Non-stationary Characteristics Research Articles

Frequency-chirprate synchrosqueezing-based scaling chirplet transform for wind turbine nonstationary fault feature time–frequency representation

As key rotational components of wind turbines, planetary gearboxes, and bearings need special health monitoring and fault diagnosis for reducing downtime and maintenance costs. However, it is still a challenging issue for time–frequency analysis (TFA) techniques to analyze nonstationary and close-spaced fault frequencies of wind turbines. Hence, a high- concentration TFA technique, termed frequency-chirprate synchrosqueezing-based scaling chirplet transform (FCSSCT) is developed. In the FCSSCT, the novel dimension of chirprate is introduced to map the signal into the three-dimensional space of time–frequency-chirprate in contrast to the time–frequency domain in the synchrosqueezing transform (SST), herein, the three-dimensional space of time, frequency and chirprate is calculated based on the scaling-basis chirplet transform (SBCT); then, a frequency-chirprate synchrosqueezing operator (FCSO) is defined in the frequency-chirprate domain to reassign the amplitude coefficients of the SBCT results and a three-dimensional representation of time–frequency-chirprate is obtained; finally, the time–frequency representation (TFR) with concentrated energy is obtained by transforming the three-dimensional representation of the time–frequency-chirprate space into the time–frequency domain. The effectiveness of the developed FCSSCT is verified by the simulated multi-component signals with close-spaced frequencies or crossover frequencies. Experimental analysis results on wind turbine planetary gearbox and bearing show that the developed technique is effective in characterizing nonstationary fault frequencies. Rényi entropies demonstrate that the FCSSCT has much better energy concentration compared with several advanced TFA methods.

Wind speed prediction utilizing dynamic spectral regression broad learning system coupled with multimodal information

As the integration of wind energy into the power system increases, accurate wind speed prediction becomes crucial to ensure the reliable and economically efficient operation of the grid. The non-stationary, chaotic, and nonlinear characteristics of wind speed pose significant challenges for prediction models in uncovering the dynamic evolution process. To address these challenges, we proposed a wind speed prediction method based on the dynamic spectral regression broad learning system coupled with multimodal information (DSR-BLS). Firstly, we proposed a frequency density clustering-based mode decomposition (FDCMD) algorithm, which automatically transforms the non-stationary wind speed into multiple relatively stationary modal components. Next, we proposed the dynamic spectral regression (DSR) algorithm, which is based on dynamic-inner latent variable modeling and spectral regression. DSR can extract features and reconstruct the dynamic characteristics of wind speed through non-uniform embedding in the phase space. Finally, DSR-BLS is proposed to enhance the deterministic point prediction accuracy of the original BLS by utilizing multimodal features and dynamic features. The experiments show that DSR-BLS outperforms the comparative prediction methods in multi-step ahead prediction results.

A novel time-frequency slice extraction method for target recognition and local enhancement of non-stationary signal features

Blind deconvolution can remove the effects of complex paths and extraneous disturbances, thus recovering simple features of the original fault source, and is used extensively in the field of fault diagnosis. However, it can only identify and extract the statistical mean of the fault impact features in a single domain and is unable to simultaneously highlight the local features of the signal in the time-frequency domain. Therefore, the extraction effect of weak fault signals is generally not ideal. In this paper, a new time-frequency slice extraction method is proposed. The method first computes a high temporal resolution spectrum of the signal by short-time Fourier transform to obtain multiple frequency slices with distinct temporal waveforms. Subsequently, the constructed harmonic spectral feature index is used to quantify and target the intensity of feature information in each frequency slice and enhance their fault characteristics using maximum correlation kurtosis deconvolution. Enhancing the local features of selected frequency slice clusters can reduce noise interference and obtain signal components with more obvious fault signatures. Finally, the validity of the method was confirmed by a simulated signal and fault diagnosis of the rolling bearing outer and inner rings was accomplished sequentially. Compared with other common deconvolution methods, the proposed method obtains more accurate and effective results in identifying fault messages.

Parallel-swath-array analysis of passive source surface waves based on beamforming

The detection of mined-out coal area remains a pivotal subject in geophysical prospecting and presents an urgent issue requiring resolution. A refined and effective approach to tackle this challenge involves conducting dispersion analysis on passive surface waves, which are derived from ambient noises. While classical passive surface wave methods, such as the Spatial Autocorrelation Method (SPAC), rely on spatial and time domain stationary assumptions, these can be difficult to fulfill. This is especially true when using ambient noises with frequencies >1 Hz, leading to a growing disparity between basic assumptions and actual scenario. To reduce this discrepancy, it's crucial to account for the non-stationary features of noise sources. In this study, we introduce a pioneering approach for parallel-swath-array analysis of passive source surface waves based on beamforming, making full use of non-stationary ambient noises. The parallel-swath array allows for efficient data collection and high-density spatial observation. The method's core concept involves: 1) The collection of noise data by a 2-D array arranged in three parallel lines; 2) The use of a plane-wave basis function to directly scan the original noise records in a time-segment mode within the time domain. These are conducive to unveil the azimuths and time-variant characteristics of the noise sources, resulting in accurate surface wave dispersion information. To ascertain the feasibility and effectiveness of this innovative method, we simulated passive surface wave records for a geological model, accommodating both time-invariant and time-variant distribution of noise sources. The results demonstrate that the method successfully reveals the time-invariant or time-variant characteristics of noise sources and the associated surface wave dispersion information. Simultaneously, we employ the preprocessed steepest-descent (PSD) algorithm to invert the dispersion curves, and the low-velocity layer in the numerical tests can be clearly revealed. In conclusion, we deployed this method in a coal mine situated in Northern China, which encompasses abandoned mined-out areas. This procedure effectively disclosed the intricate azimuthal properties of the noise sources, yielding high-resolution dispersion images. The inversion outcomes depicted a 2-D S-wave velocity section plunging to a depth of 60 m. By interpreting the low-velocity features of the mined-out area, we can accurately delineate its boundaries. The results of the interpretation align coherently with the findings from the drilling data, to verify the feasibility and effectiveness of parallel-swath-array analysis of passive source surface waves based on beamforming in detecting coal mined-out area under non-stationary ambient noises.

MetaCAE: Causal autoencoder with meta-knowledge transfer for brain effective connectivity estimation

Using machine learning methods to estimate brain effective connectivity networks from functional magnetic resonance imaging (fMRI) data has gradually become one of the hot subjects in the fields of neuroscience. In particular, the encoder–decoder based methods can effectively extract the connections in fMRI time series, which have achieved promising performance. However, these methods generally use Granger causality model, which may identify false directions due to the non-stationary characteristic of fMRI data. Additionally, fMRI datasets have limited sample sizes, which significantly constrains the development of these methods. In this paper, we propose a novel brain effective connectivity estimation method based on causal autoencoder with meta-knowledge transfer, called MetaCAE. The proposed approach employs a causal autoencoder (CAE) to extract causal dependencies from non-stationary fMRI time series, and leverages meta-knowledge transfer to improve the estimation accuracy on small-sample data. More specifically, MetaCAE first employs a temporal convolutional encoder to extract non-stationary temporal information from fMRI time series. Then it uses a structural equation model-based decoder to decode causal relationships between brain regions. Finally, it utilizes a model-agnostic meta-learning method to learn the meta-knowledge of the shared brain effective connectivity among different subjects, and transfers the meta-knowledge to the CAE to enhance its estimation ability on small-sample fMRI data. Comprehensive experiments on both simulated and real-world data demonstrate the efficacy of MetaCAE in estimating brain effective connectivity.

Influence of large-scale climate indices and regional meteorological elements on drought characteristics in the Luanhe River Basin

Frequent drought disasters have significant impacts on socio-economic and ecosystems, and it is crucial to explore the propagation characteristics of drought for disaster prevention and mitigation. In this paper, based on 0.25° × 0.25° grid-point Meteorological hydrological and large-scale climate factor data, the start-to-start, peak-to-peak, and end-to-end drought propagation times, and the periods and rates of drought development and recovery were estimated for 11 regions in the Luanhe River Basin under stationary and non-stationary conditions. The Generalized Additive Model for Location, Scale and Shape (GAMLSS) framework was used to construct stationary and non-stationary models to capture the stationary and non-stationary drought characteristics respectively, and then the drought development and recovery patterns, and drought propagation times were assessed. The results showed that under the influence of climate factors, severe drought events occurred in most study areas, the duration of meteorological drought was prolonged by 0.1–0.6 months, and the peak intensity was increased by about 0.05. The severity of hydrological drought increased by 0.2–0.8, and the peak intensity decreased by 0.1–0.2. The rate of development and recovery of hydrological drought was accelerated by 0.1–0.2 per month. The propagation time of start-to-start was shortened by 0.2 months, and the propagation time of end-to-end was extended by 1–2 months. These mean that water resource control authorities need to propose responses to droughts more quickly.

Characteristic Analysis and Modeling of Train‐to‐Train Wireless Channel in Station Scenario

In this paper, ray tracing (RT) is used to analyze the characteristics of train‐to‐train (T2T) wireless channel in 2.1 GHz frequency band, including path loss, multipath clustering, delay spread, Rice factor, angular spread, and channel nonstationarity. It is found that the change of environment has a great influence on the characteristics of the wireless channel, which not only causes the birth and death of multipath clusters but also makes the channel appear nonstationary characteristics. In order to characterize the nonstationarity of the T2T wireless channel, we introduce the time correlation coefficient (TPCC) of the power delay profile (PDP), analyze the nonstationarity of the T2T wireless channel, and give the quasi‐stationarity distance. The results are basically consistent with the measured data.

Data-Driven Joint Fault Diagnosis Based on RMK-ASSA and DBSKNet for Blast Furnace Iron-Making Process

Blast furnace iron-making process (BFIP) is one of the most critical procedures in the iron and steel industry where timely detection and accurate classification of faults have always been of core focus. However, the coupling effects of system’s nonlinear and nonstationary characteristics often cause process consistent underlying information to be buried, allowing accurate extraction to be a significant challenge. This also complicates the development of BFIP fault diagnosis model. Therefore, we propose a novel data-driven joint fault diagnosis strategy that employs regularized mutual kernel analytic stationary subspace analysis (RMK-ASSA) and deep broad stationary kernel network (DBSKNet) to eliminate this interference. To develop this method, we first construct an RMK-ASSA approach to address the poor modeling accuracy caused by standard analytic stationary subspace analysis (ASSA)’s inability to handle complex process nonlinearity. Global and local kernels are utilized to account for multiple nonlinearities in BFIP data. The weight of different nonlinear data is calculated by regularized principal component analysis, and the main information is imported into ASSA to obtain more robust and accurate modeling results by eliminating the interference of redundant noise. Subsequently, we design a DBSKNet-based classifier to implement the fault diagnosis task. This network further considers the nonlinearity by boosting kernel structure in depth and width while distinguishing the respective contributions of different kernels to fault diagnosis results. Finally, a double-layer loop parameter optimization algorithm is used for optimizing. Simulated cases and practical BFIP tests validate that RMK-ASSA eliminates the negative impact caused by nonstationary data and that the proposed joint fault diagnosis strategy outperforms other methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —BFIP’s nonlinear and nonstationary coupling properties pose unique challenges in eliminating distractions, constructing fault classifiers and accurately detecting process anomalies. To tackle these challenges, this paper proposes a joint fault diagnosis strategy based on RMK-ASSA and DBSKNet. RMK-ASSA effectively estimates nonlinear consistent features, while DBSKNet mines rich deep nonlinear information, accurately distinguishing variations in BFIP data under different working conditions. Experimental results demonstrate that this data-driven strategy can perform high-quality fault diagnosis, enabling field engineers to execute operations efficiently.

DYNAMIC SPECTRAL ANALYSIS OF HUMAN BREATHING AND HEARTBEAT BY RESCUER RADARS

Specialized rescuer radars, employed for detecting living individuals during rescue operations amid natural or man-made disasters, operate by estimating the nonstationary spectral characteristics of reflected signals induced by breathing and heartbeats. The nonstationary spectra resulting from Doppler phase shifts in reflected radar signals are attributed to the breathing and heartbeat processes of living humans. These phase fluctuations occur at ultra-low frequencies and can be effectively detected using extended pseudo-noise probing signals, such as those based on Mersenne codes. The method for tracking the power spectrum of a process, where the rates of change in the correlation function at various lags differ over time, is presented. The method is discussed in terms of its application with finite-length correlation processes. It allocates a short memory for rapidly varying terms in the correlation while concurrently employing longer-term averaging for the more stationary terms. Time-varying spectral estimates of rescuer radar signals are derived through the processing of resulting correlation estimates of signals reflected from a living human body. Examples of real spectrum estimates are provided to illustrate that improved tracking can be achieved compared to employing a constant lag-invariant averaging method.

Multi-Scale Masked Autoencoders for Cross-Session Emotion Recognition.

Affective brain-computer interfaces (aBCIs) have garnered widespread applications, with remarkable advancements in utilizing electroencephalogram (EEG) technology for emotion recognition. However, the time-consuming process of annotating EEG data, inherent individual differences, non-stationary characteristics of EEG data, and noise artifacts in EEG data collection pose formidable challenges in developing subject-specific cross-session emotion recognition models. To simultaneously address these challenges, we propose a unified pre-training framework based on multi-scale masked autoencoders (MSMAE), which utilizes large-scale unlabeled EEG signals from multiple subjects and sessions to extract noise-robust, subject-invariant, and temporal-invariant features. We subsequently fine-tune the obtained generalized features with only a small amount of labeled data from a specific subject for personalization and enable cross-session emotion recognition. Our framework emphasizes: 1) Multi-scale representation to capture diverse aspects of EEG signals, obtaining comprehensive information; 2) An improved masking mechanism for robust channel-level representation learning, addressing missing channel issues while preserving inter-channel relationships; and 3) Invariance learning for regional correlations in spatial-level representation, minimizing inter-subject and inter-session variances. Under these elaborate designs, the proposed MSMAE exhibits a remarkable ability to decode emotional states from a different session of EEG data during the testing phase. Extensive experiments conducted on the two publicly available datasets, i.e., SEED and SEED-IV, demonstrate that the proposed MSMAE consistently achieves stable results and outperforms competitive baseline methods in cross-session emotion recognition.

Modeling and Prediction of Nonstationary Ground Motions as Time–Frequency Images

Proper modeling of nonstationary characteristics of ground motions is critical in estimating the seismic performance of structures. The importance of ground motion nonstationarity is being increasingly recognized in seismic design codes and provisions. This paper develops a new method for predicting seismic ground motions in the joint time–frequency domain based on recorded ground motions. We treat wavelet energy maps of acceleration records as images and extract essential patterns from them using principal component analysis. These patterns are then linked to the seismic source, path, and site variables using general regression neural network. The resulting model predicts an image representing the expected evolutionary power spectrum conditioned on the input variables. An example application is presented using records from the Next Generation Attenuation of Ground Motions Database of the Pacific Earthquake Engineering Center. As opposed to conventional ground motion prediction models, the proposed approach retains the time domain characteristics of ground motions. The results show that the proposed model can predict significant patterns in the seismic energy distribution, acceleration time series, and 5% damped elastic spectral accelerations.

A novel methodology for emotion recognition through 62-lead EEG signals: multilevel heterogeneous recurrence analysis.

Recognizing emotions from electroencephalography (EEG) signals is a challenging task due to the complex, nonlinear, and nonstationary characteristics of brain activity. Traditional methods often fail to capture these subtle dynamics, while deep learning approaches lack explainability. In this research, we introduce a novel three-phase methodology integrating manifold embedding, multilevel heterogeneous recurrence analysis (MHRA), and ensemble learning to address these limitations in EEG-based emotion recognition. The proposed methodology was evaluated using the SJTU-SEED IV database. We first applied uniform manifold approximation and projection (UMAP) for manifold embedding of the 62-lead EEG signals into a lower-dimensional space. We then developed MHRA to characterize the complex recurrence dynamics of brain activity across multiple transition levels. Finally, we employed tree-based ensemble learning methods to classify four emotions (neutral, sad, fear, happy) based on the extracted MHRA features. Our approach achieved high performance, with an accuracy of 0.7885 and an AUC of 0.7552, outperforming existing methods on the same dataset. Additionally, our methodology provided the most consistent recognition performance across different emotions. Sensitivity analysis revealed specific MHRA metrics that were strongly associated with each emotion, offering valuable insights into the underlying neural dynamics. This study presents a novel framework for EEG-based emotion recognition that effectively captures the complex nonlinear and nonstationary dynamics of brain activity while maintaining explainability. The proposed methodology offers significant potential for advancing our understanding of emotional processing and developing more reliable emotion recognition systems with broad applications in healthcare and beyond.

HabLSTM: A Nonstationary Feature Focusing LSTM for Spatiotemporal Prediction of Harmful Algal Bloom

HabLSTM: A Nonstationary Feature Focusing LSTM for Spatiotemporal Prediction of Harmful Algal Bloom

Motor Bearing Fault Diagnosis in an Industrial Robot Under Complex Variable Speed Conditions

Abstract Motor bearing is the key vulnerable part of the servomotor in an industrial robot, which is always arranged at the joint that is the main load area. In the movement process of the robot, motor bearing bears a great impact due to the frequent movement of joints, which is easily damaged. The fault characteristic information of a bearing in these complex conditions shows strong nonstationary characteristics. Early nonstationary fault signals are often weak and submerged in background noise. The nonstationary signal processing method using computed order analysis and the weak signal enhancement method using adaptive stochastic resonance both show good performances for the above problems. Inspired by these, a hybrid diagnosis strategy for motor bearing under these speed conditions is proposed. Firstly, the nonstationary fault signals of the motor bearing are transformed into stationary angular signals via computed order analysis. Then, the fault modes are identified via resonance demodulation and variational mode decomposition in the order spectrum. Finally, adaptive stochastic resonance is used to extract the fault features reflecting the bearing operation state. Two types of typical speed conditions are considered, which are representative of the joint. Numerical simulation analysis and experiments verify the effectiveness of the diagnosis method.

Inversion of wind load on high-rise buildings under non-stationary and non-Gaussian conditions via DKF and FB-FFT

Wind-induced effects should be especially concerned for the design and maintenance of high-rise buildings, and information of wind load is sometimes prerequisite for related wind-resistant practices. Previous studies have been mainly conducted to deduce wind load on high-rise buildings under stationary and Gaussian conditions. However, due to the inherent randomness, wind load often exhibits non-stationary and non-Gaussian characteristics. This study employs two methods, namely Discrete Kalman Filter (DKF) and Fast Bayesian Fourier Transform (FB-FFT), to estimate wind load on high-rise buildings under non-stationary and/or non-Gaussian conditions. Firstly, a numerical building model is employed to evaluate the inversion performance of the two methods. Subsequently, both methods are applied to determine the wind load on a real building. Results through numerical simulation analysis demonstrate that DKF can invert the base force and modal force accurately under non-stationary conditions. For stationary non-Gaussian cases, the inverted wind load approximates the target force in terms of amplitude, but the inversion result exhibits Gaussian characteristics. FB-FFT can be basically utilized to invert the modal force under varied concerned conditions, yet the estimated wind load for stationary non-Gaussian case is slightly smaller than the target value. In reference to the real high-rise building example, DKF is found to produce similar results to those determined on the basis of wind tunnel test and in-situ measurement. Meanwhile, results of model force obtained via the two methods agree with each other. The above findings suggest that DKF and FB-FFT can be employed, at least partially, to deal with the issues of wind load inversion under non-stationary and non-Gaussian conditions.

Research on robust fault-tolerant control of the controllable suspension based on knowledge-data fusion driven

For the robust fault-tolerant control of the controllable suspension system, a control strategy driven by knowledge-data fusion is proposed. Firstly, the boundary fuzziness between perturbation type uncertainty and gain type fault is analyzed, and then a data-driven method is introduced to avoid the state estimation of system uncertainty and fault. The proximal policy optimization algorithm in reinforcement learning is selected to construct a “data control law”, to deal with uncertainty and fault. On the other hand, based on the classical sky-hook control, the “knowledge control law” for system performance optimization is designed, taking into account the nonlinear and non-stationary characteristics of the system. Furthermore, the dependency between robust fault tolerance and performance optimization control is revealed, and the two control laws are fused by numerical multiplication, to realize the performance matching optimization control of robust fault tolerance of controllable suspension system driven by knowledge-data fusion. Finally, the effectiveness and feasibility of the proposed method are verified by the simulation and real-time experiment of non-stationary excitation and near-stationary excitation under the combination of uncertainty and fault.

Real-time prediction of ship motion based on improved empirical mode composition and dynamic residual neural network

Ship motion attitude data have strong random and non-stationary characteristics under severe sea states. Real-time and accurate prediction of the ship's motion attitude can significantly improve the safety of navigation. Therefore, this article proposes a prediction model based on the improved empirical mode decomposition (IEMD) and the dynamic residual recurrent neural network with bidirectional structure and time pattern attention mechanism (TPA-Bi-DRRNN), and proposes a new algorithm: dynamic adaptive beetle swarm antennae search (DABSAS) algorithm to optimise the initial weight and threshold of the prediction model. The input data are adaptively composed into multiple intrinsic mode functions (IMFs) containing their frequency characteristics using IEMD, and a prediction is made for each IMF using TPA-Bi-DRRNN. The model structure can be regulated in real time according to the sliding window. The destroyer DTMB5415 is used as an example to conduct a performance test of the hybrid prediction model and DABSAS. The results show that no mode mixing occurred in the IMFs, the noise in each IMF was significantly reduced, thus dramatically reducing the difficulty of using the input data for prediction; and the optimization performance of DABSAS in applying the TPA-Bi-DRRNN is much better than that of the traditional algorithms. Compared with other models, the difference in the predictive accuracy of TPA-Bi-DRRNN under each condition is the smallest, suggestings that it has extremely high robustness and will always be able to maintain much higher accuracy than other models over a long period, thus meeting the needs for real-time accurate prediction of ship motion attitude.

Filter bank second-order underdamped stochastic resonance analysis for implementing a short-term high-speed SSVEP detection

ObjectiveThe progression of brain-computer interfaces (BCIs) has been propelled by breakthroughs in neuroscience, signal processing, and machine learning, marking it as a dynamic field of study over the past few decades. Nevertheless, the nonlinear and non-stationary characteristics of steady-state visual evoked potentials (SSVEPs), coupled with the incongruity between frequently employed linear techniques and nonlinear signal attributes, resulted in the subpar performance of mainstream non-training algorithms like canonical correlation analysis (CCA), multivariate synchronization index (MSI), and filter bank CCA (FBCCA) in short-term SSVEP detection. MethodsTo tackle this problem, the novel fusions of common filter bank analysis, CCA dimensionality reduction methods, USSR models, and MSI recognition models are used in SSVEP signal recognition. ResultsUnlike conventional linear techniques such as CCA, MSI, and FBCCA, the filter bank second-order underdamped stochastic resonance (FBUSSR) analysis demonstrates superior efficacy in the detection of short-term high-speed SSVEPs. ConclusionThis research enlists 32 subjects and uses a public dataset to assess the proposed approach, and the experimental outcomes indicate that the non-training method can attain greater recognition precision and stability. Furthermore, under the conditions of the newly proposed fusion method and light stimulation, the USSR model exhibits the most optimal enhancement effect. SignificanceThe findings of this study underscore the expansive potential for the application of BCI systems in the realm of neuroscience and signal processing.

Research on non-stationary characteristic test and decomposition for dynamic response of floating structures

Considering the complex influences of harsh marine environments, auxiliary structures, and various operational processes, motion response of floating structures will inevitably exhibit non-stationary behaviors. Therefore, grasping the non-stationary characteristics of motion responses is imperative for a comprehensive understanding of the operational mechanisms. This paper presents a strategy for testing non-stationary characteristics and decomposing dynamic responses, with the objective of investigating the influence of non-stationary characteristics on motion responses of floating structures. The primary contributions of this study are: (1) Proposed a cointegration analysis method for characteristics testing applicable to floating structures to investigate potential non-stationary variations. It explains the statistics of non-stationary characteristics through dimensional analysis, establishing a connection between the test statistics and the engineering intuition of non-stationary motion response. (2) Proposed a non-stationary signal decomposition method based on adaptive segmentation and decomposition control techniques to overcome mode mixing issues in the decomposition of structural motion responses. The validity and applicability of the developed strategy for testing and decomposing non-stationary responses are verified through a synthesized signal and a numerical semi-submersible platform. Numerical results demonstrate that this strategy can effectively test the non-stationarity, and the accuracy of decomposition results is greater than 99%, and the maximum normalization error is less than 2%. Finally, physical experiments are conducted on a semi-submersible platform under regular and irregular waves action, respectively, to verify the feasibility of the developed strategy when applied to measured data. Experimental results indicate that this strategy can effectively detect the non-stationary characteristics of the measured response, and realize an accurate decomposition of structural motion responses. These results will provide valuable insights into understanding non-stationary characteristics relevant to various engineering applications.

Streaming variational probabilistic principal component analysis for monitoring of nonstationary process

Modern industrial processes are characteristic of nonstationary and uncertainty. To address these issues, this paper proposes a probabilistic principal component analysis based model that utilizes streaming variational inference for online monitoring of nonstationary process. The model parameters are updated in a streaming/batch-wise manner to track the nonstationary behavior in the process. In the updating procedures, the posterior distributions obtained from the previous data batch are used as priors for the current model, whose parameters can be estimated using the variational Bayesian inference. The streaming variational inference enables recursive parameter estimation over time. Additionally, in order to improve computational efficiency, a distributed update strategy is also applied to the proposed model. For online process monitoring, the noncentral chi-square distributions are derived to estimate the statistical control limits for each data batch, resulting in better adaptation to the nonstationary characteristics. The effectiveness and superiority of the proposed method are validated through simulation example and real-world industrial application.