Search results for: inverse proportional body

Authors: K. Kiniwa, S. Kitagawa, M. Kawamoto, H. Uchiyama

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This study aims to identify phenomenologically the embodiment of soccer in order to analyze soccer games. In this paper the authors focused on the embodiment of sports and the embodiment of the goal type ball games of team sports. The authors revealed that the embodiment of sports is represented by inverse proportional body. It is possible for this structure (body scheme) of intercorporeality of sports to be compared to the symbolic figure of Uroboros which is a monster connected the tails of two snakes. The embodiment of the goal type ball games of team sports has dependency on situation and complexity. In doing this, it revealed that soccer is sensitive and emotional sports.

Keywords: intercorporeality, structure, body scheme, Uroboros, inverse proportional body, dependency on situation, complexity

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Authors: Liang Liu, Xiaopeng Luo

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In this paper, we propose an accelerated stochastic gradient method with momentum. The momentum term is the weighted average of generated gradients, and the weights decay inverse proportionally with the iteration times. Stochastic gradient descent with momentum (SGDM) uses weights that decay exponentially with the iteration times to generate the momentum term. Using exponential decay weights, variants of SGDM with inexplicable and complicated formats have been proposed to achieve better performance. However, the momentum update rules of our method are as simple as that of SGDM. We provide theoretical convergence analyses, which show both the exponential decay weights and our inverse proportional decay weights can limit the variance of the parameter moving directly to a region. Experimental results show that our method works well with many practical problems and outperforms SGDM.

Keywords: exponential decay rate weight, gradient descent, inverse proportional decay rate weight, momentum

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Authors: Adel Mohsen

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A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner.

Keywords: Broyden's updates, matrix inverse, inverse factorization, solution of linear algebraic equations, ill-conditioned matrices, preconditioning

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Authors: Bolatbek Rysbaiuly, Aliya S. Azhibekova

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Problems concerning the interpretation of the well testing results belong to the class of inverse problems of subsurface hydromechanics. The distinctive feature of such problems is that additional information is depending on the capabilities of oilfield experiments. Another factor that should not be overlooked is the existence of errors in the test data. To determine reservoir properties, some inverse problems for parabolic equations were investigated. An approach to solving the inverse problems based on the method of regularization is proposed.

Keywords: iterative approach, inverse problem, parabolic equation, reservoir properties

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Authors: Nafiseh Ebrahimi, Amir Jafari

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The study of humanoid character is of great interest to researchers in the field of robotics and biomechanics. One might want to know the forces and torques required to move a limb from an initial position to the desired destination position. Inverse dynamics is a helpful method to compute the force and torques for an articulated body limb. It enables us to know the joint torques required to rotate a link between two positions. Our goal in this study was to control a human-like articulated manipulator for a specific task of path tracking. For this purpose, the human arm was modeled with a three-link planar manipulator activated by Hill muscle model. Applying a proportional controller, values of force and torques applied to the joints were calculated by inverse dynamics, and then joints and muscle forces trajectories were computed and presented. To be more accurate to say, the kinematics of the muscle-joint space was formulated by which we defined the relationship between the muscle lengths and the geometry of the links and joints. Secondary, the kinematic of the links was introduced to calculate the position of the end-effector in terms of geometry. Then, we considered the modeling of Hill muscle dynamics, and after calculation of joint torques, finally, we applied them to the dynamics of the three-link manipulator obtained from the inverse dynamics to calculate the joint states, find and control the location of manipulator’s end-effector. The results show that the human arm model was successfully controlled to take the designated path of an ellipse precisely.

Keywords: arm manipulator, hill muscle model, six-muscle model, three-link lodel

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Authors: Faisal Yousafzai, Murad-ul-Islam Khan, Kar Ping Shum

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We introduce the concept of partially inverse AG**-groupoids which is almost parallel to the concepts of E-inversive semigroups and E-inversive E-semigroups. Some characterization problems are provided on partially inverse AG**-groupoids. We give necessary and sufficient conditions for a partially inverse AG**-subgroupoid E to be a rectangular band. Furthermore, we determine the unitary congruence η on a partially inverse AG**-groupoid and show that each partially inverse AG**-groupoid possesses an idempotent separating congruence μ. We also study anti-separative commutative image of a locally associative AG**-groupoid. Finally, we give the concept of completely N-inverse AG**-groupoid and characterize a maximum idempotent separating congruence.

Keywords: AG**-groupoids, congruences, inverses, rectangular band

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Authors: Yu Menshikov

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In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solution are analyzed. Several methods for remove the influence of uncontrollable inaccuracy have been suggested.

Keywords: inverse problems, filtration, uncontrollable inaccuracy

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Authors: Renata Masarova, Bohuslava Juhasova, Martin Juhas, Zuzana Sutova

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In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: dynamic system, transfer matrix, inverse matrix, modeling

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Authors: Abdon Choque-Rivero

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The Jacobi system with the Dirichlet boundary condition is considered on a half-line lattice when the coefficients are real valued. The inverse problem of recovery of the coefficients from various data sets containing the so-called transmission eigenvalues is analyzed. The Marchenko method is utilized to solve the corresponding inverse problem.

Keywords: inverse scattering, discrete system, transmission eigenvalues, Marchenko method

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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Authors: Fabrizio Iezzi, Claudio Valente

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The viscous damping in dynamic systems can be proportional or non-proportional. In the first case, the mode shapes are real whereas in the second case they are complex. From an engineering point of view, the complexity of the mode shapes is important in order to quantify the non-proportional damping. Different indices exist to provide estimates of the modal complexity. These indices are or not zero, depending whether the mode shapes are not or are complex. The modal density problem arises in the experimental identification when the dynamic systems have close modal frequencies. Depending on the entity of this closeness, the mode shapes can hold fictitious imaginary quantities that affect the values of the modal complexity indices. The results are the failing in the identification of the real or complex mode shapes and then of the proportional or non-proportional damping. The paper aims to show the influence of the modal density on the values of these indices in case of both proportional and non-proportional damping. Theoretical and pseudo-experimental solutions are compared to analyze the problem according to an appropriate mechanical system.

Keywords: complex mode shapes, dynamic systems identification, modal density, non-proportional damping

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Authors: Mohamed Hafid, Marcel Lacroix

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This study presents a simple inverse heat transfer procedure for predicting the wall erosion and the time-varying thickness of the protective bank that covers the inside surface of the refractory brick wall of a melting furnace. The direct problem is solved by using the Finite-Volume model. The melting/solidification process is modeled using the enthalpy method. The inverse procedure rests on the Levenberg-Marquardt method combined with the Broyden method. The effect of the location of the temperature sensors and of the measurement noise on the inverse predictions is investigated. Recommendations are made concerning the location of the temperature sensor.

Keywords: melting furnace, inverse heat transfer, enthalpy method, levenberg–marquardt method

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Authors: Fouad Inel, Lakhdar Khochemane

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This article presents a comparative response specification performance between two controllers of three and four cable based robots for various applications. The main objective of this work is: the first is to use the direct and inverse geometric model to study and simulate the end effector position of the robot with three and four cables. A graphical user interface has been implemented in order to visualizing the position of the robot. Secondly, we present the determination of static and dynamic tensions and lengths of cables required to flow different trajectories. At the end, we study the response of our systems in closed loop with a Proportional-IntegratedDerivative (PID) and Proportional-Integrated (PD) controllers then this last are compared the results of the same examples using MATLAB/Simulink; we found that the PID method gives the better performance, such as rapidly speed response, settling time, compared to PD controller.

Keywords: dynamic modeling, geometric modeling, graphical user interface, open loop, parallel cable-based robots, PID/PD controllers

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Authors: S. M. Golgoun, S. M. Taheri

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Investigation of radioactive contamination of personnel working in radiation centers to identify radioactive materials and then measure the potential contamination and eliminate it has always been considered. For this purpose, various ways have been proposed so far and different devices have been designed and built. Gas sealed proportional counter has special working conditions. In this research, a gas sealed detector of proportional counter type was made and then its various parameters were investigated. Some parameters are influential on their working conditions and one of these most important parameters is the internal pressure of the proportional gas-filled detector. In this experimental research, we produced software for examination and altering high voltage, registering data, and calculating efficiency. By this, we investigated different gas pressure effects on detector efficiency and proposed optimizing working conditions of this detector. After reviewing the results, we suggested a range between 20-30 mbar pressure for this gas sealed detector.

Keywords: gas sealed, proportional detector, pressure, counter

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Authors: Fouad. Inel, Lakhdar. Khochemane

Abstract:

This article presents a comparative response specification performance between two controllers of three and four cable based robots for various applications. The main objective of this work is: The first is to use the direct and inverse geometric model to study and simulate the end effector position of the robot with three and four cables. A graphical user interface has been implemented in order to visualizing the position of the robot. Secondly, we present the determination of static and dynamic tensions and lengths of cables required to flow different trajectories. At the end, we study the response of our systems in closed loop with a Proportional-Integrated Derivative (PID) and Proportional-Integrated (PD) controllers then this last are compared the results of the same examples using MATLAB/Simulink; we found that the PID method gives the better performance, such as rapidly speed response, settling time, compared to PD controller.

Keywords: parallel cable-based robots, geometric modeling, dynamic modeling, graphical user interface, open loop, PID/PD controllers

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Authors: Sharon-Yasotha Veerayah-Mcgregor, Valipuram Manoranjan

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A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient.

Keywords: inverse/backward equation, operator-splitting, Nagumo equation, ill-posed, finite-difference

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Authors: Ahmad Moussavi

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In this paper, we are concerned with the Jacobson semisimple skew inverse Laurent series rings R((x−1; α, δ)) and the skew Laurent power series rings R[[x, x−1; α]], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Examples to illustrate and delimit the theory are provided.

Keywords: skew polynomial rings, Laurent series, skew inverse Laurent series rings

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Authors: Muhammad Hassan Khalil, Xu Jiadong

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Early detection through screening is the best tool short of a perfect treatment against the malignant tumor inside the breast of a woman. By detecting cancer in its early stages, it can be recognized and treated before it has the opportunity to spread and change into potentially dangerous. Microwave tomography is a new imaging method based on contrast in dielectric properties of materials. The mathematical theory of microwave tomography involves solving an inverse problem for Maxwell’s equations. In this paper, we present designed antenna for breast cancer detection, which will use in microwave tomography configuration.

Keywords: microwave imaging, inverse scattering, breast cancer, malignant tumor detection

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Authors: Priscila Vitorino, Jeeziane Rezende, Edison Pereira, Adrielly Silva, Weimar Barroso

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Body composition insight during physical activity is relevant to follow up sports income since it can be important and actuate in velocity, resistance, potency, and has an effect on force and agility. The purpose of this study was to identify anthropometric profile, evaluate and correlate body mass index and bioimpedance behavior during the days of Caminhada Ecológica de Goiás - Brasil. A longitudinal study was performed with 25 male participants, with an average age of 45.6±9.1 years. All patients were actives. Body composition was evaluated by body mass index (BMI) measurement and bioimpedance procedures. Both were collected 20 days before walking beginning (A0) and in the four days along the same (A1, A2, A3 e A4). Data were collected in the end of each walking day at athletes accommodations. Final distance during walking route was 308 km in five days, with an average of 62km/day and 7,6 km/hour, and an average temperature of 30°C. Data are represented with mean and standard deviation. ANOVA (Bonferroni pos test) was used to compare frequent measurements between the days. Pearson's correlation test was used to correlate BMI with lean mass, fat mass, and water. BMI decreased from A0 to A1, A2 and A3 (p < 0,01) and increased on A4 (p < 0,01). No changes were observed concerning fat percentage (p=0,60), lean mass (p=0,10) and body water composition (p=0,09). A positive and moderate correlation between BMI and fat percentage was observed; an inverse and moderate correlation between BMI, lean mass and body water composition occurred. Total body mass increased during high intensity and long term walking distance. However, the values of body fat, lean mass and water were maintained.

Keywords: aerobic exercise, body composition, metabolism, sports

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study aimed at developing an inverse heat transfer approach for predicting the time-varying freezing front and the temperature distribution of tumors during cryosurgery. Using a temperature probe pressed against the layer of tumor, the inverse approach is able to predict simultaneously the metabolic heat generation and the blood perfusion rate of the tumor. Once these parameters are predicted, the temperature-field and time-varying freezing fronts are determined with the direct model. The direct model rests on one-dimensional Pennes bioheat equation. The phase change problem is handled with the enthalpy method. The Levenberg-Marquardt Method (LMM) combined to the Broyden Method (BM) is used to solve the inverse model. The effect (a) of the thermal properties of the diseased tissues; (b) of the initial guesses for the unknown thermal properties; (c) of the data capture frequency; and (d) of the noise on the recorded temperatures is examined. It is shown that the proposed inverse approach remains accurate for all the cases investigated.

Keywords: cryosurgery, inverse heat transfer, Levenberg-Marquardt method, thermal properties, Pennes model, enthalpy method

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Authors: Jianhua Zhou, Yuwen Zhang

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A two-step multigrid approach is proposed to solve the inverse heat conduction problem in a 3-D object under laser irradiation. In the first step, the location of the laser center is estimated using a coarse and uniform grid system. In the second step, the front-surface temperature is recovered in good accuracy using a multiple grid system in which fine mesh is used at laser spot center to capture the drastic temperature rise in this region but coarse mesh is employed in the peripheral region to reduce the total number of sensors required. The effectiveness of the two-step approach and the multiple grid system are demonstrated by the illustrative inverse solutions. If the measurement data for the temperature and heat flux on the back surface do not contain random error, the proposed multigrid approach can yield more accurate inverse solutions. When the back-surface measurement data contain random noise, accurate inverse solutions cannot be obtained if both temperature and heat flux are measured on the back surface.

Keywords: conduction, inverse problems, conjugated gradient method, laser

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Authors: Mohamed Hafid, Marcel Lacroix

Abstract:

This study presents an inverse analysis for predicting the thermal conductivities and the heat flux of a high-temperature metallurgical reactor simultaneously. Once these thermal parameters are predicted, the time-varying thickness of the protective phase-change bank that covers the inside surface of the brick walls of a metallurgical reactor can be calculated. The enthalpy method is used to solve the melting/solidification process of the protective bank. The inverse model rests on the Levenberg-Marquardt Method (LMM) combined with the Broyden method (BM). A statistical analysis for the thermal parameter estimation is carried out. The effect of the position of the temperature sensors, total number of measurements and measurement noise on the accuracy of inverse predictions is investigated. Recommendations are made concerning the location of temperature sensors.

Keywords: inverse heat transfer, phase change, metallurgical reactor, Levenberg–Marquardt method, Broyden method, bank thickness

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Authors: S. Gómez, G. Sánchez, J. Zarama, M. Castañeda Ramos, J. Escoto Alcántar, J. Torres, A. Núñez, S. Santana, F. Nájera, J. A. Lopez

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This paper shows in detail the mathematical model of direct and inverse kinematics for a robot manipulator (welding type) with four degrees of freedom. Using the D-H parameters, screw theory, numerical, geometric and interpolation methods, the theoretical and practical values of the position of robot were determined using an optimized algorithm for inverse kinematics obtaining the values of the particular joints in order to determine the virtual paths in a relatively short time.

Keywords: kinematics, degree of freedom, optimization, robot manipulator

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Authors: Wlodzimierz Ogryczak, Michal Przyluski, Tomasz Sliwinski

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In problems of portfolio selection, the reward-risk ratio criterion is optimized to search for a risky portfolio with the maximum increase of the mean return in proportion to the risk measure increase when compared to the risk-free investments. In the classical model, following Markowitz, the risk is measured by the variance thus representing the Sharpe ratio optimization and leading to the quadratic optimization problems. Several Linear Programming (LP) computable risk measures have been introduced and applied in portfolio optimization. In particular, the Mean Absolute Deviation (MAD) measure has been widely recognized. The reward-risk ratio optimization with the MAD measure can be transformed into the LP formulation with the number of constraints proportional to the number of scenarios and the number of variables proportional to the total of the number of scenarios and the number of instruments. This may lead to the LP models with huge number of variables and constraints in the case of real-life financial decisions based on several thousands scenarios, thus decreasing their computational efficiency and making them hardly solvable by general LP tools. We show that the computational efficiency can be then dramatically improved by an alternative model based on the inverse risk-reward ratio minimization and by taking advantages of the LP duality. In the introduced LP model the number of structural constraints is proportional to the number of instruments thus not affecting seriously the simplex method efficiency by the number of scenarios and therefore guaranteeing easy solvability. Moreover, we show that under natural restriction on the target value the MAD risk-reward ratio optimization is consistent with the second order stochastic dominance rules.

Keywords: portfolio optimization, reward-risk ratio, mean absolute deviation, linear programming

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Authors: Sebastian Kölbl, Thomas Reitmaier, Mathias Hartmann

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Trial and error approaches to adapt wearable support structures to human physiology are time consuming and elaborate. However, during preliminary design, the focus lies on understanding the interaction between exoskeleton and the human body in terms of forces and moments, namely body mechanics. For the study at hand, a multi-body simulation approach has been enhanced to evaluate actual forces and moments in a human dummy model with and without a digital mock-up of an active exoskeleton. Therefore, different motion data have been gathered and processed to perform a musculosceletal analysis. The motion data are ground reaction forces, electromyography data (EMG) and human motion data recorded with a marker-based motion capture system. Based on the experimental data, the response of the human dummy model has been calibrated. Subsequently, the scalable human dummy model, in conjunction with the motion data, is connected with the exoskeleton structure. The results of the human-machine interaction (HMI) simulation platform are in particular resulting contact forces and human joint forces to compare with admissible values with regard to the human physiology. Furthermore, it provides feedback for the sizing of the exoskeleton structure in terms of resulting interface forces (stress justification) and the effect of its compliance. A stepwise approach for the setup and validation of the modeling strategy is presented and the potential for a more time and cost-effective development of wearable support structures is outlined.

Keywords: assistive devices, ergonomic design, inverse dynamics, inverse kinematics, multibody simulation

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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: Phuoc Si Nguyen

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Infinite impulse response (IIR) filters can be designed from an analogue low pass prototype by using frequency transformation in the s-domain and bilinear z-transformation with pre-warping frequency; this method is known as frequency transformation from the s-domain to the z-domain. This paper will introduce a new method to transform an IIR digital filter to another type of IIR digital filter (low pass, high pass, band pass, band stop or narrow band) using a technique based on inverse bilinear z-transformation and inverse matrices. First, a matrix equation is derived from inverse bilinear z-transformation and Pascal’s triangle. This Low Pass Digital to Digital Filter Pascal Matrix Equation is used to transform a low pass digital filter to other digital filter types. From this equation and the inverse matrix, a Digital to Digital Filter Pascal Matrix Equation can be derived that is able to transform any IIR digital filter. This paper will also introduce some specific matrices to replace the inverse matrix, which is difficult to determine due to the larger size of the matrix in the current method. This will make computing and hand calculation easier when transforming from one IIR digital filter to another in the digital domain.

Keywords: bilinear z-transformation, frequency transformation, inverse bilinear z-transformation, IIR digital filters

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Authors: V. Srikanth, K. Balasubramanian, Rajath R. Bhat, A. S. Arjun, Nandhu Venugopal, Ananthu Unnikrishnan

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Indirect vector control is known to produce high performance in Permanent Magnet Synchronous Motor (PMSM) drives by decoupling flux and torque producing current components of stator current. The most commonly used controller or the vector control of AC motor is Proportional-Integral (P-I) controller. However, the P-I controller has some disadvantages such as high starting overshoot, sensitivity to controller gains and slower response to sudden disturbance. Therefore, the Integral-Proportional controller for PMSM drives to overcome the disadvantages of the P-I controller. Simulations results are presented and analyzed for both controllers and it is observed that Integral-Proportional (I-P) controllers give better responses than the traditional P-I controllers.

Keywords: PMSM, FOC, PI controller, IP controller

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Authors: Sumei Cai, Hong Li

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Either during water or gas injection into reservoir, in order to understand the areal flow pressure distribution underground, associated bounding deformation is prevalently monitored by ground or downhole tiltmeters. In this paper, an inverse solution to elastic response of far field displacements induced by reservoir pressure change due to flow injection was studied. Furthermore, the fundamental theory on inverse solution to elastic problem as well as its spatial smoothing approach is presented. Taking advantage of source code development based on Boundary Element Method, numerical analysis on the monitoring data of ground surface displacements to further understand the behavior of reservoir process was developed. Numerical examples were also conducted to verify the effectiveness.

Keywords: remote displacement, inverse problem, boundary element method, BEM, reservoir process

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Authors: D. S. Nagesh, G. L. Datta

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In the field of welding, various studies had been made by some of the previous investigators to predict as well as optimize weld bead geometric descriptors. Modeling of weld bead shape is important for predicting the quality of welds. In most of the cases, design of experiments technique to postulate multiple linear regression equations have been used. Nowadays, Genetic Algorithm (GA) an intelligent information treatment system with the characteristics of treating complex relationships as seen in welding processes used as a tool for inverse mapping/optimization of the process is attempted.

Keywords: smaw, genetic algorithm, bead geometry, optimization/inverse mapping

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