Prediction and Optimization of Electrospun Polyacrylonitrile Fiber Diameter Based on Grey System Theory

This paper provides a new method for predicting the diameter of electrospun nanofibers. Based on the grey system theory, the effects of polyacrylonitrile mass fraction, voltage, flow rate, and receiving distance on fiber diameter were studied. The GM(1,1) (grey model) model and DNGM(1,1) (The DNGM (...

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Main Authors: Qihong Zhou, Liqun Lin, Ge Chen, Zhaoqun Du
Format: Article
Language:English
Published: MDPI AG 2019-07-01
Series:Materials
Subjects:
Online Access:https://www.mdpi.com/1996-1944/12/14/2237
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spelling doaj-4758c39e132547449f27de435664b6742020-11-25T00:19:36ZengMDPI AGMaterials1996-19442019-07-011214223710.3390/ma12142237ma12142237Prediction and Optimization of Electrospun Polyacrylonitrile Fiber Diameter Based on Grey System TheoryQihong Zhou0Liqun Lin1Ge Chen2Zhaoqun Du3College of Mechanical Engineering, Donghua University, Shanghai 201620, ChinaCollege of Mechanical Engineering, Donghua University, Shanghai 201620, ChinaCollege of Mechanical Engineering, Donghua University, Shanghai 201620, ChinaCollege of Textiles, Donghua University, Shanghai 201620, ChinaThis paper provides a new method for predicting the diameter of electrospun nanofibers. Based on the grey system theory, the effects of polyacrylonitrile mass fraction, voltage, flow rate, and receiving distance on fiber diameter were studied. The GM(1,1) (grey model) model and DNGM(1,1) (The DNGM (1,1) model is based on the whitening differential equation using parameters to Directly estimate the approximate Non-homogeneous sequence Grey prediction Model) model were established to predict fiber diameter by a single-factor change, and the results showed high prediction accuracy. The multi-variable grey model MGM(1,n) (MGM(1,n) is a Multivariate Grey prediction Model) was used for prediction of fiber diameter when multiple factors change simultaneously. The results showed that the average modeling fitting error is 8.62%. The background value coefficients of the MGM(1,n) model were optimized, the average modeling fitting error was reduced to 1.01%, and the average prediction error was reduced to 1.33%. Combining the fractional optimization with the background-value coefficient optimization, the optimal background-value coefficient <inline-formula> <math display="inline"> <semantics> <mi>&#945;</mi> </semantics> </math> </inline-formula> and the order r were selected. The results showed that the average modeling fitting error is 0.85%, and the average prediction error is 0.38%. The results demonstrate that the grey system theory can effectively predict the diameter of polyacrylonitrile electrospinning fibers with high prediction accuracy. This theory can increase the control of nanofiber diameters in production.https://www.mdpi.com/1996-1944/12/14/2237electrospinningnanofiber diameter predictiongrey prediction theorybackground value optimizationfractional order accumulation
collection DOAJ
language English
format Article
sources DOAJ
author Qihong Zhou
Liqun Lin
Ge Chen
Zhaoqun Du
spellingShingle Qihong Zhou
Liqun Lin
Ge Chen
Zhaoqun Du
Prediction and Optimization of Electrospun Polyacrylonitrile Fiber Diameter Based on Grey System Theory
Materials
electrospinning
nanofiber diameter prediction
grey prediction theory
background value optimization
fractional order accumulation
author_facet Qihong Zhou
Liqun Lin
Ge Chen
Zhaoqun Du
author_sort Qihong Zhou
title Prediction and Optimization of Electrospun Polyacrylonitrile Fiber Diameter Based on Grey System Theory
title_short Prediction and Optimization of Electrospun Polyacrylonitrile Fiber Diameter Based on Grey System Theory
title_full Prediction and Optimization of Electrospun Polyacrylonitrile Fiber Diameter Based on Grey System Theory
title_fullStr Prediction and Optimization of Electrospun Polyacrylonitrile Fiber Diameter Based on Grey System Theory
title_full_unstemmed Prediction and Optimization of Electrospun Polyacrylonitrile Fiber Diameter Based on Grey System Theory
title_sort prediction and optimization of electrospun polyacrylonitrile fiber diameter based on grey system theory
publisher MDPI AG
series Materials
issn 1996-1944
publishDate 2019-07-01
description This paper provides a new method for predicting the diameter of electrospun nanofibers. Based on the grey system theory, the effects of polyacrylonitrile mass fraction, voltage, flow rate, and receiving distance on fiber diameter were studied. The GM(1,1) (grey model) model and DNGM(1,1) (The DNGM (1,1) model is based on the whitening differential equation using parameters to Directly estimate the approximate Non-homogeneous sequence Grey prediction Model) model were established to predict fiber diameter by a single-factor change, and the results showed high prediction accuracy. The multi-variable grey model MGM(1,n) (MGM(1,n) is a Multivariate Grey prediction Model) was used for prediction of fiber diameter when multiple factors change simultaneously. The results showed that the average modeling fitting error is 8.62%. The background value coefficients of the MGM(1,n) model were optimized, the average modeling fitting error was reduced to 1.01%, and the average prediction error was reduced to 1.33%. Combining the fractional optimization with the background-value coefficient optimization, the optimal background-value coefficient <inline-formula> <math display="inline"> <semantics> <mi>&#945;</mi> </semantics> </math> </inline-formula> and the order r were selected. The results showed that the average modeling fitting error is 0.85%, and the average prediction error is 0.38%. The results demonstrate that the grey system theory can effectively predict the diameter of polyacrylonitrile electrospinning fibers with high prediction accuracy. This theory can increase the control of nanofiber diameters in production.
topic electrospinning
nanofiber diameter prediction
grey prediction theory
background value optimization
fractional order accumulation
url https://www.mdpi.com/1996-1944/12/14/2237
work_keys_str_mv AT qihongzhou predictionandoptimizationofelectrospunpolyacrylonitrilefiberdiameterbasedongreysystemtheory
AT liqunlin predictionandoptimizationofelectrospunpolyacrylonitrilefiberdiameterbasedongreysystemtheory
AT gechen predictionandoptimizationofelectrospunpolyacrylonitrilefiberdiameterbasedongreysystemtheory
AT zhaoqundu predictionandoptimizationofelectrospunpolyacrylonitrilefiberdiameterbasedongreysystemtheory
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