Theoretical and Experimental Identification of Clearance Nonlinearities for a Continuum Structure

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Jie Liu ◽  
Bing Li
Keyword(s):  
Cantilever Beam ◽  
Piecewise Linear ◽  
Influence Factors ◽  
Piecewise Linear Function ◽  
Continuous Systems ◽  
Displacement Curve ◽  
Engineering Structures ◽  
Fitting Method ◽  
Nonlinear Force ◽  
Continuum Structure

Clearance is unavoidable in many engineering structures due to the manufacturing and installation errors. These clearances can cause intense impact and wear of the contacting pairs, which may change the dynamic response and eventually reduce the movement precision and the service life of the transmission system. Parameters identification of the clearance would provide better understanding of dynamic behaviors of the clearance and contribute significantly for the control of the induced disturbance and deviation. In this paper, based on dynamic characteristics of the clearance nonlinearity, the piecewise fitting method is first proposed to identify the clearance value of the continuum structure. During the proposed method, first, the rough scope of the clearance value extracted from the displacement response is divided into subintervals. And then, the nonlinear force is fitted by the piecewise linear function in the subintervals. Once the equivalent stiffness is obtained, the clearance value can be calculated by the sorting nonlinear force–displacement curve. The feasibility of the piecewise fitting method was verified by a cantilever beam system with clearances in simulation. Besides, some influence factors of this identification method, including the clearance value, exciting force level and measurement noise, are fully discussed to illustrate the robustness of this method. Moreover, an experiment system of a cantilever beam with adjustable clearances was designed to experimentally validate the effectiveness of the proposed method, and the results show that the piecewise fitting method can precisely identify the clearance value of continuous systems.

The Effect of Nonlinear Springs in Jumping Mechanisms

2018 ◽  
Author(s):  
Sahand Sadeghi ◽  
Blake D. Betsill ◽  
Phanindra Tallapragada ◽  
Suyi Li
Keyword(s):  
Piecewise Linear ◽  
Equations Of Motion ◽  
Piecewise Linear Function ◽  
Displacement Curve ◽  
Spring Stiffness ◽  
Nonlinear Spring ◽  
Jumping Performance ◽  
Nonlinear Springs ◽  
Nonlinear Force ◽  
Force Displacement

This research investigates the potential effects of utilizing nonlinear springs on the performance of robotic jumping mechanisms. As a theoretical example, we study dynamic characteristics of a jumping mechanism consisting of two masses connected by a generic nonlinear spring, which is characterized by a piecewise linear function. The goal of this study is to understand how the nonlinearity in spring stiffness can impact the jumping performance. To this end, non-dimensional equations of motion of the jumping mechanism are derived and then used extensively for both analytical and numerical investigations. The nonlinear force-displacement curve of the spring is divided into two sections: compression and tension. We examine the influences of these two sections of spring stiffness on the overall performance of the jumping mechanism. It is found that compression section of the nonlinear spring can significantly increase energy storage and thus enhance the jumping capabilities dramatically. We also found that the tension section of the nonlinear force-displacement curve does not affect the jumping performance of the center of gravity, however, it has a significant impact on the internal oscillations of the mechanism. Results of this study can unfold the underlying principles of harnessing nonlinear springs in jumping mechanisms and may lead to the emergence of more efficient hopping and jumping systems and robots in the future.

scholarly journals MINLP formulations for continuous piecewise linear function fitting

2021 ◽  
Author(s):  
Noam Goldberg ◽  
Steffen Rebennack ◽  
Youngdae Kim ◽  
Vitaliy Krasko ◽  
Sven Leyffer
Keyword(s):  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Mixed Integer ◽  
Function Fitting ◽  
Computational Performance ◽  
Integer Nonlinear Programming ◽  
Minlp Model ◽  
Necessary Constraints ◽  
Continuous Piecewise Linear Function

AbstractWe consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

scholarly journals A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Hamid Reza Erfanian ◽  
M. H. Noori Skandari ◽  
A. V. Kamyad
Keyword(s):  
Nonsmooth Optimization ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Piecewise Linear Function ◽  
Nonsmooth Equations ◽  
Smooth Functions ◽  
Generalized Derivative ◽  
Novel Approach

We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other words, nonsmooth function is approximated by a piecewise linear function based on generalized derivative. In the next step, we solve smooth linear optimization problem whose optimal solution is an approximate solution of main problem. Then, we apply the results for solving system of nonsmooth equations. Finally, for efficiency of our approach some numerical examples have been presented.

scholarly journals DESIGN OF TIME DELAYED CHAOTIC CIRCUIT WITH THRESHOLD CONTROLLER

2011 ◽  
Vol 21 (03) ◽  
pp. 725-735 ◽  
Author(s):  
K. SRINIVASAN ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
M. LAKSHMANAN ◽  
SUDESHNA SINHA
Keyword(s):  
Numerical Simulations ◽  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operational Amplifiers ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Threshold Values ◽  
Chaotic Circuit

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

High transparency flexible sensor for pressure and proximity sensing

2018 ◽  
Vol 32 (32) ◽  
pp. 1850394 ◽  
Author(s):  
Dan Bu ◽  
Si Qi Li ◽  
Yun Ming Sang ◽  
Cheng Jun Qiu
Keyword(s):  
Indium Tin Oxide ◽  
Pressure Range ◽  
Piecewise Linear ◽  
High Sensitivity ◽  
Maximum Error ◽  
Piecewise Linear Function ◽  
Good Repeatability ◽  
Flexible Pressure Sensor ◽  
Human Finger ◽  
Proximity Sensing

A high-sensitivity and high-transmittance flexible pressure sensor is presented in this paper. Using polydimethylsiloxane (PDMS) sensing film to cover indium tin oxide (ITO) electrodes interdigitated on the polyethylene terephthalate (PET) substrate, an interdigital capacitance (IDC) structure is constructed. The pressure and proximity sensing characteristics of the fabricated IDC sensor are investigated. The experiment results show that the IDC sensor has the piecewise linear function in different pressure range, especially sensitive to the low-pressure range with the pressure sensitivity of 6.64 kPa[Formula: see text]. Moreover, it has a good repeatability with the maximum error rate of 2.73% and a high transmittance over 90% in the wavelength range from 400 nm to 800 nm. As a human finger approaches or leaves, the proximity sensing characteristic emerges, with a maximum sensing distance of about 20 cm.

scholarly journals Reliably Assessing Duration of Protection for COVID-19 Vaccines

2021 ◽  
Author(s):  
Danyu Lin ◽  
Donglin Zeng ◽  
Yu Gu ◽  
Thomas Fleming ◽  
Phillip Krause
Keyword(s):  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Vaccine Effectiveness ◽  
Vaccine Protection ◽  
Time Period ◽  
Duration Of Protection ◽  
Reliable Methods ◽  
Protective Effectiveness ◽  
Vaccine Effect ◽  
Observation Period

Decision-making about booster dosing for COVID-19 vaccine recipients hinges on reliable methods for evaluating the longevity of vaccine protection. We show that modeling of protection as a piecewise linear function of time since vaccination for the log hazard ratio of the vaccine effect provides more reliable estimates of vaccine effectiveness at the end of an observation period and also more reliably detects plateaus in protective effectiveness as compared with the traditional method of estimating a constant vaccine effect over each time period. This approach will be useful for analyzing data pertaining to COVID-19 vaccines and other vaccines where rapid and reliable understanding of vaccine effectiveness over time is desired.

Dynamic Portfolio Selection

2017 ◽  
pp. 116-140
Keyword(s):  
Portfolio Optimization ◽  
Asset Allocation ◽  
Piecewise Linear ◽  
Relevant Literature ◽  
Asset Price ◽  
Piecewise Linear Function ◽  
Simple Formulation ◽  
Wolfram Mathematica ◽  
Dynamic Portfolio ◽  
Algorithmic Construction

In this chapter I recognize the importance of the stochastic programming as a significant tool in financial planning. The current practice of portfolio optimization is still limited to the simple formulation of linear programming (LR) or quadratic programming (QR) type. For that reason, relevant literature on asset-liability management (ALM) model has been reviewed and two different ALM approaches are compared: first piecewise linear function; and second a nonlinear utility function. This chapter shows that the mathematical programming methodology is ready to challenge the huge problem arising from LP portfolio optimization. A special emphasis was put on the shape of the investors' payoff functions in asset price equilibrium. The results underpin our claim that the nonlinear ALM model generated better asset allocation. An algorithmic construction of ALM model is developed in Wolfram Mathematica 9.

ReLU Networks Are Universal Approximators via Piecewise Linear or Constant Functions

2020 ◽  
Vol 32 (11) ◽  
pp. 2249-2278
Author(s):  
Changcun Huang
Keyword(s):  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Piecewise Linear Approximation ◽  
Piecewise Constant ◽  
Deep Layers ◽  
Univariate Function ◽  
Arbitrary Precision ◽  
Piecewise Constant Approximation ◽  
Neural Unit ◽  
Universal Approximators

This letter proves that a ReLU network can approximate any continuous function with arbitrary precision by means of piecewise linear or constant approximations. For univariate function [Formula: see text], we use the composite of ReLUs to produce a line segment; all of the subnetworks of line segments comprise a ReLU network, which is a piecewise linear approximation to [Formula: see text]. For multivariate function [Formula: see text], ReLU networks are constructed to approximate a piecewise linear function derived from triangulation methods approximating [Formula: see text]. A neural unit called TRLU is designed by a ReLU network; the piecewise constant approximation, such as Haar wavelets, is implemented by rectifying the linear output of a ReLU network via TRLUs. New interpretations of deep layers, as well as some other results, are also presented.

Recognition of handwritten digits using a neural network based on the piecewise linear function

1994 ◽  
Author(s):  
Hongyu Liu ◽  
Yialei Wang ◽  
Peimao Sun ◽  
Tianyun Zhang ◽  
Rong Jiang
Keyword(s):  
Neural Network ◽  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function
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