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1、使用RBF神经网络进行优化冷藏库的控制文摘:近年来,先进控制技术最优控制冷藏。但仍有许多缺点。的一个主要问题是,传统方法不能实现在线预测最优控制制冷系统的简单而有效的算法。一个RBF神经网络有很强的非线性映射能力,一个好的插值性能,价值和更高的训练速度。因此本文提出了一种两级RBF神经网络。将测量值与预测值,两级RBF神经网络用于在线预测最优控制的冷藏温度。新方法的应用效果显示一个巨大的成功。关键词:RBF神经网络、冷藏、在线预测最优控制。介绍冷库温度的预测最优控制找到了广泛应用在农业工程,特别是冷藏的水果和蔬菜保鲜的。所有的currently-used温度控制单元面临如何选择最适温度为控制对
2、象的问题，如何进行冷藏库温度的变化，和如何实现最优控制。大量的工作研究了前面的方法是基于泰勒级数理论和PID控制算法1,5。后来,毛皮商的转换方法,切比雪夫的理论和一些基础知识的系统我们得到了并且使用了更好的结论(2、3)。近年来,英国石油公司将神经网络用于冷库温度的最优控制。BP神经网络具有良好的非线性映射的性能,但它有太多的地方并不是那么理想,通常是其训练速度太慢了(2、5)。因此它不能方便地用于在线控制计算。后来也提出了一种两阶段RBF神经网络实现在线最优控制的冷藏温度。在第一阶段的使用过程中确定当前最佳制冷系统的温度,和第二个阶段是用于在未来时间点进行确定温度的值。此外, 他的解决方案
3、是用于制冷系统的直接行动，一个最难的问题是解决了。采用RBF神经网络分为两个阶段。第一阶段是用来确定最佳值的冷藏温度, 而第二个是用来预测温度。一般来说,假设n 个输入变量, 和m 个输出变量, .则： (1) (2)使用RBF神经网络最优控制冷藏，代表一个点的n维输入空间,而代表一个点的m维输出空间,假设隐藏的单位的数量是H。每个隐单元使用了两个参数,一个是标量,另一个是矢量。假设的训练样本集是。一般来说,应该满足。RBF神经网络是基于插值radius-based功能的性能。为了改善性能,使用下列方程计算出RBF神经网络的输出。 (3)在这里,分子是一种传统的RBF插值算法表达式,而分母不变
4、的插值表达式（1）通过这种分母,衰减指数函数的分子是取消了极大的分母。通过这种方式,改进的RBF神经网络具有更好的性能。3、在线计算的冷藏温度选择的目标价值冷藏温度,需要综合考虑所有的因素。为了合理地使用能源,制冷过程中应该有一个高性能系数，而和制冷量子与所需的能源的关系应该满足公式 (4)研究结果表明, 随蒸发温度和冷凝温度的下降而增加，而且一个更高的蒸发温度和冷凝温度较低有利于保持新鲜的水果和蔬菜。因此,制冷系统应该运行在更高的蒸发温度和冷凝温度较低的环境中。然而,蒸发温度显然是在冷藏条件下的温度对象的限制。为一种特殊的水果或蔬菜就进入冷藏，它的最佳储存温度可以得到正交实验方法。最佳储存温
5、度随着储存时间的增加而减小。单位水果或者蔬菜的损失满足公式 (5)式中是由水果或蔬菜被冻伤造成的，而是由于时间关系而日益恶化造成的。当环境温度升高了，降低但是会升高。这两个数据都和存储时间相关。因此， (6)在这个式子中，会随着温度的升高而降低，但是会升高。表示进入存储的时间，则表示表示存储时间,然后我们有 (7)对于水果或者蔬菜来说，其最佳储存温度应该满足以下方程 (8)设水果或蔬菜的重力是，其存储损失为，则在单位时间间隔内总存储损失为 (9)设表示最佳储存温度。它应该满足 (10)就是 (11)用上面传统的方法计算是比较费时间的，因此我们使用RBF神经网络实现的解决方案。这种RBF神经网络
6、的第一部分提出两级RBF神经网络。这种网络只有一个输出，并且有2n个输入，即, 和 ,。在这里作为隐藏的单位使用，方程（11）用于产生足够的训练样本。4、冷库温度的在线预测最优控制的关键问题之一的存储温度是如何准确预测温度。因为他们的鲁棒性,基于神经网络的预测方法吸引了越来越多的关注。BP神经网络是一种早期的神经网络用于这一目的。但它的训练时间通常是太长,和它有很多局部最小值点。因此,RBF神经网络由于其较高的训练速度吸引了越来越多的关注。本文采用两级RBF神经网络预测存储温度。在预测过程中,温度和湿度之间的耦合关系应该考虑。本文选择输出变量, 在同一时间内设置包括温度变量和湿度变量。输入变量
7、的选择考虑是否有执行控制,涉及以下两种不同的情况:案例l:自动控制系统假设有R个冷藏的操作变量和S个状态变量。考虑一个时间窗口组成的个时间点, (12)分别用和表示和 在时的值，令 (13) (14) 式中，这些预测的作用是根据（13）式中的向量确定（14）式中的，在当前时间，所有的测量结果可以用来构造预测网络的输入。假设所有的操作变量和状态变量可以被测量，但是在以后他们的值都是未知的。为了构建一个预测样本，相关的时间 应该满足公式 。否则,未知值将包含在示例将是不合理的。假设已经得到了足够多的样品，首先,计算隐藏单位的参数,然后计算存储温度的预测价值。例2:自动控制系统此时,输入变量的设置只
8、包含环境温度、湿度和量子存储的水果和蔬菜,等等。任何输入变量不出现在控制算法,而预测变量是稳定状态变量的值。RBF神经网络的非线性映射函数是用来设计稳定模型。当状态变量的稳定值,控制算法用于计算仓库的温度, 因此预测变量的集合不包含任何变量控制。这就是为什么预例2中设置预测变量和控制变量与例1的不同之处。5、在线最优控制的冷藏温度普通PID控制算法的一个变量单位需要以下公式 （15）和分别是初始值和控制变量的当前值。是分配值和控制对象的实际价值的区别,即 （16）和分别是时间点处的实际值和分配的控制对象的值，写出方程(15)的增量形式,然后我们可以得到 （17）式子中 是积分系数, 是微分系数
9、。用另一种形式写上面的方程,我们可以得到 （18）在得到控制变量的预测值的情况下，式(17)和（18）就会发生改变。表示当前时间，并且设在和 时刻变量的预测的值分别是和，令 （19）结合历史值和变量的预测值计算方程 (18) 的右边。令（20） （21） （22） 用这个方法，方程（18）可以变成一下格式 （23）上式中的值应该满足 ， ， （24）因此系统中只有6独立系数待定。选择这些系数作为条件来确保他们能够让的数学期望最小,也就是说,我们有以下方程 （25）与下面的约束条件所有的的初始值可以被选为。6、应用程序本文提出的方法已被用于最优控制温度冷藏的水果和蔬菜。表1列出了水果和蔬菜的日常
10、存储损失之前和之后使用本文提出的方法。对于一种特殊的水果或蔬菜来说,其日常损失率是指 式中表示水果和蔬菜的种类的数量, 和 分别表示每天入口的特殊水果或蔬菜的损失和市场价格，。只是损失不包括水果或蔬菜腐烂而被丢弃的部分, 而且也存在越来越不新鲜了而造成的价格降低，假设水果或蔬菜的市场价值是基于其存储容量，。每天总损失率可以根据以下公式计算。从表,我们可以看到,通过使用本文提出的控制方法,保鲜效果已经大大提高,系统运行更稳定7.结论本文提出了一种两级RBF神经网络计算的最佳冷藏温度和温度的预测。在此基础上,修改后的PID控制算法。以这种方式实现温度的在线优化控制,并得到了满意的结果。两级RBF神
11、经网络具有强大的非线性映射能力和插值的一个很好的性能值，它也有一个更高的训练速度。本文提出的方法可用于其它控制问题在农业工程与一个伟大的前景。Using RBF Neural Network for OptimumControl of a Cold StorageShi Guodong, Wang Qihong , Xu Yan & Xue GuoxinJiangsu Institution of Petrochemical Technology, Changzhou 213016, P.R.China(Received November 26, 1999)Abstract :In recen
12、t years ,advanced control technologies have been for the optimum control of a cold storage. But there are still a lot of shortcomings. One of the main problems is that the traditional methods cant realize the on-line predictive optimum control of a refrigerating system with simple and valid algorith
13、ms. An RBF neural network has a strong ability in nonlinear mapping, a good interpolating value performance, and a higher training speed. Thus a two-stage RBF neural network is proposed in this paper .Combining the measured values with the predicted values , the two-stage RBF neural network is used
14、for the on-line predictive optimum control of the cold storage temperature. The application results of the new methods show a great success.Keywords: RBF neural network, Cold storage, On-line prediction, optimum control.1. INTRODUCTIONThe predictive optimum control of cold storage temperature has fo
15、und a wide application in a agricultural engineering, especially for keeping fruits and vegetables fresh by cold storage. All of the currently-used temperature control units face the problems on how to choose the optimum temperature as the controlled object, how to predict the temperature variation
16、of the refrigerating storehouse and how to realize the optimum control. A lot of study efforts have been made. The earlier methods were based on the Taylors series theory and the PID control algorithm1,5.Later, Furriers transformation method, Chebyshevs theory and knowledge -based system were used a
17、nd better results were got 2,3.In recent years ,BP neural networks have been used for the optimum control of the cold storage temperature .A BP neural network has a good performance of nonlinear mapping, but it has too many local minimum points, and usually its training speed is too slow2,5. Hence i
18、t couldnt be used for on-line control calculation conveniently .This paper proposes a two -stage RBF neural network to realize the on-line optimum control of the cold storage temperature. The first stage is used to determine the current optimum refrigerating temperature of the system, and the second
19、 is used to predict the temperature values in the coming time points .Furthermore, an optimum problem is solved, whose solution is used to direct the action of the refrigerating system. 2. A TWO- STAGE RBF NEURAL NETWORKA two-stage RBF neural network is adopted. The first stage is used to determine
20、the optimum value of the cold storage temperature, and the second is used to predict the temperature. Generally, suppose that there are input variables , and output variables , . Let (1) (2)Using RBF Neural Network for Optimum control of a Cold Storage where denotes a point in the -dimensional input
21、 space ,while denotes a point in the dimensional output space ,Suppose that the number of the hidden units is .Every hidden unit uses two parameters, one is scalar quantity ,the other is vector .Suppose that the set of the training samples is .Generally, should be satisfied. RBF neural networks are
22、based on the interpolating value performance of radius-based functions. To improve this performance ,the following equation is used to calculate the -the output of an RBF neural network. (3)Here, the numerator is a traditional RBF interpolating algorithm expression, and the denominator is the interp
23、olating expression of constant 1.With this denominator, the attenuation of exponent functions in the numerator is canceled out greatly by that of the denominator. In this way ,the improved RBF neural network has a better performance.3. THE ON-LINE CALCULATION OF THE COLD STORAGE TEMPERATURETo choose
24、 the target value of the cold storage temperature, it is needed to take overall considerations about all factors. In order to use energy reasonably, the refrigeration process should have a high performance coefficient which is the ratio of the refrigeration quantum to the needed energy satisfying (4
25、)Research results show that increases as the evaporation temperature increases or the condensation temperature decreases 4,6,and a higher evaporation temperature and a lower condensation temperature are beneficial to keep fruits and vegetable fresh . Thus the refrigeration system should run under a
26、higher evaporation temperature and a lower condensation temperature. However the evaporation temperature is apparently limited by the temperature of the object under refrigeration.For a special kind of fruit or vegetable just entering the cold storage, its optimum storage temperature can be got with
27、 the orthogonal experimental method. The optimum storage temperature decreases with the increasing of the storage time. The loss of per unit of fruit or vegetable is (5)where is produced by frostbiting, while by deteriorating .When temperature increases , decreases and increases .Both of them are re
28、lated to the storage time , thus (6)where decreases and increases respectively when the temperature increases , denotes the time of entering the storage, while denotes the storage time, then we have (7)For fruit or vegetable, its optimum storage temperature should satisfy the following equation (8)L
29、et the gravity of fruit or vegetable be ,its storage loss , then the total storage loss in a unit time interval is (9)Let denote the optimum storage temperature in general .It should satisfy (10)that is, (11)The calculation of in above formulae with traditional methods is time consuming. Hence we us
30、e an RBF neural network to accomplish the solution of . This RBF neural network is the first part of the two-stage RBF neural network proposed in the paper .It has only one output , ,and inputs, that is , and ,.hidden units are used here .Equation(11) is used to produce enough training samples. 4、TH
31、E ON-LINE PREDICTION OF THE COLD STORAGE TEMPERATUREOne of the key problems of the optimum control over the storage temperature is how to predict the temperature accurately. Because of their robustness ,the prediction methods based on neural networks have attracted more and more attentions. BP neura
32、l network is a kind of earlier used neural network for this purpose .But its training time is usually too long, and it has many local minimum points. Thus the RBF neural network has attracted more and more attention thanks to its higher training speed. This paper employs a two-stage RBF neural netwo
33、rk to predict the storage temperature.In the prediction process, the coupling relation between the temperature and the humidity should be taken into account. The paper selects the output variables in a way that the set of the variables include the temperature variables and the humidity variables at
34、the same time. The choosing of the input variables should be taken into account no matter whether the control is performed or not, with the following two different cases involved:Case l: Automatic control system is offSuppose that there are R operating variables of the cold storage and state variabl
35、es .Consider a time window composed of time points, (12)Use and to denote the values of and at time point respectively . Let (13) (14)Where . The task of the prediction is to determine of (14)according to the vector of (13) .For the current time ,all of the measured results can be used to construct
36、the inputs of the prediction network. Suppose that all of the operating variables and state variables can be got by measuring ,and their values in the future are unknown. To construct a prediction sample ,the related time should satisfy .Otherwise, unknown values would be contained in the sample whi
37、ch would be unreasonable.Suppose that enough samples have been got .First, calculate the parameters of the hidden units, then calculate the prediction value of the storage temperature.Case2 :Automatic control system is onAt this time, the set of the input variables only contains the environmental te
38、mperature, humidity and quantum of the stored fruits and vegetables ,etc. Any of the input variables doesnt appear in the control algorithm ,while the prediction variables are the stable values of the state variables. The nonlinear mapping function of the RBF neural network is used to design the sta
39、ble models. When the stable values of the state variables have been obtained, the control algorithm is used to calculate the temperature of the storehouse, thus the set of the predicted variables wouldnt contain any variable to be controlled. Thats why the set of the predicted variables and the set
40、of the controlled variables under Case2 are different from those under Case1. 5.THE ON-LINE OPTIMUM CONTROL OF THE COLD STORAGE TEMPERATURE待添加的隐藏文字内容3The common PID control algorithm of a variable unit takes the following form （15）Where and are the initial value and the current value of the controll
41、ed variable respectively . is the difference between the assigned value and the real value of the control object, that is （16）where and are the real value at time point and the assigned value of the control object respectively. Write equation (15) in the incremental form ,then we have （17）Where is t
42、he integral coefficient, is the differential coefficient .Write the above equations in another form, then we have （18）Under the case of having got the predicted value of the controlled variable ,equations(17)and(18)should be changed .Let denote the current time ,and suppose that the predicted values
43、 at the instants and of variable with RBF neural network are and respectively ，Let （19）Combine the historic values with the predicted values of the variable to calculate the right side of equation(18).Let（20） （21） （22） In this way ,equation (18) is changed into the following form （23）The values of i
44、n above equations should satisfy ， ， （24）Hence there are only 6 independent coefficients to be determined. Choose them as the condition to determine them is that they should let the mathematical expectation of get its minimum, that is ,we have the following equation （25）with the following constraint conditionAll of the initial values of can be chosen as .6. APPLICATIONThe methods proposed in the paper have been used for the optimum control over the temperature of a cold storage for fruits and vegetables. Table 1 lists the daily storing losses of the fruits and
