The application of piecewise-linear method to some nonlinear power problems

1965 ◽  
Author(s):  
Chun-ming Shen
Keyword(s):  
Piecewise Linear ◽  
Linear Method

A New Model for Simulating AC and Surge Properties of ZnO Varistors Based on Microstructural Characteristics

2008 ◽  
Vol 368-372 ◽  
pp. 510-513 ◽  
Author(s):  
Jun Hu ◽  
Jin Liang He ◽  
Feng Chao Luo
Keyword(s):  
Numerical Simulation ◽  
Grain Boundaries ◽  
Conduction Mechanism ◽  
Piecewise Linear ◽  
Linear Method ◽  
Microstructural Characteristics ◽  
Nonlinear Resistor ◽  
Resistor Networks ◽  
Zno Varistors ◽  
The Relationship

The numerical simulation is an effective method for researching the relationship between macroscopic properties of ZnO varistors and their microstructural characteristics. However, the computing efficiency is a big problem for further researches. In this paper, a quick piecewise linear method for solving the complicated nonlinear resistor networks of ZnO varistors is proposed, which can significantly improve the computing efficiency by a hundred times. The simulating models for the microstructural characteristics of ZnO varistors are improved based on actual conduction mechanism of grain boundaries. The simulations of more bulk characteristics of ZnO varistors become possible, such as alternating current (AC) and surge properties.

scholarly journals Force Analysis and Evaluation of a Pelvic Support Walking Robot with Joint Compliance

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Jiancheng Ji ◽  
Shuai Guo ◽  
Fengfeng (Jeff) Xi
Keyword(s):  
Force Field ◽  
Piecewise Linear ◽  
Linear Method ◽  
Kinematic Model ◽  
Gait Training ◽  
Walking Robot ◽  
Force Analysis ◽  
Interaction Forces ◽  
Joint Compliance ◽  
Pelvic Support

The force analysis of a pelvic support walking robot with joint compliance is discussed in this paper. During gait training, pelvic motions of hemiplegic patients may be excessively large or out of control; however, restriction of pelvic motions is not likely to facilitate successful rehabilitation. A robot-assisted pelvic balance trainer (RAPBT) is proposed to help patients control the range of motion via force field, and force analysis is necessary for the control of the compliant joints. Thus, kinematic model and static model are developed to derive the Jacobian and the relation between the interaction forces and the pelvic movements, respectively. Since the joint compliance is realized through a nontorsional spring, a conventional (linear) Jacobian method and a piecewise linear method are derived to relate the interaction forces with the pelvis movements. Three preliminary experiments are carried out to evaluate the effectiveness of the proposed methods and the feasibility of the RAPBT. The experiment results indicate that the piecewise linear method is effective in the calculation of the interaction forces. Gait with pelvic brace strongly resembles free overground walking and partly decreases motion range via force field. The findings of this research demonstrate that the pelvic brace with joint compliance may provide effective interventions.

An Intuitionistic Fuzzy Multi-Objective Goal Programming Approach to Portfolio Selection

2021 ◽  
pp. 1-21
Author(s):  
Gao-Feng Yu ◽  
Deng-Feng Li ◽  
De-Cui Liang ◽  
Guang-Xu Li
Keyword(s):  
Portfolio Selection ◽  
Piecewise Linear ◽  
Linear Method ◽  
Multiple Objectives ◽  
Programming Approach ◽  
Binary Variables ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Solution Methods ◽  
Hard Problems

Portfolio selection can be regarded as a type of multi-objective decision problem. However, traditional solution methods rarely discussed the decision maker’s nonsatisfaction and hesitation degrees with regard to multiple objectives and they require many extra binary variables, which lead to tedious computational burden. Based on the above, the aim of this paper is to develop a new and unified intuitionistic fuzzy multi-objective linear programming (IFMOLP) model for such portfolio selection problems. The nonmembership functions are constructed by the pessimistic, optimistic, and mixed approaches so as to perfect the traditional intuitionistic fizzy (IF) inequalities and IF theory. The decision maker’s hesitation degrees with regard to multiple objectives are represented by using IF inequalities, and the new IFMOLP model based on IF inequalities is proposed. The IFMOLP problems are solved by the S-shaped membership functions without extra binary variables required by the piecewise-linear method. Finally, the portfolio selection model under IF environments based on IFMOLP is established, and a real example is analyzed to demonstrate its validity and superiority. The developed unified IFMOLP model and method can not only effectively solve multi-objective decision problems with nonsatisfaction and hesitation degrees but also remarkably reduce the complexity of the nondeterministic polynomial-hard problems.

scholarly journals Study of Dynamic Characteristics of Slow-Changing Process

2000 ◽  
Vol 7 (2) ◽  
pp. 113-117
Author(s):  
Yinong Li ◽  
Ling Zheng ◽  
Bangchun Wen
Keyword(s):  
Nonlinear System ◽  
Dynamic Characteristic ◽  
Dynamic Characteristics ◽  
Asymptotic Method ◽  
Piecewise Linear ◽  
Linear Method ◽  
Vibration System ◽  
Intelligent Structures ◽  
Resonant Region ◽  
The Relationship

A vibration system with slow-changing parameters is a typical nonlinear system. Such systems often occur in the working and controlled process of some intelligent structures when vibration and deformation exist synchronously. In this paper, a system with slow-changing stiffness, damping and mass is analyzed in an intelligent structure. The relationship between the amplitude and the frequency of the system is studied, and its dynamic characteristic is also discussed. Finally, a piecewise linear method is developed on the basis of the asymptotic method. The simulation and the experiment show that a suitable slow-changing stiffness can restrain the amplitude of the system when the system passes through the resonant region.

Simulation Study of Harmonic Compensation Device Based on Combination of FC-TCR and TSC for Drilling Rigs

2012 ◽  
Vol 566 ◽  
pp. 317-323
Author(s):  
Mao Zeng Lu ◽  
Xi Geng Ma ◽  
Jun Tao Xu ◽  
Chang Zhong Han ◽  
Meng Liu
Keyword(s):  
Reactive Power ◽  
Piecewise Linear ◽  
Linear Method ◽  
Open Loop ◽  
Harmonic Compensation ◽  
Loop Control ◽  
Switch Capacitor ◽  
Compensation Device ◽  
Drilling Rigs ◽  
Signal Switch

To solve the problem of high reactive power consumption and serious harmonic pollution of the drilling rigs, a hybrid filter device based on a combination of FC-TCR and TSC was studied. Use open loop control, take reactive power as control signal, switch capacitor at voltage’s peak and use piecewise linear method to get reactor’s firing angle. Through MATLAB/SIMULINK, compensation scheme was simulated. Simulation results verified its effectiveness and validity, and it has an important guiding significance on the development of actual devices.

scholarly journals Semiparametric methods for estimation of a non-linear exposure–outcome relationship using instrumental variables with application to Mendelian randomization

2017 ◽  
Author(s):  
James R Staley ◽  
Stephen Burgess
Keyword(s):  
Blood Pressure ◽  
Instrumental Variables ◽  
Mendelian Randomization ◽  
Causal Effect ◽  
Piecewise Linear ◽  
Linear Method ◽  
Piecewise Linear Function ◽  
Polynomial Method ◽  
Fractional Polynomial ◽  
Outcome Relationship

AbstractMendelian randomization, the use of genetic variants as instrumental variables (IV), can test for and estimate the causal effect of an exposure on an outcome. Most IV methods assume that the function relating the exposure to the expected value of the outcome (the exposure-outcome relationship) is linear. However, in practice this assumption may not hold. Indeed, often the primary question of interest is to assess the shape of this relationship. We present two novel IV methods for investigating the shape of the exposure-outcome relationship: a fractional polynomial method and a piecewise linear method. We divide the population into strata using the exposure distribution, and estimate a causal effect, referred to as a localized average causal effect (LACE), in each stratum of population. The fractional polynomial method performs meta-regression on these LACE estimates. The piecewise linear method estimates a continuous piecewise linear function, the gradient of which is the LACE estimate in each stratum. Both methods were demonstrated in a simulation study to estimate the true exposure-outcome relationship well, particularly when the relationship was a fractional polynomial (for the fractional polynomial method) or was piecewise linear (for the piecewise linear method). The methods were used to investigate the shape of relationship of body mass index with systolic blood pressure and diastolic blood pressure.Availability and implementation: https://github.com/jrs95/nlmr

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