Showing papers in "Fractal and fractional in 2022"
TL;DR: In this paper , a series of 1-g model tests were conducted to explore the lateral behavior of both soil and monopile under unidirectional cyclic loading, based on the foundation of an offshore wind turbine near the island.
Abstract: The analysis of the behavior of soil and foundations when the piles in offshore areas are subjected to long-term lateral loading (wind) is one of the major problems associated with the smooth operation of superstructure. The strength of the pile-soil system is influenced by variations in the water content of the soil. At present, there are no studies carried out analyzing the mechanical and deformational behavior of both the material of the laterally loaded piles and soil with groundwater level as a variable. In this paper, a series of 1-g model tests were conducted to explore the lateral behavior of both soil and monopile under unidirectional cyclic loading, based on the foundation of an offshore wind turbine near the island. The influence of underground water level and cyclic load magnitude on the performance of the pile–soil system was analyzed. To visualize the movements of soil particles during the experimental process, particle image velocimetry (PIV) was used to record the soil displacement field under various cyclic loading conditions. The relationship curves between pile top displacement and cyclic steps, as well as the relationship curves between cyclic stiffness and cyclic steps, were displayed. Combined with fractal theory, the fractal dimension of each curve was calculated to evaluate the sensitivity of the pile–soil interaction system. The results showed that cyclic loading conditions and groundwater depth are the main factors affecting the pile–soil interaction. The cyclic stiffness of the soil increased in all test groups as loading progressed; however, an increase in the cyclic load magnitude decreased the initial and cyclic stiffness. The initial and cyclic stiffness of dry soil was higher than that of saturated soil, but less than that of unsaturated soil. The ability of the unsaturated soil to limit the lateral displacement of the pile decreased as the depth of the groundwater level dropped. The greater the fluctuation of the pile top displacement, the larger the fractal dimension of each relationship curve, with a variation interval of roughly 1.24–1.38. The average increment of the cumulative pile top displacement between each cycle step following the cyclic loading was positively correlated with fractal dimension. Based on the PIV results, the changes in the pile–soil system were predominantly focused in the early stages of the experiment, and the short-term effects of lateral cyclic loading are greater than the long-term effects. In addition, this research was limited to a single soil layer. The pile–soil interaction under layered soil is investigated, and the results will be used in more complex ground conditions in the future.
65 citations
TL;DR: In this paper , the influence of two types of Magnesia expansion agent on the hydration, as well as the shrinkage behavior of LHP cement-based materials, were studied via pore structural and fractal analysis.
Abstract: Currently, low heat Portland (LHP) cement is widely used in mass concrete structures. The magnesia expansion agent (MgO) can be adopted to reduce the shrinkage of conventional Portland cement-based materials, but very few studies can be found that investigate the influence of MgO on the properties of LHP cement-based materials. In this study, the influences of two types of MgO on the hydration, as well as the shrinkage behavior of LHP cement-based materials, were studied via pore structural and fractal analysis. The results indicate: (1) The addition of reactive MgO (with a reactivity of 50 s and shortened as M50 thereafter) not only extends the induction stage of LHP cement by about 1–2 h, but also slightly increases the hydration heat. In contrast, the addition of weak reactive MgO (with a reactivity of 300 s and shortened as M300 thereafter) could not prolong the induction stage of LHP cement. (2) The addition of 4 wt.%–8 wt.% MgO (by weight of binder) lowers the mechanical property of LHP concrete. Higher dosages of MgO and stronger reactivity lead to a larger reduction in mechanical properties at all of the hydration times studied. M300 favors the strength improvement of LHP concrete at later ages. (3) M50 effectively compensates the shrinkage of LHP concrete at a much earlier time than M300, whereas M300 compensates the long-term shrinkage more effectively than M50. Thus, M300 with an optimal dosage of 8 wt.% is suggested to be applied in mass LHP concrete structures. (4) The addition of M50 obviously refines the pore structures of LHP concrete at 7 days, whereas M300 starts to refine the pore structure at around 60 days. At 360 days, the concretes containing M300 exhibits much finer pore structures than those containing M50. (5) Fractal dimension is closely correlated with the pore structure of LHP concrete. Both pore structure and fractal dimension exhibit weak (or no) correlations with shrinkage of LHP concrete.
62 citations
TL;DR: In this paper , a fractional model of the Capsicum annuum (C. annuum) affected by the yellow virus through whiteflies (Bemisia tabaci) is examined.
Abstract: In this article, a fractional model of the Capsicum annuum (C. annuum) affected by the yellow virus through whiteflies (Bemisia tabaci) is examined. We analyzed the model by equilibrium points, reproductive number, and local and global stability. The optimal control methods are discussed to decrease the infectious B. tabaci and C. annuum by applying the Verticillium lecanii (V. lecanii) with the Atangana–Baleanu derivative. Numerical results described the population of plants and comparison values of using V. lecanni. The results show that using 60% of V. lecanni will control the spread of the yellow virus in infected B. tabaci and C. annuum in 10 days, which helps farmers to afford the costs of cultivating chili plants.
50 citations
TL;DR: In this paper , the influence of the magnesium-phosphorus molar (M/P) ratio and water-to-binder (W/B) ratio on the hydration product is explored by the thermodynamic simulation.
Abstract: Magnesium phosphate cement (MPC) paste is hardened by the acid–base reaction between magnesium oxide and phosphate. This work collects and evaluates the thermodynamic data at 25 ℃ and a pressure of 0.1 MPa and establishes the hydration reaction model of MPC pastes. The influence of the magnesium–phosphorus molar (M/P) ratio and water-to-binder (W/B) ratio on the hydration product is explored by the thermodynamic simulation. Following this, the initial and ultimate states of the hydration state of MPC pastes are visualized, and the porosity of different pastes as well as fractal analysis are presented. The result shows that a small M/P ratio is beneficial for the formation of main hydration products. The boric acid acts as a retarder, has a significant effect on lowering the pH of the paste, and slows down the formation of hydration products. After the porosity comparison, it can be concluded that the decreasing of M/P and W/B ratios helps reduce porosity. In addition, the fractal dimension Df of MPC pastes is positively proportional to the porosity, and small M/P ratios as well as small W/B ratios are beneficial for reducing the Df of MKPC pastes.
48 citations
TL;DR: In this article , the effects of fly ash with four dosages (i.e., 10, 20, 30, and 40%) on the drying shrinkage, autogenous shrinkage and the cracking resistance of face slab concrete were studied.
Abstract: The crack resistance of face slab concretes to various shrinkages is crucial for the structural integrity and the normal operation of concrete-faced rockfill dams (CFRDs). In this work, the effects of fly ash with four dosages (i.e., 10%, 20%, 30% and 40%) on the drying shrinkage, autogenous shrinkage and the cracking resistance of face slab concrete were studied. Besides, the difference in shrinkage behavior due to fly ash addition was revealed from the viewpoint of the pore structure and fractal dimension of the pore surface (Ds). The findings demonstrate that (1) the incorporation of 10–40% fly ash could slightly reduce the drying shrinkage by about 2.2–13.5% before 14 days of hydration, and it could reduce the drying shrinkage at 180 days by about 5.1–23.2%. By contrast, the fly ash addition could markedly reduce the autogenous shrinkage at early, middle and long-term ages. (2) Increasing fly ash dosage from 0 to 40% considerably improves the crack resistance of concrete to plastic shrinkage. Nevertheless, the increase in fly ash dosage increases the drying-induced cracking risk under restrained conditions. (3) The pore structures of face slab concrete at 3 and 28 days become coarser with the increase in fly ash dosage up to 40%. At 180 days, the pore structures become more refined as the fly ash dosage increases to 30%; however, this refinement effect is not as appreciable as the fly ash dosage increases from 30% to 40%. (4) The Ds of face slab concrete is closely related with the concrete pore structures. The Ds of face slab concrete at a. late age increases from 2.902 to 2.946 with increasing of the fly ash dosage. The pore structure and Ds are closely correlated with the shrinkage of face slab concrete. (5) The fly ash dosage around 30% is optimal for face slab concretes in terms of lowering shrinkage and refining the pore structures, without compromising much mechanical property. However, the face slab concretes with a large fly ash dosage should be well cured under restrained and evaporation conditions at an initial hydration age.
43 citations
TL;DR: In this paper , the authors mainly focus on the approximate controllability of fractional semilinear integrodifferential equations using resolvent operators and show that the compactness of an associated resolver can be improved by using Gronwall's inequality.
Abstract: This article primarily focuses on the approximate controllability of fractional semilinear integrodifferential equations using resolvent operators. Two alternative sets of necessary requirements have been studied. In the first set, we use theories from functional analysis, the compactness of an associated resolvent operator, for our discussion. The primary discussion is proved in the second set by employing Gronwall’s inequality, which prevents the need for compactness of the resolvent operator and the standard fixed point theorems. Then, we extend the discussions to the fractional Sobolev-type semilinear integrodifferential systems. Finally, some theoretical and practical examples are provided to illustrate the obtained theoretical results.
34 citations
TL;DR: In this article , the influence of MgO reactivity (50 s and 300 s) and dosage (0, 4 wt.%, by weight of binder) on the air void, pore structure, permeability and freezing-thawing (F-T) resistance of concrete were studied.
Abstract: Currently, the MgO expansion agent is widely used to reduce the cracking risk of concrete. The influence of MgO reactivity (50 s and 300 s) and dosage (0, 4 wt.% and 8 wt.%, by weight of binder) on the air void, pore structure, permeability and freezing–thawing (F–T) resistance of concrete were studied. The results indicate (1) the addition of 4–8 wt.% reactive MgO (with reactivity of 50 s and termed as M50 thereafter) and weak reactive MgO (with reactivity of 300 s and termed M300 thereafter) lowers the concrete’s compressive strength by 4.4–17.2%, 3.9–16.4% and 1.9–14.6% at 3, 28 and 180 days, respectively. The increase in MgO dosage and reactivity tends to further reduce the concrete strength at all hydration ages. (2) Permeability of the concrete is closely related to the pore structure. M50 can densify the pore structure and lower the fraction of large capillary pores at an early age, thus it is beneficial for the impermeability of concrete. In contrast, M300 can enhance the 180-day impermeability of concrete since it can densify the pore structure only at a late age. (3) The influence of MgO on F–T resistance is minor since MgO could not change the air void parameters. (5) MgO concretes exhibit obvious fractal characteristics. The fractal dimension of the pore surface (Ds) exhibits a close relationship with the permeability property of concrete. However, no correlation can be found between F–T resistance and Ds.
34 citations
TL;DR: In this paper , the authors analyzed and found the solution for a suitable nonlinear fractional dynamical system that describes coronavirus (2019-nCoV) using a novel computational method.
Abstract: In this paper, we analyzed and found the solution for a suitable nonlinear fractional dynamical system that describes coronavirus (2019-nCoV) using a novel computational method. A compartmental model with four compartments, namely, susceptible, infected, reported and unreported, was adopted and modified to a new model incorporating fractional operators. In particular, by using a modified predictor–corrector method, we captured the nature of the obtained solution for different arbitrary orders. We investigated the influence of the fractional operator to present and discuss some interesting properties of the novel coronavirus infection.
32 citations
TL;DR: In this article , the effects of polyvinyl alcohol (pVA) fiber and magnesium oxide expansive agents (mgO) were used together to solve the problems of cracking and abrasive damage.
Abstract: Abrasion resistance and cracking resistance are two important properties determining the normal operation and reliability of hydropower projects that are subjected to erosion and abrasive action. In this study, polyvinyl alcohol (abbreviated as PVA) fiber and magnesium oxide expansive agents (abbreviated as MgO) were used together to solve the problems of cracking and abrasive damage. The effects of PVA fiber and MgO on the mechanical property, abrasion and cracking resistance, pore structures and fractal features of high-strength hydraulic concrete were investigated. The main results are: (1) The incorporation of 4–8% Type I MgO reduced the compressive strength, splitting tensile strength and the abrasion resistance by about 5–12% at 3, 28 and 180 days. Adding 1.2–2.4 kg/m3 PVA fibers raised the splitting tensile strength of concrete by about 8.5–15.7% and slightly enhanced the compressive strength and abrasion resistance of concrete. (2) The incorporation of 4–8% Type I MgO prolongs the initial cracking time of concrete rings under drying by about 6.5–11.4 h, increased the cracking tensile stress by about 6–11% and lowered the cracking temperature by 2.3–4.5 °C during the cooling down stage. Adding 1.2–2.4 kg/m3 PVA fibers was more efficient than adding 4–8% MgO in enhancing the cracking resistance to drying and temperature decline. (3) Although adding 4% MgO and 1.2–2.4 kg/m3 PVA fibers together could not enhance the compressive strength and abrasion resistance, it could clearly prolong the cracking time, noticeably increase the tensile stress and greatly lower the racking temperature; that is, it efficiently improved the cracking resistance to drying and thermal shrinkage compared with the addition of MgO or PVA fiber alone. The utilization of a high dosage of Type I MgO of less than 8% and PVA fiber of no more than 2.4 kg/m3 together is a practical technique to enhance the cracking resistance of hydraulic mass concretes, which are easy to crack. (4) The inclusion of MgO refined the pores, whereas the PVA fiber incorporation marginally coarsened the pores. The compressive strength and the abrasion resistance of hydraulic concretes incorporated with MgO and/or PVA fiber are not correlated with the pore structure parameters and the pore surface fractal dimensions.
31 citations
TL;DR: In this article , two geometric parameters, namely, fractal dimension and fracture entropy, are proposed to determine the spatial and temporal states of rock mass fractures caused by mining, and a spatiotemporal model is created to examine the spatial patterns of hot and cold spots of the fractures based on a Geographic Information System (GIS).
Abstract: Fractures caused by mining are the main form of water inrush disaster. However, the temporal and spatial development characteristics of fractures of the rock mass due to mining are not clearly understood at present. In this paper, two geometric parameters, namely, fractal dimension and fracture entropy, are proposed to determine the spatial and temporal states of rock mass fractures caused by mining. The spatial and temporal structure characteristics of fractures in the rock mass due to mining are simulated with physical scale model testing based on digital image processing technology. A spatiotemporal model is created to examine the spatial and temporal patterns of hot and cold spots of the fractures based on a Geographic Information System (GIS). Results indicate that the fractal dimensions and entropy of the fractures network in the rock mass increase and decrease with the progression of mining, respectively, which can be examined in three stages. When the fractal dimension of the fractures in rock mass rapidly increases, the conductive fracture zone has a saddle shape. The fracture entropy of fracture has periodic characteristics in the advancing direction of the panel, which reflects the characteristics of periodic weighting. The fractal dimension and fracture entropy of fractures of the rock mass increase with time, and the rock mass system undergoes a process of increasing entropy. When the fractal dimension and fracture entropy of the fractures increase, the spatiotemporal state of fractures in rock mass caused by mining is initiated. When the fractal dimension and fracture entropy of the fractures decrease, the spatiotemporal state of fractures in rock mass is closed.
29 citations
TL;DR: The experimental results illustrated that only PSO-FrSlEn can classify 10 kinds of bearing signals with 100% classification accuracy by using double features, which is at least 4% higher than the classification accuracies of the other four fractional entropies.
Abstract: Slope entropy (SlEn) is a time series complexity indicator proposed in recent years, which has shown excellent performance in the fields of medical and hydroacoustics. In order to improve the ability of SlEn to distinguish different types of signals and solve the problem of two threshold parameters selection, a new time series complexity indicator on the basis of SlEn is proposed by introducing fractional calculus and combining particle swarm optimization (PSO), named PSO fractional SlEn (PSO-FrSlEn). Then we apply PSO-FrSlEn to the field of fault diagnosis and propose a single feature extraction method and a double feature extraction method for rolling bearing fault based on PSO-FrSlEn. The experimental results illustrated that only PSO-FrSlEn can classify 10 kinds of bearing signals with 100% classification accuracy by using double features, which is at least 4% higher than the classification accuracies of the other four fractional entropies.
TL;DR: In this article , a new improved optimization technique, namely the quantum chaos game optimizer (QCGO) is applied to tune the gains of the proposed combination TD-TI controller in two-area interconnected hybrid power systems.
Abstract: This study presents an innovative strategy for load frequency control (LFC) using a combination structure of tilt-derivative and tilt-integral gains to form a TD-TI controller. Furthermore, a new improved optimization technique, namely the quantum chaos game optimizer (QCGO) is applied to tune the gains of the proposed combination TD-TI controller in two-area interconnected hybrid power systems, while the effectiveness of the proposed QCGO is validated via a comparison of its performance with the traditional CGO and other optimizers when considering 23 bench functions. Correspondingly, the effectiveness of the proposed controller is validated by comparing its performance with other controllers, such as the proportional-integral-derivative (PID) controller based on different optimizers, the tilt-integral-derivative (TID) controller based on a CGO algorithm, and the TID controller based on a QCGO algorithm, where the effectiveness of the proposed TD-TI controller based on the QCGO algorithm is ensured using different load patterns (i.e., step load perturbation (SLP), series SLP, and random load variation (RLV)). Furthermore, the challenges of renewable energy penetration and communication time delay are considered to test the robustness of the proposed controller in achieving more system stability. In addition, the integration of electric vehicles as dispersed energy storage units in both areas has been considered to test their effectiveness in achieving power grid stability. The simulation results elucidate that the proposed TD-TI controller based on the QCGO controller can achieve more system stability under the different aforementioned challenges.
TL;DR: In this paper , a generalized midpoint-type Hermite-Hadamard inequality and Pachpatte-type inequality via a new fractional integral operator associated with the Caputo-Fabrizio derivative are presented.
Abstract: In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type inequality via a new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, a new fractional identity for differentiable convex functions of first order is proved. Then, taking this identity into account as an auxiliary result and with the assistance of Hölder, power-mean, Young, and Jensen inequality, some new estimations of the Hermite-Hadamard (H-H) type inequality as refinements are presented. Applications to special means and trapezoidal quadrature formula are presented to verify the accuracy of the results. Finally, a brief conclusion and future scopes are discussed.
TL;DR: The scientific community has recently seen a fast-growing number of publications tackling the topic of fractional-order controllers in general, with a focus on the fractional order PID.
Abstract: The scientific community has recently seen a fast-growing number of publications tackling the topic of fractional-order controllers in general, with a focus on the fractional order PID. Several versions of this controller have been proposed, including different tuning methods and implementation possibilities. Quite a few recent papers discuss the practical use of such controllers. However, the industrial acceptance of these controllers is still far from being reached. Autotuning methods for such fractional order PIDs could possibly make them more appealing to industrial applications, as well. In this paper, the current autotuning methods for fractional order PIDs are reviewed. The focus is on the most recent findings. A comparison between several autotuning approaches is considered for various types of processes. Numerical examples are given to highlight the practicality of the methods that could be extended to simple industrial processes.
TL;DR: In this paper , the influence of FGPS and fly ash on frost resistance, pore structure and fractal features of hydraulic concretes was investigated and compared, and the results showed that FGPS concrete presented larger compressive strengths and better frost resistance than fly ash concrete at 28 and 180 days.
Abstract: Hydraulic concrete in cold regions is necessary for good frost resistance. The utilization of finely ground PS (FGPS) in the construction of hydropower projects could solve the pollution issue and the fly ash shortage problem. In this work, the influence of FGPS and fly ash on frost resistance, pore structure and fractal features of hydraulic concretes was investigated and compared. The main results are: (1) The inclusion of 15–45% FGPS reduced the compressive strength of plain cement concretes by about 21–52%, 7–23% and 0.4–8.2% at 3, 28 and 180 days, respectively. (2) The inclusion of FGPS less than 30% contributed to the enhancement of 180-day frost resistance. At the same dosage level, the FGPS concrete presented larger compressive strengths and better frost resistance than fly ash concrete at 28 and 180 days. (3) At 3 days, both the addition of FGPS and fly ash coarsened the pore structures. FGPS has a much stronger pore refinement effect than fly ash at 28 and 180 days. The correlation between frost resistance of hydraulic concrete and pore structure is weak. (4) At 28 days, the incorporation of FGPS and fly ash weakened the air void structure of hydraulic concrete. At 180 days, the presence of FGPS and fly ash was beneficial for refining the air void structure. The optimal dosage for FGPS and fly ash in terms of 180-day air void refinement was 30% and 15%, respectively. The frost resistance of hydraulic concretes is closely correlated with the air void structure. (5) The pore surface fractal dimension (Ds) could characterize and evaluate the pore structure of hydraulic concretes, but it was poorly correlated with the frost resistance.
TL;DR: By combining the rough set theory with a Gaussian mixture model, a new image segmentation algorithm with higher immunity is obtained that can obtain more image layers with concentrating information and preserve more image details than traditional algorithms.
Abstract: In the paper, an image enhancement algorithm based on a rough set and fractional order differentiator is proposed. By combining the rough set theory with a Gaussian mixture model, a new image segmentation algorithm with higher immunity is obtained. This image segmentation algorithm can obtain more image layers with concentrating information and preserve more image details than traditional algorithms. After preprocessing, the segmentation layers will be enhanced by a new adaptive fractional order differential mask in the Fourier domain. Experimental results and numerical analysis have verified the effectiveness of the proposed algorithm.
TL;DR: In this article , the existence of fractional integral inclusions that are connected to the Hermite-Hadamard and Hermite Hadamard-Fejér type inequalities for χ-pre-invex fuzzy-interval-valued functions is proved.
Abstract: The purpose of this study is to prove the existence of fractional integral inclusions that are connected to the Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for χ-pre-invex fuzzy-interval-valued functions. Some of the related fractional integral inequalities are also proved via Riemann–Liouville fractional integral operator, where integrands are fuzzy-interval-valued functions. To prove the validity of our main results, some of the nontrivial examples are also provided. As specific situations, our findings can provide a variety of new and well-known outcomes which can be viewed as applications of our main results. The results in this paper can be seen as refinements and improvements to previously published findings.
TL;DR: In this paper , the authors define a new class of harmonically convex functions, which is known as left and right harmonic convex interval-valued function (LR-𝓗-convex IV-F), and establish novel inclusions for a newly defined class of intervalvalued functions (IV-Fs) linked to Hermite-Hadamard (H-H) and Hermite Hadamard-Fejér type inequalities via intervalvalued Riemann-Liouville fractional integrals.
Abstract: The purpose of this study is to define a new class of harmonically convex functions, which is known as left and right harmonically convex interval-valued function (LR-𝓗-convex IV-F), and to establish novel inclusions for a newly defined class of interval-valued functions (IV-Fs) linked to Hermite–Hadamard (H-H) and Hermite–Hadamard–Fejér (H-H-Fejér) type inequalities via interval-valued Riemann–Liouville fractional integrals (IV-RL-fractional integrals). We also attain some related inequalities for the product of two LR-𝓗-convex IV-Fs. These findings enable us to identify a new class of inclusions that may be seen as significant generalizations of results proved by Iscan and Chen. Some examples are included in our findings that may be used to determine the validity of the results. The findings in this work can be seen as a considerable advance over previously published findings.
TL;DR: The results show that the chaotic system of FMHNN has abundant dynamic behaviors, and a chaotic audio encryption scheme under a Message Queueing Telemetry Transport (MQTT) protocol is proposed and implemented by Raspberry Pi, which has a broad future in intelligent home and other IoT applications.
Abstract: Fractional-order chaotic systems are widely used in the field of encryption because of its initial value sensitivity and historical memory. In this paper, the fractional-order definition of Caputo is introduced based on a nonideal flux-controlled memristive Hopfield neural network model, when changing the parameters of the fractional-order memristive Hopfield neural network (FMHNN) can generate a different amount of multi-scroll attractors. Some dynamical behaviors are investigated by numerical simulation, especially analyzed coexistence and bifurcation under different orders and different coupling strengths. The results show that the chaotic system of FMHNN has abundant dynamic behaviors. In addition, a chaotic audio encryption scheme under a Message Queueing Telemetry Transport (MQTT) protocol is proposed and implemented by Raspberry Pi; the audio encryption system based on FMHNN has a broad future in intelligent home and other IoT applications.
TL;DR: It is demonstrated that the FuzzDEα at different fractional orders is more sensitive to changes in the dynamics of the time series, and the proposed mixed features bearing fault diagnosis method achieves 100% recognition rate at just triple features.
Abstract: Fuzzy dispersion entropy (FuzzDE) is a very recently proposed non-linear dynamical indicator, which combines the advantages of both dispersion entropy (DE) and fuzzy entropy (FuzzEn) to detect dynamic changes in a time series. However, FuzzDE only reflects the information of the original signal and is not very sensitive to dynamic changes. To address these drawbacks, we introduce fractional order calculation on the basis of FuzzDE, propose FuzzDEα, and use it as a feature for the signal analysis and fault diagnosis of bearings. In addition, we also introduce other fractional order entropies, including fractional order DE (DEα), fractional order permutation entropy (PEα) and fractional order fluctuation-based DE (FDEα), and propose a mixed features extraction diagnosis method. Both simulated as well as real-world experimental results demonstrate that the FuzzDEα at different fractional orders is more sensitive to changes in the dynamics of the time series, and the proposed mixed features bearing fault diagnosis method achieves 100% recognition rate at just triple features, among which, the mixed feature combinations with the highest recognition rates all have FuzzDEα, and FuzzDEα also appears most frequently.
TL;DR: Wang et al. as discussed by the authors proposed a novel approach by fusing fractal dimension and UHK-Net deep learning network to conduct the semantic recognition of concrete cracks, which can not only characterize the dark crack images, but also distinguish small and fine crack images.
Abstract: Concrete wall surfaces are prone to cracking for a long time, which affects the stability of concrete structures and may even lead to collapse accidents. In view of this, it is necessary to recognize and distinguish the concrete cracks. Then, the stability of concrete will be known. In this paper, we propose a novel approach by fusing fractal dimension and UHK-Net deep learning network to conduct the semantic recognition of concrete cracks. We first use the local fractal dimensions to study the concrete cracking and roughly determine the location of concrete crack. Then, we use the U-Net Haar-like (UHK-Net) network to construct the crack segmentation network. Ultimately, the different types of concrete crack images are used to verify the advantage of the proposed method by comparing with FCN, U-Net, YOLO v5 network. Results show that the proposed method can not only characterize the dark crack images, but also distinguish small and fine crack images. The pixel accuracy (PA), mean pixel accuracy (MPA), and mean intersection over union (MIoU) of crack segmentation determined by the proposed method are all greater than 90%.
TL;DR: In this paper , the influence of five fly ash dosages (namely 10, 20, 30, 40% and 50%) on the permeability property of face slab concretes was investigated.
Abstract: Concrete-face slabs are the primary anti-permeability structures of the concrete-face rockfill dam (CFRD), and the resistance of face slab concrete to permeability is the key factor affecting the operation and safety of CFRDs. Herein, the influences of five fly ash dosages (namely 10%, 20%, 30%, 40% and 50%) on the permeability property of face slab concretes were investigated. Moreover, the difference in the permeability caused by the fly ash dosage variations is revealed in terms of the pore structure and fractal theory. The results illustrate that: (1) The inclusion of 10–50% fly ash lowered the compressive strength of face slab concretes before 28 days of hydration, whereas it contributed to the 180-day strength increment. (2) The incorporation of 10–50% fly ash raised the average water-seepage height (Dm) and the relative permeability coefficient (Kr) of the face slab concrete by about 14–81% and 30–226% at 28 days, respectively. At 180 days, the addition of fly ash improved the 180-day impermeability by less than 30%. (3) The permeability of face slab concretes is closely correlated with their pore structures and Ds. (4) The optimal fly ash dosage in terms of the long-term impermeability and pore refinement of face slab concretes is around 30%. Nevertheless, face slab concretes containing a high dosage of fly ash must be cured for a relatively long period before they can withstand high water pressure.
TL;DR: In this paper , the existence of a mild solution for a neutral partial integrodifferential nonlocal system with finite delay is presented and proved using the techniques of the Monch-Krasnosel'skii type of fixed point theorem, a measure of noncompactness and resolvent operator theory.
Abstract: In this theory, the existence of a mild solution for a neutral partial integrodifferential nonlocal system with finite delay is presented and proved using the techniques of the Monch–Krasnosel’skii type of fixed point theorem, a measure of noncompactness and resolvent operator theory. For this work, we have introduced some sufficient conditions to confirm the existence of the neutral partial integrodifferential system. An illustration of the derived results is offered at the end with a filter system corresponding to our existence result.
TL;DR: The purpose of this study is to introduce a new class of generalized convex interval-valued functions called (p, s)-convex fuzzy interval- valued functions and to establish Hermite–Hadamard (H–H) type inequalities for ( p, s)-conveX F-I-V-Fs using fuzzy order relation.
Abstract: Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called (p, s)-convex fuzzy interval-valued functions ((p, s)-(-convex F-I-V-Fs) in the second sense and to establish Hermite–Hadamard (H–H) type inequalities for (p, s)-convex F-I-V-Fs using fuzzy order relation. In addition, we demonstrate that our results include a large class of new and known inequalities for (p, s)-convex F-I-V-Fs and their variant forms as special instances. Furthermore, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions.
TL;DR: In this paper , the analytical solutions of the fractional fluid models described by the Caputo derivative were analyzed and the physical interpretations of the influence of the parameters of the model have been proposed.
Abstract: This paper studies the analytical solutions of the fractional fluid models described by the Caputo derivative. We combine the Fourier sine and the Laplace transforms. We analyze the influence of the order of the Caputo derivative the Prandtl number, the Grashof numbers, and the Casson parameter on the dynamics of the fractional diffusion equation with reaction term and the fractional heat equation. In this paper, we notice that the order of the Caputo fractional derivative plays the retardation effect or the acceleration. The physical interpretations of the influence of the parameters of the model have been proposed. The graphical representations illustrate the main findings of the present paper. This paper contributes to answering the open problem of finding analytical solutions to the fluid models described by the fractional operators.
TL;DR: In this article , the Hermite-Hadamard-type inequalities concerning a monotonic increasing function have been investigated and a new class of convexity and related integral and fractional inequalities have been discussed.
Abstract: The comprehension of inequalities in convexity is very important for fractional calculus and its effectiveness in many applied sciences. In this article, we handle a novel investigation that depends on the Hermite–Hadamard-type inequalities concerning a monotonic increasing function. The proposed methodology deals with a new class of convexity and related integral and fractional inequalities. There exists a solid connection between fractional operators and convexity because of its fascinating nature in the numerical sciences. Some special cases have also been discussed, and several already-known inequalities have been recaptured to behave well. Some applications related to special means, q-digamma, modified Bessel functions, and matrices are discussed as well. The aftereffects of the plan show that the methodology can be applied directly and is computationally easy to understand and exact. We believe our findings generalise some well-known results in the literature on s-convexity.
TL;DR: In this article , the authors presented the impacts and importance of fractional order derivatives of the SIQ model based on the coronavirus with the lockdown effects, and the stochastic solvers based on Levenberg-Marquardt backpropagation scheme (LMBS) along with the neural networks (NNs) have been implemented to solve the fractional-order SIQ mathematical system.
Abstract: The theme of this study is to present the impacts and importance of the fractional order derivatives of the susceptible, infected and quarantine (SIQ) model based on the coronavirus with the lockdown effects. The purpose of these investigations is to achieve more accuracy with the use of fractional derivatives in the SIQ model. The integer, nonlinear mathematical SIQ system with the lockdown effects is also provided in this study. The lockdown effects are categorized into the dynamics of the susceptible, infective and quarantine, generally known as SIQ mathematical system. The fractional order SIQ mathematical system has never been presented before, nor solved by using the strength of the stochastic solvers. The stochastic solvers based on the Levenberg-Marquardt backpropagation scheme (LMBS) along with the neural networks (NNs), i.e., LMBS-NNs have been implemented to solve the fractional order SIQ mathematical system. Three cases using different values of the fractional order have been provided to solve the fractional order SIQ mathematical model. The data to present the numerical solutions of the fractional order SIQ mathematical model is selected as 80% for training and 10% for both testing and validation. For the correctness of the LMBS-NNs, the obtained numerical results have been compared with the reference solutions through the Adams–Bashforth–Moulton based numerical solver. In order to authenticate the competence, consistency, validity, capability and exactness of the LMB-NNs, the numerical performances using the state transitions (STs), regression, correlation, mean square error (MSE) and error histograms (EHs) are also provided.
TL;DR: In this article, the existence and Ulam-Hyer stability of solutions of a nonlinear neutral stochastic fractional differential system were investigated by using fixed point theorems and the Banach contraction principle.
Abstract: The main purpose of this paper is to investigate the existence and Ulam-Hyers stability (U-Hs) of solutions of a nonlinear neutral stochastic fractional differential system. We prove the existence and uniqueness of solutions to the proposed system by using fixed point theorems and the Banach contraction principle. Also, by using fundamental schemes of fractional calculus, we study the (U-Hs) to the solutions of our suggested system. Besides, we study an example, best describing our main result.
TL;DR: In this paper , anomaly diffusion in fractal media is simulated using the Navier-Stokes equations (NSEs) with time-fractional derivatives of order β∈(0,1).
Abstract: Navier–Stokes (NS) equation, in fluid mechanics, is a partial differential equation that describes the flow of incompressible fluids. We study the fractional derivative by using fractional differential equation by using a mild solution. In this work, anomaly diffusion in fractal media is simulated using the Navier–Stokes equations (NSEs) with time-fractional derivatives of order β∈(0,1). In Hγ,℘, we prove the existence and uniqueness of local and global mild solutions by using fuzzy techniques. Meanwhile, we provide a local moderate solution in Banach space. We further show that classical solutions to such equations exist and are regular in Banach space.
TL;DR: In this article , a variable step size strategy is adopted in formulating a new variable step hybrid block method (VSHBM) for the solution of the Kepler problem, which is known to be a rigid and stiff differential equation.
Abstract: In this article, a variable step size strategy is adopted in formulating a new variable step hybrid block method (VSHBM) for the solution of the Kepler problem, which is known to be a rigid and stiff differential equation. To derive the VSHBM, the step size ratio r is left the same, halved, or doubled in order to optimize the total number of steps, minimize the number of formulae stored in the code, and ensure that the method is zero-stable. The method is formulated by integrating the Lagrange polynomial with limits of integration selected at special points. The article further analyzed the stability, order, consistency, and convergence properties of the VSHBM. The stability regions of the VSHBM at different values of the step size ratios were also plotted and plots showed that the method is fit for solving the Kepler problem. The results generated were then compared with some existing methods, including the MATLAB inbuilt stiff solver (ode 15 s), with respect to total number of failure steps, total number of steps, total function calls, maximum error, and computation time.