Computational Thinking - Учебное пособие, страница 5

To overcome the dependence of thelearning process on the initial settings and for a furtherimprovement of the mapping accuracy, we use a combinationof backpropagation and a genetic algorithm. The key idea isto vary the properties of each neuron in the net in addition tothe adaptation of the weights. The processing properties of aneuron are determined by its activation function. We use aspecial type of sigmoid activation function, the so-calledFermi function:The genetic algorithm optimizes the slopes (3 of the Fermifunctions). As the output of the network is essentially a sumover all weighted activation functions, we obtain a betteraccuracy by allowing to change the functions during training.The vector of slopes 0, in which the ith element denotes theslope of the Fermi function of neuron i, is treated as thestring of genetic information.

This string determines themapping capability of the network with respect to the overallmodeling error. For each slope vector 0 an appropriate set ofweights is determined by applying the improvedbackpropagation method Super SAB to the net. The training25process thus is an iteration of the genetic algorithm whichtunes the slopes and backpropagation to optimize the weightsfor each configuration of the slopes.Fermi Function.In the genetic algorithm, a population of neural nets,initialized with randomly distributed weights and slope valuesfor all neurons, is considered.

The genetic algorithm consistsof three parts:1. Determine the “fitness” of each member of the population.The member with the smallest value of E is considered thefittest.2. Generate a new population member by genetic operatorssuch as mutation and recombination from old members. Trainthis new member a certain time with the Super SAB methodand determine the fitness of the new member.3. If the new member is better than the worst old member,replace the worst old one with the new one.

Steps I to 3 arerepeated until an acceptable performance by the best memberis achieved. By this combination of the genetic algorithm anda modified gradient-based method, the average training timeto obtain a sufficiently small error is reduced considerablybecause ineffective training runs are avoided.Training Data GenerationThe aim of our work is to obtain a nonlinear black-box modelof a real process by training a neural net from measured dataonly. Other researchers in the field who treated systemidentification with neural networks for a neutralizationprocess generated the training data from applying randominputs to the process. This leads to a very sparserepresentation of the high gain area at the point ofequivalence in the training data set.

In contrast to thisapproach, we consider a training set which is generated by thesystem under closed-loop control with a reasonable PIcontroller. Instead of generating random input sequences tothe process, we changed the set point for the linear controllerrandomly during plant operation under control. This leads to26a sequence of setpoint steps which were tracked by theconventionally controlled system.

The resulting training setconsists of the two measured time series of the pumpfrequency and pH-value for 3.5 hours for this conventionallytracked setpoint sequence. The advantages of using data fromthe controlled plant go beyond the specific aspect ofneutralization plants that without control the plant can hardlybe operated within the most interesting.Experimental ResultsFor the experiments, the neural network was trained withdataset described above. The sampling time was chosen to beequal to the sampling time used for the PI-controller, whichwas T = 5 s. Thus there were 2800 data points in the trainingset. The training algorithm described above was implementedon IBM-compatible PCs running in parallel.

The requiredtraining time was 4 hours. After the completion of thetraining, the prediction of the network was tested with datawhich was not included in the training set.The extended DMC algorithm was realized using acommercial PC-based process monitoring. The predictionhorizon was chosen as NP=5, whereas the control horizonwas chosen as NU=l. In contrast to the long training time,the time required to compute the network output online forthe prediction and compute the controller output iteratively isshort enough to be performed.ConclusionsWe have presented an approach to model predictive controlof a highly nonlinear plant without a priori information aboutthe plant dynamics other than that the plant can be controlled(with unsatisfactory performance) by a conventionalcontroller. The process dynamics were identified frommeasured input/output time series only.

All we needed wasdata from 3.5 hours of normal plant operation under linearcontrol with varying setpoints. No special input sequences asrandom input signals or steps were used. We modified anonlinear extension to the standard DMC control scheme for27operation with the trained neural network. The controller wasimplemented using a small commercial PC based processcontrol system and shows a significantly improvedperformance compared to the linear controller for setpointtracking as well as for disturbance rejection. As we mentionedabove, in contrast to the time needed for prediction, thetraining time for the neural network used here was quite long.Thus our research activities concentrate on networks withshorter training time for online training of time-varyingprocess dynamics.

As the DMC approach is inherently amultivariable control strategy, we are also extending theproposed control algorithm to the MIMO case.Notes:Model Predictive Control – an advanced method of processcontrol intended to represent the behavior of complexdynamical systemsA PID (a Proportional-Integral-Derivative) Controller – acontrol loop feedback mechanism which calculates error valueand tries to minimize itThe Smith Predictor (invented by O.J.M.Smith in 1957) – atype of predictive controller for systems with pure time delayArtificial neural network – a computational model inspired bythe brain that is capable of machine learning and patternrecognitionA sigmoid function – a mathematical function having an “S”shape (a sigmoid curve)Exercises1.

Give Russian equivalents to the following words andphrases and explain them in your own words:To require more than one variable; to evaluate multipleprocess inputs; to predict the direction of the desired controlvariable;to minimize the difference between target andactual variables; the requirements increased significantly; dueto; a nonlinear behavior; to extend predictive techniques; to28incorporate nonlinear models; a feedforward network withsigmoid activation functions.2. Translate the sentences into Russian paying attention to theterms and abbreviations:1.

The main idea of MPC is to choose the control action byrepeatedly solving online optimal control problems.2. For processes that are highly nonlinear, the performance ofan MPC based on a linear model can be poor, which hasmotivated the development of Nonlinear Model PredictiveControl (NMPC), where a more accurate ( non-linear )model of the plant is used for prediction and optimization.3.

The proposed MPC control action is conceptually differentfrom the traditional robot control methods in that the controlaction is determined by optimizing a performance index overthe time horizon.4. The training data to set up the neural network model corefrom measuring the robot joint variables and torques duringthe running of a real robot.5. The research activities concentrate on networks withshorter training time for online training of time-varyingprocess design.6. In contrast to the time needed for prediction, the trainingneeded for prediction, the training time for the neuralnetwork used here was quite long.7.

The extended DMC algorithm was realized usingcommercial PC-based process monitoring and control system.8.In contrast to the long training time, the time requiredto compute the network output online for the prediction andcompute the controller output iteratively is short enough to beperformed within one sampling period in addition to thestandard tasks of the monitoring and control system on a PC.3. Give English equivalents to the following words andphrases:Методобратногораспространения;распознавание29текста; алгоритм обучения нейросети; обучение наоснове опыта; в процессе обучения величина ошибкиуменьшается; различные параметры и настройки; модельопределяет парадигму обучения; обучение за небольшоечисло шагов;оценочная функция; нейронные сетииспользуются для задач оптимизации; прогнозированиехаотических временных рядов; многослойная структуранейросети.4.

Answer the following questions:1. What is the main idea of model predictive control?2. Why is the Smith Predictor so appropriate to controlsystems with time-delay?3. What is the essence of Model-Based Predictive Controltechnology?4. How do statistical models contribute to the controlprocesses?5. What are the ways to extend predictive control techniques?6.