Xiang Wan

Remaining useful life estimation for mechanical systems based on similarity of phase space trajectory

RUL is estimated based on the similarity of phase space trajectory.Nonlinear degradation evolution is revealed by the phase space trajectory.Trajectory matching is not influenced by the scaling and shifting.The estimation accuracy is verified by simulated data and actual data. When evolving from a normal state to failure, mechanical systems undergo a gradual degradation process. Due to the nonlinearity of damage accumulation, degradation data always exhibit a distinctive trend and random fluctuations. It makes the prediction of remaining useful life (RUL) very difficult and inaccurate. The phase space trajectory reconstructed from the time series of degradation data is capable of reliably elucidating the nonlinear degradation behavior. In this paper, a novel method based on the similarity of the phase space trajectory is proposed for estimating the RUL of mechanical systems. First, the reference degradation trajectories are built with historical degradation data using the phase space reconstruction. Second, the similarities between the current degradation trajectory and the reference degradation trajectories are measured with a normalized cross correlation indicator, which is determined solely by the trajectory shape and is not interfered with the scaling and shifting of the trajectory. Trajectory shape and degradation stage matching algorithms are combined to find the optimal segments in the reference degradation trajectories compared with the current degradation trajectory. Finally, the RULs corresponding to the optimal matching segments are subjected to weighted averaging to obtain the RUL of the current degradation process. The proposed method is evaluated utilizing both simulated data in stochastic degradation processes and experimental data measured on an actual pump. The results show that the predicted RULs are very close to the actual RUL.

Numerical Simulation of Nonlinear Lamb Waves Used in a Thin Plate for Detecting Buried Micro-Cracks

Compared with conventional linear ultrasonic inspection methods, which are sensitive only to severe defects, nonlinear ultrasonic inspection methods are better for revealing micro-cracks in thin plates. However, most nonlinear ultrasonic inspection methods have only been experimentally investigated using bulk or Rayleigh waves. Numerical studies, especially numerical simulations of Lamb ultrasonic waves, have seldom been reported. In this paper, the interaction between nonlinear S0 mode Lamb waves and micro-cracks of various lengths and widths buried in a thin metallic plate was simulated using the finite element method (FEM). The numerical results indicate that after interacting with a micro-crack, a new wave-packet was generated in addition to the S0 mode wave-packet. The second harmonics of the S0 mode Lamb waves and the new wave-packet were caused by nonlinear acoustic effects at the micro-crack. An amplitude ratio indicator is thus proposed for the early detection of buried micro-cracks.

Analytical and numerical studies of approximate phase velocity matching based nonlinear S0 mode Lamb waves for the detection of evenly distributed microstructural changes

Most previous studies on nonlinear Lamb waves are conducted using mode pairs that satisfying strict phase velocity matching and non-zero power flux criteria. However, there are some limitations in existence. First, strict phase velocity matching is not existed in the whole frequency bandwidth; Second, excited center frequency is not always exactly equal to the true phase-velocity-matching frequency; Third, mode pairs are isolated and quite limited in number; Fourth, exciting a single desired primary mode is extremely difficult in practice and the received signal is quite difficult to process and interpret. And few attention has been paid to solving these shortcomings. In this paper, nonlinear S0 mode Lamb waves at low-frequency range satisfying approximate phase velocity matching is proposed for the purpose of overcoming these limitations. In analytical studies, the secondary amplitudes with the propagation distance considering the fundamental frequency, the maximum cumulative propagation distance (MCPD) with the fundamental frequency and the maximum linear cumulative propagation distance (MLCPD) using linear regression analysis are investigated. Based on analytical results, approximate phase velocity matching is quantitatively characterized as the relative phase velocity deviation less than a threshold value of 1%. Numerical studies are also conducted using tone burst as the excitation signal. The influences of center frequency and frequency bandwidth on the secondary amplitudes and MCPD are investigated. S1–S2 mode with the fundamental frequency at 1.8 MHz, the primary S0 mode at the center frequencies of 100 and 200 kHz are used respectively to calculate the ratios of nonlinear parameter of Al 6061-T6 to Al 7075-T651. The close agreement of the computed ratios to the actual value verifies the effectiveness of nonlinear S0 mode Lamb waves satisfying approximate phase velocity matching for characterizing the material nonlinearity. Moreover, the ratios derived from the primary and secondary horizontal displacements generated from nonlinear S0 mode Lamb waves are closest to the real value, which indicates that using horizontal displacements is more suitable for detecting evenly distributed microstructural changes in large thin plate-like structure. Successful application to evaluating material at different levels of evenly distributed fatigue damage is also numerically conducted.

Second harmonic reflection and transmission from primary S0 mode Lamb wave interacting with a localized microscale damage in a plate: A numerical perspective

HIGHLIGHTSExistence of interfacial nonlinearity between linear and nonlinear elastic materials is verified.Amplitudes of second harmonic generated due to interfacial nonlinearity are quantitatively evaluated.Second harmonic reflection and transmission from a localized microscale damage are investigated.The effects of the length and width of a microscale damage on WCPA of second harmonics are studied respectively.The reflected second harmonic mainly reflects the interfacial nonlinearity, while the transmitted second harmonic mainly reflects the material nonlinearity. ABSTRACT Second harmonic generation has been widely used in characterizing microstructural changes which are evenly distributed in a whole structure. However, few attention has been paid to evaluating localized micro‐scale damages. In this paper, second harmonic reflection and transmission from the primary S0 mode Lamb wave interacting with a localized microstructural damage is numerically discussed. Schematic diagram for deriving fundamental temporal waveform and reconstructing the second harmonic temporal waveform based on Morlet wavelet transform is presented. Second harmonic reflection and transmission from an interface between the zones of linear elastic and nonlinear materials is firstly studied to verify the existence of interfacial nonlinearity. Compositions contributing to second harmonic components in the reflected and transmitted waves are analyzed. Amplitudes of the reflected and transmitted second harmonic components generated at an interface due to the interfacial nonlinearity are quantitatively evaluated. Then, second harmonic reflection and transmission from a localized microscale damage is investigated. The effects of the length and width of a microscale damage on WCPA (wavelet coefficient profile area) of the reflected and transmitted second harmonic components are studied respectively. It is found that the second harmonic component in the reflected waves mainly reflects the interfacial nonlinearity while second harmonic in the transmitted waves reflects the material nonlinearity. These findings provide some basis on using second harmonic generation for characterization and detection of localized microstructural changes.

A quantitative method for evaluating numerical simulation accuracy of time-transient Lamb wave propagation with its applications to selecting appropriate element size and time step.

Lamb wave technique has been widely used in non-destructive evaluation (NDE) and structural health monitoring (SHM). However, due to the multi-mode characteristics and dispersive nature, Lamb wave propagation behavior is much more complex than that of bulk waves. Numerous numerical simulations on Lamb wave propagation have been conducted to study its physical principles. However, few quantitative studies on evaluating the accuracy of these numerical simulations were reported. In this paper, a method based on cross correlation analysis for quantitatively evaluating the simulation accuracy of time-transient Lamb waves propagation is proposed. Two kinds of error, affecting the position and shape accuracies are firstly identified. Consequently, two quantitative indices, i.e., the GVE (group velocity error) and MACCC (maximum absolute value of cross correlation coefficient) derived from cross correlation analysis between a simulated signal and a reference waveform, are proposed to assess the position and shape errors of the simulated signal. In this way, the simulation accuracy on the position and shape is quantitatively evaluated. In order to apply this proposed method to select appropriate element size and time step, a specialized 2D-FEM program combined with the proposed method is developed. Then, the proper element size considering different element types and time step considering different time integration schemes are selected. These results proved that the proposed method is feasible and effective, and can be used as an efficient tool for quantitatively evaluating and verifying the simulation accuracy of time-transient Lamb wave propagation.

FEM simulation of nonlinear lamb waves for detecting a micro-crack in a metallic plate

Nonlinear ultrasonic technique has been employed to detect micro-cracks since conventional linear elastic ultrasonic technology is just sensitive to gross defects. However, most of nonlinear ultrasonic researches to date have been experimental generally using bulk waves or Rayleigh waves, few numerical studies exist, especially for lamb wave ultrasonic. In this chapter, finite element method (FEM) is applied to simulate nonlinear lamb waves interacting with a micro-crack in a thin metallic structure. A pitch and catch approach is introduced containing two symmetric piezoelectric transition (PZT) wafers as actuators to generate single S0 mode signal and one PZT wafer as receiver. Generated S0 mode lamb waves propagate along the structure, interact with the micro-crack, obtain nonlinear features, and are picked up by the receiver. An undamaged plate and seven plates with different crack length are simulated. The received simulation signal from a micro-cracked plate contains a S0 mode wave-packet and a new wave-packet. A nonlinearity index (NI) is proposed to show the degree of nonlinear effect. The simulation results show that employing NI, a received signal of S0 mode can provide information on the damage severity of a micro-crack and the new wave-packet signal can be used as an early indicator for the existence of a micro-crack.

An Adaptive Support Vector Regression Machine for the State Prognosis of Mechanical Systems

Due to the unsteady state evolution of mechanical systems, the time series of state indicators exhibits volatile behavior and staged characteristics. To model hidden trends and predict deterioration failure utilizing volatile state indicators, an adaptive support vector regression (ASVR) machine is proposed. In ASVR, the width of an error-insensitive tube, which is a constant in the traditional support vector regression, is set as a variable determined by the transient distribution boundary of local regions in the training time series. Thus, the localized regions are obtained using a sliding time window, and their boundaries are defined by a robust measure known as the truncated range. Utilizing an adaptive error-insensitive tube, a stabilized tolerance level for noise is achieved, whether the time series occurs in low-volatility regions or in high-volatility regions. The proposed method is evaluated by vibrational data measured on descaling pumps. The results show that ASVR is capable of capturing the local trends of the volatile time series of state indicators and is superior to the standard support vector regression for state prediction.

An Adaptive Alarm Method for Tool Condition Monitoring Based on Probability Density Functions Estimated with the Parzen Window

Tool condition monitoring plays an important role in modern automatic processing for ensuring the processing quality and the machine life [1].