BP神经网络的理论及其在农业机械化中的应用研究
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摘要
BP神经网络是目前研究最为成熟、应用最为广泛的人工神经网络模型之一。由于其结构简单、可操作性强、具有较好的自学习能力、能够有效地解决非线性目标函数的逼近问题等优点,因此被广泛应用于自动控制、模式识别、图像识别、信号处理、预测、函数拟合、系统仿真等学科和领域中。但是,BP算法也存在许多不足。例如,初始学习率选取困难,收敛速度慢,接近最优解时易产生波动,有时还会出现振荡现象,对于具有增长趋势的时间序列预测问题外推效果不好等问题。因此,针对BP神经网络存在的这些问题进行深入系统的研究,不仅具有理论意义,也具有重要的应用价值。
理论已经证明,三层BP神经网络只要隐含层节点数足够多,就具有模拟任意复杂的非线性映射的能力,由此可见BP神经网络具有较强的拟合能力。但是,在实际应用中,有时人们不仅关心神经网络的拟合效果,而且也十分关心当输入为何值时,能使输出取得极大值或极小值的问题。这一问题实际是基于BP神经网络的优化问题,而对这一问题的研究,目前尚未见文献报导。虽然有些文献称为BP神经网络的优化研究,但都是关于BP神经网络权值、学习率和网络结构的优化研究；或者,根据BP神经网络的输入与输出关系,从中选择一个较好的输出值,这实际上并不是真正意义上的优化,而是一种模拟,是从模拟结果中选择一个较优方案。因此对真正的基于BP神经网络的优化方法进行探讨,不仅具有理论意义,也具有现实意义和应用价值。
本论文旨在通过研究,分析BP神经网络存在不足的原因,进而通过研究提出BP神经网络的改进算法及用于时间序列预测时的一种新方法。在此基础上,研究探讨基于BP神经网络的优化问题。最后,将BP神经网络理论上的研究成果用于黑龙江省农机总动力预测与气吸式割前摘脱联收机惯性分离室的工艺参数的优化中。
研究取得的成果主要有：
(1)分析指出了BP神经网络算法存在问题的原因和用BP神经网络进行时间序列预测时外推效果不好的原因。
(2)研究给出了一种改进的BP神经网络算法。
提出了每个权值分别对应一个学习率的改进BP算法。该算法使得负梯度方向的信息得到了更充分的利用,同时学习率实现了按需要变化,克服了BP神经网络接近最优解时产生波动和振荡现象、计算精度得到了明显提高,并且后一次的迭代计算继承了前一次迭代计算的学习率,因此可以提高学习速度。另外,改进BP算法基本不受初始学习率的影响,避免了初始学习率选取的困难。
(3)研究给出了一种基于BP神经网络的时间序列预测问题的新方法。
首先,分析指出了基于BP神经网络的预测问题存在的不足,根据基于BP神经网络的时间序列预测问题的结构特点,依据Z变换理论,给出了一种新的激活函数,并分析指出了在BP神经网络中,以y=x作为激活函数与y=a+bx作为激活函数等价的原因。其次,推导出了以y=x作为激活函数的BP算法的计算公式和模型。最后,通过示例和实例计算表明,对于具有增长趋势的时间序列预测问题,当以单极性S型函数作为激活函数时其外推效果不理想,而以y=x作为激活函数时外推效果较好。另外,y=x作为激活函数的外推效果基本不受数据处理区间的影响,而单极性S型函数作为激活函数时外推效果受处理区间的影响较大。并且以y=x作为激活函数可以克服单极性Sigmoid函数作为激活函数的BP神经网络在预测问题中存在的不足。
(4)研究给出了一种基于BP神经网络的优化方法。
该优化方法以单极性Sigmoid函数作为激活函数,以网络输出最大化为例,给出了基于BP神经网络的无约束和有约束优化问题的一般数学模型,在此基础上,给出了基于BP网络的无约束和有约束优化方法的基本思路,推导给出了BP神经网络输出对输入的偏导数,进而给出了基于BP神经网络的无约束和有约束优化方法的计算方法。
(5)编写了标准BP算法、改进BP算法、基于改进BP算法的时间序列预测方法和基于BP神经网络的优化方法的计算机程序。
(6)BP神经网络在农业机械化中的应用研究。
首先,运用编好的基于改进BP算法的时间序列预测程序对黑龙江省的农机总动力进行预测,给出了未来5年的农机总动力值。预测结果表明该预测方法具有较高的预测精度。其次,运用基于BP神经网络的优化程序对气吸式割前摘脱联收机惯性分离室的工艺参数进行优化,给出了分离室压力损失最小时的最佳工艺参数,优化结果可为此类型惯性分离室的设计和优化提供理论依据。
BP neural network is one of the most mature and widely used artificial neural network models. As it has the advantages of simple structure, easy to operate, good self-learning capability, effectively solve the approximation problems of nonlinear objective function, etc., which has been widely used in pattern recognition, signal processing, automatic control, prediction, image recognition, function approximation, system simulation and other disciplines and fields. However, BP algorithm also has many deficiencies. For example, the selection of initial learning rate is difficult, the rate of convergence is slow, the volatile appears when close to the optimal solution, and sometimes there is oscillation. It is ineffective extrapolated with growth trend of time series prediction problems. Therefore, it has not only of theoretical significance, but also important application value in further BP neural network systematic study of these issues.
It is proved that as long as the hidden nodes of three-layer BP neural network are enough, it has the capacity to simulate any complex nonlinear mapping, so the BP neural network has strong ability of the fitting ability. However, in practice, sometimes people not only care about the fitting effect of neural networks, but also very concerned about the value of the input, which can lead the output to achieve maximum or minimum. This problem is actually based on the optimization problem of BP neural network, by now, the research on this issue has not yet be reported. Although some literatures are referred to as BP neural network optimization, but they are focus on the weights, learning rate and network structure optimization of BP neural network, according to the relationship between BP neural network input and output, and to choose a better output value, which is actually not really optimization, but a simulation, it is to choose an optimal solution from simulation results. Therefore, it has not only of theoretical significance, but also important application value in exploration of real BP neural network optimization method.
This thesis aimed to analysis the reasons of BP neural network appeared shortages, and then proposed improved algorithm of BP neural network and a new method for time series prediction. On this basis, BP neural network optimization problems were discussed. Finally, the theoretical research production of BP neural network for prediction of Heilongjiang province agriculture machinery total power and processing parameters optimization of inertia separation chamber of stripper combine harvester with air suction.
The results achieved during the research were below:
(1) Analysis indicated the reasons of BP neural network algorithm appeared problems and poor extrapolation results of time series forecasting when use BP neural network.
(2) This study put forward an improved BP neural network algorithm.
It was proposed that each weight corresponds to an improved learning rate of BP algorithm. This algorithm made the negative gradient direction information was more fully utilized, while the learning rate achieved necessary changes. It overcame the fluctuation and oscillation when BP neural network close to the optimal solution, and significantly improved the calculated accuracy; also the latter iterative calculation continued the learning rate of previous iterative calculation, which can improve the learning rate. In addition, the improved BP algorithm was independent of the initial learning rate, which avoided the difficulties of learning rate selection.
(3) A new prediction method of BP neural network based time series was presented in this research.
First, the prediction shortcomings of BP neural network were indicated, according to the structural features of BP neural network time series prediction, based on Z transform theory, a new activate function was given. And in the BP neural network, as activation function was y=x, y=a+bx was the reason of equivalent to the activation function. Secondly, y=x was derived as the activation function of BP algorithm and the model formula. Finally, through examples calculation, it was showed that with the growth trend for time series prediction, the extrapolation results were not good when unipolar S-function as the activation function, but the extrapolation results were better when y=x as the activation function. In addition, the extrapolation results were not affected by data processing interval when y=x as the activation function, while the extrapolation results were influenced by the processing interval a lot when unipolar S-function as the activation function. And the y=x as the activation function can overcome the shortcomings of prediction problems of unipolar Sigmoid function as the activation.
(4) An optimization method was given based on BP neural network. The optimization method was according to unipolar Sigmoid function as the activation function, take the network maximize output for example, the general mathematical model of unconstrained and constrained optimization problem was given based on BP neural network, on this basis, the basic ideas of unconstrained and constrained optimization methods were given based on BP network, the partial derivative of BP neural network output to input was derived, and then the optimization calculation of unconstrained and constrained method was given.
(5) The standard BP algorithm was written, BP algorithm was improved, the optimization method of the computer program based on time series forecasting was improved.
(6) The application of BP neural network in agricultural mechanization was discussed.
First, the total power of Heilongjiang Province was predicted by improved BP algorithm based on programmed time series forecasting procedure, the results showed that the total power value of the next 5 years was given. Predicted results showed high prediction accuracy. Secondly, the BP neural network optimization program was used for suction stripping inertial separation chamber associated receiver to optimize the process parameters, the best technology parameters of separation chamber pressure loss minima was given, the results can provide a theoretical basis for design and optimization of this type inertial separator chamber.
理论已经证明,三层BP神经网络只要隐含层节点数足够多,就具有模拟任意复杂的非线性映射的能力,由此可见BP神经网络具有较强的拟合能力。但是,在实际应用中,有时人们不仅关心神经网络的拟合效果,而且也十分关心当输入为何值时,能使输出取得极大值或极小值的问题。这一问题实际是基于BP神经网络的优化问题,而对这一问题的研究,目前尚未见文献报导。虽然有些文献称为BP神经网络的优化研究,但都是关于BP神经网络权值、学习率和网络结构的优化研究；或者,根据BP神经网络的输入与输出关系,从中选择一个较好的输出值,这实际上并不是真正意义上的优化,而是一种模拟,是从模拟结果中选择一个较优方案。因此对真正的基于BP神经网络的优化方法进行探讨,不仅具有理论意义,也具有现实意义和应用价值。
本论文旨在通过研究,分析BP神经网络存在不足的原因,进而通过研究提出BP神经网络的改进算法及用于时间序列预测时的一种新方法。在此基础上,研究探讨基于BP神经网络的优化问题。最后,将BP神经网络理论上的研究成果用于黑龙江省农机总动力预测与气吸式割前摘脱联收机惯性分离室的工艺参数的优化中。
研究取得的成果主要有：
(1)分析指出了BP神经网络算法存在问题的原因和用BP神经网络进行时间序列预测时外推效果不好的原因。
(2)研究给出了一种改进的BP神经网络算法。
提出了每个权值分别对应一个学习率的改进BP算法。该算法使得负梯度方向的信息得到了更充分的利用,同时学习率实现了按需要变化,克服了BP神经网络接近最优解时产生波动和振荡现象、计算精度得到了明显提高,并且后一次的迭代计算继承了前一次迭代计算的学习率,因此可以提高学习速度。另外,改进BP算法基本不受初始学习率的影响,避免了初始学习率选取的困难。
(3)研究给出了一种基于BP神经网络的时间序列预测问题的新方法。
首先,分析指出了基于BP神经网络的预测问题存在的不足,根据基于BP神经网络的时间序列预测问题的结构特点,依据Z变换理论,给出了一种新的激活函数,并分析指出了在BP神经网络中,以y=x作为激活函数与y=a+bx作为激活函数等价的原因。其次,推导出了以y=x作为激活函数的BP算法的计算公式和模型。最后,通过示例和实例计算表明,对于具有增长趋势的时间序列预测问题,当以单极性S型函数作为激活函数时其外推效果不理想,而以y=x作为激活函数时外推效果较好。另外,y=x作为激活函数的外推效果基本不受数据处理区间的影响,而单极性S型函数作为激活函数时外推效果受处理区间的影响较大。并且以y=x作为激活函数可以克服单极性Sigmoid函数作为激活函数的BP神经网络在预测问题中存在的不足。
(4)研究给出了一种基于BP神经网络的优化方法。
该优化方法以单极性Sigmoid函数作为激活函数,以网络输出最大化为例,给出了基于BP神经网络的无约束和有约束优化问题的一般数学模型,在此基础上,给出了基于BP网络的无约束和有约束优化方法的基本思路,推导给出了BP神经网络输出对输入的偏导数,进而给出了基于BP神经网络的无约束和有约束优化方法的计算方法。
(5)编写了标准BP算法、改进BP算法、基于改进BP算法的时间序列预测方法和基于BP神经网络的优化方法的计算机程序。
(6)BP神经网络在农业机械化中的应用研究。
首先,运用编好的基于改进BP算法的时间序列预测程序对黑龙江省的农机总动力进行预测,给出了未来5年的农机总动力值。预测结果表明该预测方法具有较高的预测精度。其次,运用基于BP神经网络的优化程序对气吸式割前摘脱联收机惯性分离室的工艺参数进行优化,给出了分离室压力损失最小时的最佳工艺参数,优化结果可为此类型惯性分离室的设计和优化提供理论依据。
BP neural network is one of the most mature and widely used artificial neural network models. As it has the advantages of simple structure, easy to operate, good self-learning capability, effectively solve the approximation problems of nonlinear objective function, etc., which has been widely used in pattern recognition, signal processing, automatic control, prediction, image recognition, function approximation, system simulation and other disciplines and fields. However, BP algorithm also has many deficiencies. For example, the selection of initial learning rate is difficult, the rate of convergence is slow, the volatile appears when close to the optimal solution, and sometimes there is oscillation. It is ineffective extrapolated with growth trend of time series prediction problems. Therefore, it has not only of theoretical significance, but also important application value in further BP neural network systematic study of these issues.
It is proved that as long as the hidden nodes of three-layer BP neural network are enough, it has the capacity to simulate any complex nonlinear mapping, so the BP neural network has strong ability of the fitting ability. However, in practice, sometimes people not only care about the fitting effect of neural networks, but also very concerned about the value of the input, which can lead the output to achieve maximum or minimum. This problem is actually based on the optimization problem of BP neural network, by now, the research on this issue has not yet be reported. Although some literatures are referred to as BP neural network optimization, but they are focus on the weights, learning rate and network structure optimization of BP neural network, according to the relationship between BP neural network input and output, and to choose a better output value, which is actually not really optimization, but a simulation, it is to choose an optimal solution from simulation results. Therefore, it has not only of theoretical significance, but also important application value in exploration of real BP neural network optimization method.
This thesis aimed to analysis the reasons of BP neural network appeared shortages, and then proposed improved algorithm of BP neural network and a new method for time series prediction. On this basis, BP neural network optimization problems were discussed. Finally, the theoretical research production of BP neural network for prediction of Heilongjiang province agriculture machinery total power and processing parameters optimization of inertia separation chamber of stripper combine harvester with air suction.
The results achieved during the research were below:
(1) Analysis indicated the reasons of BP neural network algorithm appeared problems and poor extrapolation results of time series forecasting when use BP neural network.
(2) This study put forward an improved BP neural network algorithm.
It was proposed that each weight corresponds to an improved learning rate of BP algorithm. This algorithm made the negative gradient direction information was more fully utilized, while the learning rate achieved necessary changes. It overcame the fluctuation and oscillation when BP neural network close to the optimal solution, and significantly improved the calculated accuracy; also the latter iterative calculation continued the learning rate of previous iterative calculation, which can improve the learning rate. In addition, the improved BP algorithm was independent of the initial learning rate, which avoided the difficulties of learning rate selection.
(3) A new prediction method of BP neural network based time series was presented in this research.
First, the prediction shortcomings of BP neural network were indicated, according to the structural features of BP neural network time series prediction, based on Z transform theory, a new activate function was given. And in the BP neural network, as activation function was y=x, y=a+bx was the reason of equivalent to the activation function. Secondly, y=x was derived as the activation function of BP algorithm and the model formula. Finally, through examples calculation, it was showed that with the growth trend for time series prediction, the extrapolation results were not good when unipolar S-function as the activation function, but the extrapolation results were better when y=x as the activation function. In addition, the extrapolation results were not affected by data processing interval when y=x as the activation function, while the extrapolation results were influenced by the processing interval a lot when unipolar S-function as the activation function. And the y=x as the activation function can overcome the shortcomings of prediction problems of unipolar Sigmoid function as the activation.
(4) An optimization method was given based on BP neural network. The optimization method was according to unipolar Sigmoid function as the activation function, take the network maximize output for example, the general mathematical model of unconstrained and constrained optimization problem was given based on BP neural network, on this basis, the basic ideas of unconstrained and constrained optimization methods were given based on BP network, the partial derivative of BP neural network output to input was derived, and then the optimization calculation of unconstrained and constrained method was given.
(5) The standard BP algorithm was written, BP algorithm was improved, the optimization method of the computer program based on time series forecasting was improved.
(6) The application of BP neural network in agricultural mechanization was discussed.
First, the total power of Heilongjiang Province was predicted by improved BP algorithm based on programmed time series forecasting procedure, the results showed that the total power value of the next 5 years was given. Predicted results showed high prediction accuracy. Secondly, the BP neural network optimization program was used for suction stripping inertial separation chamber associated receiver to optimize the process parameters, the best technology parameters of separation chamber pressure loss minima was given, the results can provide a theoretical basis for design and optimization of this type inertial separator chamber.
引文
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