1,335 results
Search Results
2. Experimental Study on Forecasting Mathematical Model of Drying Shrinkage of Recycled Aggregate Concrete
- Author
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Yuanchen Guo and Xue Wang
- Subjects
Aggregate (composite) ,Article Subject ,Waste management ,lcsh:Mathematics ,General Mathematics ,General Engineering ,lcsh:QA1-939 ,Pulp and paper industry ,Drying time ,lcsh:TA1-2040 ,Error analysis ,Fly ash ,lcsh:Engineering (General). Civil engineering (General) ,Expansive ,Mathematics ,Shrinkage - Abstract
On the basis of basic law in AASHTO2007 model, the forecasting mathematical model of drying shrinkage of recycled aggregate concrete (RAC) is established by regression analysis and experimental study. The research results show that (1) with the replacement rate of RCA increases, the drying shrinkage value of RAC increases; this trend is even more obvious in the early drying time. (2) The addition of fly ash can inhibit the drying shrinkage of RAC, but the effect is not very obvious. Specifically, the addition of fly ash will increase the shrinkage to some extent when the mixing amount is 20%. (3) The addition of expansive agent can obviously inhibit the shrinkage of RAC; the inhibition affection is better than that of fly ash. (4) The forecasting mathematical models of drying shrinkage of RAC established in this paper have high accuracy and rationality according to experiment validation and error analysis.
- Published
- 2012
3. Parameter Identification of Tractor-Semitrailer Model under Steering and Braking
- Author
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Qin Shi, Yiming Li, and Duoyang Qiu
- Subjects
Tractor ,0209 industrial biotechnology ,business.product_category ,Article Subject ,General Mathematics ,02 engineering and technology ,020901 industrial engineering & automation ,0203 mechanical engineering ,Control theory ,Genetic algorithm ,medicine ,Mathematics ,lcsh:Mathematics ,Yaw ,General Engineering ,Stiffness ,020302 automobile design & engineering ,lcsh:QA1-939 ,Axle ,lcsh:TA1-2040 ,Lookup table ,medicine.symptom ,lcsh:Engineering (General). Civil engineering (General) ,business ,Test data ,Interpolation - Abstract
This paper describes a valuable linear yaw-roll tractor-semitrailer (TST) model with five-degree-of-freedom (DOFs) for control algorithm development when steering and braking. The key parameters, roll stiffness, axle cornering stiffness, and fifth-wheel stiffness, are identified by the genetic algorithm (GA) and multistage genetic algorithm (MGA) based on TruckSim outputs to increase the accuracy of the model. Thus, the key parameters of the simplified model can be modified according to the real-time vehicle states by online lookup table and interpolation. The TruckSim vehicle model is built referring to the real tractor (JAC-HFC4251P1K7E33ZTF6×2) and semitrailer (Luyue LHX9406) used in the field test later. The validation of the linear yaw-roll model of a tractor-semitrailer using field test data is presented in this paper. The field test in the performance testing ground is detailed, and the test data of roll angle, roll rate, and yaw rate are compared with the outputs of the model with maps of the key parameters. The results indicate that the error of the tractor’s roll angle and semitrailer’s roll angle between model data and test data is 1.13% and 1.24%, respectively. The roll rate and yaw rate of the tractor and semitrailer are also in good agreement.
- Published
- 2019
4. Model of Automobile Parts Sale Prediction Based on Nonlinear Periodic Gray GM(1,1) and Empirical Research
- Author
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Canlin Wang and Lixiong Gong
- Subjects
Article Subject ,Differential equation ,lcsh:Mathematics ,020209 energy ,General Mathematics ,General Engineering ,02 engineering and technology ,lcsh:QA1-939 ,Nonlinear system ,Empirical research ,lcsh:TA1-2040 ,Approximation error ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,lcsh:Engineering (General). Civil engineering (General) ,Gray (horse) ,Algorithm ,Mathematics - Abstract
The traditional predictive method cannot fully reflect the complex nonlinear characteristics and regularities of automobile and parts sales data, so the prediction precision is not high. The purpose of this paper is to propose the gray GM(1,1) nonlinear periodic predictive model by introducing the seasonal variation index to improve predictive accuracy of the single GM(1,1) model. Firstly, the paper analyzes concept of GM(1,1) and then proposes the gray GM(1,1) nonlinear periodic predictive model to forecast automobile parts sales. The model algorithm used gray theory and accumulated technology to generate new data and set up unified differential equations to find the fitting curve of automobile parts sales prediction by the seasonal variation index to remove random elements. Lastly, the gray GM(1,1) nonlinear periodic predictive model is used for empirical analysis; the result of example shows that the model proposed in the paper is feasible. The superiority of the proposed predictive model compared with the single gray GM(1,1) model is demonstrated. The reliability of this model is experienced by the accuracy test, which provides a theoretical guidance for the prediction of automobile part sales. And the average relative error is reduced by 8.52% compared with the single GM(1,1) model.
- Published
- 2019
5. Active-Side Calculation Method for a Backhoe Hydraulic Excavator with Incomplete Digging Resistance in a Normal State
- Author
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Liu Jurong, Zhang Junfeng, Sun Haoran, Ren Zhigui, Wang Junli, Liang Yang, and Jin Chen
- Subjects
0209 industrial biotechnology ,Article Subject ,General Mathematics ,02 engineering and technology ,Kinematics ,law.invention ,Stress (mechanics) ,020901 industrial engineering & automation ,Position (vector) ,law ,Mathematics ,Backhoe loader ,Normal force ,business.industry ,lcsh:Mathematics ,General Engineering ,04 agricultural and veterinary sciences ,Structural engineering ,lcsh:QA1-939 ,Digging ,Excavator ,lcsh:TA1-2040 ,040103 agronomy & agriculture ,Bending moment ,0401 agriculture, forestry, and fisheries ,lcsh:Engineering (General). Civil engineering (General) ,business - Abstract
The digging resistance in a normal state is the key to excavator design and automated excavation. It is difficult to accurately predict, simulate, or directly measure the digging resistance in a normal state due to uncertainties in the soil properties and excavation parameters. In this paper, a research idea is proposed that uses the working device as the entry point to indirectly calculate the digging resistance in a normal state by measuring the motion parameters and the cylinder pressure intensity. Based on the rule of combination for spatial force systems, a method for combining and projecting the system of the digging resistance is proposed in which the system is projected as six parts, and the tangential force, normal force, and bending moment in the plane of symmetry of the working device are the objects of the solution to avoid redundant equations. Based on kinematics and dynamics models of the excavator and the force and moment equilibrium conditions of the working device, equations for the active-side calculation of the incomplete digging resistance are derived. Based on these equations, the motion parameters of the working device and data on the cylinder pressure intensity obtained by measurement are used to calculate the incomplete digging resistance. The validation scheme and process proposed use the incomplete digging resistance as the external load to obtain the simulated stress of the working device through transient analysis. The simulated stress and the measured stress corresponding to the position of the measurement point are extracted and compared. The results show that there is a difference in the size of the numerical value between the simulated and measured stress, but the variation law is highly consistent, which validates the calculation method. In this paper, an active-side calculation method is provided for the incomplete digging resistance in a normal state without considering the soil-tool interaction relationships, which lays a theoretical foundation for the study of the digging resistance characteristics in a normal state, as well as excavator design and automated excavation.
- Published
- 2019
6. Stabilization of Discrete-Time Delayed Systems in Presence of Actuator Saturation Based on Wirtinger Inequality
- Author
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Richa Negi, Quanxin Zhu, and Vipin Chandra Pal
- Subjects
Convex hull ,0209 industrial biotechnology ,Article Subject ,Stability criterion ,lcsh:Mathematics ,General Mathematics ,General Engineering ,Linear matrix inequality ,02 engineering and technology ,lcsh:QA1-939 ,020901 industrial engineering & automation ,Discrete time and continuous time ,lcsh:TA1-2040 ,Computer Science::Systems and Control ,Control theory ,Control system ,Full state feedback ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Convex combination ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
This paper examines the stability analysis of discrete-time control systems particularly during the event of actuator saturation and time-varying state delay. With the help of Wirtinger inequality along with Lyapunov-Krasovskii functional gain of state feedback controller is determined for stabilization of above system. The saturation nonlinearity is represented in the terms of convex hull. A new linear matrix inequality (LMI) criterion is settled with reciprocally convex combination based inequality which is dependent on delay. The proposed criterion is less conservative in concern to increase the delay bound and a controller is also simulated for real time problem of missile control system in this paper. It is also attained that projected stability criterion is less conservative compared to other outcomes. Furthermore, an optimization procedure together with LMI constraints has been proposed to maximize the attraction of domain.
- Published
- 2019
7. Algebraic Formulation for Moderately Thick Elastic Frames, Beams, Trusses, and Grillages within Timoshenko Theory
- Author
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Wojciech Gilewski and Jan Pełczyński
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Article Subject ,Plane (geometry) ,lcsh:Mathematics ,General Mathematics ,Mathematical analysis ,Diagonal ,0211 other engineering and technologies ,General Engineering ,Truss ,02 engineering and technology ,lcsh:QA1-939 ,021001 nanoscience & nanotechnology ,Space (mathematics) ,Matrix (mathematics) ,Algebraic equation ,lcsh:TA1-2040 ,021105 building & construction ,Compressibility ,Algebraic number ,lcsh:Engineering (General). Civil engineering (General) ,0210 nano-technology ,Mathematics - Abstract
The paper is dedicated to the algebraic formulation of elastic frame equations. The obtained set of equations describe deformations of moderately thick frames made of both compressible and incompressible bars, grillages of rigid or pin-joined connections, and trusses. Plane as well as space structures are presented. The paper is an extension of the article of T. Lewiński written in 2001 related to thin bars. Algebraic equations with diagonal constitutive matrix are original and suitable for various engineering applications and for educational purposes.
- Published
- 2019
8. Application of Adomian Decomposition Method to Bounded and Unbounded Stokes’ Problems
- Author
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Ray-Yeng Yang and Chi-Min Liu
- Subjects
Article Subject ,lcsh:Mathematics ,General Mathematics ,General Engineering ,02 engineering and technology ,Function (mathematics) ,lcsh:QA1-939 ,01 natural sciences ,010305 fluids & plasmas ,Exact solutions in general relativity ,Flow (mathematics) ,lcsh:TA1-2040 ,Bounded function ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Padé approximant ,020201 artificial intelligence & image processing ,Boundary value problem ,lcsh:Engineering (General). Civil engineering (General) ,Adomian decomposition method ,Variable (mathematics) ,Mathematics - Abstract
The well-known Stokes’ problems are reexamined by applying the Adomian decomposition method (ADM) associated with other mathematical techniques in this paper. Both the finite-depth (bounded) and infinite-depth (unbounded) cases are analyzed. The present paper raises and deals with two major concerns. The first one is that, for Stokes’ problems, it lacks one boundary condition at the expansion point to fully determine all coefficients of the ADM solution in which an unknown function appears. This unknown function which is dependent on the transformed variable will be determined by the boundary condition at the far end. The second concern is that the derived solution begins to deviate from the exact solution as the spatial variable grows for the unbounded problems. This can be greatly improved by introducing the Padé approximant to satisfy the boundary condition at the far end. For the second problems, the derived ADM solution can be easily separated into the steady-state and the transient parts for a deeper comprehension of the flow. The present result shows an excellent agreement with the exact solution. The ADM is therefore verified to be a reliable mathematical method to analyze Stokes’ problems of finite and infinite depths.
- Published
- 2018
9. FTS and FTB of Conformable Fractional Order Linear Systems
- Author
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Omar Naifar, Bao-wei Wu, Mohamed Ali Hammami, and Abdellatif Ben Makhlouf
- Subjects
0209 industrial biotechnology ,Article Subject ,lcsh:Mathematics ,General Mathematics ,Linear system ,General Engineering ,Order (ring theory) ,010103 numerical & computational mathematics ,02 engineering and technology ,Conformable matrix ,lcsh:QA1-939 ,01 natural sciences ,Stability (probability) ,Fractional calculus ,020901 industrial engineering & automation ,lcsh:TA1-2040 ,Control theory ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
In this paper, an extension of some existing results related to finite-time stability (FTS) and finite-time boundedness (FTB) into the conformable fractional derivative is presented. Illustrative example is presented at the end of the paper to show the effectiveness of the proposed result.
- Published
- 2018
10. Novel Two-Stage Method for Low-Order Polynomial Model
- Author
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Xiuli Shen, Cheng Yan, and Fushui Guo
- Subjects
Surface (mathematics) ,Polynomial ,Article Subject ,lcsh:Mathematics ,General Mathematics ,0211 other engineering and technologies ,General Engineering ,Sampling (statistics) ,Statistical model ,02 engineering and technology ,lcsh:QA1-939 ,Nonlinear system ,020303 mechanical engineering & transports ,Polynomial and rational function modeling ,0203 mechanical engineering ,lcsh:TA1-2040 ,Applied mathematics ,Response surface methodology ,lcsh:Engineering (General). Civil engineering (General) ,Engineering design process ,021106 design practice & management ,Mathematics - Abstract
One of the most popular statistical models is a low-order polynomial response surface model, i.e., a polynomial of first order or second order. These polynomials can be used for global metamodels in weakly nonlinear simulation to approximate their global tendency and local metamodels in response surface methodology (RSM), which has been studied in various applications in engineering design and analysis. The order of the selected polynomial determines the number of sampling points (input combinations) and the resulting accuracy (validity, adequacy). This paper derives a novel method to obtain an accurate high-order polynomial while requiring fewer sampling points. This method uses a two-stage procedure such that the second stage modifies the low-order polynomial estimated in the first stage; this second stage does not require new points. This paper evaluates the performance of the method numerically by using several test functions. These numerical results show that the proposed method can provide more accurate predictions than the traditional method.
- Published
- 2018
11. Hysteresis Modelling of Mechanical Systems at Nonstationary Vibrations
- Author
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A. D. Shalashilin and A. N. Danilin
- Subjects
0209 industrial biotechnology ,Polynomial ,Article Subject ,Differential equation ,lcsh:Mathematics ,General Mathematics ,Mathematical analysis ,General Engineering ,02 engineering and technology ,lcsh:QA1-939 ,Damper ,Vibration ,Mechanical system ,Hysteresis ,020303 mechanical engineering & transports ,020901 industrial engineering & automation ,0203 mechanical engineering ,lcsh:TA1-2040 ,Black box ,Pendulum (mathematics) ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
This paper considers and reviews a number of known phenomenological models, used to describe hysteretic effects of various natures. Such models consider hysteresis system as a “black box” with experimentally known input and output, related via formal mathematical dependence to parameters obtained from the best fit to experimental data. In particular, we focus on the broadly used Bouc-Wen and similar phenomenological models. The current paper shows the conditions which the Bouc-Wen model must meet. An alternative mathematical model is suggested where the force and kinematic parameters are related by a first-order differential equation. In contrast to the Bouc-Wen model, the right hand side is a polynomial with two variables representing hysteresis trajectories in the process diagram. This approach ensures correct asymptotic approximation of the solution to the enclosing hysteresis cycle curves. The coefficients in the right side are also determined experimentally from the hysteresis cycle data during stable oscillations. The proposed approach allows us to describe hysteretic trajectory with an arbitrary starting point within the enclosed cycle using only one differential equation. The model is applied to the description of forced vibrations of a low-frequency pendulum damper.
- Published
- 2018
12. Solubility Optimal System for Supercritical Fluid Extraction Based on a New Nonlinear Temperature-Pressure Decoupling Model Constructed with Unequal-Interval Grey Optimal Models and Peng-Robinson Models
- Author
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Wen You and Binglin Li
- Subjects
Article Subject ,lcsh:Mathematics ,General Mathematics ,010401 analytical chemistry ,General Engineering ,Supercritical fluid extraction ,Mimo nonlinear systems ,02 engineering and technology ,lcsh:QA1-939 ,021001 nanoscience & nanotechnology ,01 natural sciences ,0104 chemical sciences ,Nonlinear system ,Temperature and pressure ,Singularity ,lcsh:TA1-2040 ,Control theory ,Decoupling (probability) ,Solubility ,lcsh:Engineering (General). Civil engineering (General) ,0210 nano-technology ,Nonlinear coupling ,Mathematics - Abstract
This paper presents a new solubility optimal system to improve the efficiency of supercritical fluid extraction (SFE). The major contribution is a nonlinear temperature-pressure decoupling model constructed with unequal-interval grey optimal models (UEIGOMs) and Peng-Robinson models (PRMs). The linear parts of temperature and pressure process can be constructed with UEIGOM, respectively. The nonlinear parts of temperature and pressure process can be described by PRMs, respectively. The whole nonlinear model cannot be input-output decoupled resulting from the singularity of decoupling matrix for PRM. This problem on input-output nondecoupling can be transformed to the problem on disturbance decoupling for a class of MIMO nonlinear systems. Therefore, the whole nonlinear coupling model can be disturbance decoupled. Furthermore, solubility optimal method is presented in the paper; it can calculate the optimal pressure according to the given temperature, namely, optimal working points, to maximize solubility for SFE process. The feasibility, effectiveness, and practicality of the proposed nonlinear temperature-pressure decoupling model constructed with UEIGOMs and PRMs are verified by SFE experiments in biphenyl. Experiments using the designed solubility optimal system are carried out to demonstrate the effectiveness in control scheme, simplicity in structure, and flexibility in implementation for the proposed solubility optimal system based on a new nonlinear temperature-pressure coupling model constructed with UEIGOMs and PRMs.
- Published
- 2018
13. An Improvement for Fuzzy Stochastic Goal Programming Problems
- Author
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Shu-Cheng Lin, Han-Wen Tuan, and Peterson Julian
- Subjects
Mathematical optimization ,Index (economics) ,Article Subject ,Linear programming ,lcsh:Mathematics ,General Mathematics ,General Engineering ,02 engineering and technology ,Extension (predicate logic) ,lcsh:QA1-939 ,Fuzzy logic ,020202 computer hardware & architecture ,lcsh:TA1-2040 ,Goal programming ,0202 electrical engineering, electronic engineering, information engineering ,Random environment ,020201 artificial intelligence & image processing ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
We examined the solution process for linear programming problems under a fuzzy and random environment to transform fuzzy stochastic goal programming problems into standard linear programming problems. A previous paper that revised the solution process with the lower-side attainment index motivated our work. In this paper, we worked on a revision for both-side attainment index to amend its definition and theorems. Two previous examples were used to examine and demonstrate our improvement over previous results. Our findings not only improve the previous paper with both-side attainment index, but also provide a theoretical extension from lower-side attainment index to the both-side attainment index.
- Published
- 2017
14. A Scientific Decision Framework for Supplier Selection under Interval Valued Intuitionistic Fuzzy Environment
- Author
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Raghunathan Krishankumar, Kattur Soundarapandian Ravichandran, and R. Ramprakash
- Subjects
0209 industrial biotechnology ,Mathematical optimization ,Article Subject ,lcsh:Mathematics ,General Mathematics ,General Engineering ,Intuitionistic fuzzy ,TOPSIS ,Vagueness ,02 engineering and technology ,lcsh:QA1-939 ,computer.software_genre ,Interval valued ,020901 industrial engineering & automation ,Ranking ,lcsh:TA1-2040 ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Data mining ,ELECTRE ,Decision-making ,lcsh:Engineering (General). Civil engineering (General) ,computer ,Selection (genetic algorithm) ,Mathematics - Abstract
This paper proposes a new scientific decision framework (SDF) under interval valued intuitionistic fuzzy (IVIF) environment for supplier selection (SS). The framework consists of two phases, where, in the first phase, criteria weights are estimated in a sensible manner using newly proposed IVIF based statistical variance (SV) method and, in the second phase, the suitable supplier is selected using ELECTRE (ELimination and Choice Expressing REality) ranking method under IVIF environment. This method involves three categories of outranking, namely, strong, moderate, and weak. Previous studies on ELECTRE ranking reveal that scholars have only used two categories of outranking, namely, strong and weak, in the formulation of IVIF based ELECTRE, which eventually aggravates fuzziness and vagueness in decision making process due to the potential loss of information. Motivated by this challenge, third outranking category, called moderate, is proposed, which considerably reduces the loss of information by improving checks to the concordance and discordance matrices. Thus, in this paper, IVIF-ELECTRE (IVIFE) method is presented and popular TOPSIS method is integrated with IVIFE for obtaining a linear ranking. Finally, the practicality of the proposed framework is demonstrated using SS example and the strength of proposed SDF is realized by comparing the framework with other similar methods.
- Published
- 2017
15. Synthesis of Adaptive Robust Controllers for a Class of Nonlinear Systems with Input Saturations
- Author
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Tomohiro Kubo, Tsuyoshi Matsuki, Hidetoshi Oya, and Kenta Oba
- Subjects
0209 industrial biotechnology ,Class (set theory) ,Article Subject ,Matching (graph theory) ,lcsh:Mathematics ,General Mathematics ,MathematicsofComputing_NUMERICALANALYSIS ,General Engineering ,02 engineering and technology ,Linear matrix ,lcsh:QA1-939 ,Nonlinear system ,020901 industrial engineering & automation ,lcsh:TA1-2040 ,Control theory ,Simple (abstract algebra) ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
This paper deals with a design problem of an adaptive robust controller for a class of nonlinear systems with specified input saturations. For the nonlinear system under consideration, the nonlinearity means unknown perturbations and satisfies the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed adaptive robust controller giving consideration to input saturations are given in terms of linear matrix inequalities (LMIs). Finally, simple illustrative examples are shown.
- Published
- 2017
16. The Global Optimal Algorithm of Reliable Path Finding Problem Based on Backtracking Method
- Author
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Jian Zhao, Hu Shao, Liang Shen, and Long Zhang
- Subjects
050210 logistics & transportation ,Mathematical optimization ,Correctness ,Article Subject ,Backtracking ,lcsh:Mathematics ,General Mathematics ,05 social sciences ,General Engineering ,02 engineering and technology ,Fast path ,lcsh:QA1-939 ,Longest path problem ,lcsh:TA1-2040 ,0502 economics and business ,Shortest path problem ,Path (graph theory) ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,lcsh:Engineering (General). Civil engineering (General) ,Yen's algorithm ,Algorithm ,Dijkstra's algorithm ,Mathematics - Abstract
There is a growing interest in finding a global optimal path in transportation networks particularly when the network suffers from unexpected disturbance. This paper studies the problem of finding a global optimal path to guarantee a given probability of arriving on time in a network with uncertainty, in which the travel time is stochastic instead of deterministic. Traditional path finding methods based on least expected travel time cannot capture the network user’s risk-taking behaviors in path finding. To overcome such limitation, the reliable path finding algorithms have been proposed but the convergence of global optimum is seldom addressed in the literature. This paper integrates the K-shortest path algorithm into Backtracking method to propose a new path finding algorithm under uncertainty. The global optimum of the proposed method can be guaranteed. Numerical examples are conducted to demonstrate the correctness and efficiency of the proposed algorithm.
- Published
- 2017
17. Response of Duffing Oscillator with Time Delay Subjected to Combined Harmonic and Random Excitations
- Author
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N. D. Anh and D. N. Hao
- Subjects
Stationary distribution ,Article Subject ,Computer simulation ,lcsh:Mathematics ,General Mathematics ,Mathematical analysis ,Degenerate energy levels ,General Engineering ,Duffing equation ,Probability density function ,02 engineering and technology ,Auxiliary function ,lcsh:QA1-939 ,01 natural sciences ,010305 fluids & plasmas ,020303 mechanical engineering & transports ,Transformation (function) ,0203 mechanical engineering ,lcsh:TA1-2040 ,Control theory ,0103 physical sciences ,Harmonic ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
This paper aims to investigate the stationary probability density functions of the Duffing oscillator with time delay subjected to combined harmonic and white noise excitation by the method of stochastic averaging and equivalent linearization. By the transformation based on the fundamental matrix of the degenerate Duffing system, the paper shows that the displacement and the velocity with time delay in the Duffing oscillator can be computed approximately in non-time delay terms. Hence, the stochastic system with time delay is transformed into the corresponding stochastic non-time delay equation in Ito sense. The approximate stationary probability density function of the original system can be found by combining the stochastic averaging method, the equivalent linearization method, and the technique of auxiliary function. The response of Duffing oscillator is investigated. The analytical results are verified by numerical simulation results.
- Published
- 2017
18. Infrared Dim and Small Targets Detection Method Based on Local Energy Center of Sequential Image
- Author
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Zhenming Peng, Xiangsuo Fan, Jianlin Zhang, Yongmei Huang, and Zhiyong Xu
- Subjects
020301 aerospace & aeronautics ,Article Subject ,Basis (linear algebra) ,Infrared ,business.industry ,lcsh:Mathematics ,General Mathematics ,General Engineering ,02 engineering and technology ,lcsh:QA1-939 ,Image (mathematics) ,0203 mechanical engineering ,lcsh:TA1-2040 ,0202 electrical engineering, electronic engineering, information engineering ,Preprocessor ,Clutter ,020201 artificial intelligence & image processing ,Computer vision ,Noise (video) ,Artificial intelligence ,lcsh:Engineering (General). Civil engineering (General) ,Anisotropy ,business ,Energy (signal processing) ,Mathematics - Abstract
In order to detect infrared (IR) dim and small targets in a strong clutter background, a method based on local energy center of sequential image is proposed. This paper began by using improved anisotropy for background prediction (IABP), followed by target enhancement by improved high-order cumulates (HOC). Finally, on the basis of image preprocessing, the paper constructs a sequential image energy center detection algorithm that integrates the neighborhood, continuity, area, and energy and other motion characteristics of the target. Experiments showed that the improved anisotropic background predication could be loyal to the true background of the original image to the maximum extent, presenting a superior overall performance to other background prediction methods; the improved HOC significantly increased the signal-noise ratio of images; when the signal-noise ratio (SNR) is lower than 2.5 dB, the proposed method could effectively eliminate noise and detect targets.
- Published
- 2017
19. Solution to Two-Dimensional Steady Inverse Heat Transfer Problems with Interior Heat Source Based on the Conjugate Gradient Method
- Author
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Huangchao Jia, Li Zhang, Xiaogang Sun, and Shoubin Wang
- Subjects
Observational error ,Article Subject ,Convective heat transfer ,lcsh:Mathematics ,General Mathematics ,Mathematical analysis ,General Engineering ,010103 numerical & computational mathematics ,02 engineering and technology ,Inverse problem ,lcsh:QA1-939 ,Thermal conduction ,01 natural sciences ,020303 mechanical engineering & transports ,0203 mechanical engineering ,lcsh:TA1-2040 ,Conjugate gradient method ,Heat transfer ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Gradient method ,Boundary element method ,Mathematics - Abstract
The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points’ number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.
- Published
- 2017
20. Analysis of Hull Girder Ultimate Strength and Residual Strength Based on IACS CSR-H
- Author
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Hong Zhou, Gui-jie Shi, and Da-wei Gao
- Subjects
Article Subject ,business.industry ,General Mathematics ,lcsh:Mathematics ,General Engineering ,020101 civil engineering ,02 engineering and technology ,Structural engineering ,Nonlinear finite element method ,lcsh:QA1-939 ,0201 civil engineering ,Residual strength ,Naval architecture ,020303 mechanical engineering & transports ,Shipbuilding ,0203 mechanical engineering ,lcsh:TA1-2040 ,Hull ,Girder ,Ultimate tensile strength ,business ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
In order to express the safety level of hull structures, IACS Common Structure Rules of Bulk Carriers and Oil Tankers (CSR-H) makes new requirements of hull girder ultimate strength. Compared with original CSR (i.e., CSR-OT and CSR-BC), partial safety factors of hull girder ultimate strength in CSR-H have been partly modified, and new requirements of residual strength have been added in the rules for hull safety after grounded/collided damage. This paper compares the rule requirements of ultimate strength in CSR-H and CSR-OT/CSR-BC and explains the technical background of rule requirements. The hull girder ultimate strength is mainly analyzed by SMITH method in rule requirements due to fast and stable calculation results. This paper also uses nonlinear finite element method (NFEM) to explain the critical influence factors for hull girder ultimate strength implied in the rule requirements. Based on 5 typical Bulk Carriers and 4 typical Oil Tankers, the influence of hull girder ultimate strength and residual strength in CSR-H has been evaluated for ship building industry. The actual ship evaluation results can be used to instruct the new CSR-H ship design.
- Published
- 2019
21. The Connected Detour Numbers of Special Classes of Connected Graphs
- Author
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Ali A. Ali and Ahmed Ali
- Subjects
Discrete mathematics ,Article Subject ,General Mathematics ,lcsh:Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,010103 numerical & computational mathematics ,02 engineering and technology ,0101 mathematics ,lcsh:QA1-939 ,01 natural sciences ,Mathematics - Abstract
Simple finite connected graphs G=V,E of p≥2 vertices are considered in this paper. A connected detour set of G is defined as a subset S⊆V such that the induced subgraph GS is connected and every vertex of G lies on a u−v detour for some u,v∈S. The connected detour number cdnG of a graph G is the minimum order of the connected detour sets of G. In this paper, we determined cdnG for three special classes of graphs G, namely, unicyclic graphs, bicyclic graphs, and cog-graphs for Cp, Kp, and Km,n.
- Published
- 2019
22. Applications of Fractional Lower Order Frequency Spectrum Technologies to Bearing Fault Analysis
- Author
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Junbo Long, Haibin Wang, and Peng Li
- Subjects
0209 industrial biotechnology ,Article Subject ,General Mathematics ,Gaussian ,lcsh:Mathematics ,General Engineering ,02 engineering and technology ,Covariance ,Fault (power engineering) ,lcsh:QA1-939 ,Stable distribution ,symbols.namesake ,020901 industrial engineering & automation ,Autoregressive model ,Side lobe ,lcsh:TA1-2040 ,Frequency domain ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,020201 artificial intelligence & image processing ,Autoregressive–moving-average model ,lcsh:Engineering (General). Civil engineering (General) ,Algorithm ,Mathematics - Abstract
The traditional spectral analysis method is used to study the characteristics of bearing fault signals in frequency domain, which is reasonable and effective in general cases. However, it is proved that the fault signals have heavy tails in this paper, which are α stable distribution, and 1<α<2, and even the noises belong to α stable distribution. Then the conventional spectral analysis methods degenerate and even fail under α stable distribution environment. Several improved frequency spectral analysis methods are proposed employing fractional lower order covariation or fractional lower order covariance in this paper, including fractional lower order Blackman-Tukey covariation spectrum (FLOBTCS), fractional lower order periodogram covariation spectrum (FLOPCS), and fractional lower order welch covariation spectrum (FLOWCS). In order to suppress side lobe and improve resolution, we present novel fractional lower order autoregression (FLO-AR) and fractional lower order autoregressive moving average (FLO-ARMA) parameter model frequency spectrum methods, and the calculation steps are summarized. The proposed spectrum methods are compared with the existing methods based on second-order statistics under Gaussian and SαS distribution environments, and the results show that the new algorithms have better performance than the traditional methods. Finally, the improved methods are applied to estimate frequency spectrums of the normal and outer race fault signals, and it is demonstrated that they are effective for fault diagnosis.
- Published
- 2019
23. A New Stability Analysis of Uncertain Delay Differential Equations
- Author
-
Yufu Ning and Xiao Wang
- Subjects
0209 industrial biotechnology ,Article Subject ,General Mathematics ,lcsh:Mathematics ,General Engineering ,02 engineering and technology ,Delay differential equation ,lcsh:QA1-939 ,Stability (probability) ,Measure (mathematics) ,020901 industrial engineering & automation ,lcsh:TA1-2040 ,0202 electrical engineering, electronic engineering, information engineering ,sort ,Applied mathematics ,020201 artificial intelligence & image processing ,Almost surely ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
This paper first provides a concept of almost sure stability for uncertain delay differential equations and analyzes this new sort of stability. In addition, this paper derives three sufficient conditions for uncertain delay differential equations being stable almost surely. Finally, the relationship between almost sure stability and stability in measure for uncertain delay differential equations is discussed.
- Published
- 2019
24. Two-Dimensional Far Field Source Locating Method with Nonprior Velocity
- Author
-
Xiaowen Liu, Peng Liu, Manyi Wang, Juanjuan Li, and Qing Chen
- Subjects
Article Subject ,lcsh:Mathematics ,General Mathematics ,General Engineering ,Geometry ,Near and far field ,02 engineering and technology ,lcsh:QA1-939 ,010502 geochemistry & geophysics ,01 natural sciences ,Stability (probability) ,020501 mining & metallurgy ,Hyperbola ,0205 materials engineering ,lcsh:TA1-2040 ,Position (vector) ,Convergence (routing) ,Asymptote ,lcsh:Engineering (General). Civil engineering (General) ,Algorithm ,Fuzzy locating system ,Linear equation ,0105 earth and related environmental sciences ,Mathematics - Abstract
Relative position of seismic source and sensors has great influence on locating accuracy, particularly in far field conditions, and the accuracy will decrease seriously due to limited calculation precision and prior velocity error. In order to improve the locating accuracy of far field sources by isometric placed sensors in a straight line, a new locating method with nonprior velocity is proposed. After exhaustive research, this paper states that the hyperbola which is used for locating will be very close to its asymptote when seismic source locates in far field of sensors; therefore, the locating problem with prior velocity is equivalent to solving linear equations and the problem with nonprior velocity is equivalent to a nonlinear optimization problem with respect to the unknown velocity. And then, this paper proposed a new locating method based on a one-variable objective function with respect to the unknown velocity. Numerical experiments show that the proposed method has faster convergence speed, higher accuracy, and better stability.
- Published
- 2016
25. Effective Root-Finding Methods for Nonlinear Equations Based on Multiplicative Calculi
- Author
-
Tolgay Karanfiller, Ali Özyapıcı, and Zehra B. Sensoy
- Subjects
Article Subject ,lcsh:Mathematics ,General Mathematics ,Science and engineering ,Numerical analysis ,Multiplicative function ,Mathematical analysis ,Numerical methods for ordinary differential equations ,02 engineering and technology ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Range (mathematics) ,Rate of convergence ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,0101 mathematics ,Root-finding algorithm ,Mathematics - Abstract
In recent studies, papers related to the multiplicative based numerical methods demonstrate applicability and efficiency of these methods. Numerical root-finding methods are essential for nonlinear equations and have a wide range of applications in science and engineering. Therefore, the idea of root-finding methods based on multiplicative and Volterra calculi is self-evident. Newton-Raphson, Halley, Broyden, and perturbed root-finding methods are used in numerical analysis for approximating the roots of nonlinear equations. In this paper, Newton-Raphson methods and consequently perturbed root-finding methods are developed in the frameworks of multiplicative and Volterra calculi. The efficiency of these proposed root-finding methods is exposed by examples, and the results are compared with some ordinary methods. One of the striking results of the proposed method is that the rate of convergence for many problems are considerably larger than the original methods.
- Published
- 2016
26. Periodic Event-Triggered Condition Design for the Consensus of Multiagent Systems with Communication Delays
- Author
-
Kai Gao, Weirong Liu, Liran Li, Feng Zhou, and Zhiwu Huang
- Subjects
0209 industrial biotechnology ,Mathematical optimization ,Article Subject ,lcsh:Mathematics ,General Mathematics ,Multi-agent system ,Control (management) ,General Engineering ,Stability (learning theory) ,Sampling (statistics) ,020207 software engineering ,02 engineering and technology ,lcsh:QA1-939 ,Linear dynamical system ,020901 industrial engineering & automation ,Consensus ,lcsh:TA1-2040 ,Control theory ,0202 electrical engineering, electronic engineering, information engineering ,Exponential decay ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics ,Event (probability theory) - Abstract
This paper focuses on the periodic event-triggered consensus problem for multiagent systems under undirected graph. In the periodic event-triggered control, the event condition is tested only periodically to decide when to exert the control behaviors and when to broadcast the sampling data. Two sets of event-triggered strategies combining with sampled-data control are designed based on an exponential decay function and a quadratic Lyapunov function, respectively. Some useful theorems for these two periodic event-triggered strategies about the choice of period are derived to guarantee the asymptotical stability of the closed-loop multiagent systems. In addition, this paper gives a sufficient condition about the bounds of communication delay for the multiagent systems. It is rigorously proved that the overall system will achieve the consensus under the proposed strategy if the period and time delay satisfy the theorems. Finally, we extend these solutions to general linear dynamical systems. Simulation results are presented to show the effectiveness.
- Published
- 2016
27. Modeling Portfolio Optimization Problem by Probability-Credibility Equilibrium Risk Criterion
- Author
-
Ye Wang, Yanju Chen, and YanKui Liu
- Subjects
0209 industrial biotechnology ,Mathematical optimization ,Optimization problem ,Article Subject ,lcsh:Mathematics ,General Mathematics ,General Engineering ,02 engineering and technology ,lcsh:QA1-939 ,Fuzzy logic ,Constraint (information theory) ,Variable (computer science) ,020901 industrial engineering & automation ,lcsh:TA1-2040 ,Convex optimization ,0202 electrical engineering, electronic engineering, information engineering ,Expected return ,Portfolio ,020201 artificial intelligence & image processing ,Portfolio optimization ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
This paper studies the portfolio selection problem in hybrid uncertain decision systems. Firstly the return rates are characterized by random fuzzy variables. The objective is to maximize the total expected return rate. For a random fuzzy variable, this paper defines a new equilibrium risk value (ERV) with credibility level beta and probability level alpha. As a result, our portfolio problem is built as a new random fuzzy expected value (EV) model subject to ERV constraint, which is referred to as EV-ERV model. Under mild assumptions, the proposed EV-ERV model is a convex programming problem. Furthermore, when the possibility distributions are triangular, trapezoidal, and normal, the EV-ERV model can be transformed into its equivalent deterministic convex programming models, which can be solved by general purpose optimization software. To demonstrate the effectiveness of the proposed equilibrium optimization method, some numerical experiments are conducted. The computational results and comparison study demonstrate that the developed equilibrium optimization method is effective to model portfolio selection optimization problem with twofold uncertain return rates.
- Published
- 2016
28. Problems on Solving Matrix Aggregation in Group Decision-Making by Glowworm Swarm Optimization
- Author
-
Yaping Li
- Subjects
0209 industrial biotechnology ,Mathematical optimization ,Article Subject ,lcsh:Mathematics ,General Mathematics ,media_common.quotation_subject ,Glowworm swarm optimization ,General Engineering ,02 engineering and technology ,Information loss ,lcsh:QA1-939 ,Adaptability ,Universality (dynamical systems) ,Group decision-making ,020901 industrial engineering & automation ,lcsh:TA1-2040 ,Fuzzy matrix ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Multi-swarm optimization ,lcsh:Engineering (General). Civil engineering (General) ,media_common ,Mathematics - Abstract
Judgment matrix aggregation, as an important part of group decision-making, has been widely and deeply studied due to the universality and importance of group decision-making in the management field. For the variety of judgment matrix in group decision-making, the matrix aggregation result can be obtained by using the mode of glowworm swarm optimization. First, this paper introduces the basic principle of the glowworm swarm optimization (GSO) algorithm and gives the improved GSO algorithm to solve the matrix aggregation problems. In this approach, the consistency ratio is introduced to the objective function of the glowworm swarm optimization, thus reducing the subjectivity and information loss in the aggregation process. Then, the improved GSO algorithm is applied to the solution of the deterministic matrix and the fuzzy matrix. The method optimization can provide an effective and relatively uniform aggregation method for matrix aggregation. Finally, through comparative analysis, it is shown that the method of this paper has certain advantages in terms of adaptability, accuracy, and stability to solving the matrix aggregation problems.
- Published
- 2016
29. Fuzzy Risk Analysis for a Production System Based on the Nagel Point of a Triangle
- Author
-
Handan Akyar, Anadolu Üniversitesi, Fen Fakültesi, Matematik Bölümü, and Akyar, Handan
- Subjects
0209 industrial biotechnology ,Mathematical optimization ,Fuzzy classification ,Article Subject ,lcsh:Mathematics ,General Mathematics ,General Engineering ,02 engineering and technology ,lcsh:QA1-939 ,Type-2 fuzzy sets and systems ,Defuzzification ,020901 industrial engineering & automation ,Fuzzy transportation ,lcsh:TA1-2040 ,Fuzzy mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Fuzzy set operations ,Fuzzy number ,020201 artificial intelligence & image processing ,Fuzzy associative matrix ,lcsh:Engineering (General). Civil engineering (General) ,Algorithm ,Mathematics - Abstract
WOS: 000374093400001, Ordering and ranking fuzzy numbers and their comparisons play a significant role in decision-making problems such as social and economic systems, forecasting, optimization, and risk analysis problems. In this paper, a new method for ordering triangular fuzzy numbers using the Nagel point of a triangle is presented. With the aid of the proposed method, reasonable properties of ordering fuzzy numbers are verified. Certain comparative examples are given to illustrate the advantages of the new method. Many papers have been devoted to studies on fuzzy ranking methods, but some of these studies have certain shortcomings. The proposed method overcomes the drawbacks of the existing methods in the literature. The suggested method can order triangular fuzzy numbers as well as crisp numbers and fuzzy numbers with the same centroid point. An application to the fuzzy risk analysis problem is given, based on the suggested ordering approach., Anadolu University Scientific Research Projects Commission [1403F077], This study was supported by the Anadolu University Scientific Research Projects Commission under Grant no. 1403F077.
- Published
- 2016
30. A New Method Applied to the Quadrilateral Membrane Element with Vertex Rigid Rotational Freedom
- Author
-
Xiao-Wei Gao, Jun Lv, and Yunfei Liu
- Subjects
Vertex (computer graphics) ,Article Subject ,General Mathematics ,Shell (structure) ,Geometry ,02 engineering and technology ,Topology ,01 natural sciences ,law.invention ,0203 mechanical engineering ,law ,Local coordinates ,Cartesian coordinate system ,0101 mathematics ,Mathematics ,Quadrilateral ,lcsh:Mathematics ,General Engineering ,Order (ring theory) ,lcsh:QA1-939 ,010101 applied mathematics ,020303 mechanical engineering & transports ,Membrane ,lcsh:TA1-2040 ,Element (category theory) ,lcsh:Engineering (General). Civil engineering (General) - Abstract
In order to improve the performance of the membrane element with vertex rigid rotational freedom, a new method to establish the local Cartesian coordinate system and calculate the derivatives of the shape functions with respect to the local coordinates is introduced in this paper. The membrane elements with vertex rigid rotational freedom such as GQ12 and GQ12M based on this new method can achieve higher precision results than traditional methods. The numerical results demonstrate that the elements GQ12 and GQ12M with this new method can provide better membrane elements for flat shell elements. Furthermore, this new method presented in this paper offers a new approach for other membrane elements used in flat shell element to improve the computing accuracy.
- Published
- 2016
31. Nonlinear Alignment and Its Local Linear Iterative Solution
- Author
-
Zhengming Ma, Zengrong Zhan, and Sumin Zhang
- Subjects
Article Subject ,General Mathematics ,Invariant manifold ,02 engineering and technology ,Topology ,Pseudo-Riemannian manifold ,symbols.namesake ,020204 information systems ,Local coordinates ,0202 electrical engineering, electronic engineering, information engineering ,Mathematics::Symplectic Geometry ,Mathematics ,Manifold alignment ,lcsh:Mathematics ,Mathematical analysis ,General Engineering ,lcsh:QA1-939 ,Mathematics::Geometric Topology ,lcsh:TA1-2040 ,Piecewise linear manifold ,Local tangent space alignment ,symbols ,Normal coordinates ,020201 artificial intelligence & image processing ,Mathematics::Differential Geometry ,lcsh:Engineering (General). Civil engineering (General) ,Center manifold - Abstract
In manifold learning, the aim of alignment is to derive the global coordinate of manifold from the local coordinates of manifold’s patches. At present, most of manifold learning algorithms assume that the relation between the global and local coordinates is locally linear and based on this linear relation align the local coordinates of manifold’s patches into the global coordinate of manifold. There are two contributions in this paper. First, the nonlinear relation between the manifold’s global and local coordinates is deduced by making use of the differentiation of local pullback functions defined on the differential manifold. Second, the method of local linear iterative alignment is used to align the manifold’s local coordinates into the manifold’s global coordinate. The experimental results presented in this paper show that the errors of noniterative alignment are considerably large and can be reduced to almost zero within the first two iterations. The large errors of noniterative/linear alignment verify the nonlinear nature of alignment and justify the necessity of iterative alignment.
- Published
- 2016
32. Consensus of High-Order Linear Multiagent Systems with Multitype Switching Topologies Based on the Dynamic Dwell Time Approach
- Author
-
Yaxiao Zhang, Yangzhou Chen, and Xiaojun Qu
- Subjects
0209 industrial biotechnology ,Article Subject ,lcsh:Mathematics ,General Mathematics ,Multi-agent system ,General Engineering ,Stability (learning theory) ,02 engineering and technology ,lcsh:QA1-939 ,Topology ,Network topology ,Computer Science::Multiagent Systems ,Linear map ,Dwell time ,020901 industrial engineering & automation ,Consensus ,lcsh:TA1-2040 ,Computer Science::Systems and Control ,Control theory ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,High order ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
This paper investigates the consensus problem of high-order continuous-time linear multiagent systems (LMASs) with multitype switching topologies which include both consensusable and unconsensusable communication topologies. A linear transformation is introduced, which equivalently transforms the consensus problem into the stability problem of a corresponding switched system, along with a necessary and sufficient condition to analyze the consensus problem. This paper is aimed at studying the impact of a switching rule on communication topologies for consensus of LMASs. Based on the dynamic dwell time method, a sufficient condition is derived for consensus of LMASs. It is shown that, with switching signals that satisfy this switching rule, LMASs can achieve consensus under directed switching communication topologies. A numerical example is provided to illustrate the effectiveness of the theoretical results.
- Published
- 2016
33. Sensor Location Problem for Network Traffic Flow Derivation Based on Turning Ratios at Intersection
- Author
-
Xianzhi Shao, Lijun Sun, and Minhua Shao
- Subjects
050210 logistics & transportation ,021103 operations research ,Article Subject ,Intersection (set theory) ,lcsh:Mathematics ,General Mathematics ,05 social sciences ,0211 other engineering and technologies ,General Engineering ,02 engineering and technology ,lcsh:QA1-939 ,Network topology ,Flow network ,Set (abstract data type) ,Traffic flow (computer networking) ,Flow (mathematics) ,lcsh:TA1-2040 ,0502 economics and business ,lcsh:Engineering (General). Civil engineering (General) ,Coefficient matrix ,Greedy algorithm ,Algorithm ,Simulation ,Mathematics - Abstract
The sensor location problem (SLP) discussed in this paper is to find the minimum number and optimum locations of the flow counting points in the road network so that the traffic flows over the whole network can be inferred uniquely. Flow conservation system at intersections is formulated firstly using the turning ratios as the prior information. Then the coefficient matrix of the flow conservation system is proved to be nonsingular. Based on that, the minimal number of counting points is determined to be the total number of exclusive incoming roads and dummy roads, which are added to the network to represent the trips generated on real roads. So the task of SLP model based on turning ratios is just to determine the optimal sensor locations. The following analysis in this paper shows that placing sensors on all the exclusive incoming roads and dummy roads can always generate a unique network flow vector for any network topology. After that, a detection set composed of only real roads is proven to exist from the view of feasibility in reality. Finally, considering the roads importance and cost of the sensors, a weighted SLP model is formulated to find the optimal detection set. The greedy algorithm is proven to be able to provide the optimal solution for the proposed weighted SLP model.
- Published
- 2016
34. Analysis of the Stability and Hopf Bifurcation of Currency Supply Delay in an Opened Kaldorian Business Cycle Model
- Author
-
Liming Zhao and Zhipei Zhao
- Subjects
Equilibrium point ,Hopf bifurcation ,Article Subject ,Computer simulation ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,General Engineering ,lcsh:QA1-939 ,01 natural sciences ,Stability (probability) ,symbols.namesake ,Exchange rate ,lcsh:TA1-2040 ,Currency ,0103 physical sciences ,Business cycle ,symbols ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,010301 acoustics ,Mathematical economics ,Mathematics - Abstract
First of all, we establish a three-dimension open Kaldorian business cycle model under the condition of the fixed exchange rate. Secondly, with regard to the model, we discuss the existence of equilibrium point and the stability of the system near it with a time delay in currency supply as the bifurcating parameters of the system. Thirdly, we discuss the existence of Hopf bifurcation and investigate the stability of periodic solution generated by the Hopf bifurcation; then the direction of the Hopf bifurcation is given. Finally, a numerical simulation is given to confirm the theoretical results. This paper plays an important role in theoretical researching on the model of business cycle, and it is crucial for decision-maker to formulate the macroeconomic policies with the conclusions of this paper.
- Published
- 2016
35. Novel 3-Scroll Chua’s Attractor with One Saddle-Focus and Two Stable Node-Foci
- Author
-
Kaibin Chu, Huagan Wu, Zhengwei Zhu, and Hui Qian
- Subjects
Equilibrium point ,Article Subject ,General Mathematics ,lcsh:Mathematics ,General Engineering ,Chaotic ,MathematicsofComputing_NUMERICALANALYSIS ,Topology ,lcsh:QA1-939 ,01 natural sciences ,Analog multiplier ,010305 fluids & plasmas ,law.invention ,Nonlinear Sciences::Chaotic Dynamics ,law ,lcsh:TA1-2040 ,0103 physical sciences ,Attractor ,Operational amplifier ,Node (circuits) ,lcsh:Engineering (General). Civil engineering (General) ,010301 acoustics ,Saddle ,Electronic circuit ,Mathematics - Abstract
With new three-segment piecewise-linearity in the classic Chua’s system, two new types of 2-scroll and 3-scroll Chua’s attractors are found in this paper. By changing the outer segment slope of the three-segment piecewise-linearity as positive, the new 2-scroll Chua’s attractor has emerged from one zero index-1 saddle-focus and two symmetric stable nonzero node-foci. In particular, by newly introducing a piecewise-linear control function, an improved Chua’s system only with one zero index-2 saddle-focus and two stable nonzero node-foci is constructed, from which a 3-scroll Chua’s attractor is converged. Some remarks for Chua’s nonlinearities and the generating chaotic attractors are discussed, and the stabilities at the three equilibrium points are then analyzed, upon which the emerging mechanisms of the novel 2-scroll and 3-scroll Chua’s attractors are explored in depth. Furthermore, an analog electronic circuit built with operational amplifier and analog multiplier is designed and hardware circuit experiments are measured to verify the numerical simulations. These novel 2-scroll and 3-scroll Chua’s attractors reported in this paper are completely different from the classic Chua’s attractors, which will enrich the dynamics of the classic Chua’s system.
- Published
- 2018
36. A New Approach to Derive Priority Weights from Additive Interval Fuzzy Preference Relations Based on Logarithms
- Author
-
Chengxiang Yin, Wenning Hao, Xingdang Kang, Xiuli Qi, and Hongjun Zhang
- Subjects
0209 industrial biotechnology ,Transitive relation ,Article Subject ,Logarithm ,Linear programming ,General Mathematics ,lcsh:Mathematics ,General Engineering ,Linear model ,02 engineering and technology ,Interval (mathematics) ,lcsh:QA1-939 ,Fuzzy logic ,020901 industrial engineering & automation ,Consistency (statistics) ,lcsh:TA1-2040 ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,lcsh:Engineering (General). Civil engineering (General) ,Preference (economics) ,Mathematics - Abstract
This paper investigates the consistency definition and the weight-deriving method for additive interval fuzzy preference relations (IFPRs) using a particular characterization based on logarithms. In a recently published paper, a new approach with a parameter is developed to obtain priority weights from fuzzy preference relations (FPRs), then a new consistency definition for the additive IFPRs is defined, and finally linear programming models for deriving interval weights from consistent and inconsistent IFPRs are proposed. However, the discussion of the parameter value is not adequate and the weights obtained by the linear models for inconsistent IFPRs are dependent on alternative labels and not robust to permutations of the decision makers’ judgments. In this paper, we first investigate the value of the parameter more thoroughly and give the closed form solution for the parameter. Then, we design a numerical example to illustrate the drawback of the linear models. Finally, we construct a linear model to derive interval weights from IFPRs based on the additive transitivity based consistency definition. To demonstrate the effectiveness of our proposed method, we compare our method to the existing method on three numerical examples. The results show that our method performs better on both consistent and inconsistent IFPRs.
- Published
- 2018
37. Multiple Nontrivial Solutions for a Class of Biharmonic Elliptic Equations with Sobolev Critical Exponent
- Author
-
Xiaoyong Qian, Jun Wang, and Maochun Zhu
- Subjects
Pure mathematics ,Article Subject ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,General Engineering ,MathematicsofComputing_NUMERICALANALYSIS ,Mathematics::Analysis of PDEs ,Multiplicity (mathematics) ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Sobolev space ,Elliptic curve ,lcsh:TA1-2040 ,Bounded function ,Biharmonic equation ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Critical exponent ,Mathematics - Abstract
In this paper, we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic equation with Sobolev critical exponent in a bounded domain. By using the idea of the previous paper, we generalize the results and prove the existence and multiplicity of nontrivial solutions of the biharmonic elliptic equations.
- Published
- 2018
38. Exponential Stability of Antiperiodic Solution for BAM Neural Networks with Time-Varying Delays
- Author
-
Quanxin Zhu, Xiaofei Li, and Chuan Qin
- Subjects
Lyapunov function ,Artificial neural network ,Article Subject ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,General Engineering ,02 engineering and technology ,lcsh:QA1-939 ,01 natural sciences ,symbols.namesake ,Exponential stability ,Control theory ,lcsh:TA1-2040 ,Negative feedback ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,020201 artificial intelligence & image processing ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics ,Leakage (electronics) - Abstract
In this paper, a kind of BAM neural networks with leakage delays in the negative feedback terms and time-varying delays in activation functions was considered. By constructing a suitable Lyapunov function and using inequality techniques, some sufficient conditions to ensure the existence and exponential stability of antiperiodic solutions of these neural networks were derived. These conditions extend some results recently appearing in recent papers. Lastly, an example is given to show the feasibility of these conditions.
- Published
- 2018
39. Gaussian Regularized Periodic Nonuniform Sampling Series
- Author
-
Feng Wang, Congwei Wu, and Liang Chen
- Subjects
Article Subject ,business.industry ,lcsh:Mathematics ,General Mathematics ,Gaussian ,General Engineering ,010103 numerical & computational mathematics ,02 engineering and technology ,lcsh:QA1-939 ,01 natural sciences ,Regularization (mathematics) ,symbols.namesake ,Rate of convergence ,lcsh:TA1-2040 ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Applied mathematics ,020201 artificial intelligence & image processing ,0101 mathematics ,Periodic nonuniform sampling ,lcsh:Engineering (General). Civil engineering (General) ,business ,Digital signal processing ,Mathematics - Abstract
The periodic nonuniform sampling plays an important role in digital signal processing and other engineering fields. In this paper, we introduce the Gaussian regularization method to accelerate the convergence rate of periodic nonuniform sampling series. We prove that the truncation error of the Gaussian regularized periodic nonuniform sampling series decays exponentially. Numerical experiments are presented to demonstrate our result.
- Published
- 2019
40. Fixed Points of Subadditive Maps with an Application to a System of Volterra–Fredholm Type Integrodifferential Equations
- Author
-
Hüseyin Işık, Nabil Mlaiki, Hassen Aydi, and Bahman Moeini
- Subjects
Pure mathematics ,Article Subject ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,General Engineering ,Type (model theory) ,Fixed point ,lcsh:QA1-939 ,Space (mathematics) ,01 natural sciences ,Continuous functions on a compact Hausdorff space ,010101 applied mathematics ,Nonlinear system ,lcsh:TA1-2040 ,Banach algebra ,Subadditivity ,Uniqueness ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
In this paper, some fixed-point theorems are established for strongly subadditive maps on CΩ,ϒ (where CΩ,ϒ denotes the space of ϒ-valued continuous functions on a compact Hausdorff space Ω and ϒ is a unital Banach algebra). Finally, the result is applied to prove the existence and uniqueness of a solution for a system of nonlinear integrodifferential equations.
- Published
- 2019
41. Numerical Computation and Stability Analysis for the Fractional Subdiffusions with Spatial Variable Coefficients
- Author
-
Lei Ren
- Subjects
Article Subject ,lcsh:Mathematics ,General Mathematics ,Computation ,General Engineering ,Compact finite difference ,010103 numerical & computational mathematics ,Derivative ,lcsh:QA1-939 ,Space (mathematics) ,01 natural sciences ,Stability (probability) ,010101 applied mathematics ,lcsh:TA1-2040 ,Scheme (mathematics) ,Convergence (routing) ,Applied mathematics ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics ,Variable (mathematics) - Abstract
In this paper, we propose an efficient compact finite difference method for a class of time-fractional subdiffusion equations with spatially variable coefficients. Based on the L2-1σ approximation formula of the time-fractional derivative and a fourth-order compact finite difference approximation to the spatial derivative, an efficient compact finite difference method is developed. The local truncation error and the solvability of the developed method are discussed in detail. The unconditional stability of the resulting scheme and also its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Numerical examples are provided to demonstrate the accuracy and the theoretical results.
- Published
- 2019
42. A Finite Point Method for Solving the Time Fractional Richards’ Equation
- Author
-
Xinqiang Qin and Xin Yang
- Subjects
Article Subject ,Discretization ,lcsh:Mathematics ,Computer Science::Information Retrieval ,General Mathematics ,Numerical analysis ,General Engineering ,010103 numerical & computational mathematics ,lcsh:QA1-939 ,01 natural sciences ,Stability (probability) ,Fractional calculus ,010101 applied mathematics ,lcsh:TA1-2040 ,Finite point method ,Scheme (mathematics) ,Applied mathematics ,Order (group theory) ,Richards equation ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
In this paper, we propose a numerical method for solving the time fractional Richards’ equation. We first approximate the time fractional derivative of the mentioned equations by a scheme of order O(τ2−α), 0
- Published
- 2019
43. Real Representation Approach to Quaternion Matrix Equation Involving ϕ-Hermicity
- Author
-
Zhuo-Heng He, Huajun Huang, and Xin Liu
- Subjects
Pure mathematics ,Article Subject ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,General Engineering ,010103 numerical & computational mathematics ,lcsh:QA1-939 ,01 natural sciences ,Conjugacy class ,lcsh:TA1-2040 ,Transpose ,Quaternion matrix ,Mathematics::Differential Geometry ,0101 mathematics ,Real representation ,lcsh:Engineering (General). Civil engineering (General) ,Quaternion ,Mathematics - Abstract
For a quaternion matrix A, we denote by Aϕ the matrix obtained by applying ϕ entrywise to the transposed matrix AT, where ϕ is a nonstandard involution of quaternions. A is said to be ϕ-Hermitian or ϕ-skew-Hermitian if A=Aϕ or A=−Aϕ, respectively. In this paper, we give a complete characterization of the nonstandard involutions ϕ of quaternions and their conjugacy properties; then we establish a new real representation of a quaternion matrix. Based on this, we derive some necessary and sufficient conditions for the existence of a ϕ-Hermitian solution or ϕ-skew-Hermitian solution to the quaternion matrix equation AX=B. Moreover, we give solutions of the quaternion equation when it is solvable.
- Published
- 2019
44. Acceptability Indexes for Portfolio Vectors
- Author
-
Xianfu Zeng, Yanhong Chen, and Yijun Hu
- Subjects
Multivariate statistics ,050208 finance ,Article Subject ,lcsh:Mathematics ,General Mathematics ,05 social sciences ,General Engineering ,Regular polygon ,Univariate ,Extension (predicate logic) ,lcsh:QA1-939 ,01 natural sciences ,010104 statistics & probability ,lcsh:TA1-2040 ,0502 economics and business ,Statistics ,Portfolio ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Representation (mathematics) ,Mathematics - Abstract
In this paper, we introduce two new classes of acceptability indexes, named quasi-concave acceptability indexes and coherent acceptability indexes, for portfolio vectors. We establish the one-to-one correspondence between quasi-concave (coherent, resp.) acceptability indexes and convex (coherent, resp.) risk measures for portfolio vectors. We derive the representation results for coherent and convex risk measures. Finally, based on these results, we derive the representation results for quasi-concave acceptability indexes and coherent acceptability indexes for portfolio vectors. These new acceptability indexes can be considered as a kind of multivariate extension of univariate coherent and quasi-concave acceptability indexes introduced by Cherny and Madan (2009) and Rosazza Gianin and Sgarra (2013), respectively.
- Published
- 2019
45. Lipschitz Continuity for the Solutions of Triharmonic Equation
- Author
-
Xiao Bing and Zhou Yu
- Subjects
Article Subject ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,General Engineering ,lcsh:QA1-939 ,Lipschitz continuity ,01 natural sciences ,010104 statistics & probability ,lcsh:TA1-2040 ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Mathematics - Abstract
Let D be the unit disk in the complex plane C and denote T=∂D. Write Hom+T,∂Ω for the class of all sense-preserving homeomorphism of T onto the boundary of a C2 convex Jordan domain Ω. In this paper, five equivalent conditions for the solutions of triharmonic equations ∂z∂z¯3ω=ff∈CD¯ with Dirichlet boundary value conditions ωzz¯zz¯T=γ2∈CT,ωzz¯T=γ1∈CT and ωT=γ0∈Hom+T,∂Ω to be Lipschitz continuous are presented.
- Published
- 2019
46. A Halpern-Type Iteration Method for Bregman Nonspreading Mapping and Monotone Operators in Reflexive Banach Spaces
- Author
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Lateef Olakunle Jolaoso, F. U. Ogbuisi, and F. O. Isiogugu
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TheoryofComputation_MISCELLANEOUS ,Pure mathematics ,Article Subject ,Iterative method ,lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,Hilbert space ,Banach space ,State (functional analysis) ,Bregman divergence ,Fixed point ,lcsh:QA1-939 ,Strongly monotone ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,ComputingMethodologies_PATTERNRECOGNITION ,Monotone polygon ,symbols ,0101 mathematics ,Mathematics - Abstract
In this paper, we introduce an iterative method for approximating a common solution of monotone inclusion problem and fixed point of Bregman nonspreading mappings in a reflexive Banach space. Using the Bregman distance function, we study the composition of the resolvent of a maximal monotone operator and the antiresolvent of a Bregman inverse strongly monotone operator and introduce a Halpern-type iteration for approximating a common zero of a maximal monotone operator and a Bregman inverse strongly monotone operator which is also a fixed point of a Bregman nonspreading mapping. We further state and prove a strong convergence result using the iterative algorithm introduced. This result extends many works on finding a common solution of the monotone inclusion problem and fixed-point problem for nonlinear mappings in a real Hilbert space to a reflexive Banach space.
- Published
- 2019
47. Behavior of the Correction Equations in the Jacobi–Davidson Method
- Author
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Yong Fang and Yuan Kong
- Subjects
Current (mathematics) ,Article Subject ,Property (programming) ,Iterative method ,lcsh:Mathematics ,General Mathematics ,General Engineering ,010103 numerical & computational mathematics ,02 engineering and technology ,lcsh:QA1-939 ,01 natural sciences ,Hermitian matrix ,lcsh:TA1-2040 ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Subspace topology ,Mathematics - Abstract
The Jacobi–Davidson iteration method is efficient for computing several eigenpairs of Hermitian matrices. Although the involved correction equation in the Jacobi–Davidson method has many developed variants, the behaviors of them are not clear for us. In this paper, we aim to explore, theoretically, the convergence property of the Jacobi–Davidson method influenced by different types of correction equations. As a by-product, we derive the optimal expansion vector, which imposed a shift-and-invert transform on a vector located in the prescribed subspace, to expand the current subspace.
- Published
- 2019
48. Extensions and Applications of Power-Type Aczél-Vasić-Pečarić’s Inequalities
- Author
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Hong-Ying Yue, Fei Yan, and Kun Chen
- Subjects
Article Subject ,Inequality ,lcsh:Mathematics ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,General Engineering ,Type (model theory) ,lcsh:QA1-939 ,01 natural sciences ,Power (physics) ,010101 applied mathematics ,lcsh:TA1-2040 ,0101 mathematics ,lcsh:Engineering (General). Civil engineering (General) ,Mathematical economics ,media_common ,Mathematics - Abstract
In this paper, we enrich and develop power-type Aczél-Vasić-Pečarić’s inequalities. First of all, we give some new versions of theorems and corollaries about Aczél-Vasić-Pečarić’s inequalities by quoting some lemmas. Moreover, in combination with Hölder’s inequality, we give some applications of the new version of Aczél-Vasić-Pečarić’s inequality and give its proof process.
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- 2019
49. Improved Delay-Dependent Stability and Stabilization Conditions of T-S Fuzzy Time-Delay Systems via an Augmented Lyapunov-Krasovskii Functional Approach
- Author
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Shuqian Zhu, Zifan Gao, and Jiaxiu Yang
- Subjects
0209 industrial biotechnology ,State variable ,Article Subject ,lcsh:Mathematics ,General Mathematics ,General Engineering ,02 engineering and technology ,Interval (mathematics) ,Fuzzy control system ,lcsh:QA1-939 ,Stability (probability) ,Upper and lower bounds ,Fuzzy logic ,Stability conditions ,020901 industrial engineering & automation ,lcsh:TA1-2040 ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,lcsh:Engineering (General). Civil engineering (General) ,Legendre polynomials ,Mathematics - Abstract
This paper develops some improved stability and stabilization conditions of T-S fuzzy system with constant time-delay and interval time-varying delay with its derivative bounds available, respectively. These conditions are presented by linear matrix inequalities (LMIs) and derived by applying an augmented Lyapunov-Krasovskii functional (LKF) approach combined with a canonical Bessel-Legendre (B-L) inequality. Different from the existing LKFs, the proposed LKF involves more state variables in an augmented way resorting to the form of the B-L inequality. The B-L inequality is also applied in ensuring the positiveness of the constructed LKF and the negativeness of derivative of the LKF. By numerical examples, it is verified that the obtained stability conditions can ensure a larger upper bound of time-delay, the larger number of Legendre polynomials in the stability conditions can lead to less conservative results, and the stabilization condition is effective, respectively.
- Published
- 2019
50. Stationary Distribution and Extinction of a Stochastic SIQR Model with Saturated Incidence Rate
- Author
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Qiuhua Zhang and Kai Zhou
- Subjects
Lyapunov function ,Stationary distribution ,Extinction ,Article Subject ,lcsh:Mathematics ,General Mathematics ,General Engineering ,lcsh:QA1-939 ,01 natural sciences ,010305 fluids & plasmas ,symbols.namesake ,lcsh:TA1-2040 ,0103 physical sciences ,symbols ,Applied mathematics ,Ergodic theory ,Uniqueness ,lcsh:Engineering (General). Civil engineering (General) ,010306 general physics ,Epidemic model ,Mathematics - Abstract
In this paper, we consider a stochastic SIQR epidemic model with saturated incidence rate. By constructing a proper Lyapunov function, we obtain the existence and uniqueness of positive solution for this SIQR model. Furthermore, we study the dynamical properties of this stochastic SIQR model; that is, (i) we establish the sufficient condition for the existence of ergodic stationary distribution of the model; (ii) we obtain the extinction of the disease under some conditions. At last, numerical simulations are introduced to illustrate our theoretical results.
- Published
- 2019
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