Multilevel Particle Research Articles

Multilevel Particle Filters for a Class of Partially Observed Piecewise Deterministic Markov Processes

Multilevel Particle Filters for a Class of Partially Observed Piecewise Deterministic Markov Processes

Gaussian bistable cascade double feedback stochastic resonance weak signal enhancement detection

Stochastic resonance (SR), as a nonlinear weak signal enhancement detection method, has found extensive applications in fields like fault diagnosis and biological information processing. However, further research has revealed that single stochastic resonance systems often fail to meet the requirements of practical engineering applications, leading to a growing interest in multi-system collaborative stochastic resonance. This article first constructs a cascaded SR system based on the Gaussian bistable model, and introduces the idea of feedback into the cascaded system. A Gaussian bistable cascaded dual feedback SR system is proposed to improve the output signal enhancement performance of the system. This system effectively utilizes the memory characteristics inherent in the output feedback and enables multi-level particle transitions and energy transfers in noisy input signals, thereby reducing noise and enhancing the extraction of weak signal features. Furthermore, the BSO optimization algorithm was utilized to optimize the system parameters of the model, resulting in an adaptive Gaussian bistable cascaded double feedback stochastic resonance (GBCDFSR) system. This system is applied to the processing of noisy periodic signals across various noise types. Simulation experiments and engineering applications show that the proposed model has stronger signal detection capabilities.

Antithetic multilevel particle filters

Abstract In this paper we consider the filtering of partially observed multidimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon time-discretization of the diffusion process and then the application of particle filters. Perhaps the state-of-the-art method for moderate-dimensional problems is the multilevel particle filter of Jasra et al. (SIAM J. Numer. Anal.55 (2017), 3068–3096). This is a method that combines multilevel Monte Carlo and particle filters. The approach in that article is based intrinsically upon an Euler discretization method. We develop a new particle filter based upon the antithetic truncated Milstein scheme of Giles and Szpruch (Ann. Appl. Prob.24 (2014), 1585–1620). We show empirically for a class of diffusion problems that, for $\epsilon>0$ given, the cost to produce a mean squared error (MSE) of $\mathcal{O}(\epsilon^2)$ in the estimation of the filter is $\mathcal{O}(\epsilon^{-2}\log(\epsilon)^2)$ . In the case of multidimensional diffusions with non-constant diffusion coefficient, the method of Jasra et al. (2017) requires a cost of $\mathcal{O}(\epsilon^{-2.5})$ to achieve the same MSE.

An improved unbiased particle filter

Abstract In this paper, we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process, which typically leads to filtering that is subject to discretization bias. The approach in [A. Jasra, K. J. H. Law and F. Yu, Unbiased filtering of a class of partially observed diffusions, Adv. Appl. Probab. 54 (2022), 3, 661–687] establishes that, when only having access to the time discretized diffusion, it is possible to remove the discretization bias with an estimator of finite variance. We improve on this method by introducing a modified estimator based on the recent work [A. Jasra, M. Maama and H. Ombao, Antithetic multilevel particle filters, preprint (2023), https://arxiv.org/abs/2301.12371]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls.

Numerical Modeling of Thermal Behavior during Lunar Soil Drilling

This paper presents a detailed thermal simulation analysis of the drilling process for icy soil in the lunar polar region. The aim is to investigate the temperature changes that occur in the debris removal area during the drilling process. We developed a multi-level particle size simulation model that includes a thermal sieve based on geometric constraints to evaluate the influence of specific heat capacity and thermal conductivity on particle temperature. Using the central composite design method, we carried out the simulation test design and analyzed the average temperature difference of particles within and outside the range of the thermal sieve. The parameters of the discrete element model were determined by comparing the temperature of the debris removal zone in the lunar environment with the temperature simulated by the discrete element method. The results show that the thermal conductivity of the sieve ranges from 100 to 400 W/m, and the average temperature inside the thermal sieve is negatively related to the specific heat capacity. The temperature deviation of the chip removal area is ±10 °C, which is consistent with the temperature deviation observed in the lunar environment and the lunar icy regolith drilling test. Furthermore, the addition of the thermal sieve to the multi-stage particle size simulation modeling significantly reduces the calculation time by 86%. This reduction in computational time may potentially increase the efficiency of drilling operations in the future. Our study provides insights into the thermal behavior of lunar icy regolith during drilling, and proposes a numerical model of heat transfer with a thermal sieve that can effectively reduce computational time while ensuring accurate temperature calculations.

Derivation and verification of multilevel particle packing model for Ultra-High Performance Concrete (UHPC): Modelling and experiments

This paper aims to address the conflict between gap gradation and continuous particle packing for the precise design of ultra-high performance concrete (UHPC). More exactly, a new multilevel particle packing model is proposed by deriving the modified Anderson and Andreasen (MAA) equation. The key parameters of the model are determined by Box-Behnken design method. On this basis, the dense packing states of powder and aggregate segments are achieved, and the accurate ratio of two segments are confirmed. Thus, the optimal mix proportion of UHPC matrix can be calculated. Moreover, some novel viewpoints on the development of dense particle packing theory are presented in this study, including the derivation of multilevel particle packing model with n times of gap gradation and the discussion of general mix design procedure that unifies gap gradation and continuous packing, which could further improve the design theory of UHPC composites.

Unbiased filtering of a class of partially observed diffusions

AbstractIn this article we consider a Monte-Carlo-based method to filter partially observed diffusions observed at regular and discrete times. Given access only to Euler discretizations of the diffusion process, we present a new procedure which can return online estimates of the filtering distribution with no time-discretization bias and finite variance. Our approach is based upon a novel double application of the randomization methods of Rhee and Glynn (Operat. Res.63, 2015) along with the multilevel particle filter (MLPF) approach of Jasra et al. (SIAM J. Numer. Anal.55, 2017). A numerical comparison of our new approach with the MLPF, on a single processor, shows that similar errors are possible for a mild increase in computational cost. However, the new method scales strongly to arbitrarily many processors.

A Wasserstein coupled particle filter for multilevel estimation

In this article, we consider the filtering problem for partially observed diffusions, which are regularly observed at discrete times. We are concerned with the case when one must resort to time-discretization of the diffusion process if the transition density is not available in an appropriate form. In such cases, one must resort to advanced numerical algorithms such as particle filters to consistently estimate the filter. It is also well known that the particle filter can be enhanced by considering hierarchies of discretizations and the multilevel Monte Carlo (MLMC) method, in the sense of reducing the computational effort to achieve a given mean square error (MSE). A variety of multilevel particle filters (MLPF) have been suggested in the literature, e.g., in Jasra et al., SIAM J, Numer. Anal., 55, 3068–3096. Here we introduce a new alternative that involves a resampling step based on the optimal Wasserstein coupling. We prove a central limit theorem (CLT) for the new method. On considering the asymptotic variance, we establish that in some scenarios, there is a reduction, relative to the approach in the aforementioned paper by Jasra et al., in computational effort to achieve a given MSE. These findings are confirmed in numerical examples. We also consider filtering diffusions with unstable dynamics; we empirically show that in such cases a change of measure technique seems to be required to maintain our findings.

Novel multilevel particle swarm optimization algorithm for graph partitioning

Graph partitioning is crucial step in resolving real time applications in the field of image analysis, smart city designing, wireless communications, data analysis etc. Though considerable research has been done for getting an optimal partitioning of graphs still it demands enhancement for diverse application problems. Hybrid graph partitioning approaches are promising and possess ability to partition graphs with large number of vertices. In our research we have developed multilevel particle swarm optimization algorithm for graph partitioning. Size of the graph is reduced by heavy edge matching algorithm and then greedy graph growing partitioning is used to divide the graph. Discrete particle swarm optimization used at the most important stage of refinement. Performance is evaluated by using Walshaw’s Benchmark graphs and from analysis it has been observed that proposed algorithm generates optimal partitioning with reduced cut values and computational cost.

Hybrid MPSO-CNN: Multi-level Particle Swarm optimized hyperparameters of Convolutional Neural Network

Recent advances in swarm inspired optimization algorithms have shown its extensive acceptance in solving a wide range of different real-world problems. Particle Swarm Optimization (PSO) is one of the most explored nature-inspired population-based stochastic optimization algorithm. In this paper, a Multi-level Particle Swarm Optimization (MPSO) algorithm is proposed to find the architecture and hyperparameters of the Convolutional Neural Network (CNN) simultaneously. This automated learning will reduce the overhead of human experts to find these parameters through manual analysis and experiments. The proposed solution uses multiple swarms at two levels. The initial swarm at level-1 optimizes architecture and multiple swarms at level-2 optimize hyperparameters. The proposed method has used sigmoid like inertia weight to adjust the exploration and exploitation property of particles and avoid the PSO algorithm to prematurely converge into a local optimum solution. In this paper, we have explored an approach to suggest the best well-conditioned CNN architecture and its hyperparameters using MPSO in a specified search space. The complexity and performance of MPSO-CNN will depend on the dimension of the search space. The experimental results on 5 benchmark datasets of MNIST, CIFAR-10, CIFAR-100, Convex Sets, and MDRBI have demonstrated one more effective application of PSO in learning a deep neural architecture.

Unruh effect for detectors in superposition of accelerations

The Unruh effect is the phenomenon that accelerated observers detect particles even when inertial observers experience the vacuum state. In particular, uniformly accelerated observers are predicted to measure thermal radiation that is proportional to the acceleration. Here we consider the Unruh effect for a detector that follows a quantum superposition of different accelerated trajectories in Minkowski spacetime. More precisely, we analyse the excitations of a pointlike multilevel particle detector coupled to a massless real scalar field and moving in the superposition of accelerated trajectories. We find that the state of the detector excitations is, in general, not a mere (convex) mixture of the thermal spectrum characteristics of the Unruh effect for each trajectory with well-defined acceleration separately. Rather, for certain trajectories and excitation levels, and upon the measurement of the trajectory state, the state of the detector excitations features in addition off-diagonal terms. The off-diagonal terms of these "superpositions of thermal states" are related to the distinguishability of the different possible states in which the field is left after its interaction with detector's internal degrees of the freedom.

Channel and Feature Selection for a Motor Imagery-Based BCI System Using Multilevel Particle Swarm Optimization.

Brain-computer interface (BCI) is a communication and control system linking the human brain and computers or other electronic devices. However, irrelevant channels and misleading features unrelated to tasks limit classification performance. To address these problems, we propose an efficient signal processing framework based on particle swarm optimization (PSO) for channel and feature selection, channel selection, and feature selection. Modified Stockwell transforms were used for a feature extraction, and multilevel hybrid PSO-Bayesian linear discriminant analysis was applied to optimization and classification. The BCI Competition III dataset I was used here to confirm the superiority of the proposed scheme. Compared to a method without optimization (89% accuracy), the best classification accuracy of the PSO-based scheme was 99% when less than 10.5% of the original features were used, the test time was reduced by more than 90%, and it achieved Kappa values and F-score of 0.98 and 98.99%, respectively, and better signal-to-noise ratio, thereby outperforming existing algorithms. The results show that the channel and feature selection scheme can accelerate the speed of convergence to the global optimum and reduce the training time. As the proposed framework can significantly improve classification performance, effectively reduce the number of features, and greatly shorten the test time, it can serve as a reference for related real-time BCI application system research.

Multilevel particle filters for the non-linear filtering problem in continuous time

In the following article we consider the numerical approximation of the non-linear filter in continuous-time, where the observations and signal follow diffusion processes. Given access to high-frequency, but discrete-time observations, we resort to a first order time discretization of the non-linear filter, followed by an Euler discretization of the signal dynamics. In order to approximate the associated discretized non-linear filter, one can use a particle filter (PF). Under assumptions, this can achieve a mean square error of $\mathcal{O}(\epsilon^2)$, for $\epsilon>0$ arbitrary, such that the associated cost is $\mathcal{O}(\epsilon^{-4})$. We prove, under assumptions, that the multilevel particle filter (MLPF) of Jasra et al (2017) can achieve a mean square error of $\mathcal{O}(\epsilon^2)$, for cost $\mathcal{O}(\epsilon^{-3})$. This is supported by numerical simulations in several examples.

Iterative multilevel particle approximation for McKean–Vlasov SDEs

The mean field limits of systems of interacting diffusions (also called stochastic interacting particle systems (SIPS)) have been intensively studied since McKean \cite{mckean1966class}. The interacting diffusions pave a way to probabilistic representations for many important nonlinear/nonlocal PDEs, but provide a great challenge for Monte Carlo simulations. This is due to the nonlinear dependence of the bias on the statistical error arising through the approximation of the law of the process. This and the fact that particles/diffusions are not independent render classical variance reduction techniques not directly applicable and consequently make simulations of interacting diffusions prohibitive. In this article, we provide an alternative iterative particle representation, inspired by the fixed point argument by Sznitman \cite{sznitman1991topics}. This new representation has the same mean field limit as the classical SIPS. However, unlike classical SIPS, it also allows decomposing the statistical error and the approximation bias. We develop a general framework to study integrability and regularity properties of the iterated particle system. Moreover, we establish its weak convergence to the McKean-Vlasov SDEs (MVSDEs). One of the immediate advantages of iterative particle system is that it can be combined with the Multilevel Monte Carlo (MLMC) approach for the simulation of MVSDEs. We proved that the MLMC approach reduces the computational complexity of calculating expectations by an order of magnitude. Another perspective on this work is that we analyse the error of nested Multilevel Monte Carlo estimators, which is of independent interest. Furthermore, we work with state dependent functionals, unlike scalar outputs which are common in literature on MLMC. The error analysis is carried out in uniform, and what seems to be new, weighted norms.

Real-Time Solution of Time-Varying Yau Filtering Problems via Direct Method and Gaussian Approximation

Direct method for Yau filtering system has been studied since 1990s and all these work are limited in time-invariant systems. In this work, we extend the direct method so that it is applicable to time-varying cases. We need less assumptions compared with our previous work. The novelty of this work is that we propose several transformations on the forward Kolmogorov equation so that it can be solved by means of solving some ordinary differential equations if the initial distribution is Gaussian. The corresponding results for any non-Gaussian initial distributions can be obtained via Gaussian approximation. It can be seen that our new scheme direct method can treat nearly most general Yau filtering problems under natural assumptions. Our algorithm has been compared with the extended Kalman filter, multilevel particle filter, and ensemble Kalman filter by numerical examples and the simulation results show the efficiency of our method.

Multi-level separation of particles using acoustic radiation force and hydraulic force in a microfluidic chip

Combined with acoustic separation and hydraulic separation technology, a microfluidic chip, which can achieve multi-level particle separation, is proposed in this work. The chip uses the sheath flow on both sides to align the mixed particles in the set area (near the side of the channel) of the separation channel. And then, the mixed particles successively pass through the acoustic surface wave and hydraulic action area, which are generated by modulating interdigital transducers and adjusting the flow ratio, respectively, and finally realize multiple particle separation under the acoustic radiation and hydraulic force. The corresponding separation experiments were carried out using polystyrene (PS) microparticles with diameters of 1 µm, 5 µm, and 10 µm, respectively. Moreover, we explored the influence of the peak-to-peak voltage (Vpp) and flow ratio on the PS microparticles separation effect, and the separation effect is optimal at the flowrate in the main channel is 4 mm/s, Vpp = 25 V, A1 = 0.2, A2 = 0.5. Under these conditions, the separation purity of 1 µm, 5 µm, and 10 µm PS microparticles are 95.60%, 91.67%, 93.75%, respectively, and their separation rates are 96.67%, 89.19%, and 96.77%, respectively. The combined multi-level separation chip has the advantages of simple structure, high separation accuracy, high separation efficiency, and the ability to sort multiple particles, which can be applied to chemical analysis, cell sorting, biomedicine.

Towards the Task-Level Optimal Orchestration Mechanism in Multi-Device Multi-Task Architecture for Mission-Critical IoT Applications

Internet of Things is advancing, and the augmented role of architecture in automating processes is at its vanguard. Mission-critical applications are becoming a vital category of future IoT applications, and due to the advancements in the 5G, the design of mission-critical application overcome a big hurdle. Mission-critical applications must be reliable, and the output should be known in advance. Therefore, to model such application, architecture is considered the cornerstone. One of the major requirements is the flexibility of the operation and the adaptability to new devices. In this paper, an optimal orchestration mechanism is proposed to automate the processes in a conventional multi-device and multi-task mission-critical architecture for flexible and scalable operations. The central goal of this paper is to threefold; first, to model tasks in such a way to maximize the flexibility in the operation plane. Secondly, to design a strongly correlated pair which has maximum relation and thus the chance to hit the task on the devices will be potentially maximized and also the idle time among operations is minimal. Lastly, to register devices in a network which is optimal for the group of this device in terms of correlation. We propose a multi-layer particle swarm optimization for each of the optimization objectives. Results show that the operation plan is flexible and with scaling up the problem size, the orchestration is still graceful and within the requirements of mission-critical applications. The performance of multi-level particle swarm optimization is compared with conventional single-level particle swarm optimization and it has been learned that the later is not only slower but also less accurate.

Multilevel particle filters for L\xe9vy-driven stochastic differential equations

We develop algorithms for computing expectations with respect to the laws of models associated to stochastic differential equations driven by pure Lévy processes. We consider filtering such processes as well as pricing of path dependent options. We propose a multilevel particle filter to address the computational issues involved in solving these continuum problems. We show via numerical simulations and theoretical results that under suitable assumptions regarding the discretization of the underlying driving Lévy proccess, the cost to obtain MSE mathcal {O}(epsilon ^2) scales like mathcal {O}(epsilon ^{-2}) for our method, as compared with the standard particle filter mathcal {O}(epsilon ^{-3}).

Prognosis and Remaining Useful Life Estimation of Lithium-Ion Battery with Optimal Multi-Level Particle Filter and Genetic Algorithm

Prognosis and remaining useful life (RUL) estimation of components and systems (C&S) are vital for intelligent asset-integrity management. The implementation of the traditional multi-level particle filter (TRMPF) has improved prognosis when compared with the one-step traditional particle filter that depended on the first-order state equation. However, despite this improvement, the need to enhance the accuracy of fault prognosis, diagnosis and detection cannot be overemphasized. To this end, an optimal multi-level particle filter (OPMPF) algorithm that combines genetic algorithm (GA) optimization and multi-level particle filter (MPF) techniques is used to predict the RUL of the C&S in order to enhance the accuracy of the estimation at different forms of deterioration in operation. A 9-fold cross-validation ensemble MPF that utilized lithium-ion (Li+) batteries’ charge capacity decay to test the developed OPMPF algorithm showed an improvement of over 200% in the estimated RUL when compared with the TRMPF estimation.

Design of shared unit-dose drug distribution network using multi-level particle swarm optimization.

Unit-dose drug distribution systems provide optimal choices in terms of medication security and efficiency for organizing the drug-use process in large hospitals. As small hospitals have to share such automatic systems for economic reasons, the structure of their logistic organization becomes a very sensitive issue. In the research reported here, we develop a generalized multi-level optimization method - multi-level particle swarm optimization (MLPSO) - to design a shared unit-dose drug distribution network. Structurally, the problem studied can be considered as a type of capacitated location-routing problem (CLRP) with new constraints related to specific production planning. This kind of problem implies that a multi-level optimization should be performed in order to minimize logistic operating costs. Our results show that with the proposed algorithm, a more suitable modeling framework, as well as computational time savings and better optimization performance are obtained than that reported in the literature on this subject.