Non-stationary Operating Conditions Research Articles

Vibration source inversion-based fault diagnosis: approach and application

The gear transmission system of industrial equipment is characterized by a highly integrated structure, non-stationary operating conditions, and large loads. Therefore, the attenuation of fault signal characteristics and the complexity of operating conditions in gear transmission systems significantly affect the effectiveness of vibration signal-based fault diagnosis. This paper proposes a unified diagnostic framework based on vibration source inversion for two typical transmission component fault signal phenomena: meshing frequency modulation sidebands and equally spaced fault characteristic frequency interval harmonic clusters. This approach incorporates the vibration transfer path analysis of passive subsystems and identifies bearing dynamic forces, followed by their decomposition, reconstruction, and sensitive frequency band localization. It enables accurate diagnosis of complex gear transmission systems under non-stationary conditions with limited vibration testing. The effectiveness and advantages of this method over existing mainstream signal processing techniques are validated through actual cases of gear and weak bearing fault diagnosis on a complex planetary gear transmission system test bench.

Identification of flame transfer functions during transient operation

Predicting thermoacoustic instabilities requires knowledge of the flame response to acoustic perturbations, which is characterized by the Impulse Response Function. Obtaining stability maps across an extensive parameter space is prohibitively costly with existing methods, both experimentally and numerically, as the data records must be obtained independently for each stationary operating condition. To address this problem, a nonparametric identification technique that enables the characterization of instantaneous Flame Transfer Functions (FTFs) under nonstationary operating conditions, based on a series expansion of the time-varying impulse response function (TV-IRF), is proposed. The technique is a direct extension of the Wiener-Hopf equation to nonstationary signals, yielding the linear minimum mean squared error estimator (LMMSEE) of the TV-IRF. This method is applied to data obtained from a model of a premixed, hydrogen-enriched swirl flame. It's hydrogen power fraction is rapidly varied from 12-43% over 100 milliseconds and the flame response to a band-limited, white-noise signal is computed. From the resulting input-output data, the TV-IRF is accurately estimated and the FTF for all hydrogen power fractions is obtained from a single data record. This method paves the way for cost-effective estimation of a map of FTF's from computational or experimental data, significantly reducing expenses in both cases.

Dynamic time warping based instantaneous frequency estimation for rotating machineries under non-stationary operating conditions

Abstract For tacho-less order tracking, it is crucial to achieve an accurate estimation of instantaneous phase and frequency under non-stationary conditions for fault diagnosis of mechanical systems. Therefore, an instantaneous frequency estimation method based on dynamic time warping for rotating machinery was proposed. Firstly, a mono-component signal is obtained by variational mode decomposition of multi-harmonic vibration signal generated in practical engineering. Then, a stationary reference signal is constructed by the mean frequency of the vibration signal, which is obtained by the signal spectrum. Aligning the vibration signal with the reference signal to obtain the rough phase estimation and warping path. Finally, a polynomial model is constructed to calculate the analytic expression of the smooth warping path to obtain the instantaneous frequency result. The simulation and experiment present that the dynamic time warping-based method can estimate the instantaneous frequency of the signal under non-stationary conditions. Compared with the classical Hilbert transform method, the proposed dynamic time-warping algorithm has stronger noise resistance.

ANALYSIS OF PROPYLENE GLYCOL/ETHYLENE GLYCOL HEATING IN THE CYLINDRICAL CHANNEL OF THE SOLAR HEAT COLLECTOR

When designing solar thermal collectors, non-stationary operating conditions of the solar system are considered to determine the instantaneous heat output and temperature of the heat carriers during a given day or period. It is known that the amount of useful heat absorbed by a solar thermal collector is directly dependent on the temperature of the heat carrier at the inlet and outlet of the solar thermal collector. The calculation of the heat consumption and/or storage system also requires the temperature of the heat carrier at the outlet of the solar collector. The heating of the heat carrier in a solar collector can be divided into two stages: heating of the walls of the heat exchanger (cylindrical channel) in a solar thermal collector by solar energy and heating of propylene glycol/ethylene glycol in the heat exchanger (cylindrical channel) of a solar thermal collector. This paper presents seven methods for determining the temperature field of the walls of the heat exchanger (cylindrical channel) of a solar thermal collector, depending on the initial and boundary conditions. The most general case for calculating the temperature field of propylene glycol/ethylene glycol moving in the heat exchanger of a solar heat collector assumes the presence of heat exchange on the surfaces of its contact with the walls of the cylindrical channel and with the environment. The calculation takes into account the difficulties associated with the significant nonlinearity of boundary conditions of the "given surface radiation" type. That is, it is taken into account that one surface of the heat exchanger channel is turned to solar radiation, and the opposite is turned to the back wall of the solar heat collector. The solution is found analytically using the method of Green's functions.

Nonlinear modeling for bearing fault diagnosis in non-stationary operating conditions

Nonlinear modeling for bearing fault diagnosis in non-stationary operating conditions

Experimental validation of a short-term damping estimation method for wind turbines in nonstationary operating conditions

Abstract. Modal properties and especially damping of operational wind turbines can vary over short time periods as a consequence of environmental and operational variability. This study seeks to experimentally test and validate a recently proposed method for short-term damping and natural frequency estimation of structures under the influence of varying environmental and operational conditions from measured vibration responses. The method is based on Gaussian process time-dependent auto-regressive moving average (GP-TARMA) modelling and is tested via two applications: a laboratory three-storey shear frame structure with controllable, time-varying damping and a flutter test of a full-scale 7 MW wind turbine prototype, in which two edgewise modes become unstable. Damping estimates for the shear frame compare well with estimates obtained with stochastic subspace identification (SSI) and standard impact hammer tests. The efficacy of the GP-TARMA approach for short-term damping estimation is illustrated through comparison to short-term SSI estimates. For the full-scale flutter test, GP-TARMA model residuals imply that the model cannot be expected to be entirely accurate. However, the damping estimates are physically meaningful and compare well with a previous study. The study shows that the GP-TARMA approach is an effective method for short-term damping estimation from vibration response measurements, given that there are enough training data and that there is a representative model structure.

Rotating Machinery Fault Diagnosis under Time–Varying Speed Conditions Based on Adaptive Identification of Order Structure

Rotating machinery fault diagnosis is of key significance for ensuring safe and efficient operation of various industrial equipment. However, under nonstationary operating conditions, the fault–induced characteristic frequencies are often time–varying. Conventional Fourier spectrum analysis is not suitable for revealing time–varying details, and nonstationary fault feature extraction methods are still in desperate need. Order spectrum can reveal the rotational–speed–related time–varying frequency components as spectral peaks in order domain, thus facilitating fault feature extraction under time–varying speed conditions. However, the speed–unrelated frequency components are still nonstationary after angular–domain resampling, thus causing wide–band features and interferences in the order spectrum. To overcome such a drawback, this work proposes a rotating machinery fault diagnosis method based on adaptive separation of time–varying components and order feature extraction. Firstly, the rotational speed is estimated by the multi–order probabilistic approach (MOPA), thus eliminating the inconvenience of installing measurement equipment. Secondly, adaptive separation of the time–varying frequency component is achieved through time–varying filtering and surrogate test. It effectively eliminates interference from irrelevant components and noise. Finally, a high–resolution order spectrum is constructed based on the average amplitude envelope of each mono–component. It does not involve Fourier transform or angular–domain resampling, thus avoiding spectral leakage and resampling errors. By identifying the fault–related spectral peaks in the constructed order spectrum, accurate fault diagnosis can be achieved. The Rényi entropy values of the proposed order spectrum are significantly lower than those of the traditional order spectrum. This result verifies the effective energy concentration and high resolution of the proposed order spectrum. The results of both numerical simulation and lab experiments confirm the effectiveness of the proposed method in accurately presenting the time–varying frequency components for rotating machinery diagnosing faults.

Event-Triggered Relearning Modeling Method for Stochastic System with Non-Stationary Variable Operating Conditions

This study presents a novel event-triggered relearning framework for neural network modeling, designed to improve prediction precision in dynamic stochastic complex industrial systems under non-stationary and variable conditions. Firstly, a sliding window algorithm combined with entropy is applied to divide the input and output datasets across different operational conditions, establishing clear data boundaries. Following this, the prediction errors derived from the neural network under different operational states are harnessed to define a set of event-triggered relearning criteria. Once these conditions are triggered, the relevant dataset is used to recalibrate the model to the specific operational condition and predict the data under this operating condition. When the predicted data fall within the training input range of a pre-trained model, we switch to that model for immediate prediction. Compared with the conventional BP neural network model and random vector functional-link network, the proposed model can produce a better estimation accuracy and reduce computation costs. Finally, the effectiveness of our proposed method is validated through numerical simulation tests using nonlinear Hammerstein models with Gaussian noise, reflecting complex stochastic industrial processes.

Extremely compact and lightweight triboelectric nanogenerator for spacecraft flywheel system health monitoring

The abnormal state of supporting bearings significantly affects the directional accuracy of spacecraft flywheel systems. A self-sensing triboelectric nanogenerator (TENG) offers a desirable route for on-orbit health monitoring and can potentially improve the intelligence level of spacecraft. Here, an extremely compact and lightweight TENG (CL-TENG) for the nonguided clearance of bearings is proposed and fabricated for the condition monitoring of a flywheel assembly. Using the bearing radial space allows the CL-TENG to perceive the revolution and whirling behavior of the cage; therefore, the output of the CL-TENG is simultaneously affected by the bearing speed and load. A test platform for capturing the kinematic of the cage is established to validate the effectiveness of the CL-TENG based on bearing skidding, cage rotation, and whirling instability. A negative exponential correlation between the output voltage and dynamic whirling clearance index is shown to be the basis of cage whirling sensing. The internal clearance and materials of the CL-TENG are optimized to enhance the output performance while preventing wear on the flexible electrodes. The application of the CL-TENG to an actual flywheel system in a simulated space environment and nonstationary operating conditions demonstrate its advantages in detecting the abnormal operating state of the cage.

Dynamic misalignment effects on performance of dynamically loaded journal bearings

The lubrication characteristics of dynamically loaded journal bearings are significantly affected by misalignments. However, existing research on misalignment primarily focuses on fixed misalignment models, and studies on the nonlinear dynamic response of dynamically loaded bearings under dynamic misalignment are yet to be reported. To address this research gap, this study proposed a dynamic misalignment model coupled with rotor dynamics and transient mixed elastohydrodynamic lubrication. The model comprehensively considers factors such as journal eccentric translation, surface topography, oil film cavitation, and bearing elastic deformation. Upon model validation, numerical simulations are conducted to reveal the single-cycle nonlinear tribological characteristics of dynamically loaded bearings subjected to transient time-varying dynamic loads and time-varying misalignment moments. Based on the dynamic misalignment model, a series of parameter studies were conducted to explore the influence of operating conditions such as load magnitude and rotational speed on lubrication characteristics. The research also evaluated the impact of various structural parameters, including surface roughness, bearing bush thickness, and radial clearance, on the performance of dynamically loaded bearings. The numerical results indicate that the impact of fixed-value misalignment on the performance is highly dependent on the manually set deflection angles. Under light-load and high-speed nonstationary operating conditions, the effect of dynamic misalignment on the lubrication characteristics of dynamically loaded journal bearings was significantly amplified. Furthermore, a smoother surface, thicker bearing bush, and smaller radial clearance intensify dynamic misalignment's influence, compared to fixed-value misalignment, on the transient rough contact behavior at the interface. The findings of this study provide valuable guidance and references for the theoretical analysis and optimization design of dynamically loaded journal bearings.

Short-term damping estimation for time-varying vibrating structures in nonstationary operating conditions

Various structures exhibit time-varying modal properties driven by short-term variability of environmental and operational conditions, which can cause considerable short-term variations in the modal characteristics, and modal damping, in particular. This study focuses on short-term damping estimation based on operational response measurements, for which a Gaussian process time-dependent auto-regressive moving average time series model is proposed. The model coefficients are represented by basis functions which express dependence on influencing environmental and operational variables, to account for various phenomena driving the time-varying nature of the modal characteristics. The method is verified by estimating short-term damping from the response of a simulated two-mode model. The applicability of the method for more complex cases is demonstrated by estimating the short-term damping of a multi-megawatt wind turbine in operation (and during an extreme wind gust) by means of its simulated edgewise blade response. The results demonstrate that the proposed method offers an enabling approach towards short-term damping and natural frequency estimation based on response measurements.

Feasibility Analysis of Online Uncertainty Metrics for PMU-Based State Estimation

The ever-increasing penetration of renewable energy sources and distributed generation needs developing and deploying more sophisticated and precise control techniques. The paradigm shift from high-rotational inertia towards inverter-connected facilities has made modern power systems subject to strongly non-stationary operating conditions. In this context, phasor measurement units (PMUs) represent a promising solution due to their accuracy and time synchronization. The current paper further develops the concepts recently published proposing performance assessment of PMUs relying on metrics specifically defined to quantify the estimation accuracy, reporting latency, and response time. Our focus is on determining the confidence interval associated with these metrics and thus derive a robust approach for their application in measurement-based network controlling efforts. The configuration of the used simulation model is detailed, and the state estimation results as a function of the selected measurement weighing criteria are presented, concluding as a possible application of the reliability metrics in Weighted Least Squares and Discrete Kalman Filter state estimators, highlighting the performance enhancement as well as the theoretical limits of the proposed approach.

A Hydraulic Axial Piston Pump Fault Diagnosis Based on Instantaneous Angular Speed under Non-Stationary Conditions

Due to the intense noise interference in hydraulic systems, it is extremely difficult to detect component faults through vibration signals. Diagnostic performance is also constrained by highly time-varying and non-stationary operating conditions. This study proposes to use instantaneous angular speed (IAS) signals that are both operational and state parameters as sources of information. Firstly, the instantaneous angular speed fluctuation (IASF) of a piston pump is analyzed theoretically, and it is concluded that its fluctuating components contain the health status information of the components. The IASF can then be obtained by subtracting the speed trend term from IAS signals obtained via a magneto-electric speed sensor. A synchro-extraction of the normal S transform (SNST) is proposed to process it via line-pass filtering. Finally, the filtered and reconstructed IASF signal is utilized to draw a two-dimensional polar coordinate map online. A non-stationary-condition test is carried out on the test platform to monitor the morphological characteristics of the valve plate under normal, slight, and severe wear conditions. The polar plot shows significant increases in speed fluctuations and oscillation times within a range from 180° to 270°. The relevant research results reflect that the IAS signal can provide a new method for monitoring the operating status of and conducting fault diagnoses for hydraulic equipment.

Assessment and improvement of the accuracy of tacholess instantaneous speed estimation

Accurately estimating instantaneous angular speed (IAS) is crucial for effective fault diagnosis under nonstationary operating conditions. Although numerous methods have been developed to improve the accuracy of IAS estimation, finding a suitable technique (method and vibration component) for a specific application remains challenging. This is because accurately assessing the accuracy of the estimated IAS without a tachometer is not straightforward. Thus, since the accuracy of the estimated IAS is unknown, its accuracy cannot be further improved.To address the challenge of accurately estimating and further improving the accuracy of IAS without a tachometer, this study proposes a method to enhance the accuracy of IAS obtained from different techniques (methods and vibration components). The study first investigates the influence of IAS error on order analysis. Next, it discusses three indicators that can assess the accuracy of the estimated IAS without a tachometer. These indicators are designed to compare the energy of the deterministic and random parts of the signal, assess the sparsity of the order spectrum, and quantify the smearing of the vibration component of interest on the order spectrum. The signal and all IASs are divided into windowed sections to determine the most accurate IAS in each section using the three indicators separately or a resultant indicator obtained by merging them using the entropy weighting method. The most accurate IAS are then merged together to obtain the resultant IAS.The study finds that the indicators can effectively evaluate the accuracy of the IAS without a tachometer. The proposed method also produces a more accurate IAS than the IAS candidates obtained by different techniques.

An enhanced K-SVD denoising algorithm based on adaptive soft-threshold shrinkage for fault detection of wind turbine rolling bearing

Due to nonstationary operating conditions of wind turbines and surrounding harsh working environments, the impulse features induced by bearing faults are always overwhelmed by heavy noise, which brings challenges to accurately detect rolling bearing faults. Sparse representation exhibits excellent performance in nonstationary signal analysis, but it is closely bound up with the degree of similarity between the atoms in a dictionary and signals. Therefore, this paper investigates an enhanced K-SVD denoising method based on adaptive soft-threshold shrinkage to achieve high-precision extraction of impulse signals, and applies it to fault detection of generator bearing of wind turbines. An adaptive sparse coding shrinkage soft-threshold denoising is first proposed to remove noise and harmonic interference in the residual term of dictionary updating, so that the updated atoms show obvious impact characteristics. Furthermore, a soft-threshold shrinkage function with adaptive threshold is designed to further suppress clutter in atoms of the learned dictionary, so as to obtain an optimized dictionary for recovering impulse signals. Two actual engineering cases are selected for analysis, and the envelope spectrum correlation kurtosis corresponding to the results obtained by the proposed method is significantly higher than that of other comparison methods, thus verifying its superiority in detecting rolling bearing faults.

Mono-trend mode decomposition for robust feature extraction from vibration signals of rotating Machinery

The analysis of vibration signals of rotating machinery plays an important role in equipment fault diagnosis and health monitoring. However, the decomposition of fault characteristic components often lacks robustness and accuracy under nonstationary operating conditions due to potential strong background noise and the complexity of existing components. In this paper, we address this issue by utilizing the relationships among components of vibration signals generated by rotating structures, described as the mono-trend modes (MTMs). Our proposed method, called the MTM decomposition (MTMD), enables robust feature extraction from vibration signals under nonstationary operating conditions. Initially, the instantaneous angular speed (IAS) of the input shaft is measured by tachometers or estimated by the framework of parameterized resampling time–frequency transform. The instantaneous frequencies (IFs) of the targeted components are then determined based on their orders relative to the IAS. Subsequently, the instantaneous amplitudes (IAs) of the targeted components are estimated by solving a joint optimization problem that includes a penalty term designed in consideration of the low variation characteristic of IAs. This penalty term enhances the efficient distribution of energy among close-spaced components. As a result, all targeted MTMs can be extracted simultaneously without any accumulated error. Various simulated experiments and practical experiments on a high-power planetary gearbox are conducted to analyze and validate the effectiveness of the proposed MTMD method in extracting robust features, especially in the presence of strong noise and close-spaced components.

Physics-Informed Residual Network (PIResNet) for rolling element bearing fault diagnostics

Various deep learning methodologies have recently been developed for machine condition monitoring recently, and they have achieved impressive success in bearing fault diagnostics. Despite the capability of effectively diagnosing bearing faults, most deep learning methods are tremendously data-dependent, which is not always available in industrial applications. In practical engineering, bearings are usually installed in rotating machinery where speed and load variations frequently occur, resulting in difficulty in collecting large training datasets under all operating conditions. Additionally, physical information is usually ignored in most deep learning algorithms, which sometimes leads to the generated results of low compliance with the physical law. To tackle these challenges, a novel Physics-Informed Residual Network (PIResNet) is proposed for learning the underlying physics that is embedded in both training and testing data, thus providing a physical consistent solution for imperfect data. In the proposed method, a physical modal-property-dominant-generated layer is adopted at first to generate the modal-property-dominant feature. Then, a domain-conversion layer is constructed to enable the feasibility of extracting the discriminative bearing fault features under varying operating speed conditions. Lastly, a parallel bi-channel residual learning architecture that can automatically extract the bearing fault signatures is meticulously established to incorporate the bearing fault characteristics. Experimental datasets under variable operating speeds and loads, and time-varying operating speeds are utilized to demonstrate the superiority of the PIResNet under non-stationary operating conditions.

Robust deep learning-based fault detection of planetary gearbox using enhanced health data map under domain shift problem

Abstract The conventional deep learning-based fault diagnosis approach faces challenges under the domain shift problem, where the model encounters different working conditions from the ones it was trained on. This challenge is particularly pronounced in the diagnosis of planetary gearboxes due to the complicated vibrations they generate, which can vary significantly based on the system characteristics of the gearbox. To solve this challenge, this paper proposes a robust deep learning-based fault-detection approach for planetary gearboxes by utilizing an enhanced health data map (HDMap). Although there is an HDMap method that visually expresses the vibration signal of the planetary gearbox according to the gear meshing position, it is greatly influenced by machine operating conditions. In this study, domain-specific features from the HDMap are further removed, while the fault-related features are enhanced. Autoencoder-based residual analysis and digital image-processing techniques are employed to address the domain-shift problem. The performance of the proposed method was validated under significant domain-shift problem conditions, as demonstrated by studying two gearbox test rigs with different configurations operated under stationary and non-stationary operating conditions. Validation accuracy was measured in all 12 possible domain-shift scenarios. The proposed method achieved robust fault detection accuracy, outperforming prior methods in most cases.

Latent indicators for temporal-preserving latent variable models in vibration-based condition monitoring under non-stationary conditions

Condition-based monitoring for critical assets is reliant on the quality of the indicators used for condition inference. These indicators must be sensitive to the development of faults under constant and non-stationary operating conditions. Latent variable models in the time-preserving framework offer a powerful learning-based technique for the monitoring of critical assets as they only require healthy asset data, and provide indicators from the data space for asset condition inference. However, the latent manifold of latent variable models is often disregarded in favour of data space indicators, such as reconstruction errors, which are primarily focused on measuring the likelihood of the observed data. The latent space is often unintentionally unutilised. In this work, we highlight that the latent manifold is a powerful resource for condition inference and should be utilised for condition monitoring. We conceptually categorise and identify five classes of latent space health indicators that capture various manifold perspectives. These five classes introduce and allow for latent health indicator derivation and are useful for the condition inference task. Fifteen latent health indicators are considered in this work and are applied to the fault diagnostics task on two experimental datasets. An ensemble-based inference procedure is used, which produces a modular fault diagnosis framework. The indicators are shown to be informative for condition inference in both constant and variable operating conditions. Utilising the latent manifold in condition monitoring tasks is important to further develop the learning-based condition monitoring field.

Nonlinear modeling of a misaligned rotor under non-stationary operating conditions

In this study, a novel model is developed to investigate the angular acceleration of the nonlinear misaligned rotor passing through the critical speeds under non-stationary operating conditions. The concerned rotor is modeled elastic with the effects of nonlinear inertia terms and flexible bearing. Nonlinear equations of motion are derived using the Lagrange method and solved with the finite element method. Effects of parameters such as shaft eccentricity, damping, and stiffness of the supports on the increase in the rotor angular speed passing through the critical speed are considered. The obtained results indicate that a small amount of eccentricity prevents exceeding the elastic critical speed of the rotor. According to the results, if the support parameters are not selected properly, the rotor will not even be able to pass its rigid critical speed.