Search results for: nonlinear statistical methods

Authors: Ardeshir Karami Mohammadi, Mohammadreza Saee

Abstract:

A variable structure model reference adaptive control (VS-MRAC) strategy for active steering assistance of a two wheel steering car is proposed. An ideal steering system with fixed properties and moving on an ideal road is used as the reference model, and the active steering assistance system is forced to attain the same behavior as the reference model. The proposed system can treat the nonlinear relationships between the side slip angles and lateral forces on tire, and the uncertainties on friction of the road surface, whose compensation are very important under critical situations. Simulation results show improvements on yaw rate and side slip.

Keywords: Variable Structure, Adaptive Control, Model reference, Active steering assistance.

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Authors: HoYoung Son, Ki Young Kim, Woo Young Jung

Abstract:

This study investigated the change of weir structure performances when durability of concrete, which is the main material of weir structure, decreased due to their aging by mean of seismic fragility analysis. In the analysis, it was assumed that the elastic modulus of concrete was reduced by 10% in order to account for their aged deterioration. Additionally, the analysis of seismic fragility was based on Monte Carlo Simulation method combined with a 2D nonlinear finite element in ABAQUS platform with the consideration of deterioration of concrete. Finally, the comparison of seismic fragility of model pre- and post-deterioration was made to study the performance of weir. Results show that the probability of failure in moderate damage for deteriorated model was found to be larger than pre-deterioration model when peak ground acceleration (PGA) passed 0.4 g.

Keywords: Weir, FEM, concrete, fragility, aging.

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Authors: Wang Zhanquan, Yang Zeping, Gu Chunhua, Zhu Fazhi, Guo Weibin

Abstract:

Recently, Massive Open Online Courses (MOOCs) are becoming the new trend of education. There are many problems under the environment of Database Principle curriculum teaching process in MOOCs, such as teaching ideas and theories which are out of touch with the reality, how to carry out the technical teaching and interactive practice in the MOOCs environment, thus the methods of database course under the environment of MOOCs are proposed. There are three processes to deal with problem solving in the research, which are problems proposed, problems solved, and inductive analysis. The present research includes the design of teaching contents, teaching methods in classroom, flipped classroom teaching mode under the environment of MOOCs, learning flow method and large practice homework. The database designing ability is systematically improved based on the researching methods.

Keywords: Problem solving-driven, MOOCs, teaching art, learning flow.

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Authors: Rao Fu, Jie Chen, Shutian Zeng, Yiping Zhuang, Agus Sudjianto

Abstract:

Generative Adversarial Net (GAN) has proved to be a powerful machine learning tool in image data analysis and generation. In this paper, we propose to use Conditional Generative Adversarial Net (CGAN) to learn and simulate time series data. The conditions include both categorical and continuous variables with different auxiliary information. Our simulation studies show that CGAN has the capability to learn different types of normal and heavy-tailed distributions, as well as dependent structures of different time series. It also has the capability to generate conditional predictive distributions consistent with training data distributions. We also provide an in-depth discussion on the rationale behind GAN and the neural networks as hierarchical splines to establish a clear connection with existing statistical methods of distribution generation. In practice, CGAN has a wide range of applications in market risk and counterparty risk analysis: it can be applied to learn historical data and generate scenarios for the calculation of Value-at-Risk (VaR) and Expected Shortfall (ES), and it can also predict the movement of the market risk factors. We present a real data analysis including a backtesting to demonstrate that CGAN can outperform Historical Simulation (HS), a popular method in market risk analysis to calculate VaR. CGAN can also be applied in economic time series modeling and forecasting. In this regard, we have included an example of hypothetical shock analysis for economic models and the generation of potential CCAR scenarios by CGAN at the end of the paper.

Keywords: Conditional Generative Adversarial Net, market and credit risk management, neural network, time series.

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Authors: R. Blicha

Abstract:

High Peak to Average Power Ratio (PAPR) of the transmitted signal is a serious problem in multicarrier systems (MC), such as Orthogonal Frequency Division Multiplexing (OFDM), or in Multi-Carrier Code Division Multiple Access (MC-CDMA) systems, due to large number of subcarriers. This effect is possible reduce with some PAPR reduction techniques. Spreading sequences at the presence of Saleh and Rapp models of high power amplifier (HPA) have big influence on the behavior of system. In this paper we investigate the bit-error-rate (BER) performance of MC-CDMA systems. Basically we can see from simulations that the MC-CDMA system with Iterative algorithm can be providing significantly better results than the MC-CDMA system. The results of our analyses are verified via simulation.

Keywords: MC-CDMA, Iterative algorithm, PAPR, BER, Saleh, Rapp, Spreading Sequences.

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Authors: V.V. Lyahov, V.M. Neshchadim

Abstract:

The structural stability of the model of a nonelectroneutral current sheath is investigated. The stationary model of a current sheath represents the system of four connected nonlinear differential first-order equations and thus they should manifest structural instability property, i.e. sensitivity to the infinitesimal changes of parameters and starting conditions. Domains of existence of the solutions of current sheath type are found. Those solutions of the current sheath type are realized only in some regions of sevendimensional space of parameters of the problem. The phase volume of those regions is small in comparison with the whole phase volume of the definition range of those parameters. It is shown that the offered model of a nonelectroneutral current sheath is applicable for theoretical interpretation of the bifurcational current sheaths observed in the magnetosphere.

Keywords: Distribution function, electromagnetic field, magnetoactive plasma, nonelectroneutral current sheath, structural instability, bifurcational current sheath.

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Authors: Yun Jong Choi, Nam Woong, PooGyeon Park

Abstract:

Variable Structure Control (VSC) is one of the most useful tools handling the practical system with uncertainties and disturbances. Up to now, unfortunately, not enough studies on the input-saturated system with linear-growth-bound disturbances via VSC have been presented. Therefore, this paper proposes an asymp¬totic stability condition for the system via VSC. The designed VSC controller consists of two control parts. The linear control part plays a role in stabilizing the system, and simultaneously, the nonlinear control part in rejecting the linear-growth-bound disturbances perfectly. All conditions derived in this paper are expressed with Linear Matrices Inequalities (LMIs), which can be easily solved with an LMI toolbox in MATLAB.

Keywords: Input saturation, linear-growth bounded disturbances, linear matrix inequality (LMI), variable structure control

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Authors: A.H. Akhaveissy

Abstract:

Nonlinear finite element method and Serendipity eight nodes element are used for determining of ground surface settlement due to tunneling. Linear element with elastic behavior is used for modeling of lining. Modified Generalized plasticity model with nonassociated flow rule is applied for analysis of a tunnel in Sao Paulo – Brazil. The tunnel had analyzed by Lades- model with 16 parameters. In this work modified Generalized Plasticity is used with 10 parameters, also Mohr-Coulomb model is used to analysis the tunnel. The results show good agreement with observed results of field data by modified Generalized Plasticity model than other models. The obtained result by Mohr-Coulomb model shows less settlement than other model due to excavation.

Keywords: Non-associated flow rule, Generalized plasticity, tunnel excavation, Excavation method.

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Authors: Kongsheng Zhang, Li Ge

Abstract:

It is a one-sided hypothesis testing process for assessing bioequivalence. Bootstrap and modified large-sample(MLS) methods are considered to study individual bioequivalence(IBE), type I error and power of hypothesis tests are simulated and compared with FDA(2001). The results show that modified large-sample method is equivalent to the method of FDA(2001) .

Keywords: Individual bioequivalence, bootstrap, Bayesian bootstrap, modified large-sample.

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Authors: Layla Mujahed, Gang Feng, Jianghua Wang

Abstract:

An increasing number of construction projects are adopting off-site construction techniques over traditional methods to address longstanding challenges. This research paper explores the integration of design for manufacture and assembly (DfMA), modern methods of construction (MMC), and building information modeling (BIM) within the construction industry. This study employs a mixed-methods approach, using case studies and a review of the existing literature, to examine the role and combined application of each methodology in building projects of varying scales and durations. The study focuses on application mechanisms, stakeholder engagement, knowledge sharing, feedback, and performance metrics to explore the benefits, challenges, and transformative potential of integrating these methodologies. The findings indicate that the synergy among DfMA, MMC, and BIM significantly improves project efficiency, cost reduction, and overall quality. Standardization, increased collaboration among stakeholders, and the adoption of advanced technologies are also highlighted as necessary considerations to fully realize the benefits of this integration. The paper concludes with practical recommendations for industry practitioners seeking to efficiently implement these integrated approaches.

Keywords: BIM, building information modeling, case study, DfMA, design for manufacture and assembly, MMC, modern methods of construction, prefabrication.

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Authors: Olga V. Kharchenko

Abstract:

Applicability of a KTA crystal-based laser system with optical parametric oscillators (OPO) generation to lidar sounding of the atmosphere in the spectral range 3–4 µm is studied in this work. A technique based on differential absorption lidar (DIAL) method and differential optical absorption spectroscopy (DOAS) is developed for lidar sounding of trace atmospheric gases (TAG). The DIAL-DOAS technique is tested to estimate its efficiency for lidar sounding of atmospheric trace gases.

Keywords: Atmosphere, lidar sounding, DIAL, DOAS, trace gases, nonlinear crystal.

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Authors: A. Amirov, O. Gerget, V. Kochegurov

Abstract:

One of the main biomedical problem lies in detecting dependencies in semi structured data. Solution includes biomedical portal and algorithms (integral rating health criteria, multidimensional data visualization methods). Biomedical portal allows to process diagnostic and research data in parallel mode using Microsoft System Center 2012, Windows HPC Server cloud technologies. Service does not allow user to see internal calculations instead it provides practical interface. When data is sent for processing user may track status of task and will achieve results as soon as computation is completed. Service includes own algorithms and allows diagnosing and predicating medical cases. Approved methods are based on complex system entropy methods, algorithms for determining the energy patterns of development and trajectory models of biological systems and logical–probabilistic approach with the blurring of images.

Keywords: Biomedical portal, cloud computing, diagnostic and prognostic research, mathematical data analysis.

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Authors: Shiuh-Jer Huang, Shin-Ham Lee, Sheam-Chyun Lin

Abstract:

A two wheel inverted pendulum (TWIP) vehicle is built with two hub DC motors for motion control evaluation. Arduino Nano micro-processor is chosen as the control kernel for this electric test plant. Accelerometer and gyroscope sensors are built in to measure the tilt angle and angular velocity of the inverted pendulum vehicle. Since the TWIP has significantly hub motor dead zone and nonlinear system dynamics characteristics, the vehicle system is difficult to control by traditional model based controller. The intelligent model-free fuzzy sliding mode controller (FSMC) was employed as the main control algorithm. Then, intelligent controllers are designed for TWIP balance control, and two wheels synchronization control purposes.

Keywords: Balance control, synchronization control, two wheel inverted pendulum, TWIP.

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Authors: Woo-Young Jung, Minho Kwon

Abstract:

Seismic design criteria based on performance of structures have recently been adopted by practicing engineers in response to destructive earthquakes. A simple but efficient structural-analysis tool capable of predicting both the strength and ductility is needed to analyze reinforced concrete (RC) structures under such event. A three-dimensional lattice model is developed in this study to analyze torsions in high-strength RC members. Optimization techniques for determining optimal variables in each lattice model are introduced. Pure torsion tests of RC members are performed to validate the proposed model. Correlation studies between the numerical and experimental results confirm that the proposed model is well capable of representing salient features of the experimental results.

Keywords: Torsion, non-linear analysis, three-dimensional lattice, high-strength concrete.

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Authors: M. Govindarajan

Abstract:

One of the major developments in machine learning in the past decade is the ensemble method, which finds highly accurate classifier by combining many moderately accurate component classifiers. In this research work, new ensemble classification methods are proposed with homogeneous ensemble classifier using bagging and heterogeneous ensemble classifier using arcing and their performances are analyzed in terms of accuracy. A Classifier ensemble is designed using Radial Basis Function (RBF) and Support Vector Machine (SVM) as base classifiers. The feasibility and the benefits of the proposed approaches are demonstrated by the means of standard datasets of intrusion detection. The main originality of the proposed approach is based on three main parts: preprocessing phase, classification phase, and combining phase. A wide range of comparative experiments is conducted for standard datasets of intrusion detection. The performance of the proposed homogeneous and heterogeneous ensemble classifiers are compared to the performance of other standard homogeneous and heterogeneous ensemble methods. The standard homogeneous ensemble methods include Error correcting output codes, Dagging and heterogeneous ensemble methods include majority voting, stacking. The proposed ensemble methods provide significant improvement of accuracy compared to individual classifiers and the proposed bagged RBF and SVM performs significantly better than ECOC and Dagging and the proposed hybrid RBF-SVM performs significantly better than voting and stacking. Also heterogeneous models exhibit better results than homogeneous models for standard datasets of intrusion detection. 

Keywords: Data mining, ensemble, radial basis function, support vector machine, accuracy.

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Authors: Young-Seok Choi

Abstract:

We present a refined multiscale Shannon entropy for analyzing electroencephalogram (EEG), which reflects the underlying dynamics of EEG over multiple scales. The rationale behind this method is that neurological signals such as EEG possess distinct dynamics over different spectral modes. To deal with the nonlinear and nonstationary nature of EEG, the recently developed empirical mode decomposition (EMD) is incorporated, allowing a decomposition of EEG into its inherent spectral components, referred to as intrinsic mode functions (IMFs). By calculating the Shannon entropy of IMFs in a time-dependent manner and summing them over adaptive multiple scales, it results in an adaptive subscale entropy measure of EEG. Simulation and experimental results show that the proposed entropy properly reveals the dynamical changes over multiple scales.

Keywords: EEG, subscale entropy, Empirical mode decomposition, Intrinsic mode function.

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Authors: Kaan T. Oner, Ertugrul Cetinsoy, Efe Sirimoglu, Cevdet Hancer, Taylan Ayken, Mustafa Unel

Abstract:

We present our ongoing work on the development of a new quadrotor aerial vehicle which has a tilt-wing mechanism. The vehicle is capable of take-off/landing in vertical flight mode (VTOL) and flying over long distances in horizontal flight mode. Full dynamic model of the vehicle is derived using Newton-Euler formulation. Linear and nonlinear controllers for the stabilization of attitude of the vehicle and control of its altitude have been designed and implemented via simulations. In particular, an LQR controller has been shown to be quite effective in the vertical flight mode for all possible yaw angles. A sliding mode controller (SMC) with recursive nature has also been proposed to stabilize the vehicle-s attitude and altitude. Simulation results show that proposed controllers provide satisfactory performance in achieving desired maneuvers.

Keywords: UAV, VTOL, dynamic model, stabilization, LQR, SMC

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Authors: Mahdi Fakoor, Seyed Mohammad Navid Ghoreishi

Abstract:

Investigation of fracture of wood components can prevent from catastrophic failures. Created fracture process zone (FPZ) in crack tip vicinity has important effect on failure of cracked composite materials. In this paper, a failure criterion for fracture investigation of cracked wood specimens under mixed mode I/II loading is presented. This criterion is based on maximum strain energy release rate and material nonlinearity in the vicinity of crack tip due to presence of microcracks. Verification of results with available experimental data proves the coincidence of the proposed criterion with the nature of fracture of wood. To simplify the estimation of nonlinear properties of FPZ, a damage factor is also introduced for engineering and application purposes.

Keywords: Fracture criterion, mixed mode loading, damage zone, microcracks.

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Authors: An-Jui. Li, Kelvin Lim, Chien-Kuo Chiu, Benson Hsiung

Abstract:

This paper details the utilization of artificial intelligence (AI) in the field of slope stability whereby quick and convenient solutions can be obtained using the developed tool. The AI tool used in this study is the artificial neural network (ANN), while the slope stability analysis methods are the finite element limit analysis methods. The developed tool allows for the prompt prediction of the safety factors of fill slopes and their corresponding probability of failure (depending on the degree of variation of the soil parameters), which can give the practicing engineer a reasonable basis in their decision making. In fact, the successful use of the Extreme Learning Machine (ELM) algorithm shows that slope stability analysis is no longer confined to the conventional methods of modeling, which at times may be tedious and repetitive during the preliminary design stage where the focus is more on cost saving options rather than detailed design. Therefore, similar ANN-based tools can be further developed to assist engineers in this aspect.

Keywords: Landslide, limit analysis, ANN, soil properties.

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Authors: Ashiq Rahman, Sunil Thapa, Shunyao Fan, Niloy K. Dutta

Abstract:

A 20-GHz and a 50-GHz pulse train are generated using a fiber ring laser setup that incorporates rational harmonic mode-locking (RHML). Two separate experiments were carried out using charcoal nanoparticles and graphene nanoparticles acting as saturable absorbers to reduce the pulse width generated from RHML. Autocorrelator trace shows that the pulse width is reduced from 5.6 ps to 3.2 ps using charcoal at 20 GHz, and to 2.7 ps using graphene at 50-GHz repetition rates, which agrees with the simulation findings. Numerical simulations have been carried out to study the effect of varying the linear and nonlinear absorbance parameters of both absorbers on output pulse widths. Experiments closely agree with the simulations.

Keywords: Fiber optics, fiber lasers, mode locking, saturable absorbers.

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Authors: Salsabeel F. M. Alfalah, Jannat F. Falah, Nadia Muhaidat, Amjad Hudaib, Diana Koshebye, Sawsan AlHourani

Abstract:

Educational technology is changing the way how students engage and interact with learning materials. This improved the learning process amongst various subjects. Virtual Reality (VR) applications are considered one of the evolving methods that have contributed to enhancing medical education. This paper utilizes VR to provide a solution to improve the delivery of the subject of Embryology to medical students, and facilitate the teaching process by providing a useful aid to lecturers, whilst proving the effectiveness of this new technology in this particular area. After evaluating the current teaching methods and identifying students ‘needs, a VR system was designed that demonstrates in an interactive fashion the development of the human embryo from fertilization to week ten of intrauterine development. This system aims to overcome some of the problems faced by the students’ in the current educational methods, and to increase the efficacy of the learning process.

Keywords: Virtual reality, student assessment, medical education, 3D, embryology.

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Authors: B. Farhadinia

Abstract:

Although so far, many methods for ranking fuzzy numbers have been discussed broadly, most of them contained some shortcomings, such as requirement of complicated calculations, inconsistency with human intuition and indiscrimination. The motivation of this study is to develop a model for ranking fuzzy numbers based on the lexicographical ordering which provides decision-makers with a simple and efficient algorithm to generate an ordering founded on a precedence. The main emphasis here is put on the ease of use and reliability. The effectiveness of the proposed method is finally demonstrated by including a comprehensive comparing different ranking methods with the present one.

Keywords: Ranking fuzzy numbers, Lexicographical ordering.

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Authors: Shun-Qi Zhang, Shu-Yang Zhang, Min Chen

Abstract:

Applying strong electric field on piezoelectric actuators, on one hand very significant electroelastic material nonlinear effects will occur, on the other hand piezo plates and shells may undergo large displacements and rotations. In order to give a precise prediction of piezolaminated smart structures under large electric field, this paper develops a finite element (FE) model accounting for both electroelastic material nonlinearity and geometric nonlinearity with large rotations based on the first order shear deformation (FSOD) hypothesis. The proposed FE model is applied to analyze a piezolaminated semicircular shell structure.

Keywords: Smart structures, piezolamintes, material nonlinearity, geometric nonlinearity, strong electric field.

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Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new method for solving the matrix equation AXB=F . The new method can be considered as a generalized form of the well-known global full orthogonalization method (Gl-FOM) for solving multiple linear systems. Hence, the method will be called extended Gl-FOM (EGl- FOM). For implementing EGl-FOM, generalized forms of block Krylov subspace and global Arnoldi process are presented. Finally, some numerical experiments are given to illustrate the efficiency of our new method.

Keywords: Matrix equations, Iterative methods, Block Krylovsubspace methods.

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Authors: Turan Çalban, Oral Laçin, Abdüsselam Kurtbas

Abstract:

Experimental production methods of Chevreul’s salt being an intermediate stage product in copper recovery were investigated on this article. Chevreul’s salt, Cu2SO3.CuSO3.2H2O, being a mixed valence copper sulphite compound, has been obtained by using different methods and reagents. Chevreul’s salt has an intense brick-red color. It is highly stable and expensive. The production of Chevreul’s salt plays a key role in hydrometallurgy. Thermodynamic tendency on precipitation of Chevreul’s salt is related to pH and temperature. Besides, SO2 gaseous is a versatile reagent for precipitating of copper sulphites, Using of SO2 for selective precipitation can be made by appropriate adjustments of pH and temperature. Chevreul’s salt does not form in acidic solutions if those solutions contains considerable amount of sulfurous acid. It is necessary to maintain between pH 2–4.5, because, solubility of Chevreul’s salt increases with decreasing of pH values. Also, the region which Chevreul’s salt is stable can be seen from the potentialpH diagram.

Keywords: Chevreul’s salt, copper recovery, copper sulphite, stage product.

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Authors: Aref Ghafouri, Mohammad Javad Mollakazemi, Farhad Asadi

Abstract:

In this paper, model order reduction method is used for approximation in linear and nonlinearity aspects in some experimental data. This method can be used for obtaining offline reduced model for approximation of experimental data and can produce and follow the data and order of system and also it can match to experimental data in some frequency ratios. In this study, the method is compared in different experimental data and influence of choosing of order of the model reduction for obtaining the best and sufficient matching condition for following the data is investigated in format of imaginary and reality part of the frequency response curve and finally the effect and important parameter of number of order reduction in nonlinear experimental data is explained further.

Keywords: Frequency response, Order of model reduction, frequency matching condition.

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Authors: Dariush Jafari, Seyed Ali Jafari

Abstract:

The recommended limit for cadmium concentration in potable water is less than 0.005 mg/L. A continuous biosorption process using indigenous red seaweed, Gracilaria corticata, was performed to remove cadmium from the potable water. The process was conducted under fixed conditions and the breakthrough curves were achieved for three consecutive sorption-desorption cycles. A modeling based on Artificial Neural Network (ANN) was employed to fit the experimental breakthrough data. In addition, a simplified semi empirical model, Thomas, was employed for this purpose. It was found that ANN well described the experimental data (R2>0.99) while the Thomas prediction were a bit less successful with R2>0.97. The adjusted design parameters using the nonlinear form of Thomas model was in a good agreement with the experimentally obtained ones. The results approve the capability of ANN to predict the cadmium concentration in potable water.

Keywords: ANN, biosorption, cadmium, packed-bed, potable water.

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Authors: Tomohiro Hachino, Kengo Nagatomo, Hitoshi Takata

Abstract:

This paper deals with an on-line identification method of continuous-time Hammerstein systems by using the radial basis function (RBF) networks and immune algorithm (IA). An unknown nonlinear static part to be estimated is approximately represented by the RBF network. The IA is efficiently combined with the recursive least-squares (RLS) method. The objective function for the identification is regarded as the antigen. The candidates of the RBF parameters such as the centers and widths are coded into binary bit strings as the antibodies and searched by the IA. On the other hand, the candidates of both the weighting parameters of the RBF network and the system parameters of the linear dynamic part are updated by the RLS method. Simulation results are shown to illustrate the proposed method.

Keywords: Continuous-time System, Hammerstein System, OnlineIdentification, Immune Algorithm, RBF network.

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Authors: A.O. Boudraa, J.C. Cexus, Z. Saidi

Abstract:

This paper introduces a new signal denoising based on the Empirical mode decomposition (EMD) framework. The method is a fully data driven approach. Noisy signal is decomposed adaptively into oscillatory components called Intrinsic mode functions (IMFs) by means of a process called sifting. The EMD denoising involves filtering or thresholding each IMF and reconstructs the estimated signal using the processed IMFs. The EMD can be combined with a filtering approach or with nonlinear transformation. In this work the Savitzky-Golay filter and shoftthresholding are investigated. For thresholding, IMF samples are shrinked or scaled below a threshold value. The standard deviation of the noise is estimated for every IMF. The threshold is derived for the Gaussian white noise. The method is tested on simulated and real data and compared with averaging, median and wavelet approaches.

Keywords: Empirical mode decomposition, Signal denoisingnonstationary process.

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Authors: Guang Zou, Kian Banisoleiman, Arturo González

Abstract:

Crack initiation and propagation threatens structural integrity of welded joints and normally inspections are assigned based on crack propagation models. However, the approach based on crack propagation models may not be applicable for some high-quality welded joints, because the initial flaws in them may be so small that it may take long time for the flaws to develop into a detectable size. This raises a concern regarding the inspection planning of high-quality welded joins, as there is no generally acceptable approach for modeling the whole fatigue process that includes the crack initiation period. In order to address the issue, this paper reviews treatment methods for crack initiation period and initial crack size in crack propagation models applied to inspection planning. Generally, there are four approaches, by: 1) Neglecting the crack initiation period and fitting a probabilistic distribution for initial crack size based on statistical data; 2) Extrapolating the crack propagation stage to a very small fictitious initial crack size, so that the whole fatigue process can be modeled by crack propagation models; 3) Assuming a fixed detectable initial crack size and fitting a probabilistic distribution for crack initiation time based on specimen tests; and, 4) Modeling the crack initiation and propagation stage separately using small crack growth theories and Paris law or similar models. The conclusion is that in view of trade-off between accuracy and computation efforts, calibration of a small fictitious initial crack size to S-N curves is the most efficient approach.

Keywords: Crack initiation, fatigue reliability, inspection planning, welded joints.

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