Order Polynomial Function Research Articles

Idiopathic scoliosis and brace treatment: an innovative device to assess corrective pressure

The biomechanical influence of brace treatment for scoliosis is not understood. This prospective pilot study analyzed reliability of a system based on 100% textile sensors for measurement of pressure exerted by brace on trunk. Evaluation of modifications during changes in the location of the support zones and variations in amplitude of the pressure was observed in four patients, when considering three main daily positions mimicking day and nighttime wear. A calibration step allowed the determination of a conversion law between sensor data and pressure unit using a second order polynomial function with a high r2 of 0.99. This prototype is the first of a new generation. Experimental pressure distribution could be useful for the further brace development.

Meta-model based stochastic simulation of fire barrier cold-side temperature

Meta-modeling helps to reduce the computational cost of large-scale stochastic simulations. It, however, brings froth additional uncertainty in the prediction. In this work, we illustrate the use of the Response Surface Method (RSM) and Gaussian Process (GP) regression to approximate the cold-side temperature of a fire barrier in a stochastic compartment fire scenario. The deterministic model is a 1D Finite Element Method (FEM) solving heat-diffusion. We also illustrate a method for the quantification and compensation of the meta-modeling uncertainty. Additionally, we present a simple technique to create a RSM model with an arbitrary order polynomial function. The results show that both RSM and GP model can produce accurate stochastic simulations despite only few deterministic data points. The simple polynomial-based RSM approximation, however, fails when the heat-transfer is affected by exothermic reactions. This is in contrast with GP, where the combination of various kernel functions makes the prediction flexible enough even for the highly non-linear problem. The meta-modeling uncertainty can be quantified during the testing of meta-models and later be used to improve the accuracy of stochastic predictions.

Detecting Rainfall Trend and Development of Future Intensity Duration Frequency (IDF) Curve for the State of Kelantan

Due to global warming, the existing IDF curves that were derived from historical data may no longer valid for estimating future rainfall. On the other hand, the alternative future rainfall data generated from Community Climate System Model version 3 (CCSM3) cannot be used directly due to systematic biases caused by non-inclusion of local features. Quantile mapping was used to bias correct the rainfall data generated by CCSM3 model based on the properties of observed rainfall. Only 4 out of 16 stations in the state of Kelantan have shown an increasing significant trend for 1-h annual maximum rainfall. The best transfer function used to correct bias in CCSM3 data is the second order polynomial function. The quantile mapping for bias correction is satisfactory as the highest RMSE was only 4.045, a reduction by 15% compared to the original CCSM3 data. Subsequently, a unique transfer function was developed to represent the behavior of CCSM3 and observed data for each station. The future intensity was found to increase for short and medium return periods of 2-, 5-, 10- and 25-year, where most of the stations have Climate Change Factor (CCF) larger than 1. On the contrary, for a longer return period of 50- and 100-year, the intensities are predicted to be lower.

Design, Analysis and Simulation of a 6-DOF Serial Manipulator

Within the scope of this study, firstly, mechanical structure of a six-axis serial manipulator was designed. Forward kinematic analysis was made using the Denavit-Hartenberg method, which provides the transition between cartesian coordinates, that is, the linear and angular positions of the end-effector, and joint coordinates; joint angles and linear displacements. In addition, to obtain the relation between the speed of joint variables and the speed of end effector, Jacobian matrix was derived. Dynamic analysis of the system based on Lagrange-Euler mathematical model was acquired. After the design phase was carried out in three-dimensional environment, the physical system-based dynamic model was obtained by transferring this data to the MATLAB-Simscape environment. Inverse dynamic problem was solved to verificate the 3D design of robot and suitablility of selected motors. To solve this problem, position, velocity and acceleration trajectories was given to dynamic model. As a result of this, each joint torques were obtained. The trajectories used in inverse dynamics were calculated using a fifth order polynomial function. Afterwards, in order to test the operation of the system in a simulated environment, PID based controller structures were applied to the dynamic model in MATLAB/Simulink simulation envirenmont and forward dynamic problem was reviewed and discussed.

Adaptive fixed-time control of autonomous VTOL UAVs for ship landing operations

This paper addresses the fixed-time control problem of autonomous ship landing operations of vertical take-off and landing (VTOL) unmanned aerial vehicles (UAVs) subject to external disturbances. A continuous reference altitude is planned for the UAV by introducing a high order polynomial function and a continuous differentiable switching function. To ensure a safe and precise board landing operation under bad sea condition, a landing constraint condition is designed in terms of rotational motion of the ship. By combining the planar motion of the ship with the reference altitude, the landing mission is converted into the control development for the UAV tracking. By introducing the hierarchical design, an adaptive fixed-time control algorithm is proposed for the UAV such that the trajectory and command attitude tracking are achieved, respectively. It is proved via Lyapunov stability theory that the proposed control algorithm guarantees the fixed-time trajectory tracking of the UAV subject to unknown external disturbances and inertia parameters. Simulation examples verify the proposed strategy.

Covid-19: A Dynamic Analysis of Fatality Risk in Italy.

Italy was the second country in the world to face a wide epidemic of Covid-19 after China. The ratio of the number of fatalities to the number of cases (case fatality ratio, CFR) recorded in Italy was surprisingly high and increased in the month of March. The older mean age of population, the changes in testing policy, and the methodological computation of CFR were previously reported as possible explanations for the incremental trend of CFR, a parameter theoretically expected to be constant. In this brief report, the official data provided by the Italian Ministry of Health were analyzed using fitting models and the linear fit method approach. This last methodology allowed us to reach two findings. The trend of the number of deaths followed a 1–3-day delay of positive cases. This delay was not compatible with a biological course of Covid-19 but was compatible with a health management explanation. The second finding is that the Italian number of deaths did not increase linearly with the number of positive cases, but their relationship could be modeled by a second-order polynomial function. The high number of positive cases might have a direct and an indirect effect on the number of deaths, the latter being related to the overwhelmed bed capacity of intensive care units.

Squeezed Polynomial Codes: Communication-Efficient Coded Computation in Straggler-Exploiting Distributed Matrix Multiplication

In a distributed computing environment, there may exist slow processing workers, which are known as “stragglers”, and they can slow down the whole computing process. In this article, we consider coded computation for matrix multiplication tasks in distributed computing, which can mitigate the effect of stragglers by a coding approach. We propose a new communication-efficient coded computation scheme, namely squeezed polynomial codes, for a straggler-exploiting scenario where multiple sub-tasks are assigned to the workers to partially leverage the computation capability of stragglers. The key idea of squeezed polynomial codes is to overlap the encoded matrices in assigning multiple sub-tasks with appropriate polynomial functions in order to reduce the task-allocation communication load from a master to its workers. We compare squeezed polynomial codes with the existing schemes for distributed matrix multiplication in a communication load perspective. Consequently, we show that squeezed polynomial codes can efficiently reduce the communication load while ensuring the optimal recovery condition at a master to obtain final product.

Hyperchaotic Behavior in the Novel Memristor-Based Symmetric Circuit System

A novel five-dimensional (5D) memristor-based symmetric circuit, which consists of two symmetric capacitors, two symmetric inductors and only one memristor is presented in this article. The multivariable first order and multivariable second order polynomial functions are used for the internal state function of the memristor respectively. Theoretical and simulation analyses of the novel memristive circuit are investigated using equilibrium points, phase portraits, bifurcation diagrams and Lyapunov exponent spectra, etc. Complex chaotic behaviors are observed and analyzed through simulation results. The first order internal state function memristor-based symmetric circuit system can only exhibit chaotic behavior whereas the second order internal state function memristor-based symmetric circuit system can generate not only chaotic attractors, but also hyperchaotic attractors in proper parameters.

Neutronic study of UO2-BeO fuel with various claddings

The neutronic properties of UO2-BeO fuel with various claddings are investigated through the Monte Carlo method and the Linear Reactivity Model. A second order polynomial function is suggested to describe the relationship between the difference of the reactivity at the End of Cycle and two factors, the uranium enrichment and the volume fraction of BeO in the UO2-BeO fuel. The uranium enrichment is determined to ensure the same cycle length for each BeO fraction with zircaloy, FeCrAl, and SiC claddings. Similar neutronic properties are observed between the zircaloy and SiC claddings for a given BeO fraction, including the infinite multiplication factor, the gas release, the power distribution, and the isotopic concentrations. An important feature of UO2-BeO fuel is the production of 4He, which is significant compared with current UO2 fuel. Lower production rates of xenon and krypton are found in the case of the UO2-BeO-FeCrAl fuel-cladding system, while those in the UO2-BeO-zircaloy and UO2-BeO-SiC systems are quite similar to the current UO2-zircaloy system. The power distribution in an assembly and in a fuel pellet is flatter for a higher BeO fraction with the same cladding. Higher peak power is found in fuel assemblies with FeCrAl compared to the other two claddings, while the radial power distribution is quite similar for the three claddings.

Improved Stability Criteria for Time-Varying Delay System Using Second and First Order Polynomials

This article concerns the problem of stability analysis of systems with time-varying delay. Recent developments in this direction involves approximation of a second order polynomial function of time-delay. This article proposes a new Lyapunov-Krasovskii Functional that does not introduce the second-order polynomial and thereby avoid the approximation involved in obtaining the stability criterion. Two stability criterion are presented, one introduces the second-order polynomial and the other one does not. A comparison using numerical examples shows that the avoidance of second-order polynomial formulation leads to improved results.

Damage detection of long-span bridge structures based on response surface model

In order to solve the problem of high risk and low precision of existing damage detection methods for long-span Bridges, a new method based on fourth-order polynomial response surface model is proposed. Response surface model is constructed by using fourth order polynomial function. The parameters of the finite element model of the bridge are modified according to the response surface model. Based on the finite element model, the modal strain energy before and after the damage of the element was calculated, and the damage index of the element was obtained, so as to realize the damage detection of the long-span bridge structure. Experimental results show that the proposed method can accurately detect the damage location of long-span Bridges under different damage conditions, and the detection error of damage degree is less than 1%, which has a broad application prospect.

Controllable and observable control design of wind generator system using PID algorithm

This paper describes a design process of the wind generator control system. Controlling a wind generator, fan, is important to study the design of the wind turbine. A complex wind generator model was approximated with 5th order polynomial function. The paper describes a procedure for identifying system, especially for finding the transfer function of a plant, that based on input and output. The plant’s input is an electric motor fan voltage and output is wind speed produced. It’s important to simplify control’s design of the wind generator for configuring transfer functions of the plant. The identification method that is used is Linear Regression, applying Excel program, which produces a polynomial function. And then, the Matlab’s System Identification Toolbox (SIT), which produces a transfer function. From this study, applying SIT, a model of wind generator, shows the fit estimation data is 90.78% and MSE is 0.078%. A closed-loop control system using PID controller is proposed. Controllable and Observable of the state space model were verified. The best performance of the close-loop system was achieved using Kp=0.2247, Ki=6.05*10-5, and Kd=208.75 applying Ziegler-Nichols. The results showed that the closed loop stability by applying PID can stabilize the wind generator.

Effective thermal conductivity of high porosity open-cell metal foams

In this paper, a model for effective thermal conductivity of high porosity open-cell metal foams is developed by assuming the foam morphology as 3D tetradecahedron structure. The effective thermal conductivity of metal foams is first studied using the numerical simulation method, which the geometrical model (the ratio of the edge length of node to the radius of ligament) is calibrated with the experimental data. The geometrical model is divided into four distinctive layers along the heat transfer direction. The effective thermal conductivity of four layers is then determined by fitting the numerical results. Consequently, the model for effective thermal conductivity of metal foams is proposed based on the Fourier law. Several other analytical models and the experimental data are used to verify the effectiveness of the present model. The results show that the present model can be satisfactorily accurate to calculate the effective thermal conductivity of metal foam by considering the ratio of the edge length of node to the radius of ligament as a second order polynomial function of the porosity. The effective thermal conductivity of each layer is related to the porosity of each layer and overall porosity of metal foam. Compared with the experimental data, the present model has high accuracy with relative RMS deviation of less than 10%. The finding of this study can help guide the thermal design of porous media.

Design Of Random Oracle For Block Iterated One-Way Ciphers Through Polynomial Functions

The security aspect on provably secure hash function relies upon the design principles of Random Oracle (RO). Poor design principles make the said function vulnerable to hash attacks. The conventional keyless provably secure hash functions MD-5, SHA-2 and SHA-3 use RO or Sponge principles for the design and construction of hash function. They use bitwise operators AND, OR, XOR and modulo arithmetic for processing the input blocks. These operators are simple to use and they are efficient in terms of achieving quick response time. At the same time the repeated use of them in the input blocks may invite hash collisions. The proposed design advocates the use of multi variable higher-order polynomial function for the design of round function in RO. The new design paradigm derogates the use of bitwise operators at block level processing and hardens the internal structure of RO with higher- order polynomial function to ensure better security. The results prove that, the new prototype helps the block iterated hash function to exhibit strong random behavior even for a small bit flip in the input. Therefore, performing differential analysis on the proposed design is very hard than ever before.

Stride and Step Length Obtained with Inertial Measurement Units during Maximal Sprint Acceleration.

During sprint acceleration, step length, step rate, ground contact, and airtime are key variables for coaches to guide the training process and technical development of their athletes. In the field, three of these variables are easily obtained with inertial measurement units (IMUs), but, unfortunately, valid estimates of step length with IMUs currently are limited to low speeds (<50% max). A simple method is proposed here to derive step length during maximal sprint acceleration, using IMUs on both feet and two timing gates only. Mono-exponential velocity-time functions are fitted to the 30-m (split) and 60-m times, which in combination with IMU-derived step durations yield estimates of step length. To validate this approach, sixteen well-trained athletes with IMUs on the insteps of both feet executed two 60-m maximal sprints, starting from a three-point position. As a reference, step lengths were determined from video data. The reference step lengths combined with IMU-derived step durations yielded a time series of step velocity that confirmed the appropriateness of a mono-exponential increase of step velocity (R2 ≥ 0.96). The comparison of estimated step lengths to reference measurements showed no significant difference (p > 0.05) and acceptable agreement (root mean square error, RMSE = 8.0 cm, bias ± Limits of Agreement = −0.15 ± 16 cm). Step length estimations further improved (RMSE = 5.7 cm, −0.16 ± 11 cm) after smoothing the original estimated step lengths with a third order polynomial function (R2 = 0.94 ± 0.04). In conclusion, during maximal sprint acceleration, acceptable estimates of stride and step length were obtained from IMU-derived step times and 30-m (split) and 60-m sprint times.

Synthesis on the Acceleration Energies in the Advanced Mechanics of the Multibody Systems

The present paper’s objective is to highlight some new developments of the main author in the field of advanced dynamics of systems and higher order dynamic equations. These equations have been developed on the basis of the matrix exponentials which prove to have undeniable advantages in the matrix study of any complex mechanical system. The present paper proposes some new approaches, based on differential principles from analytical mechanics, by using some important dynamics notions, regarding the acceleration energies of the first, second and third order. This study extended the equations of the higher order, which provide the possibility of applying the initial motion conditions in the positions, velocities and accelerations of the first and second order. In order to determine the time variation laws for the generalized variables, the driving forces and acceleration energies of the higher order are applied by the time polynomial functions of the fifth order. According to inverse kinematics also named control kinematics of the robots, the applications of polynomial functions lead to the kinematic control functions of mechanical motions, especially the transitory motions. They influence the dynamic behavior of multibody systems, in which robot structures are included.

Self-adaptive MRPBIL-DE for 6D robot multiobjective trajectory planning

This work presents self-adaptive multiobjective real-code population-based incremental learning hybridised with differential evolution (MRPBIL-DE) for solving a 6D robot trajectory planning multiobjective optimisation problem. The objective functions are assigned to minimise travelling time and minimise maximum jerk taking place during motion while the constraints are velocity, acceleration and jerk constraints. A five order polynomial function is used to represent a motion equation while the motion path is divided into two sub-paths; from initial to intermediate positions and from intermediate to final positions. The optimiser is used to find a set of design variables including joint positions, velocities and accelerations at intermediate positions, moving time from the initial to intermediate positions, and that from the intermediate to final positions. Several multiobjective meta-heuristics (MOMHs) along with the proposed algorithm are used to solve the trajectory optimisation problem of robot manipulators while their performances are investigated. The results indicated that the proposed algorithm is effective and efficient for multiobjective robot trajectory planning optimisation problem. The results obtained from such a method are set as the baseline for further study of robot trajectory planning optimisation.

A procedure to obtain the parameters of Curie temperature distribution from thermomagnetic and magnetocaloric data

We propose a procedure for the determination of the parameters of the Curie temperature distribution (TCD) in a compositionally inhomogeneous ferromagnetic material. Assuming a Gaussian TCD and using a mean field approach based on the Brillouin function, we report that with respect to the average value of the distribution: a) both inflection point of magnetization, Tinf, and temperature at maximum magnetic entropy change curves, TpkMCE, shift to lower temperatures and b) temperature at maximum paramagnetic susceptibility, Tpkχ, shifts to higher temperatures. Using these evolutions as a function of the TCD broadening and fitting them to a second order polynomial function, a self-consistent procedure to determine the parameters of the distribution is supplied. These predictions have been experimentally tested for a ball milled Fe70Zr30 amorphous alloy using thermomagnetic and magnetocaloric measurements. The obtained parameters using the proposed procedure agree with those directly measured using Mössbauer spectrometry.

Evaluation of a phenomenological elastic‐plastic approach for magnesium alloys under multiaxial loading conditions

AbstractMagnesium alloys are greatly appreciated due to their high strength to weight ratio, stiffness, and low density; however, they can exhibit complex types of cyclic plasticity like twinning, de‐twinning, or Bauschinger effect. Recent studies indicate that these types of cyclic plastic deformations cannot be fully characterized using the typical tools used in cyclic characterization of steels and aluminium alloys; thus, it is required new approaches to fully capture their cyclic deformation and plasticity. This study aims to propose and evaluate a phenomenological cyclic elastic‐plastic approach designed to capture the cyclic deformation of magnesium alloys under multiaxial loading conditions. Series of experimental tests were performed to characterize the cyclic mechanical behaviour of the magnesium alloy AZ31BF considering proportional loadings with different strain amplitude ratios and a nonproportional loading with a 45° phase shift. The experimental results were modulated using polynomial functions in order to implement a cyclic plasticity model for the AZ311BF based on the phenomenological approach proposed. Results show good correlations between experiments and estimates.

The flow behavior of homogenizated Al-Mg-Si-La aluminum alloy during hot deformation

AbstactThe high temperature flow behavior of Al-Mg-Si-La alloy has been studied by isothermal compression test in the temperature range bwtween 350 °C and 500 °C and at strain rates from 0.01 s−1 to 1 s−1. Based on the experimental data of thermal simulation, the true stress-true strain curve of the alloy is obtained. The constitutive model containing strain is established using Arrhenius equation and Z parameter to predict the effect of strain rate and temperature on hot deformation behavior. The good agreement between the experimental and predicted results of true strain- true stress indicated that this model can estimate the flow stress accurately. The relationship between the material constants (Q, lnA, n and α) and the true strain can be expressed by the 6th order polynomial function. In addition, it is found that the average thermal deformation activation energy in this study is lower than reported values.