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IMPROVED MODELLING OF DYNAMIC SYSTEMS

机译:动态系统的改进建模

摘要

A method of modelling a dynamic system having a plurality of components which are transformed over time according to an influence thereupon by one or more other components, the method comprising the steps of (i) representing the transformation of the components, Xm, in a regular time interval tc from state values at a previous measured state, n-1, to state values at a subsequent measured state, n, as the product of the state values of the components, Xm, at the previous measured state, n-1, and the transformation of the components due to the influence thereupon by one or more other components, thus: (ii) solving the component transformation representation, using a solution of a system of linear differential equations, to give: (iii) rewriting the solution of the component transformation representation using simple variables, to give: (iv) approximating a value of E using a regression technique, (v) using the approximation of E to obtain a value for J, the transformation of the components due to the influence thereupon by one or more other components, and (vi) obtaining a model of the dynamic system which allows prediction of transformation of a state value of any component of the system at a previous state to a subsequent state in a chosen time interval from a product of the transformation J and the state value of the component at the previous state:
机译:一种对具有多个组件的动态系统进行建模的方法,该组件根据一个或多个其他组件的影响而随时间推移而变换,该方法包括以下步骤:(i)表示组件的变换X m ,在规则的时间间隔t c 中,从先前测量状态n-1的状态值到后续测量状态n的状态值作为状态值的乘积在先前的测量状态n-1处的分量X m 中的一个,以及由于一个或多个其他分量对其的影响而导致的分量转换,因此:(ii)求解该分量变换表示,使用线性微分方程组的解,可以得出:(iii)使用简单变量重写分量变换表示的解,可以得出:(iv)使用回归技术逼近E值,(v )使用E的近似值获得J,t的值由于一个或多个其他组件的影响而对组件进行转换,以及(vi)获得动态系统模型,该模型可以预测系统中任何组件的状态值从先前状态到后续状态的转换。从转换J与组件在先前状态下的状态值的乘积,在选定的时间间隔内进入状态:

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