ПРИБОРЫ И ТЕХНИКА ЭКСПЕРИМЕНТА, 2013, № 3, с. 128-133
ЛАБОРАТОРНАЯ ТЕХНИКА
A RESEARCH OF DYNAMIC COMPENSATION OF CORIOLIS MASS FLOWMETER BASED ON BP NEURAL NETWORKS © 2013 г. Dezhi Zheng, Peng Peng*, Shangchun Fan
School of Instrument Science and Opto-electronics Engineering, Beihang University, Beijing, 100191, China *E-mail: ppjejf1987@163.com Received May 24, 2012
As a resonate sensor, Coriolis Mass Flowmeter (CMF) provides a direct measurement of mass flow and is widely used in flow measurement field. However, defect of dynamic characteristics has become the main factor which restricts its further application in batch filling processes. Based on theoretical analysis, a dynamic compensation system, BP (Back-Propagation) neural network dynamic compensation method is designed in order to solve this problem. Adding a neural network dynamic compensation segment after the sensor's output, the method uses the gradient descent method with an additional momentum factor for neural network training. Studies have shown that this method greatly improves the dynamic characteristics of the Coriolis mass flowmeter.
DOI: 10.7868/S0032816213020183
1. INTRODUCTION
Coriolis Mass Flowmeter (CMF) is a type of mass flow meter which provides a direct and high precision measurement of mass flow. When there is fluid flowing in the pipeline, Coriolis force generated by the vibration of the pipeline will cause a change of the pipeline's vibration in phase and amplitude [1]. Because of the expansion of application fields and improvement of the measurement accuracy, not only sensors need to have good static characteristics, but also should meet the requirements of the dynamic characteristics. Therefore, at present the dynamic characteristic has became an important indicator to evaluate the CMF performance. However, weakness of dynamic characteristic constrains CMF's further development [2], hence becomes one of the bottlenecks for CMF's widely application.
Generally speaking, there are two ways to improve the dynamic characteristics of sensors [3]: one is to describe the dynamic characteristics of sensors by low-level differential equations. We can use zero-pole placement method to design dynamic compensation. The other is to design the compensated part by actual characteristics of sensors. However, designing a dynamic filter depends on the compensated structure or the mathematical modeling of the system in advance [4]. The compensated filter design becomes much more complicated when the sensor model has highorders feature [5]. Once the mathematical model is determined, it is difficult to be changed and adapt to the continuous changing of the actual response. That is, the method lacks of self-adaptability. When the spectrum of this sensor has considerable amount in the
high-frequency region [6], post-processing is required to determine the applied.
Neural network is a kind of information processing paradigm that is inspired by the biological nervous systems. It has been applied in many fields such as high performance aircraft autopilots, automobile automatic guidance, breast cancer cell analysis, exploration, recognition speech and so on [7]. In recent years, to enhance and improve the dynamic characteristics of system has become an important application area of neural network. The neural network system is essentially a highly non-linear kinetics network system, self-adaptive, self-learning, self-organizing, with a huge amount of parallelism, fault tolerance.
Compared to traditional pole-zero compensation, dynamic compensation of Coriolis mass flowmeter based on neural networks does not need the mathematical model of the sensor in advance. Instead, it relies on the actual data of the dynamic response to train the neural network, so it can track the signal immediately as well as improve the dynamic response characteristics of the sensor [8]. Hence, we designed a compensation based on Back-Propagation (BP) neural network in this paper, with its feasibility been proved by the experimental results.
2. BASIC DYNAMIC COMPENSATION PRINCIPLE OF CORIOLIS MASS FLOWMETER
Figure 1 is a schematic representation of the structure of the U-tube Coriolis mass flowmeter [9]. The basic principle of the dynamic compensation of CMF is improving the dynamic response of the equivalent
system using a dynamic compensated digital filter at the end of the flow transmitter. Figure 2 is a generic compensated block diagram.
Generally, a linear dynamic compensated digital filter of the sensor can be described as a linear differential equation
y(k) + ^ aiy(k - i) biz(k - i).
(1)
From the equation (1), it can be seen that the compensated system's resonant frequency and damping ratio are different from the original one. When the parameters of the filter are chosen appropriately so that the damping ratio approaches the optimal, the dynamic measurement error of the CMF could be compensated in a large frequency range. However, the method must rely on the system's mathematical model. The poles and zeros of the system change as the flow changes, and so the accuracy online cannot be guaranteed.
This thesis adopts the approach of artificial neural network to accomplish the dynamic compensation of the CMF. In this method, the normalization and linearization of the sensor system can be realized without the specific sensor model and its parameters, and then achieve the purpose of dynamic compensation. Using this method, the application is easy to realize and the dynamic characteristics of the sensor will be improved significantly.
The method of training the neural network with the parameters caught by the sensor's dynamic response is using a dynamic compensation at the end of the output. In this way, there is an error e(k) between the output with the compensation and the expected output, shown in Fig. 3. Therefore, the design of the dynamic compensation turns to be the optimization of reducing the error between the compensated output and the expected one.
The system's block diagram is shown as follows. In Fig. 3, u(k) is the input, z(k) is the original uncompensated output, y(k) is the output which is compensated. The reference modeling is the optimal second-order system (damping ratio is 0.707), and yd(k) is the output of the reference. With the continuous learning of the neural network (NN), the compensated output gradually approaches the output of the reference model. When the error e(k) = yd(k) - y(k) tends to zero, the optimal state of the system is acquired, the dynamic response time is greatly reduced, and the dynamic compensation is realized.
3. BACK-PROPAGATION NEURAL NETWORKS
In 1980s, David Rumelhart, Geoffrey Hinton and Ronald Williams, David Parker, and Yannn Le Cun invented the BP algorithm independently [10]. BP learning algorithm is described as follows: the operating signal propagates forward, error signal propagates oppo-
Cover Support tube Box
Shunt
Distance plate
Measuring tube 1
Measuring unit 1
Measuring tube 2
Measuring unit 2
-<— direction of fluid flow <!= main vibration
Fig. 1. The structure of the U-tube CMF.
u(k) Sensor z(k) Compensator y(k)
Fig. 2. Generic compensated block diagram.
Fig. 3. NN compensated block diagram.
Input layer Hidden layer Output layer
i = 0, 1, ..., n-1 j = 0, 1, ..., p-1 l = 0, 1, ..., q-1
Fig. 4. The structure of BP neural network.
sitely. Figure 4 is a basic structural diagram of BP neural network.
130
DEZHI ZHENG h gp.
Adj wei; ust ght
t
Back propagation
N
Fig. 5. The flow chart of the NN's training.
Take three layer BP neural networks for example, the input node is xt, the hidden layer node is yj, and
the output node is Zi. The network weight values between the input layer nodes and the hidden layer nodes are wij. The network weight values between the hidden layer nodes and the output layer nodes are vjl. 01 is the neuron threshold. The expected value of the output node is yd, the model is calculated as follows: output of hidden layer nodes
y j (k) = f
X WjX(k) -0
V i
netj(k) = X wijxi(k) - 0 i
output of output layer nodes
s
X vMyi (k) -0
= f (net j (k)),
V i
h (k) = f besides,
net)(k) = S vjiyj(k) -0r
= f (net j (k)),
(2)
(3)
(4)
(5)
advantage of using ANNs with respect to traditional methods consists of the fact that no a priori information on the model of the system is required; instead, only a set of input—output measures is used to infer a general rule that models the given sensor [12].
4. IMPROVED NETWORK TRAINING
METHOD WITH ADDING MOMENTUM
For multi-layer network, BP algorithm and its variants is the most common learning algorithm. It's an algorithm based on steepest descent method, and the algorithm uses the negative gradient information as the minimization of the descent direction which has slow learning speed for its linear convergence. Figure 5 is flow chart of the NN's training. Mostly, it needs thousands of step-by-step iterations or more. Moreover, the convergence rate of the algorithm depends on parameters' selection.
Hence, one chooses the gradient descent method with an additional momentum factor for neural network training. It means that using the gradient descent method to correct the network weights with an additional momentum which makes convergence rate faster and acquisition of the global minimum easier. Let us set the learning rate as n, the momentum factor as a.
Output nodes' error:
J(k) = 2S(**(k) - h(k))2
(6)
Generally, the use of these function requires special skills in the training of the networks and their commissioning into the overall control system [13]. And we se-
1 -x
- e as transfer
Most neural network models adopt BP neural network and variations in the field of practical application of artificial neural networks. It is also the key part of the feed-forward networks, which reflects the essence of the ideology of the neural network algorithm [10]. BP neural network is computationally intensive and ca
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