非线性降维混合神经网络预测器在分布式系统中的应用

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"基于非线性降维的混合神经网络分布式参数系统预测器" 这篇研究论文主要探讨了如何利用非线性降维技术构建一个混合神经网络预测器，以应对分布式参数系统(DPSs)中的非线性动态行为、外部干扰以及慢速设定点变化等问题。在分布式参数系统中，由于其内在的复杂性和高维度特性，预测和控制通常是一项挑战。该研究提出了一种创新的方法，结合非线性主成分分析(NL-PCA)网络和神经网络，以提高预测精度和效率。首先，NL-PCA网络被设计用于处理高维度的时空数据。非线性降维是解决这一问题的关键，它能够将高维度的数据映射到低维度的时间域中，同时保留系统的非线性特性。NL-PCA不同于传统的线性主成分分析(PCA)，它能更好地捕获和表示数据的非线性结构，这对于理解和建模复杂的分布式参数系统至关重要。接下来，混合神经网络被用来构建预测模型。这种网络通常由不同的神经网络架构（如前馈神经网络、循环神经网络或卷积神经网络等）组成，它们各自负责不同的任务，例如短期预测、长期预测或异常检测。通过整合这些网络的优势，混合神经网络能够更准确地模拟系统的动态行为，并适应各种输入和输出的变化。论文中可能还涉及递归算法的应用，这种算法用于训练神经网络模型，使其能够在每次新数据点到来时更新模型参数，以适应系统状态的变化。递归学习允许预测器不断学习和改进，提高对未知未来状态的预测能力。关键词包括神经网络、非线性偏微分方程分布参数系统、非线性降维、递归算法。这些关键词表明论文的重点在于利用非线性分析方法优化神经网络预测模型，以适应具有时空依赖性的复杂系统。该研究论文为理解和预测分布式参数系统的动态行为提供了一个新颖且有效的工具。通过非线性降维和混合神经网络，研究人员能够更准确地预测和控制那些受外部扰动和慢速变化影响的系统，这在化工、能源、环境等多个领域有广泛的应用潜力。

Hybrid neural network predictor for distributed parameter system

based on nonlinear dimension reduction

Mengling Wang

, Chenkun Qi

, Huaicheng Yan

, Hongbo Shi

Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology,

130, Meilong Road, Shanghai, China

Shanghai Jiao Tong University, 800 , Dongchuan Road, Shanghai, China

article info

Article history:

Received 11 May 2015

Received in revised form

16 July 2015

Accepted 1 August 2015

Available online 10 August 2015

Keywords:

Neural network

Nonlinear parabolic distributed parameter

system

Nonlinear dimension reduction

Recursive algorithm

abstract

In this study, a hybrid neural network predictor is proposed to predict spatiotemporal dynamics of the

nonlinear distributed parameter systems (DPSs) with unwanted disturbance or slow set point changes.

First, a nonlinear principal component analysis (NL-PCA) network is designed to transform the high-

dimensional spatiotemporal data into a low-dimensional time domain, which can better represent the

nonlinearity of the system compared to the linear time/space separation method. Then the hybrid NN

models are built to identify the low-dimensional temporal data. To capture the spatiotemporal dynamics

of DPS, the four-step recursive algorithm is used to obtain the time-varying weights of the model, while

the parameters of NN model does not need to online update. The simulations demonstrated show that

the proposed approach can achieve a good performance on prediction with system slow time-varying

dynamics.

1. Introduction

Many industrial processes are distributed parameter systems

(DPSs), generally describing by sets of partial differential equations

(PDEs) [1–4]. Modeling and control of DPSs have faced many

challenges, owing to their inﬁnite dimensional, spatial-temporal

nature and nonlinearities.

The nonlinear black-bo x identiﬁcation method such as the non-

linear state-space model, the nonlinear autoregressive with exogen-

ous input (NARX) model, fuzzy models, neural network (NN) can be

used to predict t he nonlinear dynamics of system based on the

ofﬂine input/output data [5–8]. And these nonlinear black-bo x

identiﬁcation methods can be easily integrat ed for online-prediction,

ﬁlter design and control design [9–11]. Using the black -bo x identi-

ﬁcati on methods for DPS, Guo and Varshney [12,13] proposed the NN

based time/space discretization method to model nonlinear DPS.

Howev er this kind of method req uires a large number of spatial

discretization points and results in a high-order model [14,15].

Another method, time/space separation method is proposed for the

appro ximation of DPSs using spatial basis functions expansion. After

the truncation, it results in a relati ve ly low-d imensional coefﬁci ent s

modeling problem, compar e to the time/space discretization based

modeling method.

For most time/space separation based modeling approach, the

modeling performance is very dependent on the choice of spatial

basis functions. And most modeling approaches for DPS are based

on principal component analysis (PCA) or Singular value decom-

position (SVD) method [14–19]. Though these methods are the

popular approaches to ﬁnd the principal spatial structures (spatial

basis functions) from the spatiotemporal data, these linear dimen-

sion reduction method may not ﬁnd the optimal spatial structures

to model the nonlinear dynamics efﬁciently. Thus, in [19],aﬁve-

layer NL-PCA network is trained for the nonlinear dimension

reduction and time/space reconstruction, while a NN model is

built to identify the low-dimensional time series. It can help to

describe the nonlinearity of the system better than the linear time/

space separation method.

As we know , industrial processes usually have set point changes,

or un w ant ed disturbances, the model is required to adapt to the

varied dynamics. The NL-PCA based NN model we proposed was

identiﬁed by the ofﬂine spatiotempor al data sets. It has limitation for

online-predic tion under some circumstances. As we know , any one-

model based predictor has a given predictive accuracy . Especially

when the system has slow time varying beha viors, the predictive

accuracy will be affected more or less [20–23]. Thus, the idea of the

combined method is proposed to improve prediction performances

in an effective way [24–26]. Bates and Granger showed that a linear

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/ locate/neucom

Neurocomputing

http://dx.doi.org/10.1016/j.neucom.2015.08.005

Corresponding author.

E-mail address: wml_ling@ecust.edu.cn (M. Wang).

Neurocomputing 171 (2016) 1591–1597

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