Differential Equation Algorithm Research Articles

Determining Fault Location in Transmission Lines Using Differential Equation Algorithms

A transmission line, in the context of electrical engineering and power systems, is a high-voltage or high-tension line that is used to transmit electrical power over long distances from power generation sources (such as power plants) to substations, where the electricity is then distributed to homes, businesses, and industrial facilities. Transmission lines are the backbone of the electrical grid, serving as the highways for electricity delivery. Their efficient and reliable operation is essential for ensuring that electricity is generated, transmitted, and distributed effectively, meeting the needs of consumers while maintaining grid stability and resilience. Transmission line protection refers to a set of techniques and devices used in electrical power systems to detect and respond to faults or abnormal conditions that can occur in high-voltage transmission lines. These lines are a critical part of the electrical grid and are responsible for transporting electricity over long distances from power generation plants to distribution substations. This paper proposes a different differential equation algorithm to locate faulty section on transmission lines. As seen from performance curves, the proposed protection algorithm is able to distinguish normal and faulty conditions.

Research on Factory Embedded Blast Furnace Temperature Operating System Based on Functional Chain Neural Network Fractional Differential Equation Algorithm

This paper provides a comprehensive overview of fractional differential equations and their application in university economic management analysis. Initially, it offers a concise summary of relevant theories surrounding fractional differential equations, establishing a robust theoretical framework. Building on this foundation, the study delves into an in-depth analysis of seven prevalent economic management models utilized in university settings. By employing fractional differential equations, the paper not only solves these economic models but also elucidates the underlying economic implications and principles. Furthermore, the research presents a detailed analysis of economic management, drawing logical inferences and insights. The abstract concludes by showcasing practical examples that illustrate the application of fractional differential equations in the realm of economic management. This study bridges theoretical concepts with real-world applications, providing valuable insights for the advancement of economic management strategies in educational institutions.

Application of linear ordinary differential equations to the stability control of long time lag networks

Abstract Optimal control based on the exact synchronization of linear ordinary differential equations can provide conditions for the existence of optimal control of long-time lag network stability. In this paper, we first generalize network control systems, time lag systems, and modern control system stability theory to discuss long-time lag network stability analysis and control problems. The numerical solution method for solving ordinary differential equations with boundary conditions is proposed by combining the numerical solution method for initial value problems of differential equations and the iterative method for solving nonlinear equations. Finally, the fixed-time synchronization problem of complex networks with time-varying time lags under periodic intermittent control is studied. Two intermittent control strategies are designed based on the linear ordinary differential equation algorithm, and the convergence analysis of the synchronization error and the synchronization criterion are given. Numerical values show that the synchronization error converges to zero (< 1.0e − 5) in 0.32s, while the convergence times are 0.55s and 0.90s. The fixed times of the three methods are calculated to be T * = 0.52, T 1 = 0.71 and T 2 = 1.32, respectively, and the synchronization error system converges faster under the method in the paper. The numerical simulation results verify the effectiveness of linear ordinary differential equations in controlling the stability of long-time lag networks.

Research on the Construction of Financial Computing Model Based on BSDE Algorithm

Economic and social development has made financial engineering an increasingly important research area, and more and more financial problems cannot be solved directly by analytical formulas. In view of this, algorithms that apply computer technology to financial engineering have emerged. In this study, the Backward Stochastic Differential Equation (BSDE) algorithm is used to investigate and analyse the problem of option pricing calculation in finance. In the research process, GBSDE-Theta parallel algorithm composed of BSDE-Theta algorithm and GPU algorithm uses the new algorithm to establish a computing model in the financial engineering field, which applies to the calculation of enterprise option pricing. The research results show that compared with the basic algorithm, the actual option values of the option pricing data obtained by using the GBSDE-Theta parallel algorithm are more closely matched. The computational model can achieve a speedup ratio of about 230 times of the serial version with the number of time steps [Formula: see text] and the number of simulated paths 80,000. About the relative error of the GBSDE-Theta algorithm, there are 80 points within 3% and only 16 points over 3.00%, which is a relatively small error. The above results show that the financial computing system obtained in this study is highly feasible and effective, and can provide a new research idea for the progress and development of other computations in the financial field.

Indoor and Outdoor Fusion Positioning Technology Based on BeiDou Satellite Navigation

In order to solve the inaccuracy and discontinuity of BeiDou differential indoor and outdoor navigation and positioning, this article highlights an indoor and outdoor fusion positioning method based on BeiDou differential and WIFI. This positioning method combines the micro-inertial navigation positioning technology with a single positioning method such as Bluetooth, WIFI fingerprint, ZigBee, ultra-wideband UWB, etc., to correct the BeiDou pseudo range equation to reduce the spatial pseudo range error. And it can integrate BeiDou differential pseudo range equation and linear filtering algorithm to achieve precise positioning of navigation. The research results show that the method realizes the positioning of the indoor and outdoor interactive area by fusing the satellite pseudo-range equation and the base station pseudo-range equation. And it realizes the seamless integration of indoor and outdoor precise positioning, which improves the positioning accuracy and reliability.

Design Method and Application of Intelligent Sports Equipment Based on Stochastic Differential Equation

Abstract A set of intelligent sports equipment information analysis systems based on stochastic differential equation algorithms is established in this paper. Then the periodic solutions of the Fokker-Planck equation are studied in this paper. At the same time, the integral conservation problem of the finite element semi-discrete solution of the Fokker-Planck equation on R is given. Finally, the intelligent sports equipment information analysis method based on the stochastic differential equation algorithm is used in college physical education. The practical application proves that this research can support multi-source acquisition. This method has high precision. This device is helpful for exercise.

Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching

Abstract This article combines ordinary differential equations’ theoretical and practical characteristics to explore how to integrate mathematical modeling ideas in teaching materials and teaching methods. We apply the fractional differential equation algorithm to the mathematical modeling of Terman diffusion. At the same time, the article proposes a framework for obtaining accurate solutions of a class of nonlinear Sinai stochastic models with power-law diffusion through Mittag-Leffler function transformation. In this way, we have obtained great explicit and accurate solutions of some important Mittag-Leffler function power-law diffusion physical processes.

A novel directional element for transmission line connecting inverter-interfaced renewable energy power plant

The fault currents characteristics of inverter-interfaced renewable energy sources (IIRESs) such as direct-drive permanent magnetic synchronous generator and photovoltaic mainly include weak feed, the variety of source impedance and frequency deviation, which may lead to the false operation of distance protection for transmission line connecting inverter-interfaced renewable energy power plant (IIREPP). The R-L differential equation algorithm based time-domain distance protection is not affected by the fault characteristics of IIRES, but it is difficult to determine the fault direction when faults near the relay. In this paper, a directional element suitable for transmission line connecting IIREPP is proposed, and an improved time-domain distance protection composed of the directional element and the R-L differential equation algorithm based time-domain distance protection is proposed. The characteristics of fault currents of IIRES and traditional AC power grid are analyzed and summarized by deriving the analytical expressions of their fault currents in dq synchronous reference frame. The analysis results show that when the back of the relay is the IIRES and the AC power grid respectively, the change trends of the d-axis component of their fault currents are the same in a short time after faults occur in front of the relay, and the changes of q-axis component of their fault currents are obviously different. The directional element is proposed based on the characteristics of the fault currents on both sides of the transmission line connecting IIREPP. The simulation results verify effectiveness of the proposed protection scheme.

Dynamic Model of Language Propagation in English Translation Based on Differential Equations

English is the most widely used language in the world, and at the same time, English translation is becoming increasingly important. However, the traditional English translation model still has some problems, such as poor translation effect, repeated translation, translation solidification, and translation limitations caused by regional language differences in the application process of language communication. Differential equations refer to relational expressions containing unknown functions and their derivatives. Solving differential equations is to find unknown functions. Differential equations are a branch of mathematics developed along with calculus. In order to solve the problem, this paper puts forward the use of differential equation thinking research English translation language propagation dynamic model, the differential equation combines the neural network language model (NNLM) to form the language dynamic propagation using the differential equation and NNLM model algorithm of the dynamic model for the actual translation effect test (the database includes more than 3,000 indexed, abstract journals and newspapers, including nearly 3,000 full-text journals. The database covers topics, such as international business, economics, economic management, finance, accounting, labor and personnel, and banking. It is suitable for professionals in economics, business administration, financial banking, labor, and personnel management, etc.), and analyze the average code length and the first word hit rate of general language model (GLM), NNLM model, and domain model in the dynamic model in different fields. Then its statistics the overall recall rate and accuracy rate of the dynamic model. The results show that the average code length of the NNLM model is relatively shorter at 2.2 bits. The first word hit rate is higher than the other two models. The first word hit rate of the NNLM model is 85% under non-professional phrases, while 90% under professional phrases. The overall accuracy of the English translation of the dynamic model of language propagation in this paper is 86.37%, and the recall rate is 79.67. It shows that the dynamic model of language propagation combined with neural network and differential equation has a good translation effect and is feasible.

The Discussion About the Identification of the Anand Model Parameters and Two Alternative Identification Methods

Abstract The Anand model is a unified viscoplastic model, which is widely employed to describe the solder material deformation. The parameters in the Anand model for a certain material are usually identified by using the classical method based on two algebraic equations derived from the original differential equation of the Anand model. However, the second algebraic equation describing the relationship between the stress and inelastic strain is obtained with some terms about the unsteady value of internal variable neglected. But the effects induced by the omission of some unsteady terms on the effectiveness of classical method are not researched comprehensively. Therefore, in this paper, the effects of the omitted terms on the accuracy of the classical method are discussed. The inelastic deformation for the material which the second algebraic equation cannot describe due to the omission of unsteady terms is presented. The precondition for obtaining accurate results from the second algebraic equation is given out. Two criteria used to judge the effectiveness of the second algebraic equation are derived. To reduce the error related to the second algebraic equation of the classical method for some materials, two alternative identification methods are proposed. By combining the step of solving differential equation and genetic algorithm, the parameters in the Anand model originally identified by the second algebraic equation are determined in the processes of the two proposed methods. The effectiveness of the two alternative methods is presented by identifying the material Anand parameters where the classical method cannot be applied.

Mathematical and Kinetic Study of Horiuti-Polanyi Reaction Mechanism for the Methylcyclohexane Dehydrogenation Over Various Pt/Al2O3 Catalysts

The Horiuti-Polanyi (HP) mechanism has been studied for the methylcyclohexane dehydrogenation reaction over a Pt/AlO catalyst. Three HP mechanistic schemes such as competitive, non-competitive, and combined-competitive-non-competitive were used in the kinetic modeling of the experimental data. The loss of first hydrogen atom was regarded as the rate-determining step and the mathematical expressions were developed and fitted against the data. A FORTRAN routine was employed where 4th order Runge-Kutta method was used to solve the related differential equation and Marquardt algorithm was used for the parametric estimation. A kinetically and statistically best-fit HP kinetic equation was obtained with 87.96 kJ/mol of activation energy. The best-fit kinetic model was tested with five additional Pt-containing AlO catalysts and yet again found in good agreement with the experimental data.

The Security of Database Network Model Based on Fractional Differential Equations

Abstract This paper discusses a class of inhomogeneous fractional differential equations with boundary conditions. At the same time, we apply it to the database network encryption model. In this paper, the fractional differential equation algorithm segments the big data in the cloud environment, and the homomorphic algorithm is used for encryption. We encrypt the algorithms and store them in the database, respectively. When the model is queried, the corresponding ciphertext data in the database can be matched according to the type of query statement. The experimental simulation realizes the information retrieval and statistics in the case of full ciphertext on the server-side.

The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations

Abstract Fractional differential equations are one of the important contents of advanced mathematics courses. The article uses fractional differential equations to describe the effects of children’s innovative education courses. Through the qualitative analysis of the basic model, several conditions to ensure the effect of children’s innovative education courses are obtained. At the same time, combined with practical experience, the teaching curriculum case design analyzes the specific application of the fractional differential equation in the effect of children’s innovative education curriculum. Research has found that the fractional differential equation algorithm improves the efficiency of innovation.

The Composition System of Pop Music Movement Based on Finite Element Differential Equations

Abstract This paper uses finite element differential equations to control the frequency of occurrence of pop music notes. This method avoids the repetition of dissonant notes in the song. The motivation for inspiration is used as a template in the system. Various musical techniques and rules are added to the composition process. The algorithm enables the musical composition to form a variety of other representations. The finite element differential equation algorithm used the 1/f noise ratio theory to verify that the frequency of note occurrence is directly related to how people feel when listening to music.

Aeroelastic Response of Wind Turbine Rotors under Rapid Actuation of Flap-Based Flow Control Devices

The largest commercial wind turbines today are rated at powers between 12 MW to 16 MW, with rotor diameters between 220 m to 242 m, which are expected to grow beyond 250 m in the near future. Economies-of-scale factors suggest the advantages of upscaling in rotor size to effectively harvest the wind potential. An increased emphasis on studies related to improvements and innovations in aerodynamic load-control methodologies has led researchers to focus on overcoming the bottlenecks in size upscaling. Though conventional pitch control is an effective approach for long-term load variations, their application to mitigate short-term fluctuations has limitations. This is directly associated with the cubical dependence on the weight of the rotor with increasing diameter. Alternatively, active flow-control devices (FCDs) have the potential to alleviate load fluctuations through rapid aerodynamic trimming. Fractional light-weight attachments such as trailing-edge flaps promise the swift response of such rapid fluctuations and require low power of actuation. The current study investigates the performance of active in dynamic load control for utility-scale wind turbines through an aeroelastic evaluation of the turbine response to control actions in short time-scales relevant to rapid load fluctuations. The numerical platform used in the analysis is designed to consider the complex multi-physics dynamics of the wind turbine through a self-adaptive Ordinary Differential Equation (ODE) algorithm that integrates the dynamics presented by control system in to the coupled response of aerodynamics and structural deformations of the rotor. The benchmark case in consideration is the use of fractional trailing-edge flaps used on blades designed for the NREL-5MW Reference Wind Turbine, originally designed by the National Renewable Energy Laboratory.

A Novel Modeling Technique for the Forecasting of Multiple‐Asset Trading Volumes: Innovative Initial‐Value‐Problem Differential Equation Algorithms for Reinforcement Machine Learning

Liquidity risk arises from the inability to unwind or hedge trading positions at the prevailing market prices. The risk of liquidity is a wide and complex topic as it depends on several factors and causes. While much has been written on the subject, there exists no clear‐cut mathematical description of the phenomena and typical market risk modeling methods fail to identify the effect of illiquidity risk. In this paper, we do not propose a definitive one either, but we attempt to derive novel mathematical algorithms for the dynamic modeling of trading volumes during the closeout period from the perspective of multiple‐asset portfolio(s), as well as for financial entities with different subsidiary firms and multiple agents. The robust modeling techniques are based on the application of initial‐value‐problem differential equations technique for portfolio selection and risk management purposes. This paper provides some crucial parameters for the assessment of the trading volumes of multiple‐asset portfolio(s) during the closeout period, where the mathematical proofs for each theorem and corollary are provided. Based on the new developed econophysics theory, this paper presents for the first time a closed‐form solution for key parameters for the estimation of trading volumes and liquidity risk, such as the unwinding constant, half‐life, and mean lifetime and discusses how these novel parameters can be estimated and incorporated into the proposed techniques. The developed modeling algorithms are appealing in terms of theory and are promising for practical econophysics applications, particularly in developing dynamic and robust portfolio management algorithms in light of the 2007–2009 global financial crunch. In addition, they can be applied to artificial intelligence and machine learning for the policymaking process, reinforcement machine learning techniques for the Internet of Things (IoT) data analytics, expert systems in finance, FinTech, and within big data ecosystems.

Deep Learning-Based Three-dimensional Transvaginal Ultrasound in Diagnosis of Intrauterine Adhesion

This study was aimed to enhance and detect the characteristics of three-dimensional transvaginal ultrasound images based on the partial differential algorithm and HSegNet algorithm under deep learning. Thereby, the effect of quantitative parameter values of optimized three-dimensional ultrasound image was analyzed on the diagnosis and evaluation of intrauterine adhesions. Specifically, 75 patients with suspected intrauterine adhesion in hospital who underwent the hysteroscopic diagnosis were selected as the research subjects. The three-dimensional transvaginal ultrasound image was enhanced and optimized by the partial differential equation algorithm and processed by the deep learning algorithm. Subsequently, three-dimensional transvaginal ultrasound examinations were performed on the study subjects that met the standards. The March classification method was used to classify the patients with intrauterine adhesion. Finally, the results by the three-dimensional transvaginal ultrasound were compared with the diagnosis results in hysteroscope surgery. The results showed that the HSegNet algorithm model realized the automatic labeling of intrauterine adhesion in the transvaginal ultrasound image and the final accuracy coefficient was 97.3%. It suggested that the three-dimensional transvaginal ultrasound diagnosis based on deep learning was efficient and accurate. The accuracy of the three-dimensional transvaginal ultrasound was 97.14%, the sensitivity was 96.6%, and the specificity was 72%. In conclusion, the three-dimensional transvaginal examination can effectively improve the diagnostic efficiency of intrauterine adhesion, providing theoretical support for the subsequent diagnosis and grading of intrauterine adhesion.

Binarization for low-quality ESPI fringe patterns based on preprocessing and clustering.

Massive inherent speckle noise and extremely low contrast make it difficult to binarize electronic speckle pattern interferometry (ESPI) fringe patterns. In this paper, we present a binarization based on preprocessing and fuzzy C-means (FCM) clustering for low-quality ESPI fringe patterns. First, we use the multiscale retinex (MSR) algorithm to enhance the original fringe pattern to improve the contrast between the bright and dark fringes. Then, the local entropy of the enhanced fringe pattern is calculated and the second-order oriented partial differential equation algorithm is introduced to filter the local entropy map. Finally, the FCM is applied to cluster the local entropy filtering map, and the pixels of the fringe pattern are classified into two categories: bright fringes and dark fringes. To verify the reliability and universality of the proposed method, we provide a qualitative evaluation of six experimental ESPI subtraction fringe patterns and two computer-simulated ESPI addition fringe patterns. Experimental results exhibit that the proposed method can provide good binarization performances.

Video Recognition of Government Community Management Cases Based on Partial Differential Equation Method

With the development of urban economic construction and urban planning, higher requirements are put forward for the government community in the corresponding community management, community service, and other related things. As an important technical means to assist the government and community in management, video recognition technology plays an important role in the accurate management and service of the government and community. Traditional algorithms based on partial differential equations will destroy image edges and image details in video recognition. Based on this, this paper improves the traditional partial differential equation algorithm of image recognition, selects the GAC model based on image segmentation in the main function, and innovatively optimizes the stop function of its equation function, so as to improve the effect of community case image segmentation. In the image smoothing layer, this paper innovatively selects the second derivative based on image processing as the inherent feature of image recognition, so as to solve the rough problem of image edge and improve the processing efficiency of the algorithm. In order to further maintain the details of the relevant images of community cases, this paper integrates the Gaussian curvature driving function on the improved partial differential equation algorithm, so as to protect the details of the smooth region of the relevant recognition video and solve the disadvantages of the traditional algorithm. The experimental results show that the improved partial differential equation algorithm proposed in this paper improves the accuracy of video recognition by about 5% compared with the traditional algorithm. At the same time, the new algorithm can well ensure the detail integrity of the recognized video.

Multifeatured Image Retrieval Techniques Based on Partial Differential Equations for Online Shopping

In today’s rapid development of network and multimedia technology, the booming of electronic commerce, users in the network shopping species of images and other multimedia information showing geometric growth, in the face of this situation, how to find the images they need in the vast amount of online shopping images has become an urgent problem to solve. This paper is based on the partial differential equation to do the following research: Based on the partial differential equation is a kind of equation that simulates the human visual perception system to analyze images; based on the summary of the advantages and disadvantages of multifeature image retrieval technology, we propose a multifeature image retrieval technology method based on the partial differential equation to alleviate the indexing imbalance caused by the mismatch of multifeature image retrieval technology distribution. To improve the search speed of the data-dependent locally sensitive hashing algorithm, we propose a query pruning algorithm compatible with the proposed partial differential equation-based multifeature image retrieval technology method, which greatly improves the retrieval speed while ensuring the retrieval accuracy; to implement the data-dependent partial differential equation algorithm, we need to distribute the data set among different operation nodes, and to better achieve better parallelization of operations, we need to measure the similarity between categories, and we achieve the problem of distributing data among various categories in each operation node by introducing a clustering method with constraints. The purpose of this article for image recognition is for better shopping platforms for merchants. This algorithm has trained multiple samples and has data support. The experimental results show that our proposed data set allocation method shows significant advantages over the data set allocation method that does not consider category correlation. However, the image features used in image retrieval systems are often hundreds or even thousands of dimensions, and these features are not only high in dimensionality but also huge in number, which makes image retrieval systems encounter an inevitable problem—“dimensionality disaster.” To overcome this problem, scholars have proposed a series of approximate nearest neighbor methods, but multifeature image retrieval techniques based on partial differential equations are more widely used in people’s daily life.