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With the development of modern industries, the working environment of rotating machinery has become increasingly complicated. Therefore, it is very meaningful to accurately identify the type of equipment failure under variable operating conditions. This paper presents a rotating machinery fault diagnosis method based on dynamic learning rate deep belief network (DBN) with adaptive structure (PSO-DDBN). Firstly, the wavelet packet energy entropy principle was used to obtain the characteristic matrix of the original data, and then the characteristics of the data under variable conditions were distinguished. Secondly, in order to adjust the structure of DBN, the loss function of DBN was used to construct the convergence function in particle swarm optimization (PSO) adaptive process. The dynamic learning rate strategy was applied to the training process of the network. The network gradient value in each iteration was recorded and the dynamic learning rate function was constructed to achieve the purpose of dynamically adjusting the network learning rate and making the network convergence faster and more stable. Then, the performance of PSO-DDBN was verified by the data of bearing and gearbox under variable conditions. Finally, other intelligent diagnosis algorithms were compared with this method, and the results showed that this method had better universality and fault classification ability.

The characterization of complex patterns arising from electroencephalogram (EEG) is an important problem with significant applications in identifying different mental states. Based on the operational EEG of drivers, a method is proposed to characterize and distinguish different EEG patterns. The EEG measurements from seven professional taxi drivers were collected under different states. The phase characterization method was used to calculate the instantaneous phase from the EEG measurements. Then, the optimization of drivers’ EEG was realized through performing common spatial pattern analysis. The structures and scaling components of the brain networks from optimized EEG measurements are sensitive to the EEG patterns. The effectiveness of the method is demonstrated, and its applicability is articulated.

In the case of the rapid development of large machinery, the research of mechanical fault signal feature extraction is of great significance, it can not only ensure the development of the economy but also ensure safety. Stochastic resonance (SR) is of widespread use in feature extraction of mechanical fault signals due to its excellent signal extraction capability. Compared with an overdamped state, SR in an underdamped state is equivalent to one more filtering of the signal, so the signal-to-noise ratio (SNR) of the output signal will be further improved. In this article, based on the piecewise tri-stable SR (PTSR) obtained from previous studies, the feature extraction of mechanical fault signals is carried out under underdamped conditions, and it is found that the SNR of the output signal is further improved. The simulation signals and experimental signals are used to verify that PTSR has better output performance under underdamped conditions.

Stochastic resonance (SR) has been widely studied as a means of signal processing since its conception. Since SR is different from other denoising methods in nature, it can be used for not only feature extraction but also signal enhancement. Additive white Gaussian noise (AWGN) is often used as a driving source in SR research due to its convenience in numerical simulation and uniform distribution, but as a special noise, it is of great significance to study the SR principle of dichotomous noise as a driving source for nonlinear dynamics. In this paper, the method of piecewise tri-stable SR (PTSR) driven by dichotomous noise is studied, and it is verified that signal enhancement can still be achieved in the PTSR system. At the same time, the influence of the parameters of the PTSR system, periodic signal, and dichotomous noise on the mean of signal-to-noise ratio gain (SNR-GM) is analyzed. Finally, dichotomous noise and AWGN are used as the driving sources of the PTSR system, and the signal enhancement ability and noise resistance ability of the two drivers are compared.

The multi-process manufacturing of steel rolling products requires the cooperation of complicated and variable rolling conditions. Such conditions pose challenges to the fault diagnosis of the key equipment of the rolling mill. The development of transfer learning has alleviated the problem of fault diagnosis under variable working conditions to a certain extent. However, existing diagnosis methods based on transfer learning only consider the distribution alignment from a single representation, which may only transfer part of the state knowledge and generate fuzzy decision boundaries. Therefore, this paper proposes a multi-representation domain adaptation network with duplex adversarial learning for hot rolling mill fault diagnosis. First, a multi-representation network structure is designed to extract rolling mill equipment status information from multiple perspectives. Then, the domain adversarial strategy is adopted to match the source and target domains of each pair of representations for learning domain-invariant features from multiple representation networks. In addition, the maximum classifier discrepancy adversarial algorithm is adopted to generate target features that are close to the source support, thereby forming a robust decision boundary. Finally, the average value of the predicted probabilities of the two classifiers is used as the final diagnostic result. Extensive experiments are conducted on an experimental platform of a four-high hot rolling mill to collect the fault state data of the reduction gearbox and roll bearing. The experimental results reveal that the method can effectively realize the fault diagnosis of rolling mill equipment under variable working conditions and can achieve average diagnostic rates of up to 99.15% and 99.40% on the data sets of the rolling mill gearbox and bearing, which are respectively 2.19% and 1.93% higher than the rates achieved by the most competitive method.

Gear transmission is one of the most commonly used transmission methods in mechanical equipment. By analyzing the vibration data of gearbox, an improved deep belief network (DBN) algorithm for gear fault diagnosis based on wavelet packet energy entropy (WPEE) and multiscale permutation entropy (MPE) is proposed. Firstly, the vibration data of gearbox with various fault types under multiple working conditions are collected. Secondly, the energy entropy of wavelet packet and the entropy distribution of multiscale permutation are calculated respectively to form a combined feature matrix. Then, the improved threshold adaptive DBN is used to further extract the fault signal features, and finally the deep layer features are classified. By analyzing the vibration data of multi-platform gearbox, a high and stable diagnostic accuracy is obtained.

Given the complexity of the operating conditions of rolling bearings in the actual rolling process of a hot mill and the difficulty in collecting data pertinent to fault bearings comprehensively, this paper proposes an approach that diagnoses the faults of a rolling mill bearing by employing the improved sparrow search algorithm deep belief network (ISAA-DBN) with limited data samples. First, the fast spectral kurtosis approach is adopted to convert the non-stationary original vibration signals collected by the acceleration sensors installed at the axial and radial ends of the rolling mill bearings into two-dimensional (2D) spectral kurtosis time–frequency images with higher feature recognition, and the principal component analysis (PCA) technique is used to decrease the dimension of the data in order to achieve a high diagnosis rate with a limited number of samples. Subsequently, the sparrow search algorithm (SSA) is used to realize the intelligent optimized self-adaptive function of a deep belief network (DBN). Furthermore, the firefly disturbance algorithm is employed to improve the spatial search capability and robustness of SSA-DBN in order to achieve better performance of the ISSA-DBN method. Finally, the proposed approach is experimentally compared to other approaches used for diagnosis. The results show that the proposed approach not only retains the useful features of the data through dimension reduction but also improves the efficiency of the diagnosis and achieves the highest diagnosis accuracy with limited data samples. In addition, the optimal position of the sensor for diagnosing rolling mill roll faults is identified.

In the absence of a priori knowledge, manual feature selection is too blind to find the sensitive features which can effectively classify the different fault features. And it is difficult to obtain a large number of typical fault samples in practice to train the intelligent classifier. A novel intelligent fault diagnosis method based on feature selection and deep learning is proposed for rotating machine mechanical in the paper. In this method, the deep neural network is not only used for feature extraction but also for fault diagnosis. First, the deep neural network 1 is used to extract feature from the spectral signal of the original signal. In addition, the original vibration signal is decomposed to a series of intrinsic mode function components by empirical mode decomposition, and the statistical features of each intrinsic mode function component are extracted by the deep neural network 2 in time domain and frequency domain. Second, the extraction features of the original signal spectrum and the extraction features of each intrinsic mode function component are evaluated, respectively. After features evaluation, the selected sensitive features are combined together to construct a joint feature. Finally, the joint feature is put into the deep neural network 3 to realize the automatic recognition of different fault states of rotating machinery. The experimental results show that the method proposed in this paper which integrated time-domain, frequency-domain statistical characteristics, empirical mode decomposition, feature selection, and deep learning methods can obtain the fault information in detail and can select sensitive features from a large number of fault features. The method can reduce the network size, improve the mechanical fault diagnosis classification accuracy, and has strong robustness.

The advantages of stochastic resonance (SR) have received extensive attention and research in the field of weak signal extraction. It can be used to extract fault signals from rotating machinery. To deeply improve the output signal-to-noise ratio (SNR), a second-order underdamped tristable stochastic resonance (SUTSR) is proposed in the present study. The potential function, the steady-state probability density of particles and the SNR are used to evaluate the model. Firstly, the relationship between the noise intensity and the SNR of SUTSR is studied. Then, using the steady-state solution curve, the output response of the SUTSR system is discussed from the perspective of steady-state input, and the output response of the system is further studied when inputting low-frequency harmonic signals. Finally, SUTSR model is used to process bearing signal data with inner ring fault and rolling element fault, and the processing result is compared with tristable system and second-order underdamped bistable system. The results show that, in the background of strong noise, the SUTSR system can accurately identify the characteristic frequency of the fault signal and then greatly improve the energy of the weak fault signal under appropriate system parameters.

A coupled vibration model of hot rolling mill rolls under multiple nonlinear effects is established by considering the nonlinear spring force produced by the hydraulic cylinder, the nonlinear friction between the work rolls, the dynamic variation of rolling force, and the effect of external excitation as well as according to the structural constraints of a four-high hot rolling mill in the vertical and horizontal directions. The amplitude-frequency response equation of rolling mill rolls is determined by using a multiple-scale approximation method. Furthermore, use of actual data for simulation indicates that the internal resonance is the main cause of coupling vibration of the rolling mill rolls. In addition, changes in the movement displacement of the hydraulic cylinder and the coupling parameters strongly affect the coupling system of the rolling mill rolls. Finally, the study of the dynamic bifurcation characteristics of the rolling mill rolls indicates that, with varying external excitation amplitude, the vibration of rolls alternates between periodic motion, period-doubling motion, and chaotic motion in both vertical and horizontal directions. This is one of the reasons for the appearance of periodic light and dark stripes on the strip surface. Furthermore, the range of the external excitation amplitude (F0) at which the rolling mill roll system vibrates violently, that is, 5.68e5 N 6.12e5 N, must be avoided. The research results can provide a theoretical reference for further exploration of the coupling vibration mechanism of hot rolling mills.

Based on the analysis of the influence of roll vibration on the elastoplastic deformation state of a workpiece in a rolling process, a dynamic rolling force model with the hysteresis effect is established. Taking the rolling parameters of a 1780 mm hot rolling mill as an example, we analyzed the hysteresis between the dynamic rolling force and the roll vibration displacement by varying the rolling speed, roll radius, entry thickness, front tension, back tension, and strip width. Under the effect of the dynamic rolling force and considering the nonlinear effect between the backup and work rolls as well as the structural constraints on the rolling mill, a hysteretic nonlinear vertical vibration model of a four-high hot rolling mill was established. The amplitude-frequency equations corresponding to 1/2 subharmonic resonance and 1:1 internal resonance of the rolling mill rolls were obtained using a multi-scale approximation method. The amplitude-frequency characteristics of the rolling mill vibration system with different parameters were studied through a numerical simulation. The parametric stiffness and nonlinear stiffness corresponding to the dynamic rolling force were found to have a significant influence on the amplitude of the subharmonic resonance system, the bending degree of the vibration curve, and the size of the resonance region. Moreover, with the change in the parametric stiffness, the internal resonance exhibited an evident jump phenomenon. Finally, the chaotic characteristics of the rolling mill vibration system were studied, and the dynamic behavior of the vibration system was analyzed and verified using a bifurcation diagram, maximum Lyapunov exponent, phase trajectory, and Poincare section. Our research provides a theoretical reference for eliminating and suppressing the chatter in rolling mills subjected to an elastoplastic hysteresis deformation.

This study establishes a vertical–horizontal coupling vibration model of hot rolling mill rolls under multi-piecewise nonlinear constraints considering the piecewise nonlinear spring force and piecewise nonlinear friction force constraints of the hydraulic cylinder in the vertical direction of the rolls, the piecewise stiffness constraints in the horizontal direction, and the influence of the nonlinear dynamic rolling force in the rolling process. Using the average method to solve the amplitude–frequency response equation of the coupled vibration system and taking the actual parameters of a 1780 mm hot rolling mill (Chengde Steel Co., Ltd., Chengde, China) as an example, we study the amplitude–frequency characteristics of the mill rolls under different parameter settings. The results show that the amplitude and resonance region can be reduced by appropriately reducing the external disturbance force and the nonlinear spring force of the hydraulic cylinder, appropriately increasing the nonlinear friction force, and eliminating the gap between the bearing seat and the mill housing, to avoid the amplitude jump phenomenon due to piecewise variation. Furthermore, using the singularity theory to study the static bifurcation characteristics of the coupled vibration system, we establish a relationship between the vibration parameters and the topological bifurcation solution of the coupled system. The transition sets and their corresponding bifurcation topological structure in three cases are given, and the steady and unsteady process parameter regions of the rolls are obtained. The dynamic behavior of the coupled vibration system can be controlled by varying the bifurcation parameter. This study provides a theoretical basis for restraining the vibration of hot rolling mill rolls and optimizing the process parameters.

For solving detection problems of multifrequency weak signals in noisy background, a novel weak signal detection method based on variational mode decomposition (VMD) and rescaling frequency-shifted multistable stochastic resonance (RFMSR) with analytical mode decomposition (AMD) is proposed. In this method, different signal frequency bands are processed by rescaling subsampling compression to make each frequency band meet the conditions of stochastic resonance. Before the enhanced signal components are synthesized, they are processed to achieve the enhanced signal by means of AMD, leaving only the enhanced sections of the signal. The processed signal is decomposed into intrinsic mode functions (IMF) by VMD, in order to require the detection of weak multifrequency signals. The experimental analysis of the rolling bearing inner ring fault and gear fault diagnosis demonstrate that the proposed method can not only enhance signal amplitude, reduce false components, and improve the VMD algorithm’s accuracy, but also effectively detect weak multifrequency signals submerged by noise.

How to improve the accuracy and algorithm efficiency of bearing fault diagnosis has been the focus and hot topic in fault diagnosis field. Deep belief network is a typical deep learning method, which can be used to form a much higher-level abstract representation and find the distributed characteristics of data. In this article, a new method of bearing fault diagnosis is proposed based on Teager–Kaiser energy operator and the particle swarm optimization-support vector machine with deep belief network. In this method, the demodulation signal is obtained using Teager–Kaiser energy operator first. And then the time and frequency statistic characteristic of the demodulation signal is analyzed. Furthermore, the deep belief network is used to extract time and frequency feature extraction. Finally, the extracted parameters are classified by particle swarm optimization-support vector machine. The experimental results show that it not only has higher accuracy but also shortens the training time greatly, and it improves the accuracy and efficiency of fault diagnosis obviously.

For the damage identification of derrick steel structures, traditional methods often require high-order vibration information of structures to identify damage accurately. However, the high-order vibration information of structures is difficult to acquire. Based on the technology of signal feature extraction, only using the low-order vibration information, taking the right front leg as an example, we analyzed the selection of HHT marginal spectrum amplitude and the calculation process of its curvature in practical application, designed the damage conditions of a derrick steel structure, used the index and intrinsic mode function (IMF) instantaneous energy curvature method to perform the damage simulation calculation and comparison, and verified the effect of identifying the damage location in a noisy environment. The results show that the index can accurately determine the location of the damage element and weak damage element and can be used to qualitatively analyze the damage degree of the element; under the impact load, the noise hardly affects the identification of the damage location. Finally, this method was applied to the ZJ70 derrick steel structure laboratory model and compared with the IMF instantaneous energy curvature method. We verified the feasibility of this method in the damage location simulation experiment.

Stochastic resonance (SR) is investigated in a multistable system driven by Gaussian white noise. Using adiabatic elimination theory and three-state theory, the signal-to-noise ratio (SNR) is derived. We find the effects of the noise intensity and the resonance system parameters b, c, and d on the SNR; the results show that SNR is a nonmonotonic function of the noise intensity; therefore, a multistable SR is found in this system, and the value of the peak changes with changing the system parameters.

An adaptive stochastic resonance and analytical mode decomposition-ensemble empirical mode decomposition (AMD-EEMD) method is proposed for fault diagnosis of rotating machinery in this paper. Firstly, the stochastic resonance system is optimized by particle swarm optimization (PSO), and the best structure parameters are obtained. Then, the signal with noise is put into the stochastic resonance system and denoising and enhancing the signal. Secondly, the signal output from the stochastic resonance system is extracted by analytical mode decomposition (AMD) method. Finally, the signal is decomposed by ensemble empirical mode decomposition (EEMD) method. The simulation results show that the optimal stochastic resonance system can effectively improve the signal-to-noise ratio, and the number of effective components of EEMD decomposition is significantly reduced after using AMD, thus improving the decomposition results of EEMD and enhancing the amplitude of components frequency. Through the extraction of the rolling bearing fault signal feature proved that the method has a good effect.

Considering the influence caused by joint angle, nonlinear damping, and nonlinear rigidity, the nonlinear torsional vibration dynamical modeling of the multi-DOF rolling mill’s main drive system is established. To analyze the coupled equations by analytic method, the equations are decoupled by transforming them into principal coordinates. The amplitude-frequency characteristic equations are obtained by multiscale method. Furthermore, numerical example based on the 1780 rolling mill’s main drive system of some Steel Co. is given to illustrate the effects of the resonance on the response of the system. The relationship between amplitude and frequency varies according to the parameters changes of nonlinear stiffness, nonlinear friction damping, torque disturbance, and joint angle. During the rolling process, the limited joint angles range is obtained and the variation rules of the joint angle caused by the nonlinear damping, nonlinear stiffness, and the disturbance torque are gained. The results present that the rolling mill can work more stably with the joint angle at a range from 2° to 8° by controlling the value of parameters. The research results provide a theoretical basis and reference for analyzing torsional vibration of rolling mill’s transmission system caused by joint angle.

Vibration signals used for rotating machinery fault diagnosis often constitute large amount of data. It is a big challenge to extract faults feature information from these data. Recently, a new sampling framework called compressed sensing has been proposed, which enables the recovery from a small set of measured data if the signals are sparse or compressible. In reality, the sparseness of the signals is not very well due to noise, so it is difficult and unavailing to recover the whole signal. Thus, a new mechanical fault diagnosis method is proposed in this paper. First, the machine fault vibration signals are pretreated by stochastic resonance. By this way, the fault signal drowned by noise is amplified and the sparseness of the signals is enhanced, which make it possible to apply compressed sensing. Second, fault features are extracted directly from the compressed data without recovering completely, which reduces the dimensionality of the measurement data and the complexity of algorithm. Finally, the effectiveness of the proposed method is proved by the experiments. [ABSTRACT FROM AUTHOR]

A novel intelligent fault diagnosis method based on deep learning and particle swarm optimization support vectors machine (PSO-SVM) is proposed. The method uses deep learning neural network (DNN) to extract fault features automatically, and then uses support vector machine to classify diagnose faults based on extracted features. DNN consists of a stack of denoising autoencoders. Through pre-training and fine-tuning of DNN, features of input parameters can be extracted automatically. This paper uses particle swarm optimization algorithm to select the best parameters for SVM. The extracted features from multiple hidden layers of DNN are used as the input of PSO-SVM. Experimental data is derived from the data of rolling bearing test platform of West University. The results demonstrate that deep learning can automatically extract fault feature, which removes the need for manual feature selection, various signal processing technologies and diagnosis experience, and improves the efficiency of fault feature extraction. Under the condition of small sample size, combining the features of the multiple hidden layers as the input into the PSO-SVM can significantly increase the accuracy of fault diagnosis. [ABSTRACT FROM AUTHOR]

Aiming at the problem of rolling bearing fault diagnosis, a fault diagnosis method of rolling bearing is proposed based on analytical mode decomposition (AMD) and LabVIEW. For the fault feature frequency of rolling bearing is predictable, the AMD method can be used to extract the signal in the frequency band of fault characteristic frequency in rolling bearing signal, and seek frequency spectrum of vibration signal. If the spectrum contains fault characteristic frequency, then the rolling bearing fault can be diagnosed by vibration signal. A rolling bearing fault diagnosis system is developed based on LabVIEW and AMD, and the application of AMD algorithm is realized. The validity of the method is proved by the analysis of actual fault signal of rolling bearing. [ABSTRACT FROM AUTHOR]

By considering the deep groove ball bearing as the research object, and using Hertzian contact theory and elastic mechanics and geometry, a nonlinear dynamic model is established herein for the study of vibration response of deep groove ball bearings having single defect on surfaces of inner and outer races. The outer race and inner race defect size parameters are introduced into this nonlinear dynamic model, and dynamic models of localized fault on outer race, inner race of rolling element bearing are simulated and analyzed by using Runge-Kutta method. Both simulated and experimental localized fault signals (acceleration signals) are subjected to the same diagnostic techniques; namely time domain waveform comparisons and envelope analysis. Then, the impact characteristic that reflects the fault severity in rolling element bearings is obtained from the time interval between two impact points. The simulating results are in accordance with experimental results, which proves the accuracy and practicality of the models used in engineering application. The characteristic defect frequencies and related harmonics are broadly investigated and presented herein. This proposed model provides theoretical basis for monitoring and fault diagnosis of rolling bears. [ABSTRACT FROM AUTHOR]

Abstract: In order to forecast the safety loading capacity of marine derrick steel structures, a novel method is proposed, which bases on modal parameters identified from vibration measurement and updated finite element model with optimization, and takes the safety assessment theory as judgment criterion. Firstly, according to the design feature and the shock excitation mode of marine derrick steel structures, the formulas are deduced for identifying modal parameters. Secondly, taking the frequency and modal shape as the key indicators and the relevant design parameters as the updating objects, the dynamic model for the updating finite element model theory is established with optimization. Thirdly, safety judgment criterion is obtained based on formerly criterion and specification. And then, the modal test of marine derrick steel structures is carried out using ocean wave stationary random motivation. The first left to right and the first front to rear natural frequencies and mode shapes are identified. At last, safety evaluation is carried out on the marine derrick steel structures. [Copyright &y& Elsevier]

For detecting the weak fault diagnosis submerged in heavy noise, a new method called multi-scale cascaded multi-stable stochastic resonance (MCMSR) is studied. The method can effectively extract weak fault diagnosis from noise background using multi-scale wavelet noise tuning stochastic resonance (SR). Firstly, input signal with noise is decomposed by multi-scale wavelets transformation, and each scale signal is adjusted by scaling factor, then the decomposed signal is used as the input of cascaded multi-stable systems to achieve the detection of fault diagnosis. If the input signal is a large parameter signal, to conform to the conditions of SR, the decomposed signal must be processed by twice sampling. The simulation and experimental signals are carried out to test the feasibility of the method. From the signal to noise ratio (SNR) comparison curves of original signal, SR output signal and MCMSR output signal plotted together, we can find that the useful signal can be enhanced by MCMSR method than SR method. The experimental results indicate that the MCMSR can extract fault diagnosis from heavy background noise. [ABSTRACT FROM AUTHOR]