Quasi-random Research Articles

Improving horizon computation algorithm with quasirandom sequences

The topographic horizon can be used to estimate shading for applications requiring an accurate solar resource estimate, including the effects of the local terrain. With high-resolution topography data, horizon estimation significantly contributes to the computation time needed for irradiance simulations. Approximate horizon algorithms have been proposed previously, sampling topography in a finite number of directions. This paper extends this idea by presenting a sampling approach based on the quasirandom sequences. The sampling strategy is optimized with 300,000 km2 of topography data from Europe and the USA. We demonstrate that our algorithm is several orders of magnitude faster than the precise horizon calculation and significantly improves the previous approximate algorithms. In particular, at the ground level with a topography resolution of 1 m/pixel, the proposed method achieved the same accuracy as the old approximate method four times faster. The horizon is one of the key methods in geographical information science and a part of many modeling tools in the built environment. Improvements in computation time benefit all applications that require irradiance modeling, e.g., the yield of vehicle- and building-integrated photovoltaic or temperature modeling of buildings.

Quantitative Property of MF-Discrepancy and Efficient Point-Selection Strategy for the Nonlinear Stochastic Response Analysis of Structures with Random Parameters

The response analysis of high-dimensional and strongly nonlinear systems with random parameters remains a significant challenge in stochastic computational mechanics. To address this challenge, some methods based on the high-efficacy point sets have been developed, in which efficient global-point-set methods represented by low-discrepancy are of paramount importance in generating representative point sets. Several discrepancies including the extended F-discrepancy (EF-discrepancy) and the generalized F-discrepancy (GF-discrepancy) have been introduced to assess the uniformity and the efficacy of a representative point set. In such context, a maximal marginal EF-discrepancy (MF-discrepancy), which is an extended form of the GF-discrepancy, is proposed in this paper and then the properties of the MF-discrepancy are studied in detail. The probability distribution of the MF-discrepancy is derived, including a rigorous proof for random point sets and a model based on an assumption for some generic point sets. A generalized Koksma-Hlawka inequality is established accordingly to govern the worst error estimate. The lowest bound of the MF-discrepancy is given, and two intuitive quantitative indices are proposed to measure the goodness of the MF-discrepancy. Based on the lowest bound, an enhanced point-selection strategy with a unified theoretical framework for minimizing the MF-discrepancy is proposed. In this framework, locally minimizing the MF-discrepancy yields the two-step point-selection method, and a new point-selection strategy is proposed based on the global minimization of the MF-discrepancy, which is verified to be efficient and robust, especially in high-dimensional cases. Several numerical examples, including a 2-story shear frame, a 10-story shear frame, and a 10-story reinforced concrete frame structure modeled by the finite element method, are studied, verifying the efficiency and the robustness of the proposed point-selection strategy.

Numerical Simulation of Spectral Radiation for Hypersonic Vehicles

The spectral radiation of hypersonic vehicles and surrounding flow fields is crucial for optical target detection. A novel approach combines Low-Discrepancy Sequences with the Reverse Monte Carlo Method to simulate the spectral radiation of hypersonic missiles. The effects of chemical non-equilibrium reactions and high-emissivity coating failures on the spectral radiation of a typical biconical hypersonic missile were investigated. Significant differences were found among chemical equilibrium, non-equilibrium, non-reactive, and catalytic wall models. High-emissivity coating failures occur mainly in the high-temperature regions of the nose cone and fins. The non-equilibrium model shows a transition peak distribution of NO in the head shock layer within the ultraviolet gamma band, with integrated ultraviolet radiation (200–300 nm) three times higher than the equilibrium model. In the 1–3 μm band, the non-equilibrium model’s radiation intensity at a 120° horizontal detection angle is about 1.46 times that of the equilibrium model. Using real coating emissivity, the 3–5 μm band radiation intensity is about 5% higher, and the 8–14 μm band is about 8.51% lower than the uniform emissivity model. When high-emissivity coating emissivity fails by 40%, the 3–5 μm band intensity decreases by about 15.38%, and the 8–14 μm band intensity decreases by about 12.67%.

Survey of a class of iterative row-action methods: The Kaczmarz method

AbstractThe Kaczmarz algorithm is an iterative method that solves linear systems of equations. It stands out among iterative algorithms when dealing with large systems for two reasons. First, at each iteration, the Kaczmarz algorithm uses a single equation, resulting in minimal computational work per iteration. Second, solving the entire system may only require the use of a small subset of the equations. These characteristics have attracted significant attention to the Kaczmarz algorithm. Researchers have observed that randomly choosing equations can improve the convergence rate of the algorithm. This insight led to the development of the Randomized Kaczmarz algorithm and, subsequently, several other variations emerged. In this paper, we extensively analyze the native Kaczmarz algorithm and many of its variations using large-scale systems as benchmarks. Through our investigation, we have verified that, for consistent systems, various row sampling schemes can outperform both the original and Randomized Kaczmarz method. Specifically, sampling without replacement and using quasirandom numbers are the fastest techniques. However, for inconsistent systems, the Conjugate Gradient method for Least-Squares problems overcomes all variations of the Kaczmarz method for these types of systems.

Inchworm quasi Monte Carlo for quantum impurities

The inchworm expansion is a promising approach to solving strongly correlated quantum impurity models due to its reduction of the sign problem in real and imaginary time. However, inchworm Monte Carlo is computationally expensive, converging as 1/N where N is the number of samples. We show that the imaginary-time integration is amenable to quasi Monte Carlo, with parametrically better 1/N convergence, by mapping the Sobol low-discrepancy sequence from the hypercube to the simplex with the so-called Root transform. This extends the applicability of the inchworm method to, e.g., multiorbital Anderson impurity models with off-diagonal hybridization, relevant for materials simulation, where continuous-time hybridization expansion Monte Carlo has a severe sign problem. Published by the American Physical Society 2024

A deep neural network reduced order model for unsteady aerodynamics of pitching airfoils

A machine learning framework is developed to compute the aerodynamic forces and moment coefficients for a pitching NACA0012 airfoil incurring in light and deep dynamic stall. Four deep neural network frameworks of increasing complexity are investigated: two multilayer perceptrons and two convolutional neural networks. The convolutional framework, in addition to the standard mean squared error loss, features an improved loss function to compute the airfoil loads. In total, five models are investigated of increasingly complexity. The convolutional model, coupled with the loss function based on force and moment coefficients and embedding the attention mechanism, is found to robustly and efficiently predict pressure and skin friction distributions over the airfoil over the entire pitching cycle. Periodic conditions are implemented to grant the physical smoothness of the model output both in space and time. An analysis of the training dataset point distributions is performed to point out the effects of adopting low discrepancy sequences, such as Latin hypercube, Sobol', and Halton, compared to random and uniform sequences. The current model shows improved performances in predicting forces and pitching moment in a broad range of operating conditions.

A short-term power load forecasting system based on data decomposition, deep learning and weighted linear error correction with feedback mechanism

Accurate power load forecasting enables Independent System Operators (ISOs) to precisely quantify the demand patterns of users and achieve efficient management of the smart grid. However, with the increasing variety of power consumption patterns, the power load data displays increasingly irregular characteristics, which posing great challenges for accurate load forecasting. In order to solve above problem, a novel power load forecasting system is proposed based on data denoising, customized deep learning and weighted linear error correction. Specifically, we first proposed an improved optimization algorithm IGWO-JAYA which enhanced the Grey Wolf Optimizer (GWO) algorithm by using Halton low-discrepancy sequence and the mechanism of JAYA algorithm. In data denoising, the proposed optimizer was employed to optimize the Variational Mode Decomposition (VMD), enabling data-driven intelligent denoising. The customized deep learning framework contained multi-layer Convolution Neural Network (CNN), Bi-directional Long Short-Term Memory (Bi-LSTM) and Multi-Head Attention mechanism. The effective integration of these layers can significantly improve the capacity for nonlinear fitting of deep learning. In weighted linear error correction, the IGWO-JAYA algorithm was employed to determine the appropriate weight for point forecasting values and residual forecasting values. By weighting them, the forecasting precision has been further enhanced. To verify the forecasting ability of the system, we conducted experiments on power load datasets from four states in Australia and found that it has the best performance compared with all rivals. In the discussion, we demonstrated the convergence efficiency of the IGWO-JAYA algorithm by CEC test function.

Quasi-random Fractal Search (QRFS): A dynamic metaheuristic with sigmoid population decrement for global optimization

Global optimization of complex and high-dimensional functions remains a central challenge with broad applications in science and engineering. This study introduces a new optimization approach called quasi-random metaheuristic based on fractal search (QRFS), which harnesses the power of fractal geometry, low discrepancy sequences, and intelligent search space partitioning techniques. The QRFS uses fractals’ inherent self-similarity and intricate structure to guide the solution space exploration. For the proposal, a deterministic but quasi-random element is used in the search process using low discrepancy sequences, such as Sobol, Halton, Hammersley, and Latin Hypercube. This integration allows the algorithm to systematically cover the search space while maintaining the level of diversity necessary for efficient exploration. The QRFS employs a dynamic strategy of partitioning the search space and reducing the population of solutions to optimize the use of function accesses, which causes it to adapt well to the characteristics of the problem. The algorithm intelligently identifies and prioritizes promising regions within the fractal-based representation, allocating computational resources where they are most likely to yield optimal solutions. Experimental evaluations on several benchmark problems demonstrate that QRFS consistently outperforms modern, canonical metaheuristics and variants of algorithms such as differential evolution (DE), particle swarm optimization (PSO), covariance matrix adaptive evolution strategy (CMA-ES), regarding solution quality. Besides, the algorithm shows remarkable scalability, which makes it suitable for high-dimensional optimization tasks. Overall, QRFS offers a robust and efficient approach to solving complex optimization problems in various domains, paving the way for improved decision-making in real-world applications.

Safety & Efficacy of Thalidomide in Children with Transfusion DependentThalassemia: a Quasi Randomized Controlled Trial in a Tertiary Care Hospital in Bangladesh

Safety & Efficacy of Thalidomide in Children with Transfusion DependentThalassemia: a Quasi Randomized Controlled Trial in a Tertiary Care Hospital in Bangladesh

Sufficient Conditions for Central Limit Theorems and Confidence Intervals for Randomized Quasi-Monte Carlo Methods

Randomized quasi-Monte Carlo methods have been introduced with the main purpose of yielding a computable measure of error for quasi-Monte Carlo approximations through the implicit application of a central limit theorem over independent randomizations. But to increase precision for a given computational budget, the number of independent randomizations is usually set to a small value so that a large number of points are used from each randomized low-discrepancy sequence to benefit from the fast convergence rate of quasi-Monte Carlo. While a central limit theorem has been previously established for a specific but computationally expensive type of randomization, it is also known in general that fixing the number of randomizations and increasing the length of the sequence used for quasi-Monte Carlo can lead to a non-Gaussian limiting distribution. This paper presents sufficient conditions on the relative growth rates of the number of randomizations and the quasi-Monte Carlo sequence length to ensure a central limit theorem and also an asymptotically valid confidence interval. We obtain several results based on the Lindeberg condition for triangular arrays and expressed in terms of the regularity of the integrand and the convergence speed of the quasi-Monte Carlo method. We also analyze the resulting estimator’s convergence rate.

Enhancing the performance of zero energy buildings with boosted coyote optimization and elman neural networks

This research paper aims to optimize electrical system modeling to minimize CO2 emissions, improve reliability, and reduce costs. It proposes integrating Elman Neural Network (ENN) and metaheuristic algorithm to evaluate environmental impact and optimize system performance. The goal is to create a mathematical model considering renewable energy sources, grid energy, CO2 emissions, and maintenance costs, and use metaheuristic algorithms to determine the optimal combination of wind turbines and photovoltaic panels. To train the ENN model and optimize the system, a three-stage approach is proposed. Quasi-random numbers are generated using Sobol techniques to create input data, which is then processed by TRNSYS for simulation. The proposed approach incorporates an ENN with Boosted version of the Coyote optimization algorithm to accurately model and predict the behavior of Hybrid Renewable Energy Systems for Zero Energy Buildings. The results demonstrate the effectiveness of the proposed approach. Our method significantly reduces energy consumption, costs, and system reliability, achieving a 25% reduction in energy consumption and 12% reduction in system cost, and is effective in optimizing hybrid solar/wind and hydrogen storage systems. The optimal system configuration significantly reduces CO2 emissions, achieves a high level of system reliability, and minimizes costs. Comparative analysis with previous studies showcases the superiority of the proposed method in achieving comprehensive optimization. In conclusion, this study combines AI techniques and metaheuristic algorithms to optimize electrical system design, considering environmental, technical, and economic factors. The proposed approach overcomes limitations in previous studies and offers an effective solution to address the optimization problem.

Scenario analysis of local storylines to represent uncertainty in complex human-water systems

Storylines are important in evaluating the uncertainty inherent in complex human-water systems. The interrelated nature of qualitative and quantitative scenarios can enhance our ability to address the uncertainty of integrated modelling of complex systems. This study proposes a transdisciplinary approach that integrates social and environmental sciences to characterize and comprehend uncertainty in the dynamic interactions of key factors affecting a human-water system. We introduce a framework for representing uncertainty through linguistic and epistemic uncertainty quantification using storyline narratives in the context of a regional integrated dynamic model. A systematic exploration of uncertainty space is performed using storytelling, fuzzy sets, and low discrepancy sequences sampling methods. Scenario analysis is applied to the generated uncertain ensemble of projections to discover predominant storylines of interest. As a representative case of a human-water system operating in a developing country, we examine the uncertainty effects of a variety of drivers of climatic and socio-economic changes on key agriculture and water-related sectors in Pakistan’s Rechna Doab region. The findings revealed soil salinity and crop yield indices were the most uncertain and showed significant variance across all developed storylines. The 95th percentile for soil salinity in year 2100 was estimated to be nearly 60 % higher than the baseline level (year 2020). There was, however, considerable overlap in different socio-economic scenarios at the local scale, indicating that change in socio-economic conditions could not fully offset climate-related uncertainty. Our analysis provides better quantification and a deeper understanding of the uncertainty in integrated assessment modelling of coupled human-water systems and the complex relationships between inputs and outcomes.

The pair correlation function of multi-dimensional low-discrepancy sequences with small stochastic error terms

In any dimension d≥2, there is no known example of a low-discrepancy sequence which possesses Poisssonian pair correlations. This is in some sense rather surprising, because low-discrepancy sequences always have β-Poissonian pair correlations for all 0<β<1d and are therefore arbitrarily close to having Poissonian pair correlations (which corresponds to the case β=1d). In this paper, we further elaborate on the closeness of the two notions. We show that d-dimensional Kronecker sequences for badly approximable vectors α→ with an arbitrary small uniformly distributed stochastic error term generically have β=1d-Poissonian pair correlations.

Suppression of Railway Catenary Galloping Based on Structural Parameters’ Optimization

Railway catenary galloping, induced by aerodynamic instability, poses a significant threat by disrupting the electric current connection through sliding contact with the contact wire. This disruption leads to prolonged rail service interruptions and damage to the catenary’s suspension components. This paper delves into the exploration of optimizing the catenary system’s structure to alleviate galloping responses, addressing crucial parameters such as span length, stagger dropper distribution, and tension levels. Employing a finite element model, the study conducts simulations to analyze the dynamic response of catenary galloping, manipulating structural parameters within specified ranges. To ensure accurate and comprehensive exploration, the Sobol sequence is utilized to generate low-discrepancy, quasi-random, and super-uniform distribution sequences for the high-dimensional parameter inputs. Subsequent to the simulation phase, a genetic algorithm based on neural networks is employed to identify optimal parameter settings for suppressing catenary galloping, taking into account various constraints. The results gleaned from this investigation affirm that adjusting structural parameters can effectively diminish the galloping amplitude of the railway catenary. The most impactful strategy involves augmenting tension and reducing span length. Moreover, even when tension and span length are fixed, adjusting other parameters demonstrates efficacy in reducing galloping amplitudes. The adjustment of messenger-wire tension, dropper distribution, and stagger can achieve a 22.69% reduction in the maximum vertical galloping amplitude. Notably, maintaining a moderate stagger value and a short steady arm–dropper distance is recommended to achieve the minimum galloping amplitude. This research contributes valuable insights into the optimization of railway catenary systems, offering practical solutions to mitigate galloping-related challenges and enhance overall system reliability.

Development of an Artificial Intelligence Model to Predict Combustion Properties, With a Focus on Auto-Ignition Delay

Abstract Hydrogen-compatible gas turbines are one way to decarbonize electricity production. However, burning and handling hydrogen is not trivial because of its high reactivity and tendency to detonate. Mandatory safety parameters, such as auto-ignition delay times, can be estimated thanks to predictive detailed kinetic models, but with significant calculation times that limit coupling with fluid mechanic codes. An auto-ignition prediction tool was developed based on an artificial intelligence (AI) model for fast computations and an implementation into an explosion model. A dataset of ignition delay times (IDTs) was generated automatically using a recent detailed kinetic model from National University of Galway (NUIG) selected from the literature. Generated data cover a wide operating range and different compositions of fuels. Clustering problems in sample points were avoided by a quasi-random Sobol sequence, which covers uniformly the entire input parameter space. The different algorithms were trained, cross-validated, and tested using a database of more than 70,000 ignitions cases of natural gas/hydrogen blends calculated with the full kinetic model by using a common split of 70/30 for training, testing. The AI model shows a high degree of robustness. For both the training and testing datasets, the average value of the correlation coefficient was above 99.91%, and the mean absolute error (MAE) and the mean square error (MSE) were around 0.03 and lower than 0.04, respectively. Tests showed the robustness of the AI model outside the ranges of pressure, temperature, and equivalence ratio of the dataset. A deterioration is, however, observed with increasing amounts of large alkanes in the natural gas.

A novel maximum entropy method based on the B-spline theory and the low-discrepancy sequence for complex probability distribution reconstruction

The maximum entropy method (MEM) is a powerful tool for the recovery of unknown probability density functions (PDF) and has growing popularity in the reliability analysis community. However, MEM may be inaccurate for PDFs with a complex shape (e. g. multiple modals or a long tail), influencing the accuracy of the reliability analysis greatly. To overcome this deficiency, this study proposes a novel MEM paradigm based on the B-spline theory and the low-discrepancy sequence. Firstly, to enhance the performance of MEM for complex PDFs, the B-spline functions are used to construct the MEM PDF. Correspondingly, the iteration formulation is derived for the undetermined parameter estimation of the B-spline-based MEM PDF based on the closed solution for minimizing the Kullback-Leibler divergence. Then, we adopt the low-discrepancy sequence to calculate the objective function of minimizing the Kullback-Leibler divergence efficiently. Compared with MEM and other moment-based reliability analysis methods, the proposed method does not require the statistical moments, and integrates the advantages of the B-spline theory and MEM. To illustrate the benefits of our method, five examples are analyzed and compared with some classical reliability analysis methods.

High-throughput determination of grain size distributions by EBSD with low-discrepancy sampling.

Because microstructure plays an important role in the mechanical properties of structural materials, developing the capability to quantify microstructures rapidly is important to enabling high-throughput screening of structural materials. Electron backscatter diffraction (EBSD) is a common method for studying microstructures and extracting information such as grain size distributions (GSDs), but is not particularly fast and thus could be a bottleneck in high-throughput systems. One approach to accelerating EBSD is to reduce the number of points that must be scanned. In this work, we describe an iterative method for reducing the number of scan points needed to measure GSDs using incremental low-discrepancy sampling, including on-the-fly grain size calculations and a convergence test for the resulting GSD based on the Kolmogorov-Smirnov test. We demonstrate this method on five real EBSD maps collected from magnesium AZ31B specimens and compare the effectiveness of sampling according to two different low discrepancy sequences, the Sobol and R2 sequences, and random sampling. We find that R2 sampling is able to produce GSDs that are statistically very similar to the GSDs of the full density grids using, on average, only 52% of the total scan points. For EBSD maps that contained monodisperse GSDs and over 1000 grains, R2 sampling only required an average of 39% of the total EBSDpoints.

Infrared radiation characteristics of dagger-type hypersonic missile

Hypersonic vehicles emit strong infrared radiation from their high-temperature exhaust plume and body, which is critical for infrared early warning, tracking, and guidance. In this work, a comprehensive analysis is conducted on the factors involved in air dissociation reaction within the shock layer of hypersonic missile heads, as well as the multi-component afterburning effect of the exhaust plume. A novel Reverse Monte Carlo Method (RMCM) is proposed for infrared radiation calculation, which utilizes two-dimensional Low-Discrepancy Sequences (LDS) to improve computational accuracy. The numerical calculations for a dagger-type missile show that afterburning reactions increase the temperature on the centerline of the outlet exhaust plume by about 1000 K. The total infrared radiation intensity of the missile is the highest in the 1–3 μm band, with the high-temperature wall of the nozzle being the primary source of solid radiation, and gas radiation primarily coming from H2O. The radiation intensity of the missile exhaust plume in the 3–5 μm band is the highest, with radiation sources primarily coming from CO2, CO, and HCl. Afterburning reactions of the exhaust plume increase the total infrared radiation intensity of the missile by about 0.7 times. These results can provide reference for the detection and guidance of hypersonic missiles.

Application of high-credible statistical results calculation scheme based on least squares Quasi-Monte Carlo method in multimodal stochastic problems

Solving stochastic problems based on multimodal distributions with high accuracy and efficiency is the focus of current research in the stochastic field. However, since exact statistical results in practical engineering problems are unknown, how to efficiently obtain statistical results with high credibility is of great importance. Therefore, a high-credible statistical results calculation scheme is proposed in this paper. First, the multimodal model is transformed into a weighted sum form of multiple unimodal models by Gaussian mixture model. Then, a high-credible statistical results calculation scheme is designed based on the reusability of low-discrepancy sequences in the quasi-Monte Carlo (QMC) method. The scheme calculates the coefficient of variation for the random response statistical results of the unimodal model across various sample ranges. When the coefficient of variation is less than the tolerance error, which indicates low fluctuation, the statistical results are deemed to have converged to the exact solution. In order to further accelerate the calculation efficiency of the proposed scheme, this paper proposes a least squares quasi-Monte Carlo (LSQMC) method to yield high accuracy statistical moments. Compared with the averageness weights in the QMC method, the non-averageness weights obtained by LSQMC method can more effectively reflect the numerical Characteristics of the random variables and the location distribution of the sampling points in the probability space. Finally, numerical examples have demonstrated that the high-credible statistical results calculation scheme based on the LSQMC method can obtain the high accuracy statistical moments with high efficiency in multimodal stochastic problems.

Generation of irregular grid maps for fingerprinting-based mobile radio localization using farthest-first traversal and low-discrepancy sequences

Localization techniques play a fundamental role in various applications like in the development of smart cities, making the improvement of such technologies indispensable. In this context, radio frequency (RF) fingerprinting (FP)-based localization methods are attractive due to their lower implementation cost, lower energy consumption, and better performance in non-line-of-sight conditions compared to GPS. With this in mind, we propose an RF FP-based localization method using an irregular grid map generation strategy. The grid map segmentation procedure is based on the assumption that the RF measurements collected in a region carry information on how users are often spatially distributed. The algorithms employed in the irregular grid map generation are the farthest-first traversal and low-discrepancy R-sequence. Different irregular grid map generators are compared with each other and with the regular grid map. We evaluate the generators in two different scenarios: with measurements obtained through simulation with ns-3 and via a driving-test procedure in an urban area. Numerical results indicate that our proposed irregular generator presents a lower localization error in both scenarios and is the only one capable of meeting one of the accuracy requirements stated by the Federal Communications Commission that demands a localization error of up to 50m in 80% of the emergency calls.