Label GM-PHD Filter Based on Threshold Separation Clustering

Gaussian mixture probability hypothesis density (GM-PHD) filtering based on random finite set (RFS) is an effective method to deal with multi-target tracking (MTT). However, the traditional GM-PHD filter cannot form a continuous track in the tracking process, and it is easy to produce a large number of redundant invalid likelihood functions in a dense clutter environment, which reduces the computational efficiency and affects the update result of target probability hypothesis density, resulting in excessive tracking error. Therefore, based on the GM-PHD filter framework, the target state space is extended to a higher dimension. By adding a label set, each Gaussian component is assigned a label, and the label is merged in the pruning and merging step to increase the merging threshold to reduce the Gaussian component generated by dense clutter update, which reduces the computation in the next prediction and update. After pruning and merging, the Gaussian components are further clustered and optimized by threshold separation clustering, thus as to improve the tracking performance of the filter and finally realizing the accurate formation of multi-target tracks in a dense clutter environment. Simulation results show that the proposed algorithm can form a continuous and reliable track in dense clutter environment and has good tracking performance and computational efficiency.

Strategies to Enhance the Performance of Gaussian Mixture Model Fitting for Uncertainty Quantification by Conditioning to Production Data

When formulating history matching within the Bayesian framework, we may quantify the uncertainty of model parameters and production forecasts using conditional realizations sampled from the posterior probability density function (PDF). It is quite challenging to sample such a posterior PDF. Some methods e.g., Markov chain Monte Carlo (MCMC), are very expensive (e.g., MCMC) while others are cheaper but may generate biased samples. In this paper, we propose an unconstrained Gaussian Mixture Model (GMM) fitting method to approximate the posterior PDF and investigate new strategies to further enhance its performance. To reduce the CPU time of handling bound constraints, we reformulate the GMM fitting formulation such that an unconstrained optimization algorithm can be applied to find the optimal solution of unknown GMM parameters. To obtain a sufficiently accurate GMM approximation with the lowest number of Gaussian components, we generate random initial guesses, remove components with very small or very large mixture weights after each GMM fitting iteration and prevent their reappearance using a dedicated filter. To prevent overfitting, we only add a new Gaussian component if the quality of the GMM approximation on a (large) set of blind-test data sufficiently improves. The unconstrained GMM fitting method with the new strategies proposed in this paper is validated using nonlinear toy problems and then applied to a synthetic history matching example. It can construct a GMM approximation of the posterior PDF that is comparable to the MCMC method, and it is significantly more efficient than the constrained GMM fitting formulation, e.g., reducing the CPU time by a factor of 800 to 7300 for problems we tested, which makes it quite attractive for large scale history matching problems.

MEASURING KEROGEN, SOLID ORGANICS, AND OIL PRODUCTION POTENTIALS OF UNCONVENTIONAL SOURCE ROCKS USING SOLID TYPE 20-MHZ NMR TECHNIQUES

It is well known that the NMR relaxation time T2 is proportional to the molecular mobility of water or hydrocarbons in rocks. In unconventional tight rocks, water and hydrocarbons are trapped in small pores of nanometer sizes, and their molecular mobility is severely restricted, causing the NMR T2 to be much shorter than that of conventional cases where pore sizes are in micrometer ranges. There are demands for advanced NMR techniques to study those solid-like bound hydrocarbons. In the meantime, it is of great interest for petrophysicists and geochemists to understand kerogen models in order to determine thermal maturity and hydrocarbon potential of organic-rich source rocks, and always attractive to have practical techniques that are nondestructive and less time consuming. In this study, a series of NMR 1D and 2D experiments have been performed on various types of source rocks with emphasis on short NMR T2 components, from sub-milliseconds down to a few microseconds, which are associated with kerogen, heavy hydrocarbons, and small hydrocarbon molecules bound in nanopores. The results show that the NMR CPMG pulse sequence used for the T2 data acquisition is (1) not capable of detecting and measuring the very rigid solid component of the T2 shorter than 30 microseconds, which is thought from kerogen, and (2) uncertain for the NMR components with T2 between 30 microseconds and 0.1 ms, which is dependent on the inter-echo spacing time (TE). Instead, the solid echo-pulse sequence was used to acquire the early time NMR signals that represent rigid solid matters, such as kerogen, in rock samples that have short relaxation times of less than 20 microseconds. The NMR solid echo signals were fitted into a composition of a Gaussian plus exponential functions to better describe NMR responses of source rocks with the shortest relaxation time of a few microseconds. The Gaussian component in the NMR signal is the measure of rigid solids associated with kerogen in the source rock. Model rock samples of thermally immature outcrops of the Upper Jurassic Kimmeridge Clay Formation in the UK and the Green River Shale Formation in the USA were used for comparison studies between the low field solid NMR techniques and geochemical analytical methods. The thermal maturities of the samples were artificially altered through the hydrous pyrolysis method at selected temperatures. The comparison results show that the amplitude of the Gaussian component measurement by NMR strongly correlated with the S2 of pyrolysis. The NMR relaxation times of the solid portion are directly proportional to the thermal maturity determined by organic petrography. This study concludes that the nondestructive solid NMR method provides an alternative and rapid way to study solid organic matters. The combined techniques enable us to further study kerogen models and hydrocarbon-generating potentials in organic-rich source rocks.

Unsupervised Abstractive Opinion Summarization by Generating Sentences with Tree-Structured Topic Guidance

This paper presents a novel unsupervised abstractive summarization method for opinionated texts. While the basic variational autoencoder-based models assume a unimodal Gaussian prior for the latent code of sentences, we alternate it with a recursive Gaussian mixture, where each mixture component corresponds to the latent code of a topic sentence and is mixed by a tree-structured topic distribution. By decoding each Gaussian component, we generate sentences with tree-structured topic guidance, where the root sentence conveys generic content, and the leaf sentences describe specific topics. Experimental results demonstrate that the generated topic sentences are appropriate as a summary of opinionated texts, which are more informative and cover more input contents than those generated by the recent unsupervised summarization model (Bražinskas et al., 2020). Furthermore, we demonstrate that the variance of latent Gaussians represents the granularity of sentences, analogous to Gaussian word embedding (Vilnis and McCallum, 2015).

Model of the Vibration Signal of the Vibrating Sieving Screen Suspension for Condition Monitoring Purposes

Diagnostics of industrial machinery is a topic related to the need for damage detection, but it also allows to understand the process itself. Proper knowledge about the operational process of the machine, as well as identification of the underlying components, is critical for its diagnostics. In this paper, we present a model of the signal, which describes vibrations of the sieving screen. This particular type is used in the mining industry for the classification of ore pieces in the material stream by size. The model describes the real vibration signal measured on the spring set being the suspension of this machine. This way, it is expected to help in better understanding how the overall motion of the machine can impact the efforts of diagnostics. The analysis of real vibration signals measured on the screen allowed to identify and parameterize the key signal components, which carry valuable information for the following stages of diagnostic process of that machine. In the proposed model we take into consideration deterministic components related to shaft rotation, stochastic Gaussian component related to external noise, stochastic α-stable component as a model of excitations caused by falling rocks pieces, and identified machine response to unitary excitations.

SOME NEW RESULTS ON AUTOMATIC IDENTIFICATION OF VIETNAMESE FOLK SONGS CHEO AND QUANHO

Vietnamese folk songs are very rich in genre and content. Identifying Vietnamese folk tunes will contribute to the storage and search for information about these tunes automatically. The paper will present an overview of the classification of music genres that have been performed in Vietnam and abroad. For two types of very popular folk songs of Vietnam such as Cheo and Quan ho, the paper describes the dataset and GMM (Gaussian Mixture Model) to perform the experiments on identifying some of these folk songs. The GMM used for experiment with 4 sets of parameters containing MFCC (Mel Frequency Cepstral Coefficients), energy, first derivative and second derivative of MFCC and energy, tempo, intensity, and fundamental frequency. The results showed that the parameters added to the MFCCs contributed significantly to the improvement of the identification accuracy with the appropriate values of Gaussian component number M. Our experiments also showed that, on average, the length of the excerpts was only 29.63% of the whole song for Cheo and 38.1% of the whole song for Quan ho, the identification rate was only 3.1% and 2.33% less than the whole song for Cheo and Quan ho respectively.

Asymptotic kinematics of globular clusters: The emergence of a Tully–Fisher relation

ABSTRACT Using a recent homogeneous sample of 40 high-quality velocity dispersion profiles for Galactic globular clusters, we study the regime of low gravitational acceleration relevant to the outskirts of these systems. We find that a simple empirical profile having a central Gaussian component and a constant large-radius asymptote, σ∞, accurately describes the variety of observed velocity dispersion profiles. We use published population synthesis models, carefully tailored to each individual cluster, to estimate mass-to-light ratios from which total stellar masses, M, are inferred. We obtain a clear scaling, reminiscent of the galactic Tully–Fisher relation of $\sigma _{\infty }[\, \mathrm{km \, s}^{-1}]= 0.084^{+0.075}_{-0.040} (\mathrm{{\it M}/M}_{\odot })^{0.3 \pm 0.051}$, which is interesting to compare to the deep modified Newtonian dynamics (MOND) limit of $\sigma _{\infty } [\mathrm{km \, s}^{-1}]=0.2(\mathrm{{\it M}/M}_{\odot })^{0.25}$. Under a Newtonian interpretation, our results constitute a further restriction on models where initial conditions are crafted to yield the outer flattening observed today. Within a modified gravity scheme, because the globular clusters studied are not isolated objects in the deep MOND regime, the results obtained point towards a modified gravity where the external field effect of MOND does not appear, or is significantly suppressed.