Gaussian Particle Research Articles

Optimized control of hybrid energy storage systems for microgrids

Abstract The development of new energy sources is considered to be one of the important ways to solve the current energy shortage problem. Clean energy sources such as wind and light have attracted much attention. Still, the volatility and uncertainty of their output power create difficulties for the large-scale connection of the system to the power grid. Based on the microgrid system, this paper focuses on the energy optimization control problem of storage batteries and supercapacitors. A low-pass filter is used based on the charge state SOC expressed as a formula. The working state of the supercapacitor charge is divided into five regions, with each region having a corresponding reference value for output power correction. The capacity optimization model of the hybrid energy storage device is constructed, and the Gaussian variational quantum particle swarm algorithm (GM-QPSO) is used to optimize the capacity of the hybrid energy storage device. It is found that the capacity optimization method proposed in this paper not only improves the stability of the operation of the system but also ensures the overall economy of the system.

Luminosity calibration bias in van-der-Meer scan due to the beam-beam interaction for q-Gaussian beams

The accuracy of luminosity calibration is an important problem in the operation of colliders, the successful solution of which determines the accuracy of the experiments performed. In hadron colliders, luminosity calibration is performed using van-der-Meer scanning, the goal of which is to measure the overlap of the colliding beams. When two beams collide, their electromagnetic interaction leads to a change in their overlap and, consequently, the luminosity calibration is biased. Typically, this effect is accounted for under the assumption that beams have a Gaussian particle distribution. However, it is known that the particle distribution in hadron collider beams differs from Gaussian and is more generally described by q-Gaussian functions. Accurate accounting of electromagnetic interaction becomes an urgent task as the requirements for the accuracy of luminosity measurements increase (for example, in the HL-LHC project the goal is an accuracy of 1 %). This paper presents a model of the electromagnetic interaction of beams with a q-Gaussian distribution of particles, and determines the influence of this interaction on the luminosity calibration using the van der Meer scanning method. Calculations were carried out for beams with conditions of the CMS and ATLA experiments.

Unbalanced Optimal Transport For Stochastic Particle Tracking

Non-invasive flow measurement techniques, such as particle tracking velocimetry, resolve 3D velocity fields by pairing tracer particle positions in successive time steps. These trajectories are crucial for evaluating physical quantities like vorticity, shear stress, pressure, and coherent structures. Traditional approaches deterministically reconstruct particle positions and extract particle tracks using tracking algorithms. However, reliable track estimation is challenging due to measurement noise caused by high particle density, particle image overlap, and falsely reconstructed 3D particle positions. To overcome this challenge, probabilistic approaches quantify the epistemic uncertainty in particle positions, typically using a Gaussian probability distribution. However, the standard deterministic tracking algorithms relying on nearest-neighbor search do not directly extend to the probabilistic setting. Moreover, such algorithms do not necessarily find globally consistent solutions robust to reconstruction errors. This paper aims to develop a globally consistent nearest-neighborhood algorithm that robustly extracts stochastic particle tracks from the reconstructed Gaussian particle distributions in all frames. Our tracking algorithm relies on the unbalanced optimal transport theory in the metric space of Gaussian measures. Specifically, we optimize a binary transport plan for efficiently moving the Gaussian distributions of reconstructed particle positions between time frames. We achieve this by computing the partial Wasserstein distance in the metric space of Gaussian measures. Our tracking algorithm is robust to position reconstruction errors since it automatically detects the number of particles that should be matched through hyperparameter optimization. Notably, our tracking algorithm also readily applies to the standard deterministic PTV case. Finally, we validate our method using an in vitro flow experiment using a 3D-printed cerebral aneurysm.

Multi-swarm surrogate model assisted PSO algorithm to minimize distribution network energy losses

The computational analysis of real-world engineering problems often relies on time-consuming simulation calculations. This presents challenges in balancing computational burden and precision when applying traditional metaheuristic algorithms to large-scale complex problems. While there have been numerous surrogate-assisted metaheuristic optimization algorithms proposed, most of them are designed for solving expensive problems within 30–50 dimensions. In this paper, a novel approach called Parallel-multi-swarm Gaussian Process Regression surrogate-based particle swarm optimization (Parallel-MS-GPRS-PSO) is proposed for high-dimensional problems. This approach combines a standard particle swarm optimization (PSO) algorithm, multi-swarm cooperative PSO (MSCPSO), and a GPR surrogate-based PSO (PSO-GPR). By integrating PSO-GPR and MSCPSO, the proposed method aims to effectively explore and exploit the search space while enhancing the global and local performance of the surrogate model. To validate the effectiveness of the proposed algorithm, it is compared with several existing PSO algorithms on seven benchmark functions and an engineering problem. The results illustrate that the Parallel-MS-GPRS-PSO approach outperforms the existing algorithms. Moreover, the method shows promising performance in computationally expensive engineering optimization problems with 288 variables.

Enhanced Adsorption Capacity of Methylene Blue Dye onto Kaolin through Acid Treatment: Batch Adsorption and Machine Learning Studies

Algerian kaolinite, sourced from Djebel Debbagh nuance 3 (DD3), was used as a low-cost adsorbent to remove methylene blue (MB) dye from water. Its adsorption capacity was enhanced through sulfuric acid treatment (treated-DD3). In response to the urgent demand for clean water, various technologies have been developed to address dye removal from wastewater. This study, specifically delving into the treatment of textile wastewater, examined the efficacy of treated-DD3 through adsorption processes. The acid treatment increased the surface area and pore volume of DD3. X-ray diffraction showed crystalline phases in both, with treated-DD3 having higher crystallinity. Fourier-transform infrared spectroscopy found no significant differences post-acid treatment. Scanning electron microscopy revealed DD3 had large, stacked particles with low surface area, while treated-DD3 had increased porosity and a smoother surface. Various parameters affecting MB adsorption were studied. The Langmuir and Freundlich models were used for isotherm parameters. Treated-DD3 exhibited a higher MB adsorption capacity (64.58 mg/g according to the Langmuir model) than DD3 (44.48 mg/g). Thermodynamic analysis indicated spontaneous and endothermic MB adsorption onto both DD3-BM and treated-DD3-BM systems under different pH conditions. Treated-DD3 effectively reduced chemical oxygen demand (from 304.056 mg/L to 34.44 mg/L) and biological oxygen demand (from 80 mg/L to 20 mg/L) in real textile wastewater. The adsorbent exhibited rapid removal and decolorization, surpassing 93% within the first 7 min of the experiment. The Gaussian process regression and particle swarm optimization (GPR–PSO) predicted MB adsorption capacity effectively (R = 0.9989, R2 = 0.9978, adj-R2 = 0.9978, RMSE = 1.1390, and MAE = 0.3926).

Gaussian Particle Filtering for Nonlinear Systems With Heavy-Tailed Noises: A Progressive Transform-Based Approach.

The Gaussian particle filter (GPF) is a type of particle filter that employs the Gaussian filter approximation as the proposal distribution. However, the linearization errors are introduced during the calculation of the proposal distribution. In this article, a progressive transform-based GPF (PT-GPF) is proposed to solve this problem. First, a progressive transformation is applied to the measurement model to circumvent the necessity of linearization in the calculation of the proposal distribution, thereby ensuring the generation of optimal Gaussian proposal distributions in sense of linear minimum mean-square error (LMMSE). Second, to mitigate the potential impact of outliers, a supplementary screening process is employed to enhance the Monte Carlo approximation of the posterior probability density function. Finally, simulations of a target tracking example demonstrate the effectiveness and superiority of the proposed method.

Cooperative Navigation for UAV Swarm Via Simplified Gaussian Particle based Belief Propagation

Cooperative Navigation for UAV Swarm Via Simplified Gaussian Particle based Belief Propagation

Modeling and solving a multi‐objective optimal portfolio of upstream oil and gas assets

AbstractThis paper focuses on optimizing project investments in oil and gas companies. It proposes a multi‐objective method for investing in oil and gas assets, considering factors such as scale and efficiency. The model takes into account the presence of nonlinear equations and integer constraints, and establishes a nonlinear multi‐objective mixed integer programming portfolio model for oil and gas. The weights of multiple objectives are determined using support vector machines. The optimization model incorporates the displacement transfer concept of particle swarm optimizer and the mutation operation of genetic algorithm using the transfer strategy of Gaussian particle swarm. The effectiveness of the model and algorithm is demonstrated through two examples.

A hybrid-model optimization algorithm based on the Gaussian process and particle swarm optimization for mixed-variable CNN hyperparameter automatic search

A hybrid-model optimization algorithm based on the Gaussian process and particle swarm optimization for mixed-variable CNN hyperparameter automatic search

Short-term performance degradation prediction of proton exchange membrane fuel cell based on discrete wavelet transform and gaussian process regression

Proton exchange membrane fuel cell (PEMFC) is regarded as one of the most promising energy conversion devices, but cost and durability are two challenges that hinder its large-scale application. Short-term performance degradation prediction is of great importance for the optimization of operating conditions and maintenance strategies to improve the durability and reduce costs of the PEMFCs. This paper proposes a novel data-driven short-term prediction method combining discrete wavelet transform (DWT), gaussian process regression (GPR) and particle swarm optimization (PSO) algorithm. The DWT decomposes the voltage time series waveform into numerous sub-waveforms with different characteristics. The GPR is utilized to construct individual prediction models for distinct sub-waveforms and the final prediction outcomes are obtained by adding the results of each model. The PSO achieves the automatic hyper-parameters optimization in order to improve the accuracy and robustness of the GPR model. In addition, the effectiveness of the proposed method is fully validated by the degradation datasets of PEMFCs in constant and quasi-dynamic load current conditions as well as real road working conditions. Finally, compared with widely used data-driven models such as artificial neural networks (ANN), support vector machine (SVM), long short-term memory (LSTM) and newly proposed methods in relevant studies, the proposed method exhibits superior accuracy and stability for degradation prediction.

Reliability Optimization Method for Gas–Electric Integrated Energy Systems Considering Cyber–Physical Interactions

With the development in the field of energy and the growing demand for sustainable energy, gas–electric integrated energy systems are attracting attention as an emerging energy supply method. At the same time, with the deep application of information technology, the cyber–physical interactions of gas–electric integrated energy systems are increasingly enhanced. To this end, first, the reliability assessment indices of a gas–electric integrated energy system, which comprehensively considers the interactions between cyber–physical and different energy sources, are established in this paper to quantitatively assess the reliability level of the system under different fault and failure conditions. Second, to solve the reliability optimization problem, a comprehensive reliability enhancement optimization model is constructed in this paper, which targets the sum of the total penalties of the failure rate and average repair time modification. The impact of the cyber systems on the gas–electric integrated energy systems is transformed into a modification of the failure rate and the average repair time, and the model is solved by an adaptive Gaussian particle swarm optimization algorithm. Finally, the applicability and superiority of the adaptive Gaussian particle swarm optimization algorithm to the reliability optimization of the gas–electricity integrated energy system are verified by conducting simulation tests on the gas–electricity integrated energy system coupled with an 8-node distribution system and the 11-node natural gas system in Belgium. Furthermore, the effects of cyber systems and cyber-attacks on system reliability optimization are also analyzed to verify the effectiveness of the proposed method and the rationality of the newly defined reliability indices.

Multiphysics Modelling of Powder Coating of U-Profiles: Towards Simulation-based Optimization of Key-Performance Attributes by Variation of Powder-Parameters

Multiphysics simulation software has been developed to predict the key performance attributes of industrial powder coating applications based on applied process-parameter settings. The software is a Eulerian-Lagrangian finite-volume Multiphysics solver based on OpenFOAM, capable of modelling mass transfer effects between powder-coating pistols and electrically grounded metallic substrates. It considers various factors such as fluid dynamics of process airflow, coating-particle dynamics, particle-substrate interactions, and particle charging mechanisms within the corona. The software is fully compatible with Massive Simultaneous Cloud Computing technology, allowing hundreds of simulated coating scenarios to be computed simultaneously. Experimental validation efforts have been conducted, indicating a high degree of practical relevance of the technology.  The current simulation study aims to demonstrate the potential of the simulation software for adjusting coating lines and optimizing powder coating of U-profiles. Specifically, the study focuses on optimizing the key-performance-attributes of the powder coating application with respect to varying material parameters of the applied powder, namely mean particle diameter, standard deviation of Gaussian particle size distribution, and powder particle density. The software predicts and visualizes coating patterns, coating efficiencies, and the batch-based standard deviation of coating thickness on a U-shaped metallic substrate, resulting in concrete and optimized powder settings. The presented results and the applied software are highly relevant for powder material suppliers.&nbsp

3D beam-envelope approach for an asymmetric beam in a high intensity linac with a solenoid channel

Presented here is a theory model based on the beam-envelope approach to determine the global behavior of a charged beam propagating through a high intensity linac with a solenoid channel, namely, the orbital evolution of the root-mean-square beam size in the transverse and longitudinal direction. The model is applied to the Gaussian particle distribution, where the motion of an individual particle is governed by linear focusing/defocusing forces in the solenoid channel and RF fields, except for space-charge forces. In this model, highly nonlinear effects that originated from space-charge forces disappear by averaging over the harmonic motions such as the betatron motion and phase motion in the moving direction and the Gaussian distribution. All particles making up a 3D Gaussian bunch obey the same linear equations of motion where all information of nonlinearity in the space-charge forces and the particle distribution are carried in. The theory is validated using Gaussian macro-particle simulation and one of the widely used photonic integrated circuit codes, TraceWin. As an example, the model is applied to the case of an international fusion materials irradiation facility superconducting linac with solenoid guiding and half wave RF acceleration. The results are compared with results obtained by this model and other two approaches.

A Progressive Bayesian Filtering Framework for Nonlinear Systems With Heavy-Tailed Noises

This article studies the Bayesian filtering problem for nonlinear systems with heavy-tailed noises. Because of the nonlinearity and heavy tail characteristics, the Gaussian distribution or particle sets may fail to express the posterior probability density distribution; thus, the progressive Bayesian filtering framework is proposed. With the filtering framework, the measurement update is divided into several steps, and the intermediate posterior distributions are chosen as the importance proposal distributions to improve the approximation of posterior probability density distributions. Moreover, termination conditions for the progressive measurement update are also proposed to improve the robustness of the progressive Bayesian filter against outliers. Finally, a simulation example is exploited to illustrate the effectiveness and superiority of the proposed filtering framework.

A Gaussian Particle Swarm Optimization-Based Phase Unwrapping Algorithm

A Gaussian particle swarm optimization-based phase unwrapping (PU) technique is presented to recover unwrapped phases reflecting the deformation or height of the observed objects from measured interferograms composed of wrapped phases. First, the Gaussian particle swarm optimization strategy is exploited into PU for measured interferograms, and a robust PU program based on the Gaussian particle filter is constructed by combining a robust phase slope estimation technique demonstrated well previously. Second, an efficient path-following approach is exploited to route the paths of PU to improve the accuracy and efficiency in PU for interferograms. Finally, the performances of the proposed method are fully demonstrated with the experiments of PU for the simulated and measured interferograms, and the advantages of this method in the accuracy of PU for interferograms are also shown, with respect to some other traditional methods and representative methods.

Gaussian Mixture Filtering with Nonlinear Measurements Minimizing Forward Kullback-Leibler Divergence

A Gaussian mixture filter is proposed for the state estimation of dynamical systems with nonlinear measurements. The filter is derived by solving an assumed density filtering problem where Kullback-Leibler (KL) divergence from the assumed posterior, which is a Gaussian mixture, to the true posterior (which we call forward KL divergence) is minimized. The approximate solution to this problem gives an iterative measurement update by which the weights, means and covariances of the assumed posterior are optimized. The resulting Gaussian mixture filter is shown to be a generalization of the (damped) posterior linearization filter to Gaussian mixture posteriors. The performance of the proposed filter is illustrated and compared to alternatives on a challenging example of target tracking in a sensor network and on an example of tracking with a radar. The results show that the proposed filter can outperform Gaussian filters as well as the Gaussian sum filter and the Gaussian sum particle filter yielding results very close to a bootstrap particle filter when the number of components in the assumed posterior is sufficiently large.

Particle field deconvolution multiplicative algebraic reconstruction technique for tomographic particle image velocimetry reconstruction

Precision tomographic reconstruction is critical for obtaining high-accuracy velocity measurements in tomographic particle image velocimetry. Traditional tomographic reconstruction methods, such as the multiplicative algebraic reconstruction technique (MART), can only be applied at low particle concentrations, limiting the spatial resolution of velocity measurements. In addition, the actual shape of the particles is not reconstructed well due to the limited views. In this study, we propose a novel method named particle field deconvolution MART (Deconv-MART) to repair the shape of actual particles while suppressing ghost particles reconstructed by MART iterations. This method first uses the Gaussian particle shape prior to estimate the convolution kernel obtained by MART reconstruction. Then, the estimated kernel is utilized to deconvolute the particle field and suppress ghost particles based on the prior information of the lower intensity of ghost particles as well as the sparsity of the particle field. Reconstruction fields are estimated with numerical and real experiments, and the results are compared with the results of advanced reconstruction methods. Comparisons of reconstruction demonstrate that the proposed method is effective at suppressing ghost particles and restoring the shape of actual particles. Comparisons of velocity measurements reveal that Deconv-MART has good performance and high measurement accuracy.

Adaptive Kernel Kalman Filter

Sequential Bayesian filters in non-linear dynamic systems require the recursive estimation of the predictive and posterior distributions. This paper introduces a Bayesian filter called the adaptive kernel Kalman filter (AKKF). With this filter, the arbitrary predictive and posterior distributions of hidden states are approximated using the empirical kernel mean embeddings (KMEs) in reproducing kernel Hilbert spaces (RKHSs). In parallel with the KMEs, some particles, in the data space, are used to capture the properties of the dynamical system model. Specifically, particles are generated and updated in the data space, while the corresponding kernel weight mean vector and covariance matrix associated with the feature mappings of the particles are predicted and updated in the RKHSs based on the kernel Kalman rule (KKR). Simulation results are presented to confirm the improved performance of our approach with significantly reduced particle numbers, by comparing with the unscented Kalman filter (UKF), particle filter (PF) and Gaussian particle filter (GPF). For example, compared with the GPF, the proposed approach provides around 5% logarithmic mean square error (LMSE) tracking performance improvement in the bearing-only tracking (BOT) system when using 50 particles.

Structural optics design of the zoom system based on particle swarm optimization

Selection of initial structural parameters is an essential step for the zoom system design. In this paper, a new method based on Gaussian optics and Particle Swarm Optimization (PSO) algorithm is proposed to design initial structural parameters of the zoom system, and an optical automatic optimization design is carried out based on the initial structural parameters. Firstly, displacement parameters of the zoom group and the compensation group of the zoom system are derived based on Gaussian optics. Secondly, constraints of the zoom system are established using the PSO algorithm, and a fitness function is designed. Then, the initial structure parameters of the zoom system are optimized. Finally, uniform and monotonic movement of the cam curve is achieved in an example of a 6 × zoom system. The results indicate that our proposed methods improve the efficiency and accuracy of the zoom system design, which has guiding significance for the design of multi-group moving zoom system with high zoom ratio and other engineering applications.

Effect of sintering time on the microstructure and stability of Al2O3–ZrO2 composite powders under microwave-assisted sintering

The function of ceramic coating is closely related to the construction technology and the quality of ceramic powders. Generally, Al2O3–ZrO2 powders are rapidly sprayed on the material surface at high temperatures to obtain better performance. Improving the quality of Al2O3–ZrO2 powders can make them more widely used in ceramic coating. In this paper, microwave sintering was used to enhance the sintering process of the powders, and the effect of sintering time on the microstructure, properties, and stability of Al2O3–ZrO2 powders was investigated. The results proved that microwave heating could improve the crystallinity and stability of the samples. At 900 °C, the tetragonal phase content in samples with different sintering times were 63.05%, 63.25%, 62.39%, and 63.22%, respectively. The average particle sizes obtained by Gaussian fitting are 1.04 μm, 0.83 μm, 0.88 μm, 0.86 μm, respectively. The Gaussian fitting particle size data was consistent with the normal distribution. Compared with the particle size of raw material (1.10 μm), the particles were refined, and the dispersion effect was noticeable. Therefore, the best sintering time for microwave sintering Al2O3 stabilized zirconia was 2 h. This paper aims to provide reasonable data support for improving the preparation of high-quality Al2O3-PSZ ceramic powders and to guide the industrial production of Al2O3-PSZ powders.