Adaptive Gaussian Mixture Model Research Articles

An algorithm for multi-damage size estimation of composite laminates

Localization and size estimation of composite damage are challenging but essential for composite performance evaluation. This paper proposes a new methodology for the size estimation of multi-damage in composite laminates using Lamb wave technology. The pure A0 modal of Lamb wave is excited to avoid dispersion and multi-modal effects of Lamb wave. An extraction algorithm is introduced to obtain the first wave packet and time-of-flight. According to the results obtained by the extraction algorithm, the Bayesian-hybrid localization algorithm based on the reconstruction algorithm for probabilistic inspection of damage and modified delay-and-sum (MDAS) is performed to localize damages. The damage boundaries are obtained through convex enveloping a series of damage boundary points identified by MDAS. An adaptive Gaussian mixture model based on Akaike’s Information Criterion and Bayesian Information Criterion is designed to remove abnormal boundary points. The proposed method is numerically investigated and validated through multi-damage experiments. The results demonstrate that it can accurately estimate the locations and boundaries of multi-damage in composite laminates.

Estimating Vehicle Turn-In Rate of Expressway Rest Areas via ETC Gantry Data – An ADPC-GMM Approach

Vehicle turn-in rate is a critical and widely adopted input for expressway rest area design and operation. With the implementation of expressway ETC gantries, the ERA turn-in rate can be further estimated by measuring the travel speed distribution via ETC gantry data. This paper proposed an adaptive density peak clustering Gaussian mixture model (ADPC-GMM) for ERA turn-in rate estimation. The ADPC algorithm is applied to generate the GMM’s inputs accommodating to the traffic characteristic of ERA expressway segments and GMM would further provide the turn-in rate estimation results. To validate the model precision, the turn-in rate data of four selected ERAs in Sichuan, China, as well as the ETC gantry data of their corresponding expressway sections are obtained. According to the estimation results, the MAE and RMSE are 0.0228 and 0.0267 for the passenger car scenario and 0.0264 and 0.0356 for the commercial truck scenario, respectively. These results are also at the lowest level compared with the results acquired from ordinary GMM, K-Means and DBSCAN algorithms. The proposed method has good applicability for vehicle turn-in rate estimation and can be deployed at different ERAs, especially those ERAs without traffic monitoring.

Guided-wave Dynamic Probability Model-based Crack Quantification Method for Metal Structures

In the process of applying guided-wave-based aircraft online structural health monitoring, the characteristics of guided wave signals used to represent structural status exhibit random uncertainty due to the interference of loads on guided wave propagation. The trend of signal feature changes caused by damage is often obscured, making the quantification of cracks under loads one of the challenges in online structural health monitoring for aircraft. To address this challenge, this paper proposes a crack quantification method using an adaptive Gaussian mixture model (GMM) and optimized probability migration distance measurement. This method effectively mitigates the uncertainty caused by loads by constructing an adaptive Gaussian mixture model to track the probability distribution changes of guided wave signal features under different structural health conditions. Subsequently, an optimized probability migration distance measurement method is employed to characterize the structural state, further enhancing the correlation between features and the extent of structural damage. Finally, an optimized probability migration distance relationship with crack length is established to estimate the crack length of new structural specimens. The effectiveness of this method is validated using load-induced crack propagation experiments on metal structures.

Seismic fragility analysis of structures via an Adaptive Gaussian Mixture Model and its application to resilience assessment

Seismic fragility analysis and seismic resilience assessment are pivotal tasks within the performance-based earthquake engineering framework. The former aims to quantitatively assess the probability of engineering structures sustaining various degrees of damage when subjected to earthquakes of varying intensity levels. In contrast to many traditional seismic fragility methods, this paper introduces a precise and versatile approach grounded in reliability analysis, with the goal of eliminating the restrictive lognormal assumption. Initially, the proposed method involves conducting seismic reliability analysis of structures using the Fractional Exponential Moments-based Maximum Entropy Method (FEM-MEM). This approach efficiently yields failure probabilities. Subsequently, an Adaptive Gaussian Mixture Model (AGMM) is presented for fitting a set of failure probability points, producing comprehensive and continuous seismic fragility curves. Notably, AGMM offers remarkable flexibility in modeling fragility curves, ensuring precise estimations for subsequent resilience assessments. Building upon the results of the fragility analysis, the paper proceeds to assess the seismic resilience of structures. The proposed method’s feasibility and effectiveness are validated through two illustrative numerical examples. The results demonstrate that, in comparison to the conventional lognormal assumption, the proposed method offers superior accuracy and broader applicability for conducting seismic fragility analyses of structures.

Retracted: Simulation of Tennis Match Scene Classification Algorithm Based on Adaptive Gaussian Mixture Model Parameter Estimation

Retracted: Simulation of Tennis Match Scene Classification Algorithm Based on Adaptive Gaussian Mixture Model Parameter Estimation

Concept drift challenge in multimedia anomaly detection: A case study with facial datasets

Anomaly detection in multimedia datasets is a widely studied area. Yet, the concept drift challenge in data has been ignored or poorly handled by the majority of the anomaly detection frameworks. The state-of-the-art approaches assume that the data distribution at training and deployment time will be the same. However, due to various real-life environmental factors, the data may encounter drift in its distribution or can drift from one class to another in the late future. Thus, a one-time trained model might not perform adequately. In this paper, we systematically investigate the effect of concept drift on various detection models and propose a modified Adaptive Gaussian Mixture Model (AGMM) based framework for anomaly detection in multimedia data. In contrast to the baseline AGMM, the proposed extension of AGMM remembers the past for a longer period in order to handle the drift better. Extensive experimental analysis shows that the proposed model better handles the drift in data as compared with the baseline AGMM. Further, to facilitate research and comparison with the proposed framework, we contribute three multimedia datasets constituting faces as samples. The face samples of individuals correspond to the age difference of more than ten years to incorporate a longer temporal context.

Decoding Upper-Limb Movement Intention Through Adaptive Dynamic Movement Primitives: A Proof-of-Concept Study with a Shoulder-Elbow Exoskeleton.

This work presents an intention decoding algorithm that can be used to control a 4 degrees-of-freedom shoulder-elbow exoskeleton in reaching tasks. The algorithm was designed to assist the movement of users with upper-limb impairments who can initiate the movement by themselves. It relies on the observation of the initial part of the user's movement through joint angle measures and aims to estimate in real-time the phase of the movement and predict the goal position of the hand in the reaching task. The algorithm is based on adaptive Dynamic Movement Primitives and Gaussian Mixture Models. The performance of the algorithm was verified in robot-assisted planar reaching movements performed by one healthy subject wearing the exoskeleton. Tests included movements of different amplitudes and orientations. Results showed that the algorithm could predict the hand's final position with an error lower than 5 cm after 0.25 s from the movement onset, and that the final position reached during the tests was on average less than 4 cm far from the target position. Finally, the effects of the assistance were observed in a reduction of the activation of the Biceps Brachii and of the time to execute the reaching tasks.

Orbital Uncertainty Propagation Based on Adaptive Gaussian Mixture Model under Generalized Equinoctial Orbital Elements

The number of resident space objects (RSOs) has been steadily increasing over time, posing significant risks to the safe operation of on-orbit assets. The accurate prediction of potential collision events and implementation of effective and nonredundant avoidance maneuvers require the precise estimation of the orbit positions of objects of interest and propagation of their associated uncertainties. Previous research mainly focuses on striking a balance between accurate propagation and efficient computation. A recently proposed approach that integrates uncertainty propagation with different coordinate representations has the potential to achieve such a balance. This paper proposes combining the generalized equinoctial orbital elements (GEqOE) representation with an adaptive Gaussian mixture model (GMM) for uncertainty propagation. Specifically, we implement a reformulation for the orbital dynamics so that the underlying state and the moment feature of the GMM are propagated under the GEqOE coordinates. Starting from an initial Gaussian probability distribution function (PDF), the algorithm iteratively propagates the uncertainty distribution using a detection-splitting module. A differential entropy-based nonlinear detector and a splitting library are utilized to adjust the number of GMM components dynamically. Component splitting is triggered when a predefined threshold of differential entropy is violated, generating several GMM components. The final probability density function (PDF) is obtained by a weighted summation of the component distributions at the target time. Benefiting from the nonlinearity reduction caused by the GEqOE representation, the number of triggered events largely decreases, causing the necessary number of components to maintain uncertainty realism also to decrease, which enables the proposed approach to achieve good performance with much more efficiency. As demonstrated by the results of propagation in three scenarios with different degrees of complexity, compared with the Cartesian-based approach, the proposed approach achieves comparable accuracy to the Monte Carlo method while largely reducing the number of components generated during propagation. Our results confirm that a judicious choice of coordinate representation can significantly improve the performance of uncertainty propagation methods in terms of accuracy and computational efficiency.

Adaptive Gaussian mixture model for identifying outliers in historical route travel times

AbstractThe historical route travel time data contain a few outliers composed of subpopulations signifying unusual traffic conditions. These outliers compose the right tail of the distribution against the central part occupied by most normal travel times dominating usual traffic conditions likely to be composed of subpopulations. The diverse subpopulations of two types of travel times result in the structural random changes of distribution shapes. This creates the problem for fixing the boundary between the two types of travel times. To address the problem, an adaptive Gaussian mixture model was formulated with two types of components, and an algorithm was put forward to determine the critical number of components in an iterative manner by adapting two types of components to provide an adequate fit to the two parts of the distribution respectively. The determined two types of components can not only fix the boundary to identify outliers reasonably, but also quantify the latent subpopulations of two types of route travel times. Thus, the route‐level travel time variability can be measured under usual/unusual traffic conditions. Two kinds of data were used to illustrate the good effects on the identification of outliers and to demonstrate the vital role of outliers in the measure of variation of route travel time.

Vehicular visible light communications noise analysis and modeling.

Vehicular visible light communications (VVLC) is promising intelligent transportation systems technology with the utilization of light-emitting diodes. The main degrading factor for the performance of VVLC systems is noise. Traditional VVLC systems noise modeling is based on the additive white Gaussian noise assumption in the form of shot and thermal noise. In this paper, to investigate both time correlated and white noise components of the VVLC channel noise, we propose a noise analysis based on Allan variance, which provides a time-series analysis method to identify noise from the data. The results show that white noise and random walk are observed in the VVLC systems. We also propose a motion detection algorithm based on the adaptive Gaussian mixture (GM) model to generate a double Gaussian model of VVLC channel noise. We further present a study on the error performance of a VVLC system considering channel noise to be a mixture of Gaussian components. We derive the analytical expressions of probability of error for binary phase-shift keying and quadrature phase-shift keying constellations. It has been observed that, in the presence of GM noise, the system performance degrades significantly from the usual one expected in a Gaussian noise environment and becomes a function of the mixing coefficients of the GM distribution.

Adaptive Gaussian Mixture Model for Uncertainty Propagation Using Virtual Sample Generation

Orbit uncertainty propagation plays an important role in the analysis of a space mission. The accuracy and computation expense are two critical essences of uncertainty propagation. Repeated evaluations of the objective model are required to improve the preciseness of prediction, especially for long-term propagation. To balance the computational complexity and accuracy, an adaptive Gaussian mixture model using virtual sample generation (AGMM-VSG) is proposed. First, an unscented transformation and Cubature rule (UT-CR) based splitting method is employed to adaptive update the weights of Gaussian components for nonlinear dynamics. The Gaussian mixture model (GMM) approximation is applied to better approximate the original probability density function. Second, instead of the pure expensive evaluations by conventional GMM methods, virtual samples are generated using a new active-sampling-based Kriging (AS-KRG) method to improve the propagation efficiency. Three cases of uncertain orbital dynamical systems are used to verify the accuracy and efficiency of the proposed manuscript. The likelihood agreement measure (LAM) criterion and the number of expense evaluations prove the performance.

Adaptive GMM and OTWD-based structural crack quantification under random load

A challenge for online guided wave-based structural health monitoring is the reliable crack quantitative evaluation under time varying conditions (TVCs). This paper proposed an adaptive guided wave (GW)-Gaussian mixture model (GMM) and optimal transport Wasserstein distance (OTWD)-based structural crack quantification method. Firstly, adaptive GMM tracking the probability distribution of GW signal features obtained under different structural healthy states is utilized to suppress the uncertain influence caused by TVCs. Then, OTWD is proposed to measure the GMM difference with improved linearity by finding the optimal transport between two GMMs. The OTWD between GMMs established under structural healthy state and monitoring state respectively is utilized as the damage indicator, where the data discrepancy caused by TVCs is further reduced. Finally, the quantitative relationship between OTWD and crack length is established to estimate the crack length. The overall method is demonstrated on the aircraft attachment lug specimens under random load. The generalization and necessity of the method is verified by cross validation and comparison with existing methods. The results illustrate the improved reliability and accuracy of the proposed method in crack quantitative evaluation under the uncertain influence of random load.

Soft Sensing of NOx Emissions From Thermal Power Units Based on Adaptive GMM Two-Step Clustering Algorithm and Ensemble Learning

The accurate measurement of NOx concentration is the basis of accurate ammonia injection in selective catalytic reduction (SCR) system of thermal power unit. Excessive or too little ammonia injection will cause ammonia escape or exceeding the standard of NOx emission, and cause environmental pollution. There exist a large measurement lag and errors during the purging process in the measurement of NOx concentration in the SCR system of thermal power units. Therefore, to enable the intelligent control of the SCR system, it is necessary to carry out soft sensing of NOx emissions. This paper proposes a soft sensing algorithm for NOx emissions of thermal power units based on an adaptive Gaussian Mixture Model (GMM) two-step clustering algorithm and ensemble learning. Adaptive GMM two-step clustering (AGTSC) algorithm is used to softly divide the historical data into working conditions. Temporal Pattern Attention Long Short-Term Memory (TPA-LSTM) is also adopted to construct individual learners for each working condition. Here we use the parameter regression algorithm to train the combiner based on the output of the individual learner and the membership signal of the working condition as the input of the combiner. The clustering algorithm is tested with three datasets. The results show that this algorithm addresses the shortcomings of GMM including not being applicable to the clustering of non-convex datasets and manual selection of the number of clusters. The soft sensing algorithm is verified by using the historical data of the SCR system of 1000 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MW</i> thermal power units. The results show that the proposed method has higher accuracy and stronger generalization ability than the conventional method, hence providing an effective method for soft sensing of NOx emissions of thermal power units.

A Small Sample-Based Multiclass Change Detection Method Using Change Vector Analysis With Adaptive Weight Gaussian Mixture Model

A Small Sample-Based Multiclass Change Detection Method Using Change Vector Analysis With Adaptive Weight Gaussian Mixture Model

Combining robust level extraction and unsupervised adaptive classification for high-accuracy fNIRS-BCI: An evidence on single-trial differentiation between mentally arithmetic- and singing-tasks.

Functional near-infrared spectroscopy (fNIRS) is a safe and non-invasive optical imaging technique that is being increasingly used in brain-computer interfaces (BCIs) to recognize mental tasks. Unlike electroencephalography (EEG) which directly measures neural activation, fNIRS signals reflect neurovascular-coupling inducing hemodynamic response that can be slow in time and varying in the pattern. The established classifiers extend the EEG-ones by mostly employing the feature based supervised models such as the support vector machine (SVM) and linear discriminant analysis (LDA), and fail to timely characterize the level-sensitive hemodynamic pattern. A dedicated classifier is desired for intentional activity recognition of fNIRS-BCI, including the adaptive acquisition of response relevant features and accurate discrimination of implied ideas. To this end, we herein propose a specifically-designed joint adaptive classification method that combines a Kalman filtering (KF) for robust level extraction and an adaptive Gaussian mixture model (a-GMM) for enhanced pattern recognition. The simulative investigations and paradigm experiments have shown that the proposed KF/a-GMM classification method can effectively track the random variations of task-evoked brain activation patterns, and improve the accuracy of single-trial classification task of mental arithmetic vs. mental singing, as compared to the conventional methods, e.g., those that employ combinations of the band-pass filtering (BPF) based feature extractors (mean, slope, and variance, etc.) and the classical recognizers (GMM, SVM, and LDA). The proposed approach paves a promising way for developing the real-time fNIRS-BCI technique.

HOG-SVM Impurity Detection Method for Chinese Liquor (Baijiu) Based on Adaptive GMM Fusion Frame Difference.

Chinese liquor (Baijiu) is one of the four major distilled spirits in the world. At present, liquor products containing impurities still exist on the market, which not only damage corporate image but also endanger consumer health. Due to the production process and packaging technologies, impurities usually appear in products of Baijiu before entering the market, such as glass debris, mosquitoes, aluminium scraps, hair, and fibres. In this paper, a novel method for detecting impurities in bottled Baijiu is proposed. Firstly, the region of interest (ROI) is cropped by analysing the histogram projection of the original image to eliminate redundant information. Secondly, to adjust the number of distributions in the Gaussian mixture model (GMM) dynamically, multiple unmatched distributions are removed and distributions with similar means are merged in the process of modelling the GMM background. Then, to adaptively change the learning rates of the front and background pixels, the learning rate of the pixel model is created by combining the frame difference results of the sequence images. Finally, a histogram of oriented gradient (HOG) features of the moving targets is extracted, and the Support Vector Machine (SVM) model is chosen to exclude bubble interference. The experimental results show that this impurity detection method for bottled Baijiu controls the missed rate by within 1% and the false detection rate by around 3% of impurities. Its speed is five times faster than manual inspection and its repeatability index is good, indicating that the overall performance of the proposed method is better than manual inspection with a lamp. This method is not only efficient and fast, but also provides practical, theoretical, and technical support for impurity detection of bottled Baijiu that has broad application prospects.

GMM based low-complexity adaptive machine-learning equalizers for optical fiber communication

The demand for high-speed data transmission has increased rapidly over the past few years, leading to advanced optical communication techniques. However, most of machine learning based equalizers which are trained with offline dataset mainly focus on achieving low BER, neglecting the generalization ability when the properties of optical link change. In this paper, we propose Gaussian Mixture model (GMM) based low-complexity adaptive machine-learning equalizers. The proposed online training strategy can fine-tune the parameters in GMM with a small amount of training sequence by introducing Maximum a posteriori probability (MAP) algorithm and sliding window. The size of online training sequence can be reduced by utilizing the parameters trained from offline data as the priori information to reduce the size of online training sequence. The proposed adaptive GMM based equalizers can not only show an excellent capability of mitigating nonlinear distortions but also show the ability to update parameters automatically according to the channel conditions. In addition, experimental results show that by introducing MAP algorithm and sliding window, the convergence speed of the proposed equalizers have been accelerated by 2 times, compared with the case that the traditional Expectation Maximization (EM) algorithm is used for online parameter update. On the other hand, there is no significant increase in computational complexity during the online stage.

Adaptive Gaussian mixture model based structural damage monitoring method under time-varying conditions

Abstract The low reliability of damage monitoring under Time-Varying Conditions (TVCs) is a key challenge for the practical application of Structural Health Monitoring (SHM) technology to aircraft structures. Among the existing SHM methods, Guided Wave (GW) and piezoelectric sensor based SHM technique is a promising method due to its high damage sensitivity and long monitoring range. Nevertheless the reliability problem still should be addressed. To deal with this problem, an adaptive Gaussian Mixture Model (GMM) based structural damage monitoring method is proposed. The probability distribution of GW features under TVCs is represented by the GMM. The center of each Gaussian component in a GMM is determined adaptively first. Then a global optimal GMM which could change with TVCs is constructed by the expectation maximization algorithm. Finally, along with damage monitoring process, the variation of GMMs is measured by a probabilistic similarity based damage index which allows normalized detection of structural damage. The utility of the proposed method is validated in the hole-edge crack monitoring of an aluminum tension sample under varying loading condition.

Data driven adaptive Gaussian mixture model for solving Fokker-Planck equation.

The Fokker-Planck (FP) equation provides a powerful tool for describing the state transition probability density function of complex dynamical systems governed by stochastic differential equations (SDEs). Unfortunately, the analytical solution of the FP equation can be found in very few special cases. Therefore, it has become an interest to find a numerical approximation method of the FP equation suitable for a wider range of nonlinear systems. In this paper, a machine learning method based on an adaptive Gaussian mixture model (AGMM) is proposed to deal with the general FP equations. Compared with previous numerical discretization methods, the proposed method seamlessly integrates data and mathematical models. The prior knowledge generated by the assumed mathematical model can improve the performance of the learning algorithm. Also, it yields more interpretability for machine learning methods. Numerical examples for one-dimensional and two-dimensional SDEs with one and/or two noises are given. The simulation results show the effectiveness and robustness of the AGMM technique for solving the FP equation. In addition, the computational complexity and the optimization algorithm of the model are also discussed.

Adaptive Gaussian mixture model and convolution autoencoder clustering for unsupervised seismic waveform analysis

Seismic facies analysis can effectively estimate reservoir properties, and seismic waveform clustering is a useful tool for facies analysis. We have developed a deep-learning-based clustering approach called the modified deep convolutional embedded clustering with adaptive Gaussian mixture model (AGMM-MDCEC) for seismic waveform clustering. Trainable feature extraction and clustering layers in AGMM-MDCEC are implemented using neural networks. We fuse the two independent processes of feature extraction and clustering, such that the extracted features are modified simultaneously with the results of clustering. We use a convolutional autoencoder for extracting features from seismic data and to reduce data redundancy in the algorithm. At the same time, weights of clustering network are fine-tuned through iteration to obtain state-of-the-art clustering results. We apply our new classification algorithm to a data volume acquired in western China to map architectural elements of a complex fluvial depositional system. Our method obtains superior results over those provided by traditional K-means, Gaussian mixture model, and some machine-learning methods, and it improves the mapping of the extent of the distributary system.