基于神经模糊系统的多模型建模方法及在软测量中的应用
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摘要
近年来,对于具有多变量、非线性、变量间有多重相关性特点的复杂系统的建模,采用较多的是利用神经网络、模糊逻辑等智能方法建立单一模型。然而,对辅助变量采用单一的函数关系来拟合输出,而不考虑数据组之间的联系和差异,会造成建模偏差,而且不同网络在不同输入空间中的预测性能会有所不同。当样本数量很多时,仅用一个网络来建立模型,会造成网络结构过于庞大,训练时间也会随之变长。
本文所做的工作是福建省自然科学基金项目“具有自学习功能的快速知识建模”的一部分。主要针对单模型结构建模方法存在的问题,对多模型结构建模方法进行了研究。首先采用多变量统计方法中利用偏最小二乘方法(PLS)对异常数据进行检测并剔除。在对建模数据进行分类时,提出了一种基于减法聚类改进的模糊C-均值(FCM)聚类方法,得到了合理的聚类数目;在建模方法的选择上,本文采用了结合减法聚类算法的ANFIS模型,该方法能以任意精度逼近非线性函数;针对多模型加权结构中权值较难确定的问题,提出了多模型非加权结构,通过仿真实验表明多模型非加权结构能有效提高模型的泛化能力,具有比单模型更好的建模效果;并提出了一种基于ANFIS的分类器,用于对现场数据进行判别分析,仿真表明这种判别分析方法理论意义明确、时间反应迅速、误判率低,具有很好的判别分析效果。针对输入变量多且具有多重相关性的复杂系统,提出了一种基于PLS的神经模糊多模型建模方法,并通过仿真应用表明,模型具有输出误差小、泛化能力强等特点,从而证明该建模方法的有效性。
最后,将这两种神经模糊多模型建模方法分别应用于厌氧消化过程中挥发性脂肪酸浓度的预测和飞机燃油箱剩余油量的预测中,通过与单模型网络的对比分析,得出多模型建模方法可以改进模型的泛化能力,具有更好的效果。
In recent years, the common method in modeling the complex systems which have characters of high dimension of inputs, nonlinearity and strong correlation between the inputs, is use intelligent methods such as neural network, fuzzy logic to establish a single model. However, the model would cause deviation if we use the single function to the secondary variable to fit the output, and without considering the links between the data sets. Moreover different networks in different input space, the forecast performance will be different. And when the samples are huge, only uses a network to establish a model will cause large network architecture, and we have to use the longer time for training.
In this paper, the author introduced multi-model technology based on the modeling problem of single-model structure. Firstly, the author used Partial Least Squares (PLS) method to detect outlier. And then proposed a modified Fuzzy C-Means clustering (FCM) based on Substractive Clustering, and received a reasonable cluster. The model which combined Substractive Clustering and ANFIS was introduced; this kind of model is fit for the nonlinear system.
Aiming at the dificultness to determine the weight in weighted multi-model structure, the non-weighted multi-model structure is proposed. Simulation results show that compared to the single model the non-weighted multi-model structure can enhance the model forecast ability effectively. And then the author proposed a classifier based on ANFIS. This classifier is tested efectively and fast and has less cluster error through simulation.
Aiming at the complex systems which have characters of high dimension and strong correlation between the inputs, a multi-model neuro-fuzzy modeling method based on PLS was proposed (PLS_MANFIS). Simulation results indicated that compared to the single model the PLS_MANFIS has a higher approaching precision and a stronger generalization capacity, thus proves the validity of this modeling method.
Finally, the multi-model neuro-fuzzy modeling methods proposed aboved were applied to predict the Volatile Fatty Acid (VFA) Concentration in Anaerobic Digestion Process and measure the aircraft fuel volume during flight, respectively. Both of the proposed methods were compared to the single model. The obtained results were strongly manifested that the multi-model modeling methods proposed had gotten better performance.
本文所做的工作是福建省自然科学基金项目“具有自学习功能的快速知识建模”的一部分。主要针对单模型结构建模方法存在的问题,对多模型结构建模方法进行了研究。首先采用多变量统计方法中利用偏最小二乘方法(PLS)对异常数据进行检测并剔除。在对建模数据进行分类时,提出了一种基于减法聚类改进的模糊C-均值(FCM)聚类方法,得到了合理的聚类数目;在建模方法的选择上,本文采用了结合减法聚类算法的ANFIS模型,该方法能以任意精度逼近非线性函数;针对多模型加权结构中权值较难确定的问题,提出了多模型非加权结构,通过仿真实验表明多模型非加权结构能有效提高模型的泛化能力,具有比单模型更好的建模效果;并提出了一种基于ANFIS的分类器,用于对现场数据进行判别分析,仿真表明这种判别分析方法理论意义明确、时间反应迅速、误判率低,具有很好的判别分析效果。针对输入变量多且具有多重相关性的复杂系统,提出了一种基于PLS的神经模糊多模型建模方法,并通过仿真应用表明,模型具有输出误差小、泛化能力强等特点,从而证明该建模方法的有效性。
最后,将这两种神经模糊多模型建模方法分别应用于厌氧消化过程中挥发性脂肪酸浓度的预测和飞机燃油箱剩余油量的预测中,通过与单模型网络的对比分析,得出多模型建模方法可以改进模型的泛化能力,具有更好的效果。
In recent years, the common method in modeling the complex systems which have characters of high dimension of inputs, nonlinearity and strong correlation between the inputs, is use intelligent methods such as neural network, fuzzy logic to establish a single model. However, the model would cause deviation if we use the single function to the secondary variable to fit the output, and without considering the links between the data sets. Moreover different networks in different input space, the forecast performance will be different. And when the samples are huge, only uses a network to establish a model will cause large network architecture, and we have to use the longer time for training.
In this paper, the author introduced multi-model technology based on the modeling problem of single-model structure. Firstly, the author used Partial Least Squares (PLS) method to detect outlier. And then proposed a modified Fuzzy C-Means clustering (FCM) based on Substractive Clustering, and received a reasonable cluster. The model which combined Substractive Clustering and ANFIS was introduced; this kind of model is fit for the nonlinear system.
Aiming at the dificultness to determine the weight in weighted multi-model structure, the non-weighted multi-model structure is proposed. Simulation results show that compared to the single model the non-weighted multi-model structure can enhance the model forecast ability effectively. And then the author proposed a classifier based on ANFIS. This classifier is tested efectively and fast and has less cluster error through simulation.
Aiming at the complex systems which have characters of high dimension and strong correlation between the inputs, a multi-model neuro-fuzzy modeling method based on PLS was proposed (PLS_MANFIS). Simulation results indicated that compared to the single model the PLS_MANFIS has a higher approaching precision and a stronger generalization capacity, thus proves the validity of this modeling method.
Finally, the multi-model neuro-fuzzy modeling methods proposed aboved were applied to predict the Volatile Fatty Acid (VFA) Concentration in Anaerobic Digestion Process and measure the aircraft fuel volume during flight, respectively. Both of the proposed methods were compared to the single model. The obtained results were strongly manifested that the multi-model modeling methods proposed had gotten better performance.
引文
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[2] Brosillow C B. Inferential Control of Process .AICHE [J], 1978, 24(3):485-509.
[3] T.J.Mcavoy. Contemplative Stance for Chemical Process Control. Automatic [J]. 1992, 28(2):441-442.
[4] 王旭东,邵惠鹤. 神经元网络建模与软测量技术[J]. 化工自动化及仪表,1996, 23(2):28-31.
[5] Tham M T. et al. Soft-sensing a Solution to the Problem of Measurement Delays [J]. Chem.Eng.Res and Des, 1989, 67(6):547-554.
[6] Yingxu You and Tianyou Cai. Soft sensing based on artificial neural network[C]. Proceedings of the American Control Conference, Albuquerque, New Mexico, June 1997.
[7] Luo Jianxu, Shao Huihe. Soft sensing modeling using neurofuzzy system based on rough set theory[C], Proceedings of the American Control Conference, Anchorage, AK May 8-10, 2002.
[8] Bates J M, Granger C W J. The Combination of Forecasts [J]. Operations Research Quarterly, 1969, 20:319-323.
[9] Cho S B, Kim J H. Combining Multiple Neural Networks by Fuzzy integral for Robust Classification [J]. IEEE Trans on Systems, Man and Cybernetics,1995, 25(2): 380-38.
[10] 吕立华,宋执环等. 用于过程软测量的多小波网络[J]. 仪器仪表学报,2002,23(5):508-51.
[11] 仲蔚,俞金寿. 基于模糊 C 均值聚类的多模型软测量建模[J]. 华东理工大学学报, 2000,26(l):83-87.
[12] 高林,顾幸生. 基于模糊聚类分析的多模型软测量技术及其应用[J]. 自动化仪表,2003,24(08):10-13.
[13] 张笑天,颜学峰,钱锋. 基于多神经网络模型的石脑油干点软测量[J]. 控制工程,2004,11(S1):52-54.
[14] 张宇,李柠,黄道. 基于多神经网络模型的酯化反应软测量[J]. 华东理工大学学报,2006,31(2):208-211.
[15] 阚晓旭,金晓明. RBF 多模型神经网络软测量技术在湿法磷酸生产中的应用[J]. 化工自动化与仪表,2006,33(1):64-66.
[16] 曲雨水,黄德先,金以慧. 多神经网络在软测量仪表中的应用[J]. 计算机工程与应用,2004,(10):208-210.
[17] 常玉清,王小刚,王福利. 基于多神经网络模型的软测量方法及应用[J]. 东北大学学报,2005,26(6):519-522.
[18] 林金星,沈炯,李益国. 基于递阶 G_K 聚类的热工过程多模型建模方法[J]. 中国电机工程学报,2006,26(11):23-27.
[19] 高林,顾幸生. 神经网络多模型软测量技术及其应用[J]. 华东理工大学学报,2004,30(5):559-563.
[20] 李柠,李少远,席裕庚. 基于 LPF 算法的多模型建模方法[J]. 控制与决策,2002,17(1):11-14.
[21] 王旭东,邵惠鹤,罗荣富. 分布式 RBF 神经网络及其在软测量方面的应用[J]. 控制理论与应用,1998,15(4):558-563.
[22] 许皖. 多模型软测量方法与应用[D]. 上海:华东理工大学硕士学位论文,2004.
[23] Cho S B, Kim J H, Combining multiple neural networks by fuzzy integral for recognition [J]. IEEE Transactions on System, Man and Cybernetics, 1995, 25(2):380-384.
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