FACTORS AND LEVELS ON DESIGN OF EXPERIMENT, EFECTIVE CHOICE UNDER CONSTRAINS

2021 ◽  
Vol 6 ◽  
pp. 122-128
Author(s):  
Sergey Smirnov ◽  
◽  
Keyword(s):  
Design Of Experiment ◽  
Iterative Process ◽  
Resource Constraints ◽  
Iterative Solution ◽  
Solution Procedure ◽  
Simple Expression ◽  
Iterative Refinement ◽  
Abbreviated Description ◽  
Main Ideas ◽  
Intermediate Value

The problem of design of experiment with resource constraints is investigated. For a complex system intended for experimental research, before using the well known advanced methods of factorial design, you must first create a simplified mathematical model that represents an incomplete abbreviated description of the system. At the same time, on this simplification from all objectively existing independent parameters of the system remain only the most important parameters, which is a forced procedure due to the natural limitations of the resources available to perform the experimental study. The same constraints limit the number of values assigned to each of the parameters (factor levels number). The article is devoted to the modification of the existing method of discretization of such a model with a rational choice of discretization parameters in accordance with the existing limitations, but with an extremely unreliable in terms of convergence iterative solution procedure. The main ideas of the modified approach are as follows: 0) The choice of the number of levels of factors is proportional to the importance of the relevant parameters and the reduction to the problem of finding a fixed point (as in the known method). 1) Probability partition (instead of partition into equal length intervals) for discretization and selection of representative values of the parameter, which allows to find an exact simple expression for its Shannon entropy. 2) Transition from multi- to one-parameter (coefficient of proportionality as an indicator of parameterization) representation of nonlinear mapping, its decomposition and simplification of the iterative process. 3) Finding the initial value of the coefficient of proportionality for a factor with average relevance and calculations for other factors, followed by iterative refinement. The iterative process is guaranteed to coincide, because the consideration of small and large values of the scalar parameter allows us to use the theorem on the intermediate value of a continuous function. Then, with the help of the developed procedure, two tasks on the assignment of the number of factor levels for situations with small and large resource constraints are solved, the corresponding complications in the calculations and ways to overcome them are indicated.

scholarly journals Self-updated four-node finite element using deep learning

2021 ◽  
Author(s):  
Jaeho Jung ◽  
Hyungmin Jun ◽  
Phill-Seung Lee
Keyword(s):  
Finite Element ◽  
Deep Learning ◽  
Iterative Solution ◽  
Solution Procedure ◽  
Element Formulation ◽  
Zero Energy ◽  
Energy Mode ◽  
Bending Modes ◽  
Solution Accuracy ◽  
Iterative Solution Procedure

AbstractThis paper introduces a new concept called self-updated finite element (SUFE). The finite element (FE) is activated through an iterative procedure to improve the solution accuracy without mesh refinement. A mode-based finite element formulation is devised for a four-node finite element and the assumed modal strain is employed for bending modes. A search procedure for optimal bending directions is implemented through deep learning for a given element deformation to minimize shear locking. The proposed element is called a self-updated four-node finite element, for which an iterative solution procedure is developed. The element passes the patch and zero-energy mode tests. As the number of iterations increases, the finite element solutions become more and more accurate, resulting in significantly accurate solutions with a few iterations. The SUFE concept is very effective, especially when the meshes are coarse and severely distorted. Its excellent performance is demonstrated through various numerical examples.

scholarly journals An Agile Approach to Improve the Usability of a Physical Telerehabilitation Platform

2019 ◽  
Vol 9 (3) ◽  
pp. 480 ◽  
Author(s):  
Hennry Pilco ◽  
Sandra Sanchez-Gordon ◽  
Tania Calle-Jimenez ◽  
Jorge Pérez-Medina ◽  
Yves Rybarczyk ◽  
...  
Keyword(s):  
Iterative Process ◽  
Usability Evaluation ◽  
Iterative Refinement ◽  
Smart Sensors ◽  
Therapeutic Exercise ◽  
Usability Problems ◽  
Kinect Camera ◽  
Development Cycle ◽  
Refinement Process ◽  
Agile Approach

The goal of a telerehabilitation platform is to safely and securely facilitate the rehabilitation of patients through the use of telecommunication technologies complemented with the use of biomedical smart sensors. The purpose of this study was to perform a usability evaluation of a telerehabilitation platform. To improve the level of usability, the researchers developed and proposed an iterative process. The platform uses a digital representation of the patient which duplicates the therapeutic exercise being executed by the patient; this is detected by a Kinect camera and sensors in real time. This study used inspection methods to perform a usability evaluation of an exploratory prototype of a telerehabilitation platform. In addition, a cognitive workload assessment was performed to complement the usability evaluation. Users were involved through all the stages of the iterative refinement process. Usability issues were progressively reduced from the first iteration to the fourth iteration according to improvements which were developed and applied by the experts. Usability issues originally cataloged as catastrophic were reduced to zero, major usability problems were reduced to ten (2.75%) and minor usability problems were decreased to 141 (38.74%). This study also intends to serve as a guide to improve the usability of e-Health systems in alignment with the software development cycle.

Research on the Convergence Condition of Iterative Solution for the Mathematical Model of Reservoir Power Generation Optimization

2020 ◽  
Author(s):  
Anqi Tan ◽  
Senlin Chen
Keyword(s):  
Mathematical Model ◽  
Power Generation ◽  
Iterative Process ◽  
Iterative Solution ◽  
Scheduling Optimization ◽  
Convergence Conditions ◽  
Generation Scheduling ◽  
Solution Convergence ◽  
Calculation Results ◽  
The Mathematical Model

<p>Discrete differential dynamic programming algorithm is widely used in reservoir power generation dispatching, but the problem of "dimensional disaster" still exists, and there are different degrees of limitations such as premature convergence and uncertainty of convergence. In the existing monographs and literature, there is little research on the algorithm itself. The iterative solution convergence conditions, initial parameters, and initial trajectory selection of the mathematical model for reservoir power generation scheduling optimization have important effects on the iterative process and results. The convergence conditions directly determine when the iterative process converges and its calculation results. In this paper, the solution convergence conditions are studied. Based on the calculation results of the mathematical model of reservoir power generation scheduling optimization, the method of iteratively solving the convergence conditions when different state quantities are used as control factors is systematically studied. Shuibuya Hydropower Station Scheduling results show that using this method to determine the termination step size can shorten the calculation time and obtain an optimization result close to the ideal value, avoid the randomness of the convergence process of the iterative solution, and improve the accuracy of the DDDP algorithm and the efficiency of the target value.</p>

An Interfacial Tracking Method for Ultrashort Pulse Laser Melting and Resolidification of a Thin Metal Film

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Yuwen Zhang ◽  
J. K. Chen
Keyword(s):  
Metal Film ◽  
Laser Energy ◽  
Film Surface ◽  
Iterative Solution ◽  
Coupling Factor ◽  
Solution Procedure ◽  
Thin Metal Film ◽  
Solidification Temperature ◽  
Ultrashort Pulse Laser ◽  
Tracking Method

An interfacial tracking method was developed to model rapid melting and resolidification of a freestanding metal film subject to an ultrashort laser pulse. The laser energy was deposited to the electrons near thin film surface, and subsequently diffused into a deeper part of the electron gas and transferred to the lattice. The energy equations for the electron and lattice were coupled through an electron-lattice coupling factor. Melting and resolidification were modeled by considering the interfacial energy balance and nucleation dynamics. An iterative solution procedure was employed to determine the elevated melting temperature and depressed solidification temperature in the ultrafast phase-change processes. The predicted surface lattice temperature, interfacial location, interfacial temperature, and interfacial velocity were compared with those obtained by an explicit enthalpy model. The effects of the electron thermal conductivity models, ballistic range, and laser fluence on the melting and resolidification were also investigated.

A New Testability Optimization Allocation Approach

2013 ◽  
Vol 328 ◽  
pp. 444-449 ◽  
Author(s):  
Gang Liu ◽  
Fang Li
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Iterative Process ◽  
Resource Constraints ◽  
Optimal Solution ◽  
Improved Genetic Algorithm ◽  
Numerical Example ◽  
Set Up ◽  
Optimization Allocation ◽  
Allocation Approach

This paper describes a methodology based on improved genetic algorithms (GA) and experiments plan to optimize the testability allocation. Test resources were reasonably configured for testability optimization allocation, in order to meet the testability allocation requirements and resource constraints. The optimal solution was not easy to solve of general genetic algorithm, and the initial parameter value was not easy to set up and other defects. So in order to more efficiently test and optimize the allocation, migration technology was introduced in the traditional genetic algorithm to optimize the iterative process, and initial parameters of algorithm could be adjusted by using AHP approach, consequently testability optimization allocation approach based on improved genetic algorithm was proposed. A numerical example is used to assess the method. and the examples show that this approach can quickly and efficiently to seek the optimal solution of testability optimization allocation problem.

Delamination Onset and Growth Prediction of Advanced Composite Materials With a Fabrication Flaw

2007 ◽  
Author(s):  
Jim Lua ◽  
Jagannathan Sankar
Keyword(s):  
Failure Load ◽  
Iterative Solution ◽  
Material Model ◽  
Solution Procedure ◽  
Model Parameters ◽  
Component Level ◽  
Cohesive Model ◽  
Advanced Composite ◽  
Fracture Parameters ◽  
Cohesive Models

The delamination failure mode is particularly significant in the damage tolerance design of advanced composite, since manufacturing flaws and in-service damage most often manifest themselves as interlaminar cracks. The primary goal of this paper is to evaluate the validity and accuracy of the developed cohesive interface model in predicting the fracture parameters at coupon and component level. To capture crack initiation and growth under mixed mode loading, a cohesive model based on a bi-linear constitutive material law is implemented in LSDYNA via a user-defined material model. The cohesive model parameters and the associated fracture toughness are determined for both primary and secondary bond coupons subjected to double cantilever beam and end notch flexure loading. An iterative solution procedure is used to determine the cohesive parameters by matching the failure load/displacement prediction with the observed test data. To explore the feasibility of using coupon level fracture parameters for fracture prediction at component level, the determined cohesive models are used to predict the critical failure load associated with delamination onset and growth of doubler specimens under axial and bending loads.

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