Research on prediction method of sensorless measurement of centrifugal pump operational state based on hybrid model

Centrifugal pumps are widely used in various fields such as industrial production and urban water supply. In order to achieve the monitoring of operational state of pumping systems, as well as the problems of inability to install sensors or high cost of sensors in practical engineering, the sensorless estimation method of centrifugal pump operational state provides a new opportunity for the monitoring and control of pumping systems. In this paper, a hybrid model based on QP model and neural network model is proposed to estimate the flow rate of rational pump by dividing the speed region. Taking a centrifugal pump as the research object, the operational points of the pump at different rotational speeds are acquired by experiments. Using the proposed method, a prediction model is established to predict the operational state of the pump. The prediction results are verified through experiments, and the error analysis of the prediction results is carried out. The results show that the proposed hybrid model can improve the prediction accuracy of centrifugal pump operational state and has certain practical value of engineering.


Introduction
Because centrifugal pumps have the advantages of simple structure, low installation and maintenance costs, they are widely used in various fields [1].According to the International Energy Agency, electric motors consume about 46% of the worlds electricity and account for nearly 70% of total industrial electricity consumption , while pump systems consume 22% of the electricity used by industrial motors [2].Therefore, improving the efficiency of pump and pumping system has a great potential for energy saving and carbon reduction [3].Currently, it is common to use inverters to optimize the control strategy map to reduce the energy consumption of pump system, and this optimization method requires real-time monitoring of the centrifugal pumps operating status [4].For some scenarios using sensors for monitoring is a challenging task, due to the impossibility to find a suitable location for sensor installation.Estimating the operating status of centrifugal pumps by monitoring a number of parameters of the motor makes sensorless monitoring methods possible [5].Sensorless monitoring technology for centrifugal pumps greatly improves the efficiency of monitoring, enhances the reliability of monitoring, and is the focus of the current research and future development trend of pump monitoring technology [6].
Currently, the main methods for monitoring centrifugal pump flow without sensing include the QP method [7], the QP extension method [8], and the artificial neural network-based estimation method [9], etc.The QP model is based on the characteristic curves QP and QH curves that can be measured for the pump itself.The mechanical power and speed of motor are estimated by means of a variable-speed drives(VSD), without using any additional measurements of the fluid handling system to estimate the operating point of pump.Since the operating point of a centrifugal pump depends on the operation at the intersection of pump characteristic curve QH and the process characteristic curve, Tamminen [10] proposed a method based on process curve to predict the state of centrifugal pump.The method automatically selects the more accurate of the QP or QH methods for operating point estimation, thereby reducing the risk of misestimation.Neural networks have good nonlinear fitting ability and are one of the most commonly used methods for fitting models [9].Wu [11] proposed a centrifugal pump flow prediction method with a two-layer neural network structure based on Bayesian regularized back propagation.Compared with the traditional QP estimation model, the new model has better nonlinearity and higher estimation accuracy.
When the velocity difference is too large, the affinity law does not apply.Therefore, we propose a hybrid model based on the prediction of different speed regions.A neural network model is used to predict flow rate when it is above the speed threshold, and a QP model is used to predict flow rate when it is below the speed threshold.The experimental results proved that the model has high prediction accuracy compared to the basic QP model and neural network model model.

QP-curve-based estimation method
The characteristic curve of the pump at the nominal speed is determined and can be converted to the current speed by the affinity law in equations (1).
where Q is the actual flow rate, H is the actual head, P is the actual power, n is the actual speed, Q 0 is the rated flow rate, H 0 is the rated head, P 0 is the rated power, n 0 is the rated speed.
As shown in figure 1, the flow rate Q est is calculated using power P act by transforming the curves QP and QH through the affinity law, and then the head H est can be calculated from the above flow rate Q est .In the QP method, the transformation of the QP curves based on the speed of the motor and the calculation of the flow rate using the power are the two key steps.Therefore, centrifugal pump speed and power are important variables in flow prediction.
where a 0 -a 9 and b 0 -b 9 are the fitting coefficients, f is the frequency.

Hybrid-model estimation method
When the actual speed does not differ significantly from the rated speed, the predictions of the QP model meet the requirements for monitoring and control.The affinity law is used under the condition that the efficiency of the centrifugal pump is constant.However, when the actual speed differs too much from the rated speed, the efficiency of the centrifugal pump has changed.The prediction results of the QP model will have a large deviation from the actual operating condition.Therefore, a hybrid model is proposed to predict the operating state of centrifugal pumps more accurately.
As shown in figure 2, firstly, a rotational speed threshold nc is set to differentiate between high and low rotational speed regions, so that a more appropriate method can be used to predict the flow rate in different regions.In the high speed region, the prediction of flow rate by affinity law has higher accuracy, so the artificial neural network (ANN) with stronger nonlinear fitting ability is used as the prediction model.In the low speed region, the prediction of flow rate by affinity law has a large error.Therefore, several characteristic curve QP with different input frequencies are introduced with equations (4) [12], the centrifugal pump characteristic curve at the current rotational speed is corrected by the affinity law, and the predicted values obtained at different rotational speeds are weighted and averaged to obtain the final predicted value of the centrifugal pump operating state.To simplify the model, two characteristic curves adjacent to the current speed are used as reference transformations.The closer the curves are to each other, the more weighted they are as predicted flows.Since the head prediction error mainly comes from the predicted flow value, the QP model is accurate enough to predict the head.Therefore, for the prediction of head, equation ( 2) is used as the model to predict the head over the entire range.

Q c c P c P c P
where c 0 -c 9 is the fitting coefficients, n l is adjacent low curves, n l is adjacent high curves, flow value Q 1 is predicted by the hiogh curve, flow value Q 2 is predicted by the low curve.

Experimental measurement
In this study, measured data from one branch of a small pumping station configured with four pumps was selected as the object of study.As shown in figure 3, the test bench mainly consists of centrifugal circulating pumps HB36-12B, variable speed drive, gauge flow meter, inlet/discharge pressure sensor, control discharge valve, water tank, power supply equipment, signal acquisition card and so on.Due to the specificity of the pump, the speed varies linearly with the control voltage, so the control voltage is considered as an input value instead of frequency or speed.Each sensors have an error of no more than 1%.

Prediction steps
Due to the specificity of the pump, we use the control voltage as an input parameter instead of speed or frequency, and the speed threshold is set to 3.8V.Therefore, in the high speed region, a neural network is used to fit the data of pump at control voltages of 4.4V and 3.8V.The control voltage and power are used as input parameters and the flow rate as the output value.In the low speed region, equation ( 4) was used to fit the curves of QP1 and QP2.Thus, QP1 corresponds to a speed control voltage of 3.8V, and QP2 corresponds to a speed control voltage of 3.2V.Equation ( 5) is used to calculate the weighted flow values.Equation ( 2) is used to fit all baseline data points and as a model for head prediction.

Results and discussion
To verify the reliability of the model, the proposed hybrid model is compared with the basic QP model and neural network model.Prediction of 8 flow points (form small to large) at control voltages of 4.1V and 3.5V.In addition, it is verified by another pump-2 on the test bench.As shown in figure 5 and figure 6, the overall performance of the hybrid model is the best.Meanwhile, the flow estimation of the neural network is affected by the sample number, data fluctuation, etc., the prediction results are very unstable, and the error is very large at small flow rates.Overall, three prediction models show that the relative error of prediction decreases with flow increases, the relative error of the prediction decreases gradually.The average relative error for the hybrid model, QP model, and ANN models are 1.46%, 2.68% and 10.18%.
As shown in figure 7 and figure 8, the predicted flow rate is determined to predict value of head.The average relative error for the hybrid model, QP model, and ANN models are 1.52%, 2.78% and 6.48%.
The maximum relative error of the hybrid model does not exceed 5% and still performs well compared to the other two models.As the three prediction methods in the prediction of head are flow rate prediction results are realized on the basis of the results, therefore, the results of ANN head prediction are also very unstable, and the accuracy of the prediction results fluctuates greatly.

Figure 1 .
Figure 1.QP characteristic curve method: (a) Q-P curves and (b) Q-H curve.The polynomial fitting equations of QP and QH at different rotational frequencies are shown in equations (2)-(3).

Q
b b f b P b f b fP b P b f P b fP b P b f

Figure 2 .
Figure 2. Flowchart of hybrid model predicting the state of centrifugal pumps.

Figure 3 .
Figure 3. Schematic diagram of test bench branch.In order to establish the prediction model, the rotational speed control voltages of 4.4V, 3.8V, and 3.2V are selected as the reference.To ensure the reliability of the data, ten data points were measured at each speed and each data point was repeated eight times.The QP and QH curve is shown in figure4.