Sequential Monte Carlo Research Articles

Monte Carlo simulation convergences’ percentage and position in future reliability evaluation

<span lang="EN-US">Reliability assessment is a needed assessment in today's world. It is required not only for system design but also to ensure the power delivered reaches the consumer. It is usual for fault to occur, but it is best if the fault can be predicted and the way to overcome it can be prepared in advance. Monte Carlo simulation is a standard method of assessing reliability since it is a time-based evaluation that nearly represents the actual situation. However, sequential Monte Carlo (SMC) typically took long-time simulation. A convergence element can be implemented into the simulation to ensure that the time taken to compute the simulation can be reduced. The SMC can be done with and without convergence. SMC with convergence has high accuracy compared to the SMC without convergence, as it takes a long time and has a high possibility of not getting accurate output. In this research, the SMC is subjected to five different convergence items to determine which converge simulation is the fastest while providing better performance for reliability evaluation. There are two types of convergence positions, namely input convergence and output convergence. Overall, output convergence shows the best result compared to input convergence.</span>

Voltage profile assessment in smart distribution grids considering BESS and communication network failures

• Sequential monte carlo simulation for assessing voltage profile of smart grids. • modeling failures in the BESS systems and the communication network (CN). • BESS optimization models for day ahead scheduling and voltage profile correction. • The results shows that communication failures have impact on the voltage profile. Battery energy storage systems (BESSs) are expected to play a major role in voltage control of smart distribution grids (SDGs) due to the high penetration of intermittent renewable energy. However, neither these devices nor the communication infrastructure needed for their control, are fully reliable. Due to this, BESS unavailability might occur, degrading voltage profile. This paper presents a new fixed-time sequential Monte Carlo simulation for assessing indices of SDGs’ long-duration voltage variations (LDVVs) considering both failures in BESS systems and in the communication network (CN). Results show that these failures have significant impact on the LDVV indices of the SDG.

A unified performance analysis of likelihood-informed subspace methods

The likelihood-informed subspace (LIS) method offers a viable route to reducing the dimensionality of high-dimensional probability distributions arising in Bayesian inference. LIS identifies an intrinsic low-dimensional linear subspace where the target distribution differs the most from some tractable reference distribution. Such a subspace can be identified using the leading eigenvectors of a Gram matrix of the gradient of the log-likelihood function. Then, the original high-dimensional target distribution is approximated through various forms of marginalization of the likelihood function, in which the approximated likelihood only has support on the intrinsic low-dimensional subspace. This approximation enables the design of inference algorithms that can scale sub-linearly with the apparent dimensionality of the problem. Intuitively, the accuracy of the approximation, and hence the performance of the inference algorithms, are influenced by three factors—the dimension truncation error in identifying the subspace, Monte Carlo error in estimating the Gram matrices, and Monte Carlo error in constructing marginalizations. This work establishes a unified framework to analyze each of these three factors and their interplay. Under mild technical assumptions, we establish error bounds for a range of existing dimension reduction techniques based on the principle of LIS. Our error bounds also provide useful insights into the accuracy of these methods. In addition, we analyze the integration of LIS with sampling methods such as Markov Chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC). We also demonstrate the applicability of our analysis on a linear inverse problem with Gaussian prior, which shows that all the estimates can be dimension-independent if the prior covariance is a trace-class operator. Finally, we demonstrate various aspects of our theoretical claims on two nonlinear inverse problems.

FMCW-MIMO Radar-Based Pedestrian Trajectory Tracking Under Low- Observable Environments

Pedestrian trajectory perception is always a challenging task for autonomous urban driving since the weak echoes from pedestrians may be masked by strong background clutters, for example, road infrastructures and other vehicles. As a consequence, this article presents a frequency-modulated continuous wave-multiple input multiple output (FMCW-MIMO) radar-based trajectory tracking method to realize continuous pedestrian detection and tracking under low-observable environments. More specifically, the keystone transform-constant false alarm ratio (KT-CFAR) is first proposed to maximize the output signal-to-interference plus noise ratio (SINR) depending on the time–space correlations of a sequence of consecutive echoes, for the sake of improving the pedestrian detection probability under low-observable conditions. Then, the multiple signal classification (MUSIC) algorithm is employed to provide a high azimuth resolution to improve the multitarget resolving ability. After that, a pedestrian trajectory tracking framework is constructed by means of Bayesian theory and sequential Monte Carlo (SMC) sampling. Finally, simulation and experimental results show that the proposed method can obtain high-precision pedestrian trajectory tracking under low SINR conditions compared with conventional Kalman filter (KF)-based tracking methods.

Sequential estimation of temporally evolving latent space network models

Dynamic network data describe interactions among a fixed population through time. This data type can be modelled using the latent space framework, where the probability of a connection forming is expressed as a function of low-dimensional latent coordinates associated with the nodes, and sequential estimation of model parameters can be achieved via Sequential Monte Carlo (SMC) methods. In this setting, SMC is a natural candidate for estimation which offers greater scalability than existing approaches commonly considered in the literature, allows for estimates to be conveniently updated given additional observations and facilitates both online and offline inference. A novel approach to sequentially infer parameters of dynamic latent space network models is proposed by building on techniques from the high-dimensional SMC literature. The scalability and performance of the proposed approach is explored via simulation, and the flexibility under model variants is demonstrated. Finally, a real-world dataset describing classroom contacts is analysed using the proposed methodology.

A Stochastic and Bayesian Inference Toolchain for Uncertainty and Risk Quantification of Rare Autoignition Events in Dry Low-Emission Premixers

Abstract Quantification of aleatoric uncertainties due to the inherent variabilities in operating conditions and fuel composition is essential for designing and improving premixers in dry low-emissions (DLE) combustion systems. Advanced stochastic simulation tools require a large number of evaluations in order to perform this type of uncertainty quantification (UQ) analysis. This task is computationally prohibitive using high-fidelity computational fluid dynamic (CFD) approaches such as large eddy simulation (LES). In this paper, we describe a novel and computationally efficient toolchain for stochastic modeling using minimal input from LES, to perform uncertainty and risk quantification of a DLE system. More specially, high-fidelity LES, chemical reactor network (CRN) model, beta mixture model, Bayesian inference and sequential Monte Carlo (SMC) are integrated into the toolchain. The methodology is applied to a practical premixer of low-emission combustion system with dimethyl ether (DME)/methane–air mixtures to simulate auto-ignition events at different engine conditions. First, the benchmark premixer is simulated using a set of LESs for a methane/air mixture at elevated pressure and temperature conditions. A partitioning approach is employed to generate a set of deterministic chemical reactor network (CRN) models from LES results. These CRN models are then solved at the volume-average conditions and validated by LES results. A mixture modeling approach using the expectation-method of moment (E-MM) is carried out to generate a set of beta mixture models and characterize uncertainties for LES-predicted temperature distributions. These beta mixture models and a normal distribution for DME volume fraction are used to simulate a set of stochastic CRN models. The Bayesian inference approach through SMC method is then implemented on the results of temperature distributions from stochastic CRN models to simulate the probability of auto-ignition in the benchmark premixer. The results present a very satisfactory performance for the stochastic toolchain to compute the auto-ignition propensity for a few events with a particular combination of inlet temperature and DME volume fraction. Characterization of these rare events is computationally prohibitive in the conventional deterministic methods such as high-fidelity LES.

Reliability Evaluation of Standalone Microgrid Based on Sequential Monte Carlo Simulation Method

In order to analyze the influence of uncertainty and an operation strategy on the reliability of a standalone microgrid, a reliability evaluation method based on a sequential Monte Carlo (SMC) simulation was developed. Here, the duty cycles of a microturbine (MT), the stochastic performance of photovoltaics (PV), and wind turbine generators (WTG) were considered. Moreover, the time-varying load with random fluctuation was modeled. In this method, the available capacity of an energy storage system (ESS) was also comprehensively considered by the SMC simulation. Then, the reliability evaluation framework was established from the perspectives of probability, frequency, and duration, and reliability evaluation algorithms under different operation strategies were formulated. Lastly, the influence of WTG and PV penetration and equipment capacity on the reliability was evaluated in the test system. The results showed that the complementary characteristics of wind and solar and the enhancement of the equipment capacity can both improve the reliability; but, with the increase in the penetration rate of WTG and PV, more ESS capacity is needed to cope with the randomness of WTG and PV. In addition, load shedding minimization strategies can minimize the probability and the number of reductions and achieve optimal reliability, which can provide a reference for the formulation of microgrid operation strategies.

Multiple targets tracking by using improved labeled multi-target multi-Bernoulli filter with FDA-MIMO radar

In the traditional multi-target multi-Bernoulli (MeMBer) filter, only the radar signal after constant false alarm rate (CFAR) is considered. In addition, it is also necessary to assume that the detection probability of the target and the covariance matrix of the measurement noise are known. In fact, the detection probability of the target and the covariance matrix of the noise are difficult to determine. Therefore, this paper proposes an improved labeled multi-target multi-Bernoulli (IL-MeMBer) filter that can avoid considering the detection probability of the target and the covariance matrix of the measurement noise. Firstly, the multi-target superposition measurement model of FDA-MIMO is given in the presence of false targets. Secondly, the target likelihood function under the superposition measurement model is derived by analyzing the characteristics of the traditional point measurement likelihood function and the Music spatial spectrum. Thirdly, considering the unknown and time-varying number of targets, the original echo signals without detection probability before (CFAR) processing, and no target tracks output by the traditional MeMBer filter, we put forward an analytical solution of the IL-MeMBer filter. Finally, a fusion strategy based on Euclidean distance is proposed to solve the problem that the same target can be estimated to have multiple tracks in the IL-MeMBer filter. In addition, the sequential Monte Carlo (SMC) implementation of the IL-MeMBer filter is provided. Numerical experiences verify the effectiveness and superiority of the proposed methods.

Accelerating astronomical and cosmological inference with preconditioned Monte Carlo

ABSTRACT We introduce preconditioned Monte Carlo (PMC), a novel Monte Carlo method for Bayesian inference that facilitates efficient sampling of probability distributions with non-trivial geometry. PMC utilizes a Normalizing Flow (NF) in order to decorrelate the parameters of the distribution and then proceeds by sampling from the preconditioned target distribution using an adaptive Sequential Monte Carlo (SMC) scheme. The results produced by PMC include samples from the posterior distribution and an estimate of the model evidence that can be used for parameter inference and model comparison, respectively. The aforementioned framework has been thoroughly tested in a variety of challenging target distributions achieving state-of-the-art sampling performance. In the cases of primordial feature analysis and gravitational wave inference, PMC is approximately 50 and 25 times faster, respectively, than nested sampling (NS). We found that in higher dimensional applications, the acceleration is even greater. Finally, PMC is directly parallelisable, manifesting linear scaling up to thousands of CPUs.

Hidden Markov Pólya Trees for High-Dimensional Distributions

The Pólya tree (PT) process is a general-purpose Bayesian nonparametric model that has found wide application in a range of inference problems. It has a simple analytic form and the posterior computation boils down to beta-binomial conjugate updates along a partition tree over the sample space. Recent development in PT models shows that performance of these models can be substantially improved by (i) allowing the partition tree to adapt to the structure of the underlying distributions and (ii) incorporating latent state variables that characterize local features of the underlying distributions. However, important limitations of the PT remain, including (i) the sensitivity in the posterior inference with respect to the choice of the partition tree, and (ii) the lack of scalability with respect to dimensionality of the sample space. We consider a modeling strategy for PT models that incorporates a flexible prior on the partition tree along with latent states with Markov dependency. We introduce a hybrid algorithm combining sequential Monte Carlo (SMC) and recursive message passing for posterior sampling that can scale up to 100 dimensions. While our description of the algorithm assumes a single computer environment, it has the potential to be implemented on distributed systems to further enhance the scalability. Moreover, we investigate the large sample properties of the tree structures and latent states under the posterior model. We carry out extensive numerical experiments in density estimation and two-group comparison, which show that flexible partitioning can substantially improve the performance of PT models in both inference tasks. We demonstrate an application to a mass cytometry dataset with 19 dimensions and over 200,000 observations. Supplementary Materials for this article are available online.

Highly Efficient MIMO-OFDM with Index Modulation

Index modulation (IM) is a novel digital modulation technique, which inactivates some subcarriers in orthogonal frequency division multiplexing (OFDM) to exploit the indices of the subcarriers to transmit bits implicitly, and has potential to further improve the energy efficiency and error performance. For the multiple-input multiple-output- (MIMO-) aided IoT devices, a highly efficient and low-complexity IM-aided scheme is needed to reduce the computational complexity at the receiver sides. In this paper, we propose a novel highly efficient MIMO-OFDM with IM scheme by performing IM on each transmit antenna subgroup, which contains two transmit antennas, to achieve two transmit diversity order and significant reduction in computational complexity at the cost of a minor spectral efficiency. To reduce the demodulation complexity, a low-complexity sequential Monte Carlo (SMC) theory-based detector is proposed, which exploits the null space submatrix of the preprocessed channel response matrix by using QR decomposition, to calculate the most likely transmitted IM patterns before the detection of the modulated symbols. Computer simulation results and complexity analysis show that the proposed IM-aided scheme achieves better error performance with extremely low computational complexity under the same constellation and the proposed SMC detector has potential to achieve near optimal bit error rate performance with considerably low demodulation complexity.

Robust extended Cubature Kalman multi-Bernoulli filter for joint detection and tracking ISAR images of small UAVs

ABSTRACT A novel approach to joint detection and tracking the moving extended small vehicles such as drones and unmanned aerial vehicles (UAVs) using inverse synthetic aperture radar (ISAR) images is proposed in this work. Recently, a random matrices model (RMM) for extended object tracking (EOT) has been proposed. Under the RMM, the object shape is assumed to be an ellipse. The RMM is chosen to describe the EOT shape because it was a good combination of an informative shape model and low computational complexity. Since conventional EOT algorithm using RMM is not accurate enough to reconstruct the object’ extension by one ellipse, an appropriate technique needs to be developed for ISAR imaging and tracking of extended drones tracking (EDTs). Therefore, we applied a new tracking-before-detection (TBD) algorithm for EDT as multiple ellipses or sub-RMM with non-linear ISAR observations and unknown orientation angle due to Doppler effect. In the recent year, the Cubature Kalman multi-Bernoulli (CK-MB) algorithm with a third-degree spherical-radical cubature rule has been applied to solve the non-linearity due to Doppler effect, the CK-MB filter is more accurate compared to state-of-the-art algorithms such as sequential Monte Carlo (SMC)-MB and Gaussian mixture (GM)-MB filters. An approach to joint detection and tracking of moving EDTs using ISAR images with the robust extended CK (ECK)-Sub-RMM-MB-based TBD algorithm is proposed and evaluated in this paper. We describe the EDT state through the ECK-Beta Gaussian inverse Wishart model. Simulation results demonstrates this remarkable performance.

Enhancing Ligand and Protein Sampling Using Sequential Monte Carlo.

The sampling problem is one of the most widely studied topics in computational chemistry. While various methods exist for sampling along a set of reaction coordinates, many require system-dependent hyperparameters to achieve maximum efficiency. In this work, we present an alchemical variation of adaptive sequential Monte Carlo (SMC), an irreversible importance resampling method that is part of a well-studied class of methods that have been used in various applications but have been underexplored in computational biophysics. Afterward, we apply alchemical SMC on a variety of test cases, including torsional rotations of solvated ligands (butene and a terphenyl derivative), translational and rotational movements of protein-bound ligands, and protein side chain rotation coupled to the ligand degrees of freedom (T4-lysozyme, protein tyrosine phosphatase 1B, and transforming growth factor β). We find that alchemical SMC is an efficient way to explore targeted degrees of freedom and can be applied to a variety of systems using the same hyperparameters to achieve a similar performance. Alchemical SMC is a promising tool for preparatory exploration of systems where long-timescale sampling of the entire system can be traded off against short-timescale sampling of a particular set of degrees of freedom over a population of conformers.

Recursive Bayesian inference and learning for target tracking with unknown maneuvers

SummaryThis paper addresses the problem of target tracking under completely unknown maneuvering behavior to cope with the complicated target maneuvers. The actual but unknown motion model is formulated as a linear stochastic model with unknown transition matrix and modeling error covariance. Considering the diversity and time‐varying of maneuvers, both the transition matrix and covariance are random. Accordingly, the tracker design amounts to recursively updating the joint posterior of target state and unknown parameters (i.e., the transition matrix and covariance). Since it is difficult to obtain the analytical joint posterior, a Bayesian inference and learning scheme is proposed in the sequential Monte Carlo (SMC) framework to alternatively update the state posterior and the unknown parameters posterior. Particularly, it is revealed that the state prediction density used in the SMC obeys a Student's t‐distribution, thus ensuring the effective sampling of particle trajectories. Finally, a maneuvering benchmark shows that the proposed tracker can significantly reduce the peak tracking error, which is one of the most important performance indices for preventing tracking failure.

Limits of Accuracy for Parameter Estimation and Localization in Single-Molecule Microscopy via Sequential Monte Carlo Methods

Assessing the quality of parameter estimates for models describing the motion of single molecules in cellular environments is an important problem in fluorescence microscopy. In this work, we consider the fundamental data model, where molecules emit photons at random time instances and these photons arrive at random locations on the detector according to complex point spread functions (PSFs). The randomness and non-Gaussian PSF of the detection process, and the random trajectory of the molecule, make inference challenging. Moreover, the presence of other closely spaced molecules causes further uncertainty in the origin of the measurements, which impacts the statistical precision of the estimates. We quantify the limits of accuracy of model parameter estimates and separation distance between closely spaced molecules (known as the resolution problem) by computing the Cramér--Rao lower bound (CRLB), or equivalently the inverse of the Fisher information matrix (FIM), for the variance of estimates. Results on the CRLB obtained from the fundamental model are crucial, in that they provide a lower bound for more practical scenarios. While analytic expressions for the FIM can be derived for static and deterministically moving molecules, the analytical tools to evaluate the FIM for molecules whose trajectories follow stochastic differential equations are still for the most part missing. We address this by presenting a general sequential Monte Carlo (SMC) based methodology for both parameter inference and computing the desired accuracy limits for nonstatic molecules and a non-Gaussian fundamental detection model. For the first time, we are able to estimate the FIM for stochastically moving molecules observed through the Airy and Born and Wolf detection models. This is achieved by estimating the score and observed information matrix via SMC. We summarize the outcome of our numerical work by delineating the qualitative behaviors for the accuracy limits as functions of various experimental settings like collected photon count, molecule diffusion, etc. We also verify that we can recover known results from the static molecule case.

ISAR images tracking for extended small vehicles using cubature Kalman MB filter

This work provides a new approach for extended drone targets (EDTs) tracking from inverse synthetic aperture radar (ISAR) images based on robust extended cubature Kalman multi-Bernoulli track-before-detect (ECK-MB-TBD) algorithm that handling of the non-linear ISAR observations with Doppler effect. During this work, we present the drone's extension as multiple ellipses with a time-varying orientation angle and solve the resulting inference problem, which involves data association between the nonlinear measurements and sub-ellipses or sub-random matrices model (RMM). In addition, we give a new implementation of the proposed robust ECK-Sub-RMM-MB-TBD filter to estimate the change in the nonlinear orientation of target's shape based on ECK-Beta Gaussian inverse Wishart. Tracking performance is compared to state-of-the-art algorithms on EDTs such as sequential Monte Carlo (SMC)-Sub-RMM-MB-TBD and histogram probabilistic multi-hypothesis (H-PMHT)-TBD. The simulation results confirm the effectiveness and robustness of the proposed algorithm. From the results, the SMC-Sub-RMM-MB-TBD algorithm take significantly more time to compute than the proposed algorithm, because the first algorithm needs a large number of the particles for EDTs. The average running times were 88.63 s for SMC-Sub-RMM-MB-TBD, 38.54 s for ECK-Sub-RMM-MB-TBD and 55.34 s for H-PMHT-TBD.

Bayesian optimization with informative parametric models via sequential Monte Carlo

AbstractBayesian optimization (BO) has been a successful approach to optimize expensive functions whose prior knowledge can be specified by means of a probabilistic model. Due to their expressiveness and tractable closed-form predictive distributions, Gaussian process (GP) surrogate models have been the default go-to choice when deriving BO frameworks. However, as nonparametric models, GPs offer very little in terms of interpretability and informative power when applied to model complex physical phenomena in scientific applications. In addition, the Gaussian assumption also limits the applicability of GPs to problems where the variables of interest may highly deviate from Gaussianity. In this article, we investigate an alternative modeling framework for BO which makes use of sequential Monte Carlo (SMC) to perform Bayesian inference with parametric models. We propose a BO algorithm to take advantage of SMC’s flexible posterior representations and provide methods to compensate for bias in the approximations and reduce particle degeneracy. Experimental results on simulated engineering applications in detecting water leaks and contaminant source localization are presented showing performance improvements over GP-based BO approaches.

A Logistic Regression Approach to Field Estimation Using Binary Measurements

In this letter, we consider the problem of field estimation using binary measurements. Previous work has formulated the problem as a parameter estimation problem, which can be solved in an online manner using sequential Monte Carlo (SMC) techniques. In the current work, we consider an alternative approach to the parameter estimation problem based on online logistic regression. The developed algorithm is less computationally intensive than the SMC approach, while having more reliable estimation performance.

A Multisource Multi-Bernoulli Filter for Multistatic Radar

Compared with conventional monostatic or bistatic radar, multistatic radar has wider coverage and better performance localization and tracking accuracy. However, the multistatic radar architecture poses challenges to the implementation for multitarget tracking in coping with highly uncertainty of data association for the fusion of multisource information. In this paper, the theoretically rigorous formulas for the multisource multi-Bernoulli (MeMBer) filter are derived by using the Finite set statistics (FISST) calculus built on the standard MeMBer filter. The multisource MeMBer filter propagates a set of MeMBer parameters approximately characterizing the multisource corrected posterior multitarget random finite set (RFS). Since the equations for the proposed filter multisource corrector are computationally intractable, we go further to develop an analytic Sequential Monte Carlo (SMC) implementation of multisource MeMBer recursion. The theoretical analysis and simulations show that the proposed filter perform well and accommodate nonlinear multistatic radar tracking scenario under the approximate conditions.

Smart Cooperative Energy Supply Strategy to Increase Reliability in Residential Stand-Alone Photovoltaic Systems

In reliability studies of isolated energy supply systems for residential buildings, supply failures due to insufficient generation are generally analysed. Recent studies conclude that this kind of analysis makes it possible to optimally design the sizes of the elements of the generation system. However, in isolated communities or rural areas, it is common to find groups of dwellings in which micro-renewable sources, such as photovoltaic (PV) systems, can be installed. In this situation, the generation and storage of several houses can be considered as an interconnected system forming a cooperative microgrid (CoMG). This work analyses the benefits that sharing two autonomous installations can bring to each one, from the point of view of reliability. The method consists of the application of a random sequential Monte Carlo (SMC) simulation to the CoMG to evaluate the impact of a simple cooperative strategy on the reliability of the set. The study considers random failures in the generation systems. The results show that the reliability of the system increases when cooperation is allowed. Additionally, at the design stage, this allows more cost-effective solutions than single sizing with a similar level of reliability.