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Chakraborty, Uday Kumar, Kalyanmoy Deb, and Mandira Chakraborty. "Analysis of Selection Algorithms: A Markov Chain Approach." Evolutionary Computation 4, no. 2 (June 1996): 133–67. http://dx.doi.org/10.1162/evco.1996.4.2.133.
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A Markov chain framework is developed for analyzing a wide variety of selection techniques used in genetic algorithms (GAs) and evolution strategies (ESs). Specifically, we consider linear ranking selection, probabilistic binary tournament selection, deterministic s-ary (s = 3,4, …) tournament selection, fitness-proportionate selection, selection in Whitley's GENITOR, selection in (μ, λ)-ES, selection in (μ + λ)-ES, (μ, λ)-linear ranking selection in GAs, (μ + λ)-linear ranking selection in GAs, and selection in Eshelman's CHC algorithm. The analysis enables us to compare and contrast the various selection algorithms with respect to several performance measures based on the probability of takeover. Our analysis is exact—we do not make any assumptions or approximations. Finite population sizes are considered. Our approach is perfectly general, and following the methods of this paper, it is possible to analyze any selection strategy in evolutionary algorithms.
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Field, R. V., P. G. Voulgaris, and L. A. Bergman. "Methods to Compute Probabilistic Measures of Robustness for Structural Systems." Journal of Vibration and Control 2, no. 4 (October 1996): 447–63. http://dx.doi.org/10.1177/107754639600200405.
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Model uncertainty, if ignored, can seriously degrade the performance of an otherwise well-designed control system. If the level of this uncertainty is extreme, the system may even be driven to instability. In the context of structural control, performance degradation and instability imply excessive vibration or even structural failure. Robust control has typically been applied to the issue of model uncertainty through worst- case analyses. These traditional methods include the use of the structured singular value (μ-analysis), as applied to the small gain condition, to provide estimates of controller robustness. However, this emphasis on the worst-case scenario has not allowed a probabilistic understanding of robust control. Because of this, an attempt to view controller robustness as a probability measure is presented. As a result, a much more intuitive insight into controller robustness can be obtained. In this context, the joint probability distribution is of dimension equal to the number of uncertain parameters, and the failure hypersurface is defined by the onset of instability of the closed-loop system in the eigenspace. A first-order reliability measure (FORM) of the system is computed and used to estimate controller robustness. It is demonstrated via an example that this FORM method can provide accurate results on the probability of failure despite the potential complexity of the closed-loop. In addition to the FORM method, a probabilistic measure of robustness is developed based on the fundamentals of μ-analysis. It is shown that the μ-analysis based method is inferior to the FORM method and can only have qualitative value when assessing control system robustness in a probabilistic framework.
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Pinus, B. I., I. G. Korneeva, and V. D. Balheeva. "Fatigue life of bending reinforced concrete elements with fibre-reinforced matrices." Journal «Izvestiya vuzov. Investitsiyi. Stroyitelstvo. Nedvizhimost» 12, no. 3 (2022): 362–67. http://dx.doi.org/10.21285/2227-2917-2022-3-362-367.
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An experimental-probabilistic analysis of variations in the load-bearing capacity of bending reinforced concrete elements with matrices reinforced by polypropylene fibres was carried out. A numerical ex-periment was conducted using the normative methodology of multi-link and layerwise modelling of el-ement cross-sections and experimental "σ-ε" diagrams of fibrocomposites in initial and post-cyclic (50 cycles with η = 0.8 amplitude and zero asymmetry) states. Probabilistic changes in the load-bearing capacity of bending elements subjected to cyclic loads were estimated by the numerical strength modelling of rectangular beams (b × h = 100 × 200 mm) with the one-sided reinforcement (A400 class) of varying intensity. The observed high value of fatigue life of reinforced concrete ele-ments with fibre-reinforced matrices was found to be associated with the presence of mechanisms compensatory for structural changes, i.e., a decrease in the strength is accompanied by an increase in the ability to redistribute internal forces. A post-cyclic reduction in the strength of concrete causes practically no effect on the load-bearing capacity of bending elements with a large and economically preferable range of their structural reinforcement. The reliability kinetics of elements, estimated by the level of the realised concrete strength potential, was analysed. Moderate (μ ≤ μR) reinforcement was found to result in objective conditions for increasing the completeness of the stress diagram in the compressed cross-sectional part due to the redistribution of forces along the height. In this case, de-spite a significant decrease in the strength of concrete, the load-bearing capacity of elements at μ ≤ 2.5% reinforcement remains practically the same after cyclic effects.
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Mussardo, Giuseppe, and André LeClair. "Randomness of Möbius coefficients and Brownian motion: growth of the Mertens function and the Riemann hypothesis." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 11 (November 1, 2021): 113106. http://dx.doi.org/10.1088/1742-5468/ac22fb.
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Abstract The validity of the Riemann hypothesis (RH) on the location of the non-trivial zeros of the Riemann ζ-function is directly related to the growth of the Mertens function M ( x ) = ∑ k = 1 x μ ( k ) , where μ(k) is the Möbius coefficient of the integer k; the RH is indeed true if the Mertens function goes asymptotically as M(x) ∼ x 1/2+ϵ , where ϵ is an arbitrary strictly positive quantity. We argue that this behavior can be established on the basis of a new probabilistic approach based on the global properties of the Mertens function, namely, based on reorganizing globally in distinct blocks the terms of its series. With this aim, we focus attention on the square-free numbers and we derive a series of probabilistic results concerning the prime number distribution along the series of square-free numbers, the average number of prime divisors, the Erdős–Kac theorem for square-free numbers, etc. These results point to the conclusion that the Mertens function is subject to a normal distribution as much as any other random walk. We also present an argument in favor of the thesis that the validity of the RH also implies the validity of the generalized RH for the Dirichlet L-functions. Next we study the local properties of the Mertens function, i.e. its variation induced by each Möbius coefficient restricted to the square-free numbers. Motivated by the natural curiosity to see how closely to a purely random walk any sub-sequence is extracted by the sequence of the Möbius coefficients for the square-free numbers, we perform a massive statistical analysis on these coefficients, applying to them a series of randomness tests of increasing precision and complexity; together with several frequency tests within a block, the list of our tests includes those for the longest run of ones in a block, the binary matrix rank test, the discrete Fourier transform test, the non-overlapping template matching test, the entropy test, the cumulative sum test, the random excursion tests, etc, for a total of 18 different tests. The successful outputs of all these tests (each of them with a level of confidence of 99% that all the sub-sequences analyzed are indeed random) can be seen as impressive ‘experimental’ confirmations of the Brownian nature of the restricted Möbius coefficients and the probabilistic normal law distribution of the Mertens function analytically established earlier. In view of the theoretical probabilistic argument and the large battery of statistical tests, we can conclude that while a violation of the RH is strictly speaking not impossible, it is however extremely improbable.
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Gvozdarev, Aleksey, and Pavel Patralov. "PROBABILISTIC ANALYSIS OF GENERALISED STATISTIC MODEL FOR MULTIPATH CHANNEL OF SIMO SISTEMS WITH FADING AND CORRELATED SHADOWING." Informatics and Automation 20, no. 3 (May 28, 2021): 727–49. http://dx.doi.org/10.15622/ia.2021.3.8.
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The paper considers the problem of analysis of the information transmission process by multi-element communication systems in presence of a multipath signal propagation channel. To generalize the propagation effects, the model of the κ–μ fading channel with correlated shadowing was assumed, and the technology used for organizing a multi-element system was the SIMO system, equipped with the maximum-ration combiner of the signal on the receiving side. To describe the characteristics of the information transfer process, an approach based on the higher-order statistics of the ergodic capacity was used. Closed-form analytical expressions for arbitrary-order capacity higher-order statistics were obtained for the channel model under consideration. The behavior of the first four statistics (ergodic capacity, its reliability, skewness and kurtosis coefficients) is analyzed depending on the channel parameters (the number of multipath propagation clusters, the ratio of power of the dominant components to the total power of multipath waves, the degree of shadowing of the dominant components, and the shadowing correlation coefficient). Within the framework of the study, 4 distinct situations of the assumed channel model behavior were considered, which significantly differ in their properties. It is noted that, in contrast to the capacity, its higher-order statistics are significantly more sensitive to the channel parameters and, as a result, are more significant indicators of fluctuations in the information transfer rate within the communication channel. The existence of a pronounced extremum (minimum) of the reliability ergodic capacity dependence from the signal-to-noise ratio was established. It should be accounted for in practical applications, when the requirements of the signal-to-noise ratio that guarantees the desired communication link quality are set.
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Volkov, Serhiy, Yuliia Simonova, Anton Korol, Yevgen Podkopayev, Oleksiy Kayun, and Oleksandr Tkachuk. "STRUCTURING EXPERIMENTAL DATA ON THE PERFORMANCE OF ARCH SUPPORTS FOR PROBABILISTIC ASSESSMENT OF THE STATE OF RETRACTABLE DRIFTS." JOURNAL of Donetsk Mining Institute, no. 1 (2022): 16–31. http://dx.doi.org/10.31474/1999-981x-2022-1-16-31.
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Purpose. Structuring of experimental data of mine observations of the performance of arched flexible supports to establish a probabilistic assessment of the state of haulage drifts of steep coal seams in the excavation areas of a coal mine. Methods. The methodological basis of the research is an integrated approach, including the analysis and generalization of scientific achievements on the problem under study; mine observations of the state of development workings; analytical calculations using the basic provisions of probability theory, mathematical statistics using differential equations. Results. A probabilistic assessment of the state of the haulage drift under different protection methods, used to predict the stability of section development workings, was obtained from the experimental data of mine observations (observation time t = 4280 hours) of the performance of the arched pliable lining installed in the working along the length of the excavation section. After the sample was formed, the calculation of a statistical assessment of the reliability of the support operation was performed: the indicators of the failure rate λ and the recovery rate μ were established. Dependencies are obtained that allow assessing the state of development workings along the length of the excavation section and in the zone of influence of the stopping operations. It is proved that in the steady mode of operation of the haulage drift, with an increase in the failure rate of the arch support by 5 times, the availability factor, as a function of the reliability and maintainability of the support, changes from 0.9 to 0.5, which leads to a deterioration in time, approximately by 60 %, operational characteristics of the support in the supported development. Novelty. The probabilistic assessment of the loss of stability of the haulage drift along the length of the excavation section is based on the structuring of the data on the performance of arched supports and depends on the method of protection of the working, the intensity of failures of the arched supple support and the frequency of its damage, when in the desired interval of observations when forming the sample, the position of the stopping front is taken into account. Practical relevance. For the reuse of development workings with a store method of preparing steep seams and a descending order of mining floors, a conceptual model is proposed that allows predicting the state of haulage drifts along the length of the excavation area, taking into account the method of protection.
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Falcoz, Alexandre, Daniel Alazard, and Christelle Pittet. "Probabilistic μ-analysis for system performances assessment. * *This work has been done in the scope of a CNES R&D activity cojointly funded by Airbus Defence and Space and CNES, Toulouse." IFAC-PapersOnLine 50, no. 1 (July 2017): 399–404. http://dx.doi.org/10.1016/j.ifacol.2017.08.181.
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Ostermeyer, Georg-Peter, Michael Müller, Stephan Brumme, and Tarin Srisupattarawanit. "Stability Analysis with an NVH Minimal Model for Brakes under Consideration of Polymorphic Uncertainty of Friction." Vibration 2, no. 1 (March 6, 2019): 135–56. http://dx.doi.org/10.3390/vibration2010009.
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In brake systems, some dynamic phenomena can worsen the performance (e.g., fading, hot banding), but a major part of the research concerns phenomena which reduce driving comfort (e.g., squeal, judder, or creep groan). These dynamic phenomena are caused by specific instabilities that lead to self-excited oscillations. In practice, these instabilities can be investigated using the Complex Eigenvalues Analysis (CEA), in which positive real parts of the eigenvalues are identified to characterize instable regions. Measurements on real brake test benches or tribometers show that the coefficient of friction (COF), μ , is not a constant, but dynamic, system variable. In order to consider this aspect, the Method of Augmented Dimensioning (MAD) has been introduced and implemented, which couples the mechanical degrees of freedom of the brake system with the degrees of freedom of the friction dynamics. In addition to this, instability prediction techniques can often determine whether a system is stable or instable, but cannot eliminate the instability phenomena on a real brake system. To address this, the current work deals with the quantification of the relevant polymorphic uncertainty of the friction dynamics, wherein the aleatory and epistemic uncertainties are described simultaneously. Aleatory uncertainty is concerned with the stochastic variability of the friction dynamics and incorporated with probabilistic methods (e.g., a Monte Carlo simulation), while the epistemic uncertainty resulting from model uncertainties is modeled via fuzzy methods. The existing measurement data are collected and processed through Data Driven Methods (DDM) for the identification of the dynamic friction models and corresponding parameters. Total Variation Regularization is used for the evaluation of derivatives within noisy data. Using an established minimal model for brake squealing, this paper addresses the question of probabilities for instabilities and the degree of certainty with which this conclusion can be made. The focus is on a comparison between the conventional Coulomb friction model and a dynamic friction model in combination with the MAD. This shows that the quality of the predictive accuracy improves dramatically with the more precise friction model.
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Liu, Yuqi, Xuehua Li, and Huan Li. "N-Widths of Multivariate Sobolev Spaces with Common Smoothness in Probabilistic and Average Settings in the Sq Norm." Axioms 12, no. 7 (July 17, 2023): 698. http://dx.doi.org/10.3390/axioms12070698.
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In this article, we give the sharp bounds of probabilistic Kolmogorov N,δ-widths and probabilistic linear N,δ-widths of the multivariate Sobolev space W2A with common smoothness on a Sq norm equipped with the Gaussian measure μ, where A⊂Rd is a finite set. And we obtain the sharp bounds of average width from the results of the probabilistic widths. These results develop the theory of approximation of functions and play important roles in the research of related approximation algorithms for Sobolev spaces.
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Liu, Yuqi, Huan Li, and Xuehua Li. "Approximation Characteristics of Gel’fand Type in Multivariate Sobolev Spaces with Mixed Derivative Equipped with Gaussian Measure." Axioms 12, no. 9 (August 22, 2023): 804. http://dx.doi.org/10.3390/axioms12090804.
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In this paper, we study the probabilistic Gel’fand N,δ-width of multivariate Sobolev spaces MW2rTd with mixed derivative that are equipped with Gaussian measure μ in LqTd. The sharp asymptotic estimates are determined by employing the discretization method.
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M. Gaddi, Carlo, and Marcelo F. Costa. "Criação de Escalas Quantitativas para Estudos de Eventos Mentais: Uma Revisão da Lei do Julgamento Comparativo." Cadernos de Psicologia 4, no. 2 (2024): 01–17. http://dx.doi.org/10.9788/cp2024.2-02.
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Louis Leon Thurstone (1887-1955) was a pioneer in developing scales for non-metric stimuli, creating an experimental model centered on the subject without the need for physical units of comparison. This model, known as the Law of Comparative Judgment, relies on probabilistic measures rather than discrete ones, making it a powerful tool for quantifying psychological attributes through interval scales. Thurstone proposed that sensory organs operate probabilistically, infl uenced by an inherent noise within the organism, which can be either internally or externally induced. This noise impacts the hypothetical psychological continuum, causing the observer’s response to be not absolute but based on information received at the moment. His model functions analogously to a statistical sample. The Law of Comparative Judgment is structured around three fundamental premises: (i) each stimulus initiates a discriminative process represented on a psychological continuum; (ii) momentary fl uctuations, both internal and among diff erent observers, can cause a stimulus to be perceived variably, characterized by a normal distribution; (iii) the mean (μ) and standard deviation (σ) of this distribution represent the scale value and its discriminative dispersion, respectively. One of the most widely adopted experimental methods derived from Thurstone’s model is the pairwise comparison protocol. In this protocol, the observer’s task is to discriminate between two stimuli presented simultaneously. In each trial, the observer must judge which of the two stimuli is superior in a specifi ed dimension. The process involves comparing each possible pair of stimuli, with each pair being repeated a specifi c number of times. To organize and analyze the results, a matrix is constructed to capture the diff erences between all stimuli in the pairwise comparison. The fi nal value assigned to each stimulus is determined by the average diff erence between that stimulus and all others in the set. The comparative judgment equation provides a method for transforming these diff erences from all pairwise comparisons into scalar values, whether metric or non-metric. This protocol not only off ers a systematic and rigorous approach for measuring psychological attributes but also allows for a detailed and quantitative analysis of the observer’s perceptions and preferences. Faced with the challenge of conducting pairwise comparisons under various experimental conditions, Thurstone developed a statistical approach to transform data from a simple ranking task into a binary matrix of comparisons. This method allows for the application of the comparative judgment equation, overcoming the challenges of traditional psychophysical methods related to the duration and complexity of experimental sessions. The ranking method, by simplifying data collection, has proven highly eff ective in obtaining interval scales in various psychological and social measurements, particularly in contexts of limited experimental control. This effi ciency suggests that the method could be adapted for large-scale studies and outside laboratory environments, enhancing research in applied fi elds of psychology and related areas.Keywords: Law of Comparative Judgment, ranking order procedure, interval scale; quantitative measure, psychophysics.Creación de Escalas Cuantitativas para Estudios de Eventos Mentales: Una Revisión de la Ley del Juicio ComparadoResumenLouis Leon Thurstone (1887-1955), interesado en cuantifi car actitudes, creencias, preferencias y opiniones, creó una ecuación conocida como la Ley del Juicio Comparativo. El modelo de escala
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Biannic, Jean-Marc, Clément Roos, Samir Bennani, Fabrice Boquet, Valentin Preda, and Bénédicte Girouart. "Advanced probabilistic μ-analysis techniques for AOCS validation." European Journal of Control, July 2021. http://dx.doi.org/10.1016/j.ejcon.2021.06.019.
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Nurfauzan, Arsyi Fatiha, and Sutawanir Darwis. "Clustering Probabilistic Seismic Hazard Analysis Temporal Epidemic-Type Aftershock Sequence untuk Premi Asuransi." Jurnal Riset Statistika, July 31, 2024, 41–48. http://dx.doi.org/10.29313/jrs.v4i1.3864.
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Abstract. An earthquake is an event that releases energy in the earth's crustal rocks, which can trigger aftershocks. The economic losses caused by earthquakes can be mitigated through earthquake insurance. However, conventional premium calculations only take into account the main earthquake (mainshock), while aftershocks are excluded through a declustering process. This article presents the development of Clustering Probabilistic Seismic Hazard Analysis (CPSHA) to evaluate earthquake risk by incorporating aftershock effects using a temporal Epidemic-Type Aftershock Sequence (ETAS) model. The approach is an improvement on traditional earthquake insurance premium calculations, which generally only consider the main earthquake. The ETAS model, with parameters θ=(μ,K,c,α,p), is estimated through Maximum Likelihood Estimation (MLE). This analysis combines seismic hazard ETAS with structural damage data to determine the pure premium of earthquake insurance with aftershock. The study uses West Java earthquake data from 21 November 2022 to 18 February 2023, sourced from the BMKG catalogue. The results indicate that customers in the Cianjur area must pay a total insurance premium (TP) of Rp 28.263.945,00 per year for clusters. This approach enhances the comprehension of earthquake risk and can aid in the calculation of more precise insurance premiums. Abstrak. Gempa bumi merupakan peristiwa pelepasan sejumlah energi pada batuan kerak bumi yang dapat memicu gempa susulan (aftershock). Dampak dari gempa bumi dapat menyebabkan kerugian ekonomi. Salah satu cara untuk menanggulangi hal tersebut dengan asuransi gempa bumi. Perhitungan premi konvensional hanya memperhitungkan gempa utama (mainshock) sementara aftershock disisihkan melalui proses declustering. Artikel ini menyajikan pengembangan Clustering Probabilistic Seismic Hazard Analysis (CPSHA) untuk mengevaluasi risiko gempa bumi dengan memasukkan efek aftershock menggunakan model Epidemic-Type Aftershock Sequence (ETAS) secara temporal. Perhitungan premi asuransi gempa bumi umumnya hanya mempertimbangkan gempa utama, namun pendekatan ini menyertakan aftershock dalam estimasi premi. Model ETAS dengan parameter θ=(μ,K,c,α,p) diestimasi melalui Maximum Likelihood Estimation (MLE). Analisis ini menggabungkan seismic hazard ETAS dengan data kerusakan struktur untuk menentukan premi murni asuransi gempa bumi dengan aftershock. Data yang digunakan adalah data gempa bumi Jawa Barat 21 November 2022 sampai 18 Februari 2023 melalui katalog BMKG. Hasil yang diperoleh menunjukkan total premi (TP) asuransi yang harus dibayarkan oleh nasabah untuk cluster di wilayah Cianjur sebesar Rp 28.263.946,00 per tahun. Pendekatan ini memberikan kontribusi pada pemahaman risiko gempa bumi dan dapat digunakan dalam perhitungan premi asuransi yang lebih akurat.
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Hamid, Mohammed O. A., and Anil Kunwar. "Enhanced spray-wall interaction model for port fuel injection under medium load conditions." Journal of Thermal Analysis and Calorimetry, December 5, 2024. https://doi.org/10.1007/s10973-024-13671-x.
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AbstractThis study presents an Eulerian-Lagrangian framework for the numerical analysis of spray dynamics, with a focus on droplet movement, spray-wall interactions, and the effects of varying injection parameters associated with port fuel injection (PFI) system. A grid-independent criterion is introduced to optimize mesh analysis for accurate predictions of fuel penetration length. The size distribution of secondary droplets is described using a probability density function, and statistical optimization is subsequently implemented to estimate their mean size. This probabilistic approach enhances the Lagrangian wall film (LWF) model, leading to accurate predictions of the Sauter mean diameter (SMD) at a given radial width ($$R_\text{{w}}$$ R w ), with results closely matching experimental data. For $$8.0 ~\text {mm} \le R_\text{{w}} \le 24.0 ~\text {mm}$$ 8.0 mm ≤ R w ≤ 24.0 mm , the maximum SMD of 21.67 $$\mu$$ μ m corresponds to $$R_\text{{w}} = 14.0, \text {mm}$$ R w = 14.0 , mm , while the smallest SMD of 12.68 $$\mu$$ μ m is computed for a radial position of $$R_\text{{w}} = 24.0 ~\text {mm}$$ R w = 24.0 mm . The numerical investigation quantifies the role of spray-wall interactions in determining the trajectory of fuel distribution, particularly in the formation of wall films and the relative spatio-temporal diesel concentration (F/A) %. The study explores aspects such as droplet size variations, heat transfer during evaporation, and film behavior under different injection pressures, providing insights into the multiphysical characteristics of spray-wall systems. Near the impingement site ($$2.0 ~\text {mm} \le R_\text{{w}} \le 4.0 ~\text {mm}$$ 2.0 mm ≤ R w ≤ 4.0 mm ), the plume height ($$H_\text{{w}}$$ H w ) slightly decreases with an increase in injection pressure. While the CFD methodology in this current work has been primarily developed for automotive engineering sector (PFI engines), it also has potential applications in areas such as additive manufacturing, hydropower engineering, climate science, and environmental engineering.
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Hopkin, Charlie. "Defining a maximum heat release rate probability distribution function for design fires in sprinkler‐protected residential buildings." Fire and Materials, October 27, 2024. http://dx.doi.org/10.1002/fam.3251.
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AbstractIn fire safety engineering analysis of sprinkler‐protected residential buildings, the maximum heat release rate is a key parameter requiring consideration. Several documents provide advice for estimating the heat release rate of a sprinkler‐controlled fire, with a prevailing suggestion that it is fixed upon activation of the first sprinkler. When carrying out deterministic analysis, this requires the engineer to assume fixed fire parameters and consider that sprinklers limit fire growth. To explore these assumptions, the study uses three deterministic models to estimate a sprinkler‐controlled maximum heat release rate for a representative apartment layout. The models include Alpert's correlation, a B‐RISK zone model and a computational fluid dynamics model in the Fire Dynamics Simulator. These deterministic models are compared to a probabilistic model in B‐RISK, where Monte Carlo simulations are used to generate a range of maximum heat release rates from distribution functions for fire and sprinkler properties. An output distribution function is generated with a mean of 296.6 kW and a standard deviation of 503.8 kW, with a lognormal distribution (μ = 5.014, σ = 1.165) estimated as a best‐fit. The deterministic models are estimated to sit in the 92–98 percentile range of this function, indicating that common deterministic assumptions are reasonably conservative. The article concludes with suggesting that, for deterministic analysis, a percentile between the 80th and 99th (340–2640 kW) could be qualitatively selected based on the design objectives, building situation and relative consequence of a fire. Further research is needed to establish guidelines for selecting appropriate percentiles across various building scenarios.
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Alghfeli, Abdalla, and Timothy S. Fisher. "Sequential Bayesian-optimized graphene synthesis by direct solar-thermal chemical vapor deposition." Scientific Reports 14, no. 1 (February 13, 2024). http://dx.doi.org/10.1038/s41598-024-54005-z.
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AbstractThis work reports the use of a high-flux solar simulator that mimics the solar spectrum and a cold-wall CVD reactor to demonstrate the feasibility of utilizing a renewable energy resource in synthesizing graphene under various conditions. A parametric study of process parameters was conducted using a probabilistic approach. Gaussian process regression serves as a surrogate to establish a prior for Bayesian optimization, and an information acquisition function is employed to identify conditions that yield high-quality products. Backscattered electron images and Raman mapping were used to assess the effects of growth conditions on graphene characteristic sizes, film quality, and uniformity. We report the synthesis of high-quality single-layer graphene (SLG) and AB-stacked bilayer graphene films in a one-step, short-time process with $$I_{D}/I_{G}$$ I D / I G ratios of 0.21 and 0.14, respectively. Electron diffraction analysis shows peak intensities that resemble SLG and AB-bilayer graphene with up to 5 and 20 $${\upmu }$$ μ m grain sizes, respectively. The optical transmissivities of SLG and AB-bilayer graphene fall between 0.959–0.977 and 0.929–0.953, whereas the sheet resistances measured by a 4-point probe with 1 mm spacing are 15.5 ± 4.6 and 3.4 ± 1.5 k$$\Omega$$ Ω /sq, respectively. Further scale-up of the optimized graphene growth area was achieved by flattening the insolation profile, leading to spatial uniformity up to 13 mm in radius. Direct solar capture for CVD synthesis enable a practical and sustainable option for synthesizing graphene films applicable for photonic and electronic applications.