Search results for: nonlinear equation system

Authors: A. Seleem, M. Mortada, M. El-Morsi, M. Younan

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Diffusion stills have been effective in water desalination. The present work represents a model of the distillation process by using vertical single-effect diffusion stills. A semi-analytical model has been developed to model the process. A software computer code using Engineering Equation Solver EES software has been developed to solve the equations of the developed model. An experimental setup has been constructed, and used for the validation of the model. The model is also validated against former literature results. The results obtained from the present experimental test rig, and the data from the literature, have been compared with the results of the code to find its best range of validity. In addition, a parametric analysis of the system has been developed using the model to determine the effect of operating conditions on the system's performance. The dominant parameters that affect the productivity of the still are the hot plate temperature that ranges from (55-90 °C) and feed flow rate in range of (0.00694-0.0211 kg/m2-s).

Keywords: analytical model, solar distillation, sustainable water systems, vertical diffusion still

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Authors: Ana Clara Santos, Maria Manuela Portela, Bettina Schaefli

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This work assesses the performance of an analytical model framework to generate daily flow duration curves, FDCs, based on climatic characteristics of the catchments and on their streamflow recession coefficients. According to the analytical model framework, precipitation is considered to be a stochastic process, modeled as a marked Poisson process, and recession is considered to be deterministic, with parameters that can be computed based on different models. The analytical model framework was tested for three case studies with different hydrological regimes located in Switzerland: pluvial, snow-dominated and glacier. For that purpose, five time intervals were analyzed (the four meteorological seasons and the civil year) and two developments of the model were tested: one considering a linear recession model and the other adopting a nonlinear recession model. Those developments were combined with recession coefficients obtained from two different approaches: forward and inverse estimation. The performance of the analytical framework when considering forward parameter estimation is poor in comparison with the inverse estimation for both, linear and nonlinear models. For the pluvial catchment, the inverse estimation shows exceptional good results, especially for the nonlinear model, clearing suggesting that the model has the ability to describe FDCs. For the snow-dominated and glacier catchments the seasonal results are better than the annual ones suggesting that the model can describe streamflows in those conditions and that future efforts should focus on improving and combining seasonal curves instead of considering single annual ones.

Keywords: analytical streamflow distribution, stochastic process, linear and non-linear recession, hydrological modelling, daily discharges

Procedia PDF Downloads 162

Authors: Pujari Muruga, T. K. Radhakrishnan, N. Samsudeen

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Hydrogen is considered as the most important energy carrier and fuel of the future because of its high energy density and zero emission properties. Microbial Electrolysis Cell (MEC) is a new and promising approach for hydrogen production from organic matter, including wastewater and other renewable resources. By utilizing anode microorganism activity, MEC can produce hydrogen gas with smaller voltages (as low as 0.2 V) than those required for electrolytic hydrogen production ( ≥ 1.23 V). The hydrogen production processes of the MEC reactor are very nonlinear and highly complex because of the presence of microbial interactions and highly complex phenomena in the system. Increasing the hydrogen production rate and lowering the energy input are two important challenges of MEC technology. The mathematical model of the MEC is based on material balance with the integration of bioelectrochemical reactions. The main objective of the research is to produce biohydrogen by selecting the optimum current and controlling applied voltage to the MEC. Precise control is required for the MEC reactor, so that the amount of current required to produce hydrogen gas can be controlled according to the composition of the substrate in the reactor. Various simulation tests involving multiple set-point changes disturbance and noise rejection were performed to evaluate the performance using PID controller tuned with Ziegler Nichols settings. Simulation results shows that other good controller can provide better control effect on the MEC system, so that higher hydrogen production can be obtained.

Keywords: microbial electrolysis cell, hydrogen production, applied voltage, PID controller

Procedia PDF Downloads 247

Authors: Walid M. Adel, Liang Guo-Zhu

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To investigate the characterization of the mechanical properties of composite solid propellant (CSP) based on hydroxyl-terminated polybutadiene (HTPB) at different temperatures and strain rates, uniaxial tensile tests were conducted over a range of temperatures -60 °C to +76 °C and strain rates 0.000164 to 0.328084 s^-1 using a conventional universal testing machine. From the experimental data, it can be noted that the mechanical properties of AP/HTPB propellant are mainly dependent on the applied strain rate and the temperature condition. The stress-strain responses exhibited an initial yielding followed by the viscoelastic phase, which was strongly affected by the strain rate and temperature. It was found that the mechanical properties increased with both increasing strain rate and decreasing temperature. Based on the experimental tests, the master curves of the tensile properties are drawn using predetermined shift factor and the results were discussed. This work is a first step in preliminary investigation the nonlinear viscoelasticity behavior of CSP.

Keywords: AP/HTPB composite solid propellant, mechanical behavior, nonlinear viscoelastic, tensile test, strain rate

Procedia PDF Downloads 231

Authors: A. Nuchitprasittichai, N. Lerdritsirikoon, T. Khamsing

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Simulation modeling can be used to solve real world problems. It provides an understanding of a complex system. To develop a simplified model of process simulation, a suitable experimental design is required to be able to capture surface characteristics. This paper presents the experimental design and algorithm used to model the process simulation for optimization problem. The CO₂ liquefaction based on external refrigeration with two refrigeration circuits was used as a simulation case study. Latin Hypercube Sampling (LHS) was purposed to combine with existing Central Composite Design (CCD) samples to improve the performance of CCD in generating the second order model of the system. The second order model was then used as the objective function of the optimization problem. The results showed that adding LHS samples to CCD samples can help capture surface curvature characteristics. Suitable number of LHS sample points should be considered in order to get an accurate nonlinear model with minimum number of simulation experiments.

Keywords: central composite design, CO2 liquefaction, latin hypercube sampling, simulation-based optimization

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Authors: O. G. Omogunloye, J. B. Olaleye, O. E. Abiodun, J. O. Odumosu, O. G. Ajayi

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The focus of the study is to proffer easy formulation and computation of least square observation equation’s design matrix by using an efficient book keeping strategy. Usually, for a large network of many triangles and stations, a rigorous task is involved in the computation and placement of the values of the differentials of each observation with respect to its station coordinates (latitude and longitude), in their respective rows and columns. The efficient book keeping strategy seeks to eliminate or reduce this rigorous task involved, especially in large network, by simple skillful arrangement and development of a short program written in the Matlab environment, the formulation and computation of least square observation equation’s design matrix can be easily achieved.

Keywords: design, differential, geodetic, matrix, network, station

Procedia PDF Downloads 356

Authors: G. De Matteis, L. Martina, V. Turco

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The work is focused on determining and comparing special nonlinear static configurations in cholesteric liquid crystals (CLCs), confined between two parallel plates and in the presence of an external static electric/magnetic field. The solutions are stabilised by topological and non-topological conservation laws since they are described in terms of integrable or partially integrable nonlinear boundary value problems. In cholesteric liquid crystals which are subject to geometric frustration; anchoring conditions at boundaries, i.e., homeotropic conditions, are incompatible with the cholesteric twist. This aspect turns out to be essential in the admissible classes of solutions, allowing also for disclination type singularities. Within the framework of Frank-Oseen theory, we study the static configurations for CLCs. First, we find numerical solutions for isolated axisymmetric states in confined CLCs with weak homeotropic anchoring at the boundaries. These solutions describe 3-dimensional modulations, namely spherulites or cholesteric bubbles, actually observed in these systems, of standard baby skyrmions. Relations with well-known nonlinear integrable systems are found and are used to explore the asymptotic behavior of the solutions. Then we turn our attention to extended periodic static configurations called Helicoids or cholesteric fingers, described by an elliptic sine-Gordon model with appropriate boundary conditions, showing how their period and energies are determined by both the thickness of the cell and the intensity of the external electric/magnetic field. We explicitly show that helicoids with π or 2π of rotations of the molecular director are different in many aspects and are not simply algebraically related. The behaviour of the solutions, their energy and the properties of the associated disclinations are discussed in detail, both analytically and numerically.

Keywords: cholesteric liquid crystals, geometric frustration, helicoids, skyrmions

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Authors: El Amine Nebbat

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A void is a dust-free region in dusty plasma, a medium formed of electrons, ions, and charged dust (grain). This structure appears in multiple experimental works. Several researchers have developed models to understand it. Recently, Nebbat and Annou proposed a nonlinear model that describes the void in non-viscos plasma, where the particles of the dusty plasma are treated as a fluid. In fact, the void appears even in dense dusty plasma where viscosity exists through the strong interaction between grains, so in this work, we augment the nonlinear model of Nebbat and Annou by introducing viscosity into the fluid equations. The analysis of the data of the numerical resolution confirms the important effect of this parameter (viscosity). The study revealed that the viscosity increases the dimension of the void for certain dimensions of the grains, and its effect on the value of the density of the grains at the boundary of the void is inversely proportional to their radii, i.e., this density increase for submicron grains and decrease for others. Finally, this parameter reduces the rings of dust density which surround the void.

Keywords: voids, dusty plasmas, variable charge, density, viscosity

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Authors: Y. T. Tsai, Jin H. Huang

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The sound pressure level (SPL) of the moving-coil loudspeaker (MCL) is often simulated and analyzed using the lumped parameter model. However, the SPL of a MCL cannot be simulated precisely in the high frequency region, because the value of cone effective area is changed due to the geometry variation in different mode shapes, it is also related to affect the acoustic radiation mass and resistance. Herein, the paper presents the inverse method which has a high ability to measure the value of cone effective area in various frequency points, also can estimate the MCL electroacoustic parameters simultaneously. The proposed inverse method comprises the direct problem, adjoint problem, and sensitivity problem in collaboration with nonlinear conjugate gradient method. Estimated values from the inverse method are validated experimentally which compared with the measured SPL curve result. Results presented in this paper not only improve the accuracy of lumped parameter model but also provide the valuable information on loudspeaker cone design.

Keywords: inverse problem, cone effective area, loudspeaker, nonlinear conjugate gradient method

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Authors: Ali Y Al-Attraqchi, P. Rajeev, M. Javad Hashemi, Riadh Al-Mahaidi

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This paper presents a probabilistic incremental dynamic analysis (IDA) of a full reinforced concrete building subjected to column loss scenario for the assessment of progressive collapse. The IDA is chosen to explicitly account for uncertainties in loads and system capacity. Fragility curves are developed to predict the probability of progressive collapse given the loss of one or more columns. At a broader scale, it will also provide critical information needed to support the development of a new generation of design codes that attempt to explicitly quantify structural robustness.

Keywords: fire, nonlinear incremental dynamic analysis, progressive collapse, structural engineering

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Authors: Charline David, Alexandre Blondin Massé, Arnaud Zinflou

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In 2016, Clements, Hurn, and Li proposed a multiple equation time series approach for the short-term load forecasting, reporting an average mean absolute percentage error (MAPE) of 1.36% on an 11-years dataset for the Queensland region in Australia. We present an adaptation of their model to the electrical power load consumption for the whole Quebec province in Canada. More precisely, we take into account two additional meteorological variables — cloudiness and wind speed — on top of temperature, as well as the use of multiple meteorological measurements taken at different locations on the territory. We also consider other minor improvements. Our final model shows an average MAPE score of 1:79% over an 8-years dataset.

Keywords: short-term load forecasting, special days, time series, multiple equations, parallelization, clustering

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Authors: Mohammadreza Salek Faramarzi, Touraj Taghikhany

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In this paper, seismic fragility assessment of a recently developed hybrid structural system, known as the strongback system (SBS) is investigated. In this system, to mitigate the occurrence of the soft-story mechanism and improve the distribution of story drifts over the height of the structure, an elastic vertical truss is formed. The strengthened members of the braced span are designed to remain substantially elastic during levels of excitation where soft-story mechanisms are likely to occur and impose a nearly uniform story drift distribution. Due to the distinctive characteristics of near-field ground motions, it seems to be necessary to study the effect of these records on seismic performance of the SBS. To this end, a set of 56 near-field ground motion records suggested by FEMA P695 methodology is used. For fragility assessment, nonlinear dynamic analyses are carried out in OpenSEES based on the recommended procedure in HAZUS technical manual. Four damage states including slight, moderate, extensive, and complete damage (collapse) are considered. To evaluate each damage state, inter-story drift ratio and floor acceleration are implemented as engineering demand parameters. Further, to extend the evaluation of the collapse state of the system, a different collapse criterion suggested in FEMA P695 is applied. It is concluded that SBS can significantly increase the collapse capacity and consequently decrease the collapse risk of the structure during its life time. Comparing the observing mean annual frequency (MAF) of exceedance of each damage state against the allowable values presented in performance-based design methods, it is found that using the elastic vertical truss, improves the structural response effectively.

Keywords: IDA, near-fault, probabilistic performance assessment, seismic fragility, strongback system, uncertainty

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Authors: Dalvinder Kaur Mangal

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For the past decade, noise corrupted output measurements have been a fundamental research problem to be investigated. On the other hand, the estimation of the parameters for linear dynamic systems when also the input is affected by noise is recognized as more difficult problem which only recently has received increasing attention. Representations where errors or measurement noises/disturbances are present on both the inputs and outputs are usually called errors-in-variables (EIV) models. These disturbances may also have additive effects which are also considered in this paper. Parameter estimation of false EIV problem using equation error, output error and iterative prefiltering identification schemes with and without additive uncertainty, when only the output observation is corrupted by noise has been dealt in this paper. The comparative study of these three schemes has also been carried out.

Keywords: errors-in-variable (EIV), false EIV, equation error, output error, iterative prefiltering, Gaussian noise

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Authors: Hyun-Woo Cho

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The real-time fault monitoring and diagnosis of large scale production processes is helpful and necessary in order to operate industrial process safely and efficiently producing good final product quality. Unusual and abnormal events of the process may have a serious impact on the process such as malfunctions or breakdowns. This work try to utilize process measurement data obtained in an on-line basis for the safe and some fault-free operation of industrial processes. To this end, this work evaluated the proposed intelligent process data monitoring framework based on a simulation process. The monitoring scheme extracts the fault pattern in the reduced space for the reliable data representation. Moreover, this work shows the results of using linear and nonlinear techniques for the monitoring purpose. It has shown that the nonlinear technique produced more reliable monitoring results and outperforms linear methods. The adoption of the qualitative monitoring model helps to reduce the sensitivity of the fault pattern to noise.

Keywords: process data, data mining, process operation, real-time monitoring

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Authors: Bavneet Kaur Sidhu, Manoj Tiwari

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Global Developmental Delay (GDD) is a common pediatric condition. Etiologies of GDD might, however, differ in developing countries. In the last decade, sporadic families are being reported in various countries. As to the author’s best knowledge, many risk factors and their correlation with the prevalence of GDD have been studied but its statistical correlation has not been done. Thus we propose the present study by targeting the risk factor, prevalence and their statistical correlation with GDD. FMR1 gene was studied to confirm the disease and its penetrance. A complete questionnaire-based performance was designed for the statistical studies having a personal, past and present medical history along with their socio-economic status as well. Methods: We distributed the children’s age in 4 different age groups having 5-year intervals and applied structural equation modeling (SEM) techniques, Spearman’s rank correlation coefficient, Karl Pearson correlation coefficient, and chi-square test.Result: A total of 1100 families were enrolled for this study; among them, 330 were clinically and biologically confirmed (radiological studies) for the disease, 204 were males (61.8%), 126 were females (38.18%). We found that 27.87% were genetic and 72.12 were sporadic, out of 72.12 %, 43.277% cases from urban and 56.72% from the rural locality, the mothers' literacy rate was 32.12% and working women numbers were 41.21%. Conclusions: There is a significant association between mothers' age and GDD prevalence, which is also followed by mothers' literacy rate and mothers' occupation, whereas there was no association between fathers' age and GDD.

Keywords: global developmental delay, FMR1 gene, spearman’ rank correlation coefficient, structural equation modeling

Procedia PDF Downloads 135

Authors: Mary Chriselda A

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This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: K. Yathish, K. G. Binu, B. S. Shenoy, D. S. Rao, R. Pai

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Load carrying capacity of an oil lubricated two-axial groove journal bearing is simulated by taking into account the viscosity variations in lubricant due to the addition of TiO2 nanoparticles as lubricant additive. Shear viscosities of TiO2 nanoparticle dispersions in oil are measured for various nanoparticle additive concentrations. The viscosity model derived from the experimental viscosities is employed in a modified Reynolds equation to obtain the pressure profiles and load carrying capacity of two-axial groove journal bearing. Results reveal an increase in load carrying capacity of bearings operating on nanoparticle dispersions as compared to plain oil

Keywords: journal bearing, TiO2 nanoparticles, viscosity model, Reynold's equation, load carrying capacity

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Authors: Byungmin Cho, Dongchul Lee, Taejin Kim, Minhee Lee

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The procedure for the seismic retrofit of existing buildings includes the seismic evaluation. In the evaluation step, it is assessed whether the buildings have satisfactory performance against seismic load. Based on the results of that, the buildings are upgraded. To evaluate seismic performance of the buildings, it usually goes through the model transformation from elastic analysis to inelastic analysis. However, when the data is not delivered through the interwork, engineers should manually input the data. In this process, since it leads to inaccuracy and loss of information, the results of the analysis become less accurate. Therefore, in this study, the process for the seismic evaluation of existing buildings using structural information modeling is suggested. This structural information modeling makes the work economic and accurate. To this end, it is determined which part of the process could be computerized through the investigation of the process for the seismic evaluation based on ASCE 41. The structural information modeling process is developed to apply to the seismic evaluation using Perform 3D program usually used for the nonlinear response history analysis. To validate this process, the seismic performance of an existing building is investigated.

Keywords: existing building, nonlinear analysis, seismic performance, structural information modeling

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Authors: R. I. Liban, N. Tayşi

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This paper deals with a nonlinear finite element analysis to examine the behavior up to failure of cantilever composite steel-concrete beams which are prestressed externally. 'Pre-' means stressing the high strength external tendons in the steel beam section before the concrete slab is added. The composite beam contains a concrete slab which is connected together with steel I-beam by means of perfect shear connectors between the concrete slab and the steel beam which is subjected to static loading. A finite element analysis will be done to study the effects of external prestressed tendons on the composite steel-concrete beams by locating the tendons in different locations (profiles). ANSYS version 12.1 computer program is being used to analyze the represented three-dimensional model of the cantilever composite beam. This model gives all these outputs, mainly load-displacement behavior of the cantilever end and in the middle span of the simple support part.

Keywords: composite steel-concrete beams, external prestressing, finite element analysis, ANSYS

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Authors: Muath Awadalla, Maen Awadallah

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Banking sector covers different activities including lending money to customers. However, it is commonly known that customers pay money they have borrowed including an added amount called interest. Compound interest rate is an approach used in determining the interest to be paid. The instant compounded amount to be paid by a debtor is obtained through a differential equation whose main parameters are the rate and the time. The rate used by banks in a country is often defined by the government of the said country. In Switzerland, for instance, a negative rate was once applied. In this work, a new approach of modeling the compound interest is proposed using Hadamard fractional derivative. As a result, it appears that depending on the fraction value used in derivative the amount to be paid by a debtor might either be higher or lesser than the amount determined using the classical approach.

Keywords: compound interest, fractional differential equation, hadamard fractional derivative, optimization

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Authors: Justin Nwabanne, Sam Omenyi, Jeremiah Chukwuneke

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This work presents structural nonlinear static analysis of a horizontal taut cable using Finite Element Analysis (FEA) method. The FEA was performed analytically to determine the tensions at each nodal point and subsequently, performed based on finite element displacement method computationally using the FEA software, ANSYS 14.0 to determine their behaviour under the influence of aerodynamic forces imposed on the cable. The convergence procedure is adapted into the method to prevent excessive displacements through the computations. The work compared the two FEA cases by examining the effectiveness of the analytical model in describing the response with few degrees of freedom and the ability of the nonlinear finite element procedure adopted to capture the complex features of cable dynamics with reference to the aerodynamic external influence. Results obtained from this work explain that the analytic FEM results without aerodynamic influence show a parabolic response with an optimum deflection at nodal points 12 and 13 with the cable weight at nodes 12 and 13 having the value -1.002936N while for the cable tension shows an optimum deflection value for nodes 12 and 13 at -189396.97kg/km. The maximum displacement for the cable system was obtained from ANSYS 14.0 as 4483.83 mm for X, Y and Z components of displacements at node number 2 while the maximum displacement obtained is 4218.75mm for all the directional components. The dynamic behaviour of a taut cable investigated has application in a typical power transmission line. Aerodynamic influences on the cables were considered using FEA approach by employing ANSYS 14.0 showed a complex modal behaviour as expected.

Keywords: aerodynamics, cable tension and weight, finite element analysis, nodal, non-linear model, optimum deflection, suspended cable, transmission line

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Authors: E. Dehghan, R. Dehghan

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Generally, the slender structural walls have flexural behavior. Since behavior of bending members can be explained by moment–curvature relation, therefore, an analytical model is proposed based on moment–curvature relation for slender structural walls. The moment–curvature relationships of RC sections are constructed through section analysis. Governing equations describing the bond-slip behavior in walls are derived and applied to moment–curvature relations. For the purpose of removing the imprecision in analytical results, the plastic hinge length is included in the finite element modeling. Finally, correlation studies between analytical and experimental results are conducted with the objective to establish the validity of the proposed algorithms. The results show that bond-slip effect is more significant in walls subjected to larger axial compression load. Moreover, preferable results are obtained when ultimate strain of concrete is assumed conservatively.

Keywords: nonlinear analysis, slender structural walls, moment-curvature relation, bond-slip, plastic hinge length

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Authors: Malki Fatima Zahra Nadia, Kellal Cheiimaa, Brahimi Houria

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Total Quality Management (TQM) is one of the most important modern management systems in marketing, that help organizations to survive and remain competitive in the dynamic market with frequent changes. It assists them in gaining a competitive advantage, growth, and excellence compared to their competitors. To understand the impact of TQM on competitive advantage in economic companies, a study was conducted in Ooredoo Telecommunications Company. A questionnaire was designed and distributed to OOredoo' 75 employees in each of the departments of leadership, quality assurance, quality control, research and development, production, customer service, Similarly, resulting in the retrieval of 72 questionnaires. To analyze the descriptive results of the study, the SPSS software version 25 was used. Additionally, Structural Equation Modeling (SEM) with the help of Smart Pls4 software was utilized to test the study's hypotheses. The study concluded that there is an impact between total quality management and competitive advantage in Ooredoo company to different degrees. On this basis, the study recommended the need to implement the total quality management system at the level of all organizations and in various fields.

Keywords: total quality management, ISO system, competitive advantage, competitive strategies

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Authors: M. Derayatifar, M. Packirisamy, R.B. Bhat

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Role of piezoelectric energy harvesters has gained interest in supplying power for micro devices such as health monitoring sensors. In this study, in order to enhance the piezoelectric energy harvesting in capturing energy from broader range of excitation and to improve the mechanical and electrical responses, bimorph piezoelectric energy harvester beam with magnetic mass attached at the end is presented. In view of overcoming the brittleness of piezo-ceramics, functionally graded piezoelectric layers comprising of both piezo-ceramic and piezo-polymer is employed. The nonlinear equations of motions are derived using energy method and then solved analytically using perturbation scheme. The frequency responses of the forced vibration case are obtained for the near resonance case. The nonlinear dynamic responses of the MEMS scaled functionally graded piezoelectric energy harvester in this paper may be utilized in different design scenarios to increase the efficiency of the harvester.

Keywords: energy harvesting, functionally graded piezoelectric material, magnetic force, MEMS (micro-electro-mechanical systems) piezoelectric, perturbation method

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Authors: Jan Henrik Wosnitza

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The logistic regression has developed into a standard approach for estimating conditional probabilities in a wide range of applications including credit risk prediction. The article at hand contributes to the current literature on logistic regression fourfold: First, it is demonstrated that the binary logistic regression automatically meets its model assumptions under very general conditions. This result explains, at least in part, the logistic regression's popularity. Second, the requirement of homoscedasticity in the context of binary logistic regression is theoretically substantiated. The variances among the groups of defaulted and non-defaulted obligors have to be the same across the level of the aggregated default indicators in order to achieve linear logits. Third, this article sheds some light on the question why nonlinear logits might be superior to linear logits in case of a small amount of data. Fourth, an innovative methodology for estimating correlations between obligor-specific log-odds is proposed. In order to crystallize the key ideas, this paper focuses on the example of credit risk prediction. However, the results presented in this paper can easily be transferred to any other field of application.

Keywords: correlation, credit risk estimation, default correlation, homoscedasticity, logistic regression, nonlinear logistic regression

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Authors: Nassim Bessaad, Qilian Bao, Zhao Jiangkang

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The fiber optics gyroscope in the strap-down inertial navigation system (FOG-SINS) suffers from precision degradation due to the influence of random errors. In this work, an enhanced Allan variance (AV) stochastic modeling method combined with discrete wavelet transform (DWT) for signal denoising is implemented to estimate the random process in the FOG signal. Furthermore, we devise a measurement-based iterative adaptive Sage-Husa nonlinear filter with augmented states to integrate a star tracker sensor with SINS. The proposed filter adapts the measurement noise covariance matrix based on the available data. Moreover, the enhanced stochastic modeling scheme is invested in tuning the process noise covariance matrix and the augmented state Gauss-Markov process parameters. Finally, the effectiveness of the proposed filter is investigated by employing the collected data in laboratory conditions. The result shows the filter's improved accuracy in comparison with the conventional Kalman filter (CKF).

Keywords: inertial navigation, adaptive filtering, star tracker, FOG

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Authors: Ibrahim Alsendid, Rob Sturman, Benjamin Sharp

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In this paper, we consider a family of 2-dimensional nonlinear area-preserving transformations on the torus. A single parameter η varies between 0 and 1, taking the transformation from a hyperbolic toral automorphism to the “Cerbelli-Giona” map, a system known to exhibit multifractal properties. Here we study the multifractal properties of the family of maps. We apply a box-counting method by defining a grid of boxes Bi(δ), where i is the index and δ is the size of the boxes, to quantify the distribution of stable and unstable manifolds of the map. When the parameter is in the range 0.51< η <0.58 and 0.68< η <1 the map is ergodic; i.e., the unstable and stable manifolds eventually cover the whole torus, although not in a uniform distribution. For accurate numerical results, we require correspondingly accurate construction of the stable and unstable manifolds. Here we use the piecewise linearity of the map to achieve this, by computing the endpoints of line segments that define the global stable and unstable manifolds. This allows the generalized fractal dimension Dq, and spectrum of dimensions f(α), to be computed with accuracy. Finally, the intersection of the unstable and stable manifold of the map will be investigated and compared with the distribution of periodic points of the system.

Keywords: Discrete-time dynamical systems, Fractal geometry, Multifractal behaviour of the Perturbed map, Multifractal of Dynamical systems

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Authors: Francys Souza, Alberto Ohashi, Dorival Leao

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We present a general solution for finding the ε-optimal controls for non-Markovian stochastic systems as stochastic differential equations driven by Brownian motion, which is a problem recognized as a difficult solution. The contribution appears in the development of mathematical tools to deal with modeling and control of non-Markovian systems, whose applicability in different areas is well known. The methodology used consists to discretize the problem through a random discretization. In this way, we transform an infinite dimensional problem in a finite dimensional, thereafter we use measurable selection arguments, to find a control on an explicit form for the discretized problem. Then, we prove the control found for the discretized problem is a ε-optimal control for the original problem. Our theory provides a concrete description of a rather general class, among the principals, we can highlight financial problems such as portfolio control, hedging, super-hedging, pairs-trading and others. Therefore, our main contribution is the development of a tool to explicitly the ε-optimal control for non-Markovian stochastic systems. The pathwise analysis was made through a random discretization jointly with measurable selection arguments, has provided us with a structure to transform an infinite dimensional problem into a finite dimensional. The theory is applied to stochastic control problems based on path-dependent stochastic differential equations, where both drift and diffusion components are controlled. We are able to explicitly show optimal control with our method.

Keywords: dynamic programming equation, optimal control, stochastic control, stochastic differential equation

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Authors: Seyed M. Khatami, H. Naderpour, R. Vahdani, R. C. Barros

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Many previous studies have been carried out to calculate the impact force and the dissipated energy between two neighboring buildings during seismic excitation, when they collide with each other. Numerical studies are an important part of impact, which several researchers have tried to simulate the impact by using different formulas. Estimation of the impact force and the dissipated energy depends significantly on some parameters of impact. Mass of bodies, stiffness of spring, coefficient of restitution, damping ratio of dashpot and impact velocity are some known and unknown parameters to simulate the impact and measure dissipated energy during collision. Collision is usually shown by force-displacement hysteresis curve. The enclosed area of the hysteresis loop explains the dissipated energy during impact. In this paper, the effect of using different types of impact models is investigated in order to calculate the impact force. To increase the accuracy of impact model and to optimize the results of simulations, a new damping equation is assumed and is validated to get the best results of impact force and dissipated energy, which can show the accuracy of suggested equation of motion in comparison with other formulas. This relation is called "n-m". Based on mathematical relation, an initial value is selected for the mentioned coefficients and kinetic energy loss is calculated. After each simulation, kinetic energy loss and energy dissipation are compared with each other. If they are equal, selected parameters are true and, if not, the constant of parameters are modified and a new analysis is performed. Finally, two unknown parameters are suggested to estimate the impact force and calculate the dissipated energy.

Keywords: impact force, dissipated energy, kinetic energy loss, damping relation

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Authors: Shiyun Liu

Abstract:

Radiant heating systems work fundamentally differently from air systems by taking advantage of both radiant and convective heat transfer to remove space heating load. There are rare studies on differences of heating systems between all-air system and radiant floor system. This paper uses the method of simulation based on state-space to calculate the indoor temperature and wall temperature of each system and shows how the dynamic heat transfer in rooms conditioned by a radiant system is different from an air system. Then this paper analyses the changes of indoor temperature of these two systems, finding out the differences between all-air heating system and radiant floor heating system to help the designer choose a more suitable heating system.

Keywords: radiant floor, all-air system, thermal comfort, simulation, heating system

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