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首页> 外文期刊>IEEE transactions on systems, man, and cybernetics. Part A, Systems and humans >Constructing a model hierarchy with background knowledge for structural risk minimization: application to biological treatment of wastewater
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Constructing a model hierarchy with background knowledge for structural risk minimization: application to biological treatment of wastewater

机译：使用背景知识构建模型层次结构以最小化结构风险：在废水生物处理中的应用

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This article introduces a novel approach to the issue of learning from empirical data coming from complex systems that are continuous, dynamic, highly nonlinear, and stochastic. The main feature of this approach is that it attempts to integrate the powerful statistical learning theoretic methods and the valuable background knowledge that one possesses about the system under study. The learning machines that have been used, up to now, for the implementation of Vapnik's inductive principle of structural risk minimization (IPSRM) are of the "black-box" type, such as artificial neural networks, ARMA models, or polynomial functions. These are generic models that contain absolutely no knowledge about the problem at hand. They are used to approximate the behavior of any system and are prodigal in their requirements of training data. In addition, the conditions that underlie the theory of statistical learning would not hold true when these "black-box" models are used to describe highly complex systems. In this paper, it is argued that the use of a learning machine whose structure is developed on the basis of the physical mechanisms of the system under study is more advantageous. Such a machine will indeed be specific to the problem at hand and will require many less data points for training than their black-box counterparts. Furthermore, because this machine contains background knowledge about the system, it will provide better approximations of the various dynamic modes of this system and will, therefore, satisfy some of the prerequisites that are needed for meeting the conditions of statistical learning theory (SLT). This paper shows how to develop such a mechanistically based learning machine (i.e., a machine that contains background knowledge) for the case of biological wastewater treatment systems. Fuzzy logic concepts, combined with the results of the research in the area of wastewater engineering, will be utilized to construct such a machine. This machine has a hierarchical property and can, therefore, be used to implement the IPSRM.
机译：本文介绍了一种新颖的方法，可以从连续，动态，高度非线性和随机的复杂系统中的经验数据中学习。这种方法的主要特征是它试图将强大的统计学习理论方法与人们对所研究系统拥有的宝贵背景知识进行整合。迄今为止，用于实现Vapnik的结构化风险最小化（IPSRM）归纳原理的学习机属于“黑匣子”型，例如人工神经网络，ARMA模型或多项式函数。这些是通用模型，完全不包含有关当前问题的知识。它们用于近似任何系统的行为，并且对训练数据的要求不高。此外，当这些“黑匣子”模型用于描述高度复杂的系统时，统计学习理论的基础条件将不成立。在本文中，有人认为使用一种学习机是更有利的，该学习机的结构是根据所研究系统的物理机制开发的。这样的机器确实是针对当前问题的，与黑匣子机器相比，所需的训练数据点更少。此外，由于该机器包含有关系统的背景知识，它将提供该系统各种动态模式的更好近似，因此将满足满足统计学习理论（SLT）的条件所需的一些先决条件。本文说明了如何针对生物废水处理系统开发这种基于机械的学习机（即包含背景知识的机器）。模糊逻辑概念，结合废水工程领域的研究结果，将被用于构建这种机器。该计算机具有分层属性，因此可以用于实现IPSRM。

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