Ebook: Applied Mathematics, Modeling and Computer Simulation

This book contains the proceedings of the 2021 International Conference on Applied Mathematics, Modeling and Computer Simulation (AMMCS 2021) which was held on November 13–14, 2021, as a virtual conference. It provides the scholars and researchers with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines. More than 150 participants were able to exchange knowledge and discuss the latest developments at the conference.

The book contains 115 peer-reviewed papers, selected from more than 250 submissions and ranging from the theoretical and conceptual to strongly pragmatic and addressing industrial best practice. It covers Mathematical Modelling and Application, Engineering Applications and Scientific Computations, Simulation of Intelligent Systems.

The book shares practical experiences and enlightening ideas and will be of interest to researchers in and practitioners everywhere.

Professor Chi-Hua Chen

College of Mathematics and Computer Science, Fuzhou University, China

The detection of composite insulator defects in substations still relies on manual inspection. In this paper, we propose a detection method for insulator crack shape features by improving the RCNN convolution kernel. The method can meet the premise of insufficient training sample data, but also can get better CNN training effect, and finally achieve accurate crack recognition. In the training phase, the RGB three-channel decomposition method is used to expand the training data set; the median filtering method is used to remove the noise; the improved convolutional kernel is used to train the CNN; in the test phase, the images are decomposed by RGB three-channel decomposition and input to CNN to get the exact crack center coordinates and length; the NMS algorithm is used to de-weight the images to get the final crack recognition results. The example analysis shows that the method in this paper can still achieve good recognition accuracy and accurately identify the specific location of cracks under the premise of insufficient training samples.

For the relay platen state identification problem, whether it is a camera or a designated track driving robot inspection, will be affected by the glass door reflection, foreign object obstruction, angle blind area and other platen can not be correctly identified, manual inspection is inevitable. In addition, the current platen image recognition requires a huge background structure, and the inspectors cannot immediately obtain the verification information at the operation site, which greatly affects the work efficiency. In this paper, in response to the above problems, an embedded-based handheld terminal solution is proposed, which uses a miniature intelligent HD camera to achieve multi-angle photography of the pressure plate screen cabinet, effectively solving the problem of obstructing photography due to glass door reflection, foreign object obstruction, angle, etc. In addition, this paper proposes a relay platen status field identification method based on embedded and YOLO Nano algorithm, and selects a high-performance computing core and a special vision recognition module as the hardware platform to avoid a huge background architecture and realize the operation field identification and verification. The test results show that the system has a 100% accuracy rate of relay platen status identification, which effectively solves the operation site identification problem of relay platen status and has strong practicality and applicability.

The construction of a Y-type urban rail transit line can effectively solve the problems of low line coverage and low utilization in suburban areas. The purpose of this paper is to study and analyze the effect of different operation modes of the Y-type line of suburban urban rail transit. In this paper, the objective function is to minimize value of passenger travel time costs and enterprise operating costs, and the main and branch train frequencies are used as decision variables to establish a selection model for Y-type operation mode, and design an improved multi-objective optimization algorithm based on NSGA-II. A case study was carried out on the Y-type line to evaluate the effect of each scheme. The results of the study found that there is no obvious difference between the advantages and disadvantages of the three operation modes. The passenger waiting time under the independent operation plan is the highest but the comfort level is greater, and the train travel distance is the lowest. The partial- through operation accommodates the interests of both passenger and business. Therefore, the corresponding operating mode should be selected according to the preferences of passengers and enterprises.

With the rapid development of artificial intelligence, in order to solve the problems of many questions from trainees, poor efficiency of teachers in answering questions and high work intensity in the process of thermal power plant simulation practice, this paper proposes an intelligent training expert guidance system for thermal power plant simulation, and this paper uses Visual C++ software programming to implement an intelligent training expert guidance system with voice interaction and video presentation functions, using the speech development package Microsoft Speech SDK, in-depth study of the SAPI it provides, design and implementation of speech recognition function and speech synthesis function. The XML file is used to define the types of questions and the corresponding Q&A test statements for keyword extraction; the video presentation function is realized with the help of Windows Media Player. The test results show that, based on the successful speech recognition, the system can simulate the way of dialogue between teachers and learners and answer learners’ questions in real time. The system has an open function, users can add questions independently, expand the database in real time, jump out of the traditional limitations of space, time and geography, and increase the interest of learning.

To compensate for the lack of abstraction in the field of origami, in this paper, we propose a categorical description that can be introduced to map folding. Specifically, we use a particular expression to abstract the folding process of a map with logical matrices. When the folding operations are restricted to two certain kinds, the simple folds and the simple unfolds, we can define categories of partly folded states of the map as poset categories. The property of posets induces many general categorical concepts, such as (co)product, opposite category, direct system, and so on. We then introduce how these general concepts are specified in the proposed categories. These conceptions and specifications brought us the hope to solve and study the map folding with contemporary mathematical methods, such as the (co)homology. Furthermore, our categorical description can potentially be applied to a more generalized version of the map folding, the flat-folding.

Music, as a kind of cultural heritage, has become an indispensable element in human life. How to intuitively understand the role of music in human collective has become a difficult issue in the field of music research. In this paper, a quantitative model of music influence, which is based on directed graph, Euclidean distance and correlation analysis, is proposed for the development of some genres. In this model, the influences of genre leaders on music development are obtained by evaluating the parameters of the directed graph among artists. Then, the similarity analysis of music within and between schools is con-ducted to get the musical characteristics of different schools. Then the correlation analysis of music features is carried out by SPSS to get the most “infectious” index of music. Finally, based on the time series, the visual analysis of music evolution is made to quantify the influence of music. In this paper, we’ve verified the model for many times according to the music development results, which proves that the model has strong guidance for the analysis of music development.

This paper mainly studies the existence of multiple positive solutions of a class of Riemann-Liouville fractional q-difference equations under the four-point boundary value condition with p-Laplacian operator. The existence of two positive solutions of the q-difference equation is verified by the monotonic iterative method. Finally, an example is used to prove the validity of the main results obtained.

Transition is the basic phenomena of complex flow regime changes in fluid mechanics. So far, the axiomatic expression and rigorous mathematical description of transition and separation are important basic scientific problems, which are also of great significance to the development of Applied Science. This article obtaining the basic conditions and general conditions for transition through the excited state theory of flowfield, which is derivation based on the N-S equations, combined with Euler’s description point of view, applied tensor analysis and with the help of the basic principles of superposition states of quantum mechanics. The research of this paper provide a theoretical view for the study of turbulence mechanism.

The safe and stable operation of power system is related to the national economy and people’s livelihood of the whole country. Blackouts are almost always caused by cascading failures. This paper first analyzes the global blackouts in the past 20 years, and points out that the scale and probability distribution of blackouts obey the power-law relationship. Secondly, it is concluded that transmission line fault, bus fault, large-scale power flow transfer and relay protection device misoperation are the main factors causing cascading failures. Then, the five stages of cascading failure evolution are analyzed, which are slow successive interruption process, fast successive interruption process, transient oscillation, avalanche blackout and long recovery. Finally, the research results of cascading failure at home and abroad in recent years are analyzed from three research points: small world network, topological network and two-layer coupling network.

The regional characteristics of middle-aged women in Xinjiang are obvious, and the phenomenon of incompatible clothing is prominent. In order to avoid the information loss of principal component analysis or factor analysis during body type classification, this study uses the LightGBM algorithm to establish a body type recognition model based on the results of K-Means clustering, and compares it with random forest and linear regression recognition models. It is found that the LightGBM model has the best body type recognition effect. it is good. Through correlation analysis and regression analysis, regression equations between variables are obtained. Based on the new cultural prototype, Liu Ruipu women’s clothing prototype, and Donghua prototype, a clothing prototype suitable for middle-aged women in Xinjiang is established. Through virtual fitting evaluation and actual fitting, the experimental prototypes established based on the Donghua prototype and the Liu Ruipu prototype can meet the needs of middle-aged women for the comfort and aesthetics of clothing. The experimental prototype established by the Donghua prototype has the best effect.

In this paper, we provide an analysis on the partial overlapping order problem in a strip, i.e., whether a given partial order involving only part of the squares of the strip corresponds to a valid flat-folded state of the strip or not. On the contrary to the general intractability of partial orders, we investigated the partial orders onto some particular sets to obtain tractable results. To rapidly get access to the solution, our methodology is based on the abstracted visualized folded states rather than a mathematical explanation by matrix. In conclusion, a strip having at least three disordered squares aligning on the strip between any two of its ordered squares always corresponds to a final flat-folded state.

By introducing the Vehicle Routing, Scheduling & Dispatching Problem for Multiples Depot (VRSDP/MD) and the description of formalization, it is helpful to offer a solution to solve the complex situation in practical transportation problem. In order to decrease the influence of the problem, A computing model embodying Hierarchical Multiplex Structure to take shape with an object-oriented multiple paradigms (HIMS+ model) are put forward as a proposal. And HIMS+ is divided into three layers: the first layer is the system cost adjusting area, the second layer is formation area for the system state, and that, the third layer is decision-making area for the system optimization. Two methods of meta-heuristic and fuzzy inference are proposed as an optimality calculation for HIMS+ architecture. There are two types of 24 tank lorries in the metropolis of Japan (Tokyo area), where two types of experiments are scheduled for 3-day of actual order data. Experiments results show that the HIMS+ model increase acceleration by 10 percent and decreases fast by 75 percent compared to what experts predict. The HIMS+ model has become a very reliable computing architecture for the multi objective and multi constraint optimization to real world transportation problems.

In this paper, threshold function denoising algorithm and wavelet neural network edge detection algorithm are combined to apply to image edge detection. Firstly, an improved threshold function is constructed in this paper, compared with the traditional soft and hard threshold functions and some existing improved threshold functions, the improved threshold function is adjustable and differentiable everywhere. It approximates the soft threshold function and the image at the threshold point is smoother. It can retain more true information and have an obvious effect in image de-noising. Finally, this paper presents wavelet neural network edge detection algorithm. Selecting the modulation Gaussian function wavelet as its excitation function, which is applied to extract the edge of the image after threshold de-noising. Thus, a new edge detection algorithm is proposed, which combines threshold function de-noising algorithm and wavelet neural network edge detection algorithm. The simulation results show that the edges detected by the new algorithm are clearer, contain less noise, and the continuity and accuracy are also improved.

Aiming at the inaccurate clock calibration of electric meters and the shortcomings of traditional clock synchronization methods, this article briefly summarizes the reasons of inaccurate meter clocks, and proposes a method of electric meter clock calibration based on wireless communication, which solves the problem of meter clock synchronization accuracy. It is verified by field test. The test results show that the error of electric meters clock after clock calibration can be controlled at the second level. And the data error of collected import active electrical energy is smaller, which meets the requirements of real-time analysis of electricity spot trading and other businesses, providing more accurate data to ensure the results reliability.

In order to make up for the deficiency of traditional passive jamming, a new electronic jamming mode is proposed, which mainly absorbs electromagnetic waves. Firstly, based on the traditional interference corridor model of radar electromagnetic signal power attenuation, the absorber as a whole is analyzed and its interference mechanism is obtained; With reference to the idea of studying the electromagnetic characteristics of stealth metamaterials by Floquet port method, the electromagnetic simulation software HFSS is used to establish an electromagnetic model for simulation verification, and the scaled method is used to simplify the model. The experimental results are consistent with the theory, which shows that the interference mechanism and the interference simulation model are correct.

The Yigong landslide is simulated and analyzed with a combined finite-discrete method (FDEM) under seismic loading. Determination of computing model and parameters are introduced. The final distances of six reference points are given showing a special distribution in accord with the results of field investigation. Also, the velocity time-history curves of these points are depicted, where two trends are captured for these points matching with the sliding process of the Yigong landslide. Inconsistencies of displacements and velocities of these points result from the generation and propagation of cracks, initiating the landslide eventually. The FDEM works well in the simulation of this landslide, revealing its applicability and advantages.

In the financial market, investors often do not consider the market environment, but only invest based on the investment behavior of others. This is commonly known as Herd behavior. The herd behavior not only takes part in traditional financial markets but also in cryptocurrency markets. This paper aims to build a model which is applicable in cryptocurrency markets. To research the herd behavior in cryptocurrency markets and the dynamic relationship between the investors and the value of cryptocurrency with the model.

Water brake technology has great significance on monorail rocket sled test, which coupling nonlinear process between high-speed flow impact and structure response. In this paper Finite element method(FEM) and Smoothed particle hydrodynamics(SPH) model is used to analyze the braking force performance and the structure response during the monorail rocket sled braking process. The results show that the FEM-SPH method has high accuracy, which braking force error between numerical simulation and experiment is 3.92% when velocity of rocket sled is 750m/s. The safe braking distance of numerical simulation is 100m, while the real distance of experiment is 105m. The error between numerical simulation and experiment is just about 5%.

Rebate, as a significant method to enhance cooperation between retailers and suppliers, has been widely applied among different commercial agencies. In this paper, we studied the effect of rebate on the evolution of cooperation in spatial social dilemmas. With a rebate mechanism, cooperators will share a part of payoff to cooperative neighbors. Simulation results shows that the rebate mechanism can promote cooperation significantly. When rebate mechanism works, the low-payoff boundary cooperators could receive extra rebates from the high-payoff cooperators in cooperator cluster. This helps cooperators defend the invasion of defectors. As a result, cooperators could survive and even dominate the system. The research can provide a new insight to explore the widespread cooperative behavior in the natural world.

In the DC power system, the circuit breaker must not only complete the rapid disconnection and isolation of the high short-circuit fault current, but also undertake the frequent switching tasks of the small load rated current. First of all, this research adopts the topological structure of double-breaker series connection and introduction of auxiliary oscillating branch on the basis of forced commutation.Different control strategies can be adopted according to different current levels, which can realize the rapid breaking of small currents while improving high current breaking performance.Secondly, through the mathematical analysis of the working process of the circuit structure, and based on the PSCAD/EMTDC electromagnetic transient simulation software, the influence of different branch parameters on the breaking process is analyzed, and the circuit parameter optimization design is carried out for the breaking process of different load current levels.

In order to reveal the lubrication characteristics of high-speed ball bearings under the sub-ring lubrication mode and improve the lubrication efficiency of ball bearings, a three-dimensional geometric model of high-speed ball bearings was established. By using multiple reference frame and VOF model, the two-phase flow field and temperature field of inner and outer ring in the bearing under different conditions were investigated, and the correlation law of lubricating oil flow and heat transfer was obtained. At the same time, the definition of the penetration rate was given quantitatively for the lubrication efficiency of the outer ring. The lubrication efficiency of ball bearings under-race lubrication was evaluated from the aspects of rotation speed and penetration rate. The results showed that the oil and gas distribution and temperature distribution in the lubrication under the ring are not uniform, and there was an obvious correlation between the two; the increase of speed reduced the oil volume fraction in the bearing. The oil distribution was more uniform which was useful for reducing the temperature difference between the inner and outer rings.

In order to solve the problems of large rendering load and low frame rate caused by the large screen of the power system five-sided LED-CAVE immersive virtual simulation platform, the article proposes a 1+N cluster rendering synchronization for the power system five-sided LED-CAVE Display management system. Configure the five-sided LED-CAVE with 1+N high-performance graphics rendering workstations and synchronous display cards according to the size and resolution of each screen. Through the synchronous rendering display system and 3D optical tracking and positioning system, achieve the effect that 5 screens refresh the stereo display simultaneously. This method improves the efficiency and immersive experience of power system virtual reality simulation rendering.

A general optimization method, based on the power series method, is presented for computing the conformal mappings with explicit expressions from: (a) the unit disc onto an infinite domain exterior of a closed Jordan curve, (b) the circular annulus domain onto a finite doubly-connected domain bounded by two closed Jordan curves, (c) the infinite domain bounded by two circular curves onto an infinite domain bounded by two non-circular closed Jordan curves. The unknown mapping functions are approximated by the power series method. The problem of solving the mapping function coefficients is transformed into the problem of determining the image points on the image plane by means of the least square method. Different from most of the previous optimization methods, the angles are set as the design variables rather than the mapping function coefficients in the paper. The influence of the terms of the series on the calculation accuracy is investigated. The successful applications of the proposed method are shown by a large number of numerical examples.

This paper established a one-dimensional model of a coaxial dielectric barrier discharge (DBD) with a single dielectric layer covering the high-voltage electrode. The mixture of Ar and a small amount of CH₄ was used as working gas, the influence of different voltage amplitude on the discharge characteristics was studied by 10.0 kHz microsecond pulsed power. The simulation results show that the discharge current curve presents bipolar characteristics with different intensities are generated in a single microsecond pulse period, and the primary discharge is much intense. The discharge current, discharge power can enhance by increasing the discharge voltage amplitude. The equivalent capacitance C_g also increases, the discharge voltage has no significant effect on C_d. In the experiment, it can be observed that the number of discharge filaments in the discharge gap increases with the increase of voltage amplitude, and photoionization is formed near the anode. The result of the current experimental trend is almost the same as the simulated current.