摘要
加工尺寸的预报建模是进行机械加工质量在线监控的必要条件，也是实现加工误差预报补偿控制的关键技术。因此，不断探索具有高精度和高速度、适用于现场应用的新型预报建模技术是非常必要的。
本文从机械加工过程的动态特征出发，对几种常用的加工尺寸预报模型的适用性进行了深入分析，在此基础上提出了三种适用于不同应用场合的加工尺寸在线建模预报方法。
针对灰色GM(1，1)模型对尺寸序列随机项反映不灵敏，预报精度不足的问题，根据灰色模型建模原理，重点分析了模型维数和背景值对改善GM(1，1)模型预报精度的作用，通过引入背景值参数，给出了GM(1，1)模型背景值的一般表达式。在此基础上，提出了GM(1，1)模型的优化问题，建立了以平均绝对预报误差最小为目标的GM(1，1)模型维数与背景值参数的优化模型，并根据该优化问题的特点，采用遗传算法实现模型维数与背景值参数的优化。用Matlab编制了相应的软件。
为进一步提高GM(1，1)模型的预报精度，研究了GM(1，1)模型残差修正算法。通过分析GM(1，1)模型残差序列的动态特征，根据时间序列组合预报的建模理论，提出了一种基于灰色模型与时间序列模型的GM(1，1)-AR组合预报模型，其中用GM(1，1)模型对加工尺寸进行等维递补动态预报，用离线建立的AR模型对GM(1，1)模型残差进行在线预报和修正。
研究了基于神经网络的加工尺寸非线性预报建模问题。针对神经网络对尺寸序列趋势项反应不灵敏的问题，提出了一种基于神经网络与GM(1，1)模型的GM(1，1)-ANN组合预报模型，利用神经网络对GM(1，1)模型残差进行非线性预报和修正，以进一步提高组合模型的适用性。
采用遗传算法对神经网络连接权进行了离线优化。为提高遗传算法的收敛速度，采用了实数编码法、正态变异算子、稳态遗传算法，改进了期望值选择法，提
出一种匹配群体规模可变的选择策略。用BC编制了相应的软件。
在数控车床上连续加工了一批试件，利用试件外圆车削尺寸的实测数据，对
提出的三种建模方法进行了应用分析。根据实验结果，GM＊＊）优化模型与标准
GM＊＊）模型相比，模型误差减小3 0％以上，GM＊＊卜ANN与GM （卜AR组合模
型与标准GM＊＊）模型相比，其模型误差均减小50％以上，表明三种预报模型均具
有较高的精度。
在保持 GM＊＊）模型快速建模性能的前提下，通过优化、组合提出了三种用于
机械加工尺寸在线建模的新型预报模型。根据其相应的建模机理，GM＊万优化模
型适用于一般加工过程的尺寸序列预报建模，两种组合预报模型适用于具有强随
机干扰下的加工尺寸预报建模，其中GM＊，l卜ANN组合模型也是对复杂非线性加
工过程进行质量监控的一种有效方法。此外，本文的研究结果对其它领域的预报
建模问题亦有借鉴意义。
Forecasting of machining dimension is the necessary requisite in machining on-line quality control, the key technique in realizing forecasting compensatory control. So it's very essential to find out a new forecasting modeling technique with high accuracy and high speed, and which can be applied in on-the-spot application.
This essay, starting from the dynamic feature of machining process, made a careful analysis of the application of several common forecasting modeling finish size. On the basis of it, three forecasting model of machining dimension applicable to different occasions were put forward.
Due to GM(1,1) model's not responding well to machining dimension sequence random and lack of forecasting accuracy, and on the basis of grey model theory, the essay focused on modeling dimension and background value 's effect on improving GM(1,1) model forecasting precision . By introducing the parameter of background value of GM(1,1), the general expression formula of background value was given. Based on that, GM(1,1) optimization was raised. The background value and dimension parameter optimization model aimed at minimizing mean absolute forecasting error was established. By taking into account the optimization features, the optimization of modeling dimension and parameter of background value was realized by using Genetic Algorithms. The corresponding software was drawn up by using Matlab.
To improve GM(l,l)'s accuracy, the essay studied error correction method. Through analyzing the dynamic character of GM(1,1) error sequence and the theory of time sequence combination forecasting modeling, a kind of GM(1,1)-AR combination forecasting model based on GM(1,1) and time sequence model, in which GM(1,1) was used to carry out dynamic forecasting with the recursive compensation by the grey numbers of identical dimensions, and in which AR model built up by left-line was used to forecast and on-line correct GM(1,1) error.
The essay also studied nonlinear forecasting model based on neural networks . Because of neural networks not responding well to size sequence tendency item, a kind of GM(1,1)-ANN combination forecasting modeling based on neural networks and GM(1,1) was given. To make combination model application into full play, the essay carried out non-linear forecast and correction on GM(l,l)model error by using neural networks.
Genetic algorithms was used to left-line optimizing weights of neural networks. To
enhance the converging speed of genetic algorithms, real number code, normal mutation operator, steady-state genetic algorithms were used to improve expectation selecting method and matching group changeability alternate strategy was showed. The corresponding software was drawn up by using BC.
A batch of samples were processed continuously on NC turing machine tool. Then, application analysis was made on three modeling methods. Experiment result showed that, comparing with GM(1,1) optimizing model with standard GM(l,l)model, model error was reduced by over 30%.Comparing GM(1,1)-ANN and GM(1,1)-AR combination model with Standard GM(1,1), model error was reduced by over 50%. These showed, the three models all have high accuracy.
On the condition that GM(1,1) on-line modeling high speed was maintained, by optimization and combination, three new on-line forecasting modeling were put forward. According to its corresponding modeling mechanism, GM(1,1) optimizing model could be applied to general machining dimension modeling and forecasting; the two combination forecasting models could be applied to machining dimension forecasting modeling with strong random disturbance, in which GM(1,1)-ANN was more suitable to the application requirement of quality control in complicated non-linear machining process. In addition, this essay's research result can serve as a reference to forecasting modeling in other fields.
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