发布时间 : 星期三 文章外文翻译--通过BP神经网络算法和改进的BP算法研究预测电渗析过程中分离百分比更新完毕开始阅读a06404a1856a561252d36f89
inputs[20,21]. BP algorithm is based on minimization of errors in neural networks. The errors are described as difference between the desired outputs and the actual ones [22]. The training is completed when the precision of the training is met (Fig. 1).
BPNs can be operated with better generalization and fault-tolerant capabilities, however, it has some shortcomings:
(1) Slow astringency can lead to a longer training time.
(2) Local extremum point may emerge in the training process.
So in this study, improved BP algorithms were used to improve the prediction capability of separation percent in the electrodialysis process. In this paper, adaptive learning rate method and flexible BP algorithm were the methods of improved BP algorithms to be applied in the electrodialysis process. 2. Materials and methods
2.1. Experimental instruments and materials
In the electrodialysis process, the experimental instruments and materials were shown in Table 1.
Moreover, other experimental materials were measuring cylinders, beakers, deionized water and so on. The purpose of these experiments was to study the effects of feed concentration, temperature, voltage and flow rate on the electrodialysis cell performance.
2.2. Cell and membranes
A plate and frame of electrodialysis cell which was made from polymethylmethacrylate (PMMA) was used to conduct the electrodialysis experiments (Fig. 2). The electrodialysis cell consisted of three parts and packed with a pair of CEM (cation exchange membrane) and AEM (anion exchange membrane) and a pair of electrodes. The overall dimensions of length, width and height of the electrodialysis cell were 0.191 m, 0.021 m and 0.181 m, respectively. The effective areas of the CEM and AEM were both 0.11 ×0.09 m 2 . Both electrodes were made of pure platinum. The surface area of each electrode was 0.115× 0.09 m 2 . And the volumes of dilute and concentrate compartments were 0.12 ×0.1 × 0.003 m3 and 0.12 × 0.1 ×0.006 m 3 , respectively.
NaCl (sodium chloride) solution was entered into the three compartments of the cell. Cation-exchange (CEM) and anion-exchange (AEM) membranes were permeable to cationic and anionic species, respectively. The two membranes were immersed in parallel, and an electric current was passed through the solution. The cations migrated to the cathode, and the anions migrated to the anode. The feed solution was divided into two streams. One stream was diluted water, and the other was concentrated water. Under a certain flow rate, the electrodialysis cell could operate to remove electrolytic ions. The ions were electrolyzed in the electrodialysis cell, so the cathode and anode occurred reactions as follows: Anode reactions: 2Cl ? ?2e→Cl2↑ H2O?2e→1=2O2↑ t2H t Cathode reaction: 2H2Ot2e→H2↑t2OH ? .
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In the anode reaction, Cl2 and O2 were produced. Moreover, H2 was produced in the cathode reaction. These gases could increase the resistance of the electrodialysis cell, so two little holes were used to release gases on the plate of the electrodialysis cell. And the concentrated streams were disposed off to prevent accumulation of these gases. List the physical and chemical characteristics of the membranes (Table 2). 2.3. Electrodialysis setup
Electrodialysis setup consisted of a tank of feed solution (TK-01), a DC power supply and two valves (GB-01, GB-02) for controlling flow rates of feed solution (Fig. 3). The total height of the electrodialysis process was 0.5 m. No cyclic regime was used for two concentrated streams and a diluted stream, and the diluted stream was collected for conductivities to predict and analysis. 2.4. Experimental principle
The electrodialysis process was one of membrane separation technologies. Under the direct electric field, electrodialysis technology utilized the selectivity ability of ion-exchange membranes to separate electrolytes from the solution, in order to realize the purposes of dilution, concentration or purification of the solution (Fig. 4). 2.5. Determination of the limiting current densities
The limiting current densities (LCDs) in the electrodialysis process are an important parameter which determines the electrical resistance and the current utilization. Usually, LCDs depend on membrane and solution properties as well as on the electrodialysis stack construction and various operational parameters such as the flow velocity of the diluted solution[23]. The methods of measurements of the limiting current density are voltage–current method, pH–current method and so on. In this paper, voltage–current method was used to determine the LCDs, the specific steps were as follows.
In the condition of constant temperature, concentration, and flow rate, adjust the buttons of voltmeter, and record the groups of voltages and currents. When the voltages were low, the currents had a linear relationship with the voltages. And as the voltages increased, the currents changed slightly. The limiting currents were determined by inflection points, and the limiting current densities were also obtained. For example, T=35 °C, C=0.5 g/L, Q=0.5 mL/s, as the voltages increased, the currents had a linear relationship with the voltages. The current was up to 0.51 A, the voltages had slight influence on the currents, so the limiting current, namely, the inflection point was 0.51 A (Fig. 5). The effective areas of the membranes were both 0.11×0.09 m 2 ,so LCD was 51.515 A/m 2 .
In the experiments, the operating currents could not exceed the limiting current. Otherwise, polarization occurred in the electrodialysis process and the prediction of separation percent would be meaningless. Using voltage–current method, LCDs were obtained in all the experimental conditions (Table 3).
To prevent the occurrence of polarization of the electrodialysis cell, all operating currents were controlled under the limiting currents. And in the electrodialysis experiments, the maximum limiting current was 0.80 A, and the effective areas of
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ion-exchange membranes were 0.11 ×0.09 m 2 , so the maximum limiting current density was 80.808 A/m 2 . 2.6. Experimental data
Experiments were carried out under the limiting current densities (Table 4). Four factors were studied: feed concentration (0.5 g/L, 1 g/L and 1.5 g/L),flow rate of dilute compartment (0.05 mL/s, 0.25 mL/s, 0.5 mL/s, 0.75 mL/s and 1 mL/s), reaction temperature (20 °C, 25 °C, 30 °C, 35 °C, 40 °C and 45 °C), and applied voltage (2 V, 5 V and 8 V).
3. BP neural networks and improved BP algorithms 3.1. BP neural networks
A typical BP neural network was a full-connected neural network including an input layer, a hidden layer and an output layer[24,25].The goal of the training process was to adjust the weights. The networks training was an unconstrained nonlinear minimization issue[26].Some researchers claimed that the networks with a single hidden layer could approximate any continuous function to any desired accuracy[27–29]. BP neural networks were composed of two parts which were forward and error back propagation. In the forward propagation, the inputs spread from the input layer, after being processed by some hidden layers, then reaching the output layer, the predictive values of the outputs in the output layer were compared with the actual outputs and the differences between them were aggregated to generate the errors. In the error back propagation, when the errors were not in the ranges of errors, the errors were back propagated by adjusting the weights. The learning process continued until the errors converged to a targeted value (Fig. 6). 3.2. Construction of BP neural networks
There were some precautions about BP neural networks:
(1) Pretreat samples. Usually samples were not used directly for network training, but engaged in pretreatment for raw data. The experimental data contained some uncertain factors in BPN training. A preprocessing method was so necessary for preparing the training and testing data to enhance the reliability.
(2) Optimize initial weights. Initial weights of the networks had impact on final training results, and affected the networks whether to achieve an acceptable accuracy or not.
(3) Select a number of hidden layers and neurons of hidden layers. The selection of hidden layers and neurons of hidden layers which affected mapping capabilities of complex issues directly were the most critical step. Now the reliable algorithm was to start with a few hidden layers and a number of neurons, train and test, then increase their numbers. Comparing the results of different training and test samples, select more appropriate numbers of hidden layers and their neurons. In this study, three-layer neural networks which had different neurons of a hidden layer were applied in the electrodialysis experiments.
(4) Choose training samples. The required samples of the networks depended on complex degrees of mapping relationships. Generally, the more complicated mapping relationships, the more training samples required. When choosing samples from all
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data, BPNs needed to obey the following principles: sufficient numbers, representative, and well-distributed. 3.3. Improved BP algorithms
BPNs were based on solid theory and rigorous derivation, however, it was found that there were many shortcomings in the training process of BPNs, including slow convergence, the emergence of local extremum and so on. In the practical application, BP algorithm was difficult to be competent, so some improved BP algorithms were raised to enhance prediction capability. There were some methods about improved BP algorithms, such as, additional momentum method, adaptive learning rate method ,flexible BP algorithm and so on. In this paper, adaptive learning rate method and flexible BP algorithm were used to predict separation percent in the electrodialysis process and compared prediction capability with that of BPNs. 3.3.1. Adaptive learning rate method
The training process of BP algorithm had a shortcoming of slow convergence which was affected by an inappropriate learning rate. In BP algorithm, the adjustments of weights depended on learning rates and gradients. And learning rate was constant in BP algorithm. In fact, when learning rate was lower, training time got longer and convergence became slower. When learning rate was too high, oscillation and divergence had emerged, this caused an unstable system. Adaptive learning rate was shown in Fig. 7.
The basic principle of adaptive learning rate: when learning rate (η) was increased, this caused shortening learning time; the higher the learning rate, the harder the convergence, and in this condition, learning rate should be decreased until the convergence of the training process. Learning rate was adjusted by the changing of errors and gradients, and also by the gradients of the learning rate according to error function. Moreover, the changing of the total error may be proceeded by adjusting heuristically, the rules were as follows:
(1) If the total error (E) decreased, learning rate needed to increase. (2) If the total error (E) increased, learning rate needed to decrease.
When the ratio of a new error to the original error exceeded a certain value (e.g. 1.04), learning rate decreased rapidly. 3.3.2. Flexible BP algorithm
Generally speaking, Sigmoid function was used to transfer data from the input layer to the hidden layer. Moreover, Sigmoid function kept infinite inputs within the limited realms of the outputs. When input variables were large, the slope of Sigmoid function would be close to 0. Even if the gradient changed slightly, this could induce the weights to make great changes, so the weights deviated gradually from the most optimistic value, and even made the weights of the networks cease in the amendment process.
When the training process vibrated, variable quantities of the weights would be decreased. And when the changing direction of the weights is kept constant in several iterations, the variable quantities of the weights would be increased. Therefore, the convergence speed of flexible BP algorithm had an advantage over other improved BP algorithms.
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