Time-varying Operating Conditions Research Articles

Synchronous Decomposition Match-Reassigning Transform and Its Application in Planetary Gearbox Fault Diagnosis

Abstract Under time-varying operating conditions, the instantaneous frequency (IF) of the vibration signal of the planetary gearbox exhibits non-stationary time-varying closely spaced characteristics as well as non-proportional and non-synchronous characteristics, making it difficult for traditional time-frequency analysis (TFA) methods to accurately identify its fault features and obtain accurate time-frequency representations (TFR). To address this challenge, this paper proposes a TFA method based on Synchronous Decomposition Match-Reassigning Transform (SDMRT). Firstly, the successive variational mode decomposition (SVMD) is used to adaptively separate non-synchronous frequency components in the original vibration signal. Then, the chirp rate (CR) describing the signal harmonic structure is used to synchronously match each frequency component, obtaining the TFR corresponding to each component. Next, all TFRs are merged to obtain a complete TFA result. Finally, Finally, the energy spread is re-aggregated to the ridge of the IF using the reassignment principle, resulting in a new frequency estimation operator called the Synchronous Decomposition Match-Reassigning Operator (SDMRO). SDMRT can adaptively separate non-proportional and non-synchronous IFs and achieve precise matching of time-varying closely spaced IFs, thereby completing the TFR of the vibration signal generated by the planetary gearbox. By analyzing simulated signals and measured vibration signals from planetary gearboxes, the method proposed in this paper is significantly superior to other TFA methods, thereby validating the effectiveness and superiority of SDMRT.

A model for remaining useful life interval prediction of servo turret power head system of turn-milling center under time-varying operating conditions

With the diversification of machining tasks in turn-milling centers, the service conditions of the servo turret power head system are complex and changeable, and there are multi-source uncertainties in the degradation monitoring process. Based on the improved conditionally parameterized convolutions and nonlinear Wiener process, this paper proposes an interval prediction model suitable for the remaining useful life (RUL) under time-varying operating conditions. Firstly, a method for making sample performance degradation labels based on operating condition classification is proposed, and the labels under continuously identical operating conditions are linearized according to the classification results of operating conditions to solve the problem of inconsistent degradation rate under time-varying operating conditions. Then, a conditionally parameterized convolutions module considering global–local features (GL-CondConv) is proposed, and the convolution kernel parameters are adaptively learned according to the input samples, so that the model fully considers the influence of the features of each sample on the prediction results under time-varying operating conditions. Finally, the nonlinear Wiener process is used to estimate the RUL interval of the equipment to quantify the RUL uncertainty. The effectiveness of the proposed method is verified on the servo turret power head system dataset and PHM bearing dataset.

A hybrid battery degradation model combining arrhenius equation and neural network for capacity prediction under time-varying operating conditions

Capacity degradation modeling and remaining useful life (RUL) prediction play a pivotal role in enhancing the safety of battery energy storage systems. Lithium-ion batteries utilized in the systems are subjected to intricate and variable operating conditions, including temperature, charging/discharging rates and depth, which result in time-varying degradation rates. However, most existing models for battery capacity prediction have the limitation of ignoring the quantitative effects of time-varying operating conditions on degradation. Therefore, a hybrid battery capacity degradation model combining Arrhenius equation and lightweight Transformer is constructed. The effects of operating conditions on capacity degradation rates are introduced by an improved Arrhenius degradation equation. The coordinate ascent method embedded with Newton descent is used for estimating the model parameters. Then, the unknown mapping relationships between the degradation statistical features extracted from monitoring data and the degradation factors are captured by the light-weight Transformer. Finally, a novel framework consisting of future capacity and RUL predicting is constructed based on sequential importance resampling (SIR). For the purpose of verification, the cyclic charge-discharge experiments of eight battery cells under two distinct operating profiles are designed and conducted. Compared with other models, the proposed model achieves the best prognostics performance on the tested cells.

Stability analysis of grid-connected inverter under full operating conditions based on small-signal stability region

Impedance analysis is a practical approach for assessing the small-signal stability of renewable energy power systems. However, existing research predominantly focuses on specific operating conditions, neglecting the fundamental principles governing stability evolution under time-varying operating conditions. This paper presents a methodology to develop the small-signal stability region (SSSR) for grid-connected inverters using the impedance method. A comprehensive stability analysis for grid-connected inverter systems is performed based on the stability region. Firstly, the multi-parameter SSSR of the grid-connected inverter is defined according to both the aggregated impedance criterion and the generalized Nyquist criterion. Furthermore, a polynomial approximation expression for the SSSR boundary is derived. Secondly, the sensitivity analysis of operating points and control parameters is performed under full operating conditions to investigate their impact on stability based on the quantified boundary. The analyses reveal that the stability of the grid-connected inverter system near the SSSR boundary decreases with increasing active power and decreasing reactive power but exhibits an initial increase followed by a decrease with a larger PLL bandwidth. Finally, the accuracy of the stability region and the influence of key parameters are verified through case studies and experiments. The study in this paper can be used for quantitative analysis of stability margins and decision guidance of control optimization for grid-connected inverters.

High-dimensional process monitoring under time-varying operating conditions via covariate-regulated principal component analysis

High-dimensional process monitoring, which aims to raise warnings for faulty events, is a fundamental tool in ensuring the safety of large-scale industrial systems. Over the last few decades, there has been significant interest in Principal Component Analysis (PCA)-based Statistical Process Control (SPC) charts. However, most of them rely on PCA’s optimal properties in homogeneous data, which often fails when dealing with heterogeneous data from industrial processes under time-varying operating conditions. To address this issue, this study proposes a Covariate-regulated PCA model (CrPCA) seamlessly integrated into a process monitoring framework. The main idea is to adjust the principal component directions smoothly according to the time-varying operating conditions, resulting in significantly less information loss in the principal component scores compared to existing methods. This approach further yields a low-dimensional feature vector that follows a distribution with fixed parameters, regardless of covariates, for real-time surveillance. We validate the performance of our methodology through a comprehensive numerical study and two real-world applications: wind turbine condition monitoring and hot rolling process monitoring.

The loose slipper fault diagnosis of variable-displacement pumps under time-varying operating conditions

Variable-displacement pumps (VDPs) are widely used as core power components of high-pressure hydraulic systems due to their superior power density. The loose slipper fault is a typical failure type of the VDP, which can cause premature damage or even unexpected shutdown. The on-site VDPs usually work under time-varying operating conditions (TVOCs), and their pressure varies with the changing speed. These unique characteristics pose a new challenge to the fault diagnosis (FD) of the VDPs. This study introduces an innovative FD method named the multi-scale attention mechanism residual network (MSARN). The MSARN is equipped with three well-chosen components: multi-scale convolution module (MSCM), attention mechanism (AM), and residual connection. The integration of these three components facilitates the efficient extraction and fusion of meaningful multi-scale fault features, thereby preventing the overfitting problem. The experimental results obtained on the VDP validate the effectiveness and accuracy of the MSARN. The suggested method trains the model using data collected under partial constant and representative operating conditions, enabling the achievement of FD under TVOCs.

On-line Updated Guided Wave-Based Gaussian Process Method for Damage Evaluation of Aircraft Structure

Accurate damage evaluation for an aircraft by using guided wave-based structural health monitoring (SHM) technology is in critical demand. An aircraft experiences various uncertainties during its service life, such as the time-varying environment, operational conditions, and different flight missions. Additionally, the actual aircraft structure involves complex structural forms such as varied thickness, stiffeners, ribs, and large cutouts, leading to a strong uncertainty of damage initiation and propagation. Consequently, when applied to an individual aircraft structure, the diagnosis model trained by prior data inevitably introduces errors, and the errors accumulate as the damage propagates, which brings challenges in engineering application. To achieve individual aircraft structure’s more accurate damage evaluation, an on-line updated guided wave-based Gaussian process (GP) damage evaluation method is investigated in this paper. Multi-source data from the design, service, and maintenance stages are utilized to continuously update and evolve the GP model, enabling its accurate evaluation throughout the long-term service life.

An Optimal-Subdomain Generalization Method for Remaining Useful Life Prediction of Machinery Under Time-Varying Operation Conditions

An Optimal-Subdomain Generalization Method for Remaining Useful Life Prediction of Machinery Under Time-Varying Operation Conditions

Asynchronous deep reinforcement learning with gradient sharing for State of Charge balancing of multiple batteries in cyber–physical electric vehicles

This work targets the State of Charge (SoC) imbalance issue due to the mismatch across multiple batteries in cyber–physical electric vehicles (EVs) arisen from a variety of practical factors such as manufacturing tolerance, nonuniform aging process and uneven operation temperature. While most of existing SoC balancing approaches are model-based and require accurate prior knowledge, a data-driven asynchronous deep reinforcement learning (DRL) with gradient sharing is proposed to equilibrate the SoC of multiple battery packs in cyber–physical EVs under time-varying operating conditions, and the transmission of control signals in the EVs is formulated by ISO/IEC 15118 standards to ensure the security of the cyber–physical EVs. The gradient sharing (GS) based exploration scheme can expand the exploration space to diversify the actor policies in the training process and in turn reduce the entropy loss value and guarantee the convergence to the optimal policy in the long term. The proposed asynchronous advantage actor-critic with gradient sharing (A3C-GS) based SoC balancing approach trains the agents based on the output data of the multiple bidirectional DC–DC converter buck-boost circuit to avoid the use of vehicle dynamics and cumbersome operating modes that are difficult to accurately model. Furthermore, the DC bus voltage regulation is integrated simultaneously with the SoC balancing scheme. Comparison results based on simulating three/six batteries based EV system show that the proposed A3C-GS based SoC balancing scheme can achieve the highest steady-state rewards while the oscillation in the early training stage is larger resulted from a larger exploration range.

Degradation modeling under time-varying operating conditions: Inference and prognosis with particle filter

The health state estimation and remaining useful life prediction have always been challenging when a mechanical system works under time-varying operating conditions (TVOC). TVOC can not only influence the amplitude of degradation growth, but also have an impact on how the baseline degradation process is observed. In this paper, we propose a state-space model to estimate the health state of a single-unit system under continuous TVOC. Compared to most existing works where only one discrete operating condition is considered, our model accounts for multi-dimensional and continuous TVOC. The baseline (hidden) degradation is described by stochastic processes or general path models, and the observations are subject to TVOC-related observation bias and noise. Given the raw observations and the TVOC sequences, a particle filter (PF) is used to estimate the hidden degradation process. When the model parameters are unknown, Monte Carlo Expectation-Maximization is used for parameter estimation. As a result, the health state at any time and any TVOC can be estimated. The proposed method is applied to a real choke valve erosion dataset, showing a significant improvement in the health state estimation compared to traditional methods.

Gas Turbine Anomaly Detection under Time-Varying Operation Conditions Based on Spectra Alignment and Self-Adaptive Normalization

Gas turbine vibration data may exhibit considerable differences under time-varying conditions, which poses challenges for neural network anomaly detection. We first propose a framework for a gas turbine vibration frequency spectra process under time-varying operation conditions, assisting neural networks’ ability to capture weak information. The framework involves scaling spectra for aligning all frequency components related to rotational speed and normalizing frequency amplitude in a self-adaptive way. Degressive beta variational autoencoder is employed for learning spectra characteristics and anomaly detection, while a multi-category anomaly index is proposed to accommodate various operating conditions. Finally, a dataset of blade Foreign Object Damage (FOD) fault occurring under time-varying operating conditions was used to validate the framework and anomaly detection. The results demonstrate that the proposed method can effectively reduce the spectra differences under time-varying conditions, and also detect FOD fault during operation, which are challenging to identify using conventional methods.

Order-frequency Holo-Hilbert spectral analysis for machinery fault diagnosis under time-varying operating conditions

Holo-Hilbert spectral analysis (HHSA) has been demonstrated to be an effective instantaneous feature demodulation tool for revealing the coupling relationship between the frequency-modulated (FM) carriers and amplitude-modulated (AM) characteristics within nonlinear and non-stationary mechanical vibration signals. However, it is unable to acquire the time varying AM characteristics from the vibration signals of the equipment operates under variable speed conditions. To decode such signals, inspired by HHSA, a novel angle-time double-layer decomposition structure termed order-frequency HHSA (OFHHSA) is established to demodulate the fault information from the time varying vibration signals in this paper. The corresponding spectrogram, namely, order-frequency Holo-Hilbert spectrum (OFHHS) is acquired for describing the interaction relationship between time and angle domains. Besides, the order AM-marginal spectrum is derived from the OFHHS via integrating the carrier variable to exhibit the fault characteristic-related orders. Moreover, the differences between OFHHSA and angle-time cyclo-stationary framework-based order-frequency spectral correlation (OFSC) are analyzed for time varying machinery fault diagnosis. Finally, from the analyses of simulated and tested data of mechanical equipment, the OFHHSA method has avoided the limitations of the two OFSC estimators on periodic assumption and the maximum cut-off order, and the proposed method obtained a more accurate rate in fault identification and more robust ability of anti-noise.

A whole service time SHM damage quantification model hierarchical evolution mechanism

Accurate damage quantification for an individual aircraft by using structural health monitoring (SHM) technology poses a persistent challenge in practical engineering. Existing damage quantification models typically rely on prior data acquired from ground design and tests. However, an individual aircraft is subject to diverse uncertainties throughout its whole service time, such as time-varying environmental and operational conditions, different flight missions, and different damage morphologies. Consequently, employing a prior trained model for damage quantification inevitably introduces errors, thereby limiting the engineering applicability of SHM. To improve the damage quantification accuracy for individual aircraft under the influence of uncertainty, a new whole lifetime data-based damage quantification model hierarchical evolution mechanism is proposed in this paper. Multi-source data from the design, service, and maintenance stages of individual aircraft are adopted to continuously evolve the probabilistic damage diagnosis model, enabling it to characterize the specific data distribution and track the damage propagation. The proposed method is validated through fatigue tests of a landing gear beam structure, which is an important aircraft load-carrying component, with guided wave monitoring based hidden Markov model quantifying its crack propagation. The validation result demonstrates the effectiveness of the proposed method in ensuring the long-term reliability of the model and achieving more accurate damage quantification for an individual aircraft.

Remaining Useful Life Prediction Method Based on Multisensor Fusion Under Time-Varying Operating Conditions

Remaining Useful Life Prediction Method Based on Multisensor Fusion Under Time-Varying Operating Conditions

An Adaptation-Aware Interactive Learning Approach for Multiple Operational Condition-Based Degradation Modeling.

Although degradation modeling has been widely applied to use multiple sensor signals to monitor the degradation process and predict the remaining useful lifetime (RUL) of operating machinery units, three challenging issues remain. One challenge is that units in engineering cases usually work under multiple operational conditions, causing the distribution of sensor signals to vary over conditions. It remains unexplored to characterize time-varying conditions as a distribution shift problem. The second challenge is that sensor signal fusion and degradation status modeling are separated into two independent steps in most of the existing methods, which ignores the intrinsic correlation between the two parts. The last challenge is how to find an accurate health index (HI) of units using previous knowledge of degradation. To tackle these issues, this article proposes an adaptation-aware interactive learning (AAIL) approach for degradation modeling. First, a condition-invariant HI is developed to handle time-varying operation conditions. Second, an interactive framework based on the fusion and degradation model is constructed, which naturally integrates a supervised learner and an unsupervised learner. To estimate the model parameters of AAIL, we propose an interactive training algorithm that shares learned degradation and fusion information during the model training process. A case study that uses the degradation data set of aircraft engines demonstrates that the proposed AAIL outperforms related benchmark methods.

Hybrid system response model for condition monitoring of bearings under time-varying operating conditions

Hybrid system response model for condition monitoring of bearings under time-varying operating conditions

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.

Construction of bearing health indicator under time-varying operating conditions based on Isolation Forest

While there have been extensive studies in the health assessment of the bearings using the vibration signal, most have focused on the constant operating conditions. The field, however, operates often under time-varying conditions as is the case of the automotive wheel bearing. In this study, a novel health indicator (HI) is proposed to address this problem based on the Isolation Forest algorithm, which was originally developed for anomaly detection. The method is advantageous in two aspects: the HI is not influenced by the type of operating conditions whether it is constant or time-varying. Only the data under normal condition are used to construct the HI without the need of run-to-failure data. The method is demonstrated by the three cases with different types of bearing and operating conditions ranging from constant to the highly variable conditions. As a result, monotonic trends are obtained for the HI in all cases, which may be useful for the prognostic monitoring. Furthermore, in comparison with the HI constructed by the run-to-failure data in the previous literature, it is found that the trends of HI agree reasonably well with each other, which supports the validity of the method.

On data-driven modeling and control in modern power grids stability: Survey and perspective

Modern power grids are fast evolving with the increasing volatile renewable generation, distributed energy resources (DERs) and time-varying operating conditions. The DERs include rooftop photovoltaic (PV), small wind turbines, energy storages, flexible loads, electric vehicles (EVs), etc. The grid control is confronted with low inertia, uncertainty and nonlinearity that challenge the operation security, efficacy and efficiency. The ongoing digitization of power grids provides opportunities to address the challenges with data-driven and control. This paper provides a comprehensive review of emerging data-driven dynamical modeling and control methods and their various applications in power grid. Future trends are also discussed based on advances in data-driven control.

On-line tool wear monitoring under variable milling conditions based on a condition-adaptive hidden semi-Markov model (CAHSMM)

Since tool wear during machining process imposes a significant limitation on production quality as well as efficiency, on-line tool wear monitoring (TWM) is one of considerably crucial issues for intelligent manufacturing system. However, there is still a lack of universal on-line TWM techniques appropriate for the practical production process with variable machining parameters. Therefore, this study proposes a highly condition-adaptive method for tool wear state monitoring and remaining useful life (RUL) estimation under time-varying operation conditions. Multi-domain features are first extracted from vibration, acoustic emission and sound signals, and subsequently fused by the kernel principal component analysis (KPCA) to highlight discriminative information correlated to tool wear. A condition-adaptive hidden semi-Markov model (CAHSMM) is established to describe the evolution of tool wear, in which the accelerated failure time model (AFTM) embedded with Taylor tool life equation is utilized to determine the state transition probabilities that are strongly dependent on cutting parameters and duration time. Moreover, to extrapolate the Gaussian mixture models (GMMs) used to represent the observation probability beyond the range where they were trained, a Moment matching based on-line unsupervised transfer learning (OUTL) method is developed. After obtaining the state transition and observation probabilities, a modified forward algorithm is eventually implemented so as to assess tool wear online. Both the dataset from milling experiments of Ti6Al4V and PHM 2010 are employed for verifying the effectiveness of the proposed method. The results show that the presented method enables to reliably evaluate wear state and RUL of the cutter even under time-switching operation parameters, which demonstrates its promising potential for industrial applications.