing signal into mono-components under an orthogonal basis and non-dyadic partition scheme. However, the pre-defined segment way of Fourier spectrum without dependence on analyzed signals may result in inaccurate mono-component identification. In this paper, the modified EWT (MEWT) method via data-driven adaptive Fourier spectrum segment is proposed for mechanical fault identification. First, inner product is calculated between the Fourier spectrum of analyzed signal and Gaussian function for scale representation. Then, adaptive spectrum segment is achieved by detecting local minima of the scale representation. Finally, empirical modes can be obtained by adaptively merging mono-components based on their envelope spectrum similarity. The adaptively extracted empirical modes are analyzed for mechanical fault identification. A simulation experiment and two application cases are used to verify the effectiveness of the proposed method and the results show its outstanding performance.

The implementation of condition monitoring and fault diagnosis system (CMFDS) on wind turbine is significant to lower the unscheduled breakdown. Generator is one of the most important components in wind turbine, and generator bearing fault identification always draws lots of attention. However, non-stationary vibration signal of weak fault and compound fault with a large amount of background noise makes this task challenging in many cases. So, effective signal processing method is essential in the accurate diagnosis step of CMFDS. As a novel signal processing method, empirical Wavelet Transform (EWT) is used to extract inherent modulation information by decomposing signal into mono-components under an orthogonal basis, which is seen as a powerful tool for mechanical fault diagnosis. Moreover, in order to avoid the inaccurate identification the internal modes caused by the heavy noise, wavelet spatial neighboring coefficient denoising with data-driven threshold is applied to increase Signal to Noise Ratio (SNR) before EWT. The effectiveness of the proposed technique on weak fault and compound fault diagnosis is first validated by two experimental cases. Finally, the proposed method has been applied to identify fault feature of generator bearing on wind turbine in wind farm successfully.

As a significant role in industrial equipment, rotating machinery fault diagnosis (RMFD) always draws lots of attention for guaranteeing product quality and improving economic benefit. But non-stationary vibration signal with a large amount of noise on abnormal condition of weak fault or compound fault in many cases would lead to this task challenging. As one of the most powerful non-stationary signal processing techniques, wavelet transform (WT) has been extensively studied and widely applied in RMFD. Numerous publications about the study and applications of WT for RMFD have been presented to academic journals, technical reports and conference proceedings. Many previous publications admit that WT can be realized by means of inner product principle of signal and wavelet base. This paper verifies the essence on inner product operation of WT by simulation and field experiments. Then the development process of WT based on inner product is concluded and the applications of major developments in RMFD are also summarized. Finally, super wavelet transform as an important prospect of WT based on inner product are presented and discussed. It is expected that this paper can offer an in-depth and comprehensive references for researchers and help them with finding out further research topics.

Fault identification timely of rolling mill drivetrain is significant for guaranteeing product quality and realizing long-term safe operation. So, condition monitoring system of rolling mill drivetrain is designed and developed. However, because compound fault and weak fault feature information is usually sub-merged in heavy background noise, this task still faces challenge. This paper provides a possibility for fault identification of rolling mills drivetrain by proposing customized maximal-overlap multiwavelet denoising method. The effectiveness of wavelet denoising method mainly relies on the appropriate selections of wavelet base, transform strategy and threshold rule. First, in order to realize exact matching and accurate detection of fault feature, customized multiwavelet basis function is constructed via symmetric lifting scheme and then vibration signal is processed by maximal-overlap multiwavelet transform. Next, based on spatial dependency of multiwavelet transform coefficients, spatial neighboring coefficient data-driven group threshold shrinkage strategy is developed for denoising process by choosing the optimal group length and threshold via the minimum of Stein’s Unbiased Risk Estimate. The effectiveness of proposed method is first demonstrated through compound fault identification of reduction gearbox on rolling mill. Then it is applied for weak fault identification of dedusting fan bearing on rolling mill and the results support its feasibility.

The electrostatic force at head–disk interface (HDI) becomes increasingly significant when the head–disk clearance is dropping into 1 nm scheme. Therefore, detecting and eliminating the electric potential in the HDI is a critical task for hard disk drives. To that end, this paper proposed an in situ measurement method for electric potential at HDI using a thermal asperity (TA) sensor. When calibrating the electric potential, both dc and ac components of the external voltage were supplied to the disk. As a result, the output of the TA sensor to the first harmonic of the ac component was linearly increasing with the decrease in the dc components. Experimental results show that this method is more efficient and flexible than the traditional methods.

Recently, to achieve a stable slider dynamics and a high recording density, a contact (lubricant surfing) recording scheme has been proposed in the literature. However, under contact/surfing condition, the interaction between the head and the disk may bring new tribological issues, which has not been fully understood so far. To amend that, this paper experimentally investigates the relation between the interfacial dynamics and the wear behaviors of head/disk at different contact conditions. To investigate the interfacial dynamics, slider was then flown at different contact stages, and slider vibrations in both the vertical and the downtrack directions were monitored using two laser Doppler vibrometers. The wear depth of slider was inspected after the experiment to correlate interfacial dynamics at different contact stages. According to our results, a severe contact is not necessary to generate serious wear, which has strong correlation with the interfacial dynamics. Compared with the structure modes, the air-bearing modes were found to have a dominant impact on slider wear. Moreover, nonlinear vibration has a much more detrimental effect on the slider wear, although this type of vibration accompanies small amplitude at high-frequency band. This paper helps understand the wear mechanisms of slider under different slider/disk contact conditions, and thus expands new designs for surfing/contact recording technologies.

The escalator is one of the most popular travel methods in public places, and the safe working of the escalator is significant. Accurately predicting the escalator failure time can provide scientific guidance for maintenance to avoid accidents. However, failure data have features of short length, non-uniform sampling, and random interference, which makes the data modeling difficult. Therefore, a strategy that combines data quality enhancement with deep neural networks is proposed for escalator failure time prediction in this paper. First, a comprehensive selection indicator (CSI) that can describe the stationarity and complexity of time series is established to select inherently excellent failure sequences. According to the CSI, failure sequences with high stationarity and low complexity are selected as the referenced sequences to enhance the quality of other failure sequences by using dynamic time warping preprocessing. Secondly, a deep neural network combining the advantages of a convolutional neural network and long short-term memory is built to train and predict quality-enhanced failure sequences. Finally, the failure-recall record of six escalators used for 6 years is analyzed by using the proposed method as a case study, and the results show that the proposed method can reduce the average prediction error of failure time to less than one month.

With the increasing distance and time of voyage, component maintenance of shipborne antenna plays a crucial role in ship communication for navigation safety. However, most maintenance strategy studies which only focus on reducing maintenance cost or improving operating revenue are not applicable for transmission system of shipborne antenna. Therefore, a multiple-component maintenance policy for shipborne antenna is proposed to maximize the operating revenue under the requirement of the antenna's availability in this paper. First, the maintenance model based on performance-guided policy is built, and the relevant maintenance parameters are derived under the special working condition of shipborne antenna. Second, three criterions, including maintenance cost, system availability and system operating revenue, are structured to assess the proposed model's performance. Then, the policy iteration method is applied to search the optimal decision. Finally, an illustrative case is analyzed by the proposed model and the traditional model respectively, and the comparative result shows the superiority of the proposed method.

Lithium-ion battery (LIB) is one of the mainstream of rechargeable batteries and has been widely used in electronics and electric vehicles due to its promising properties. Although the endurance and reliability are the everlasting pursuits, the performance fade of battery is inevitable. What's more, the performance diversity on capacity and fading rate make the general evaluation of battery intractable. To further investigate the inherent properties of the battery, this paper carries out a thorough analysis on battery's behavior at different discharge rates based on a set of multi-discharge rates degradation test of LIBs. The influence of discharge rate and cycling on battery performance are highlighted with the discussion on issues of capacity diversity, capacity fading, and charge/discharge time behaviors. A dynamic version of Peukert's law, which summarizes the general degradation characteristics of Peukert coefficient (PC) and eliminates batteries' discrepancies on life cycle is proposed. Using the proposed dynamic Peukert's equation, capacity can be transferred to the desired discharge rate level and capacities at different discharge rates become comparable. The findings reveal LIB's behavior and establish the numerical correlation for capacities at different discharge rates, which helps to better understand battery's performance and is a powerful technique for battery condition monitoring.

Early detection of faults developed in gearboxes is of great importance to prevent catastrophic accidents. In this paper, a sparsity-based feature extraction method using the tunable Q-factor wavelet transform with dual Q-factors is proposed for gearbox fault detection. Specifically, the proposed method addresses the problem of simultaneously extracting periodic transients and high-resonance component from noisy data for the gearboxes fault detection purpose. Firstly, a sparse optimization problem is formulated to jointly estimate the useful components from the noisy observation. In order to promote wavelet sparsity, non-convex regularizations are employed in the cost function of the optimization problem. Then, a fast converging, computationally efficient iterative algorithm which termed SpaEdualQA (the sparsity-based signal extraction algorithm using dual Q-factors) is developed to solve the formulated optimization problem. The derivation of the proposed fast algorithm combines the split augmented Lagrangian shrinkage algorithm (SALSA) with majorization–minimization (MM). Finally, the effectiveness of the proposed SpaEdualQA is validated by analyzing numerical signals and real data collected from engineering fields. The results demonstrated that the proposed SpaEdualQA can effectively extract periodic transients and high-resonance component from noisy vibration signals.

As a significant role in industrial equipment, rotating machinery fault diagnosis (RMFD) always draws lots of attention for guaranteeing product quality and improving economic benefit. But non-stationary vibration signal with a large amount of noise on abnormal condition of weak fault or compound fault in many cases would lead to this task challenging. As one of the most powerful non-stationary signal processing techniques, wavelet transform (WT) has been extensively studied and widely applied in RMFD. Many previous publications admit that WT can be realized by means of inner product principle of signal and wavelet base. This paper verifies the essence on inner product operation of WT by simulation experiments. Then the newer development of WT based on inner product is introduced. The construction and applications of major developments on adaptive multiwavelet in RMFD are presented. Finally, super wavelet transform as an important prospect of WT based on inner product are presented and discussed.

Remaining useful life (RUL) prognostics is a core problem in prognostics and health management (PHM). Accurate RUL prediction is crucial not only to the verification of mission goals but also to failure prevention and maintenance decision in a more effective and efficient manner. However, the substantial nonlinearity is one of most important challenges in deterioration modeling and RUL estimation of nonlinear mechanical system. An interesting contribution is the improvement of RUL prediction accuracy by the use of both greedy kernel principal components analysis (GKPCA) for dimensional reduction to extract feature from multi dimension data set of monitored nonlinear mechanical system and nonhomogeneous hidden semi-Markov model (NHSMM) to model the multistate deterioration process. A case study with the data set from turbofan engines is analyzed using the methodology, and by comparing the prediction accuracy with the previously linear PCA-NHSMM's, the result verifies the effectiveness (closer to actual RUL, earlier tracked health state, smaller boundary width) and efficiency(higher prognostics robustness) of the methodology.

Confusion of frequency spectrum under varying speed condition leads to the efficacy degradation of fault recognition for rolling element bearings. Meanwhile, a widely-used method is transforming non-stationary vibration signals into angular domain based on angular re-sampling to reduce influence of speed fluctuation. However, single domain usually cannot describe health information comprehensively. Thus a multi-domain indexes description method is proposed in this paper to improve fault recognition by multi-domain fusion. First the input indexes of multiple domains including time domain, frequency domain, angular domain and order domain are organized to train SOM neural network. Then an optimized fault cognition model is established based on the SOM input planes. Finally, faults are recognized based on multi-domain indexes model and extra complexity indexes are added to enhance recognition of compound faults. Experimental results show that the proposed method can distinguish different faults effectively and have good practical significance.