Nonlinear Mathematical Modeling and Sensitivity Analysis of Hydraulic Drive Unit

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

A mathematical model for optimized operation and controlin a CDQ-Boiler system

Based on analyzing the thermal process of a CDQ （coke dry quenching）-Boiler system, the mathematical model for opti-mized operation and control in the CDQ-Boiler system was developed. It includes a mathematical model for heat transferring process in the CDQ unit, a mathematical model for heat transferring process in the boiler and a combustion model for circulating gas in the CDQ-Boiler system. The model was verified by field data, then a series of simulations under several typical operating conditions of CDQ-Boiler were carried on, and in turn, the online relation formulas between the productivity and the optimal circulating gas, and the one between the productivity and the optimal second air, were achieved respectively. These relation equations have been success- fully used in a CDQ-Boiler computer control system in the Baosteel, to realize online optimized guide and control, and meanwhile high efficiency in the CDQ-Boiler system has been achieved.

MATHEMATICAL MODEL OF SELF-REPAIRING FLIGHT CONTROL

The most prospective method for certain structural failures and damages that cannot employ redundancy is self-repairing techniques, to ensure especially the maximum flight safety. Based on the characters of self-repairing aircraft, this paper states some basic assumptions of the self-repairing aircraft, and puts forward some special new conceptions concerning the self-repairing aircraft: control input, operating input, command input, repair input and operating and control factor as well as their relationships. Thus it provides a simple and reliable mathematical model structure for the research on the self-repairing control of the aircraft.

Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19in Nigeria Using Atangana-Baleanu Operator

We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.

Mathematical Models for a Social Partitioning Problem

In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of company employees as an effective way to curb the spread, and use integer programming techniques to model it. The goal of the model is to maximize the number of direct interactions between employees who are essential for company’s work subject to the constraint that all employees should be partitioned into components of no more than a certain size implied by the regulations. Then we further develop the basic model to take into account different restrictions and provisions. We also give heuristics for solving the problem. Our computational results include sensitivity analysis on some of the models and analysis of the heuristic performance.

Energy Factor and Mathematical Modeling for Power DC/DC Converters

Mathematical modelling for power DC/DC converters is a historical problem accompanying DC/DC conversion technology since 1940’s. The traditional mathematical modelling is not available for complex structure converters since the differential equation order increases very high. We have to search other way to establish mathematical modelling for power DC/DC converters.We have theoretically defined a new concept-Energy Factor （EF） in this paper and researched the relations between EF and the mathematical modelling for power DC/DC converters. EF is a new concept in power DC/DC conversion technology, which thoroughly differs from the traditional concepts such as power factor （PF）, power transfer efficiency （η）, total harmonic distortion （THD） and ripple factor （RF）. EF and the subsequential EFV (and EFVD) can illustrate the system stability, reference response and interference recovery. This investigation is very helpful for system design and DC/DC converters characteristics foreseeing. Two DC/DC converters: Buck converter and Super-Lift Luo-Converter as the samples are analysed in this paper to demonstrate the applications of EF, EFV (and EFVD), PE, SE, VE （and VED）, time constant τ and damping time constant τd.

Application of PCM-based Thermal Energy Storage System in Buildings: A State of the Art Review on the Mathematical Modeling Approaches and Experimental Investigations

This review paper critically analyzes the most recent literature(64% published after 2015) on the experimentation and mathematical modeling of latent heat thermal energy storage(LHTES) systems in buildings. Commercial software and in-built codes used for mathematical modeling of LHTES systems are consolidated and reviewed to provide details on the selection of appropriate tools. Insights on software’s computing speed, model simplicity, accuracy(by considering the convective term in the melting process), and application of artificial neural networks are reviewed in detail. Moreover, the overall research status of the experiments conducted on the phase change material-based LHTES systems with different experiment configurations is reviewed. The analysis shows that ANSYS Fluent is the most widely used software for specific heat transfer phenomenon in storage tanks, while self-developed models with simplified terms are evaluated as more flexible and easier to apply. For hybrid systems, self-developed MATLAB, mature parts in ESP-r, TRNSYS, and EnergyPlus are compatible. Further, most of the experimental investigations are conducted on the laboratory scale, providing data for model validation. To provide a clear guidance for the future market application, the scope for future works is presented. With this review, it would be easier to develop a unified, simplified, visual, and accurate simulation platform for the PCM-based thermal energy storage in buildings.

Mathematical modeling of fuel cells fed with an electrically rechargeable liquid fuel

Lately,utilizing a novel electrically rechargeable liquid fuel(e-fuel),a fuel cell has been designed and fabricated,which is demonstrated to achieve a much better performance than alcoholic liquid fuel cells do.However,its current performance,which thus hampers its wide application,demands further improvement to meet up with industrial requirement.Therefore,to attain a better performance for this system,an in-depth understanding of the complex physical and chemical processes within this fuel cell is essential.To this end,in this work,a two-dimensional transient model has been developed to gain an extensive knowledge of a passive e-fuel cell and analyze the major factors limiting its performance.The effects of various structural parameters and operating conditions are studied to identify the underlying performance-limiting factors,where deficient mass transport is found to be one of the major causes.The increment of anode porosity and thickness are found to be effective methods of improving the cell performance.This study therefore provides insights on achieving further per-formance advancement of the fuel cell in the future.

Predictive Mathematical and Statistical Modeling of the Dynamic Poverty Problem in Burundi: Case of an Innovative Economic Optimization System

The mathematical and statistical modeling of the problem of poverty is a major challenge given Burundi’s economic development. Innovative economic optimization systems are widely needed to face the problem of the dynamic of the poverty in Burundi. The Burundian economy shows an inflation rate of -1.5% in 2018 for the Gross Domestic Product growth real rate of 2.8% in 2016. In this research, the aim is to find a model that contributes to solving the problem of poverty in Burundi. The results of this research fill the knowledge gap in the modeling and optimization of the Burundian economic system. The aim of this model is to solve an optimization problem combining the variables of production, consumption, budget, human resources and available raw materials. Scientific modeling and optimal solving of the poverty problem show the tools for measuring poverty rate and determining various countries’ poverty levels when considering advanced knowledge. In addition, investigating the aspects of poverty will properly orient development aid to developing countries and thus, achieve their objectives of growth and the fight against poverty. This paper provides a new and innovative framework for global scientific research regarding the multiple facets of this problem. An estimate of the poverty rate allows good progress with the theory and optimization methods in measuring the poverty rate and achieving sustainable development goals. By comparing the annual food production and the required annual consumption, there is an imbalance between different types of food. Proteins, minerals and vitamins produced in Burundi are sufficient when considering their consumption as required by the entire Burundian population. This positive contribution for the latter comes from the fact that some cows, goats, fishes, ···, slaughtered in Burundi come from neighboring countries. Real production remains in deficit. The lipids, acids, calcium, fibers and carbohydrates produced in Burundi are insufficient for consumption. This negative contribution proves a Burundian food deficit. It is a decision-making indicator for the design and updating of agricultural policy and implementation programs as well as projects. Investment and economic growth are only possible when food security is mastered. The capital allocated to food investment must be revised upwards. Demographic control is also a relevant indicator to push forward Burundi among the emerging countries in 2040. Meanwhile, better understanding of the determinants of poverty by taking cultural and organizational aspects into account guides managers for poverty reduction projects and programs.

MODEL-BASED DEVELOPMENT OF REAL-TIME SOFTWARE SYSTEM FOR ELECTRONIC UNIT PUMP SYSTEM

A real-time operating system （RTOS）, also named OS, is designed based on the hardware platform of MC68376, and is implemented in the electronic control system for unit pump in diesel engine. A parallel and time-based task division method is introduced and the multi-task software architecture is built in the software system for electronic unit pump （EUP） system. The V-model software development process is used to control algorithm of each task. The simulation results of the hardware-in-the-loop simulation system （HILSS） and the engine experimental results show that the OS is an efficient real-time kernel, and can meet the real-time demands of EUP system; The built multi-task software system is real-time, determinate and reliable. V-model development is a good development process of control algorithms for EUP system, the control precision of control system can be ensured, and the development cycle and cost are also decreased.

SEIHCRD Model for COVID-19 Spread Scenarios,Disease Predictions and Estimates the Basic Reproduction Number,Case Fatality Rate,Hospital,and ICU Beds Requirement

We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartments have added death,hospitalized,and critical,which improves the basic understanding of disease spread and results.We have studiedCOVID-19 cases of six countries,where the impact of this disease in the highest are Brazil,India,Italy,Spain,the United Kingdom,and the United States.After estimating model parameters based on available clinical data,the modelwill propagate and forecast dynamic evolution.Themodel calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries’age-category scenario.Themodel calculates two types of Case fatality rate one is CFR daily,and the other is total CFR.The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection.The SEIHCRD model outperforms the classic ARXmodel and the ARIMA model.RMSE,MAPE,andRsquaredmatrices are used to evaluate results and are graphically represented using Taylor and Target diagrams.The result shows RMSE has improved by 56%–74%,and MAPE has a 53%–89%improvement in prediction accuracy.

Characteristics Analysis of the Operational Parameters of a Novel Rectifier Transformer With Filters

新型整流变压器及其滤波系统由网侧、阀侧绕组,独立滤波绕组及与之相连的滤波器组构成,其特殊的滤波支路能够在滤波和无功补偿的同时改善变压器的运行特性。首先推导以谐波抑制因子为表达方式的谐波电流抑制模型以考察谐波传递情况;然后构建网侧绕组电流和负载电流之间的数学关系,藉此研究无功补偿特性,并分析相关的运行参数;之后建立阀侧电压与网侧电压的数学关系,以研究滤波器对阀侧电压的影响。理论分析表明,新型整流变压器及其滤波系统可以有效抑制谐波,降低网侧电流和视在功率,提高网侧功率因数并增加负载电压。实际应用在工业直流供电系统中的新型整流变压器的现场实测结果,验证了理论分析的正确性。该文更全面地揭示了新型整流变压器能改善整流系统的运行特性,所推导的数学模型将为新型整流变压器在降噪节能等方面的进一步研究提供理论依据。

INVERSE PROBLEM STABILITY OF A CONTINUOUS-IN-TIME FINANCIAL MODEL

In this work, we study the inverse problem stability of the continuous-in-time model which is designed to be used for the finances of public institutions. We discuss this study with determining the Loan measure from algebraic spending measure in Radon measure space M([tI,Θmax]), and in Hilbert space L2([tI,Θmax]) when they are density measures. For this inverse problem we prove the uniqueness theorem, obtain a procedure for constructing the solution and provide necessary and sufficient conditions for the solvability of the inverse problem in L2([tI,Θmax]).

Re-Parameterization the Logistic Model in Assessing Changes in the Baroreceptor Reflex

The logistic model is frequently used to describe the nonlinear relationship between systemic arterial pressure (SAP) and carotid sinus pressure (CSP). In this paper, we propose using maximum gain and saturation as parameters in the logistic model. By this method, the estimates and standard errors together with confidence intervals for maximum gain and saturation are direct outputs from the curve fitting, which also makes it easy to perform various hypotheses testing on these quantities. The method is illustrated by real life data from a study on the carotid baroreflex function during infusion of sodium nitroprusside, in which seven healthy, young men who were clinically proved to be free from any disease were studied. Their heart rate, arterial blood pressure and central venous pressure were measured. Neck pressure and neck suction protocol was carried out to selectively elicit changes in CSP and the responsiveness of SAP. Data were analyzed and compare before and after nitroprusside infusion. Our results showed that nitroprusside significantly decreased arterial blood pressure and central venous pressure, and significantly increased heart rate, and significantly augmented maximum gain of the carotid baroreflex function.

抽油机井恒功率变频控制系统研究

抽油机作为陆上油田最重要的机械采油装备之一,近年来已发展出一系列的变频节能技术,但其研究主要集中在硬件方面,缺乏相关基础理论,导致现场应用普适性差,应用效果参差不齐。为此,研究有杆泵变频测控机理,优选了主要部件,对测试数据提出了要求,形成了有杆泵抽油变频控制系统。构建BP神经网络系统对正常井和漏失、柱塞碰泵、气体影响等异常井进行识别,分类提出变频计算模型:考虑负扭矩和抽油机冲次界限等建立了正常井恒功率变频计算模型,实例对比分析了变频后抽油机速度、加速度变化规律,产液量一定时,负功功率和有功功率分别下降了65%和44%。建立了上行程漏失的异常井变频计算模型,针对性地提高上行程冲次,形成“上快下慢”运行模式。实例计算表明:该系统缩短上行程时间2.6 s,较好地解决有杆泵上行程漏失和变频节能的问题。研究成果可为抽油机变频技术提供理论支持,对油田节能和提产具有指导意义。

基于数学表达式和文档关键词的英文文献检索模型设计

为实现针对英文学术文献的准确检索,提出一套基于数学表达式和文档关键词的英文文献检索模型。通过FDS算法对数学表达式进行结构化描述,扩大英文文献的检索范围,同时通过基于Word2Vec的词嵌入模型对英文单词进行向量化表示,采用余弦定理来计算查询关键词向量与文档单词向量之间的相似度,根据相似度的高低来对单词进行排序,进而输出查询结果。最后通过NTCIR语料库对英文文献检索模型的有效性加以验证,根据实验结果可知,该模型在查准率和查全率两方面均达到了较为理想的效果,且显著优于常规SearchOnMath模型,具有一定的应用价值。

可解释的变负荷下燃煤机组SCR反应器入口NO_(x)质量浓度预测模型

燃煤电厂灵活调峰过程NO_(x)测量往往存在滞后现象,导致选择性催化还原(selective satalytic reduction,SCR)脱硝喷氨控制系统响应不及时,易造成喷氨量过高或过低,从而造成SCR反应器出口NO_(x)质量浓度波动剧烈和氨逃逸率增大。为实现喷氨阀门的提前快速调节并考虑影响燃煤锅炉NO_(x)排放量的因素存在耦合性,提出了一种基于卷积神经网络(convolutional neural network,CNN)和长短时记忆(long short-term memory,LSTM)神经网络混合模型的SCR反应器入口NO_(x)预测模型。利用一台330 MW燃煤电站锅炉的运行参数,通过Pearson系数法计算特征变量之间的相关性,筛选出相关性较大的特征,并定义模型的输入矩阵和输出矩阵,采用随机搜索算法进行优化,以提高预测性能。进一步利用SHAP算法对黑箱模型进行解释,并通过Simulink仿真验证了带有NO_(x)预测的控制效果。结果表明:CNN-LSTM预测模型在调峰负荷变化时,能够以较高的精度预测SCR反应器入口NO_(x)质量浓度的变化,并能提前25s为喷氨控制系统提供反馈;优化后的喷氨控制策略降低了出口NO_(x)质量浓度与设定值间的标准差(降低28%),并提升了NH_(3)/NO_(x)的响应速度,减小最大氨逃逸量22%。该研究结果可为灵活调峰机组的智慧SCR脱硝技术及燃烧优化提出有效的指导。

兴隆水利枢纽下游围堰缺口封堵后对河道运行的影响研究

兴隆水利枢纽工程被迫降低水库水位运行,影响了枢纽综合效益的正常发挥,亟需研究解决的办法。依据工程现状,采用河流动力学数学模型,研究壅高枢纽下游水位应采取的工程措施,以及实施后对下游河道运行的影响。根据模拟结果,对兴隆水利枢纽工程下游横向围堰缺口段采用土工包方案进行封堵,封堵高程27.8m。封堵方案实施后,较好地解决了河床下切导致的枢纽通航和发电安全等问题,实现了工程正常运行和效益发挥的目标。

基于藻菌共生废水处理技术的MBRM反应模型

将藻菌共生的微生物代谢体系用在废水的水质处理中,能快速同步去除碳氮磷等易造成水体富营养化的污染物,因此藻菌共生水处理技术具有广阔的应用前景。而数学模型能够对相关的藻菌水处理过程进行精准的抽象描述,发掘其中的变化规律,总结适宜的参数优化策略,对于工艺后续的效果强化和扩大应用具有重要意义。尽管已有许多基于生化处理的数学模型作为基础,藻菌模型在应对水质更为复杂的情况下的表现较少,需要在原有的模型体系中针对不同的水质特性和应用场景加以改良。本研究是基于藻菌共生水处理技术应用在畜禽养殖废水处理中的一系列物理化学反应和生长代谢过程,针对其反应器开发了一个MBRM数学模型。通过30 d连续运行实验研究对模型进行验证和校准,验证了该模型能根据反应器的运行参数条件和进出水水质,并且准确地模拟其中的微生物处理过程中的相关的水质变化和微生物的生长情况。

基于PRSEUS构型翼身融合机体结构多学科优化设计方法与应用

针对翼身融合(BWB)布局机体结构承载效率低、结构增重以及高后置背撑发动机带来的大载荷和舱内噪声等问题,基于新型材料和新型高效承载结构(PRSEUS),开展以提高结构承载效率和轻量化为目标,兼顾气动、噪声、振动及工艺等多学科约束的非常规圆截面机体结构多学科优化设计方法研究。基于自适应代理模型构建技术建立了机体结构气动、噪声子系统性能分析代理模型,实现了对机体结构气动载荷、噪声性能的预测,并将气动、噪声性能的基本要求转化为几何尺寸及力学响应等约束条件,从而把多学科问题集成到一套有限元分析模型,配合高效数学规划法,解决了多学科高精度模型分析耗时问题,实现了翼身融合机体结构的多学科优化设计。通过机体结构有限元分析验证,在满足各学科约束条件前提下,结构的承载效率得到较大幅度提升,中央机体结构减质率达到了8.7%。