This paper discusses a least square support vector machine (LSSVM) approach for forecasting stability parameters of Francis turbine unit. To achieve training and testing data for the models, four field tests were presented, especially for the vibration in
Hydroelectric power’s low cost, nearzero pollution emissions, and ability to quickly respond to peak loads make it a valuable renewable energy source [
Hydropower generation varies greatly between years with varying inflows, as well as competing water uses, such as flood control, water supply, recreation, and instream flow requirements [
There are some parameters to describe the unit stability, such as vibration, pressure, and noise. When the parameters exceed a certain value, the unit would run in an instability condition. The serious vibration of rotating parts will cause the shaft misalignment. Excessive vibration of generator rotor will increase the abrasion between slip ring and brush, and the brush would spark. What is worse, the whole plant house and equipment would be damaged when the resonance occurs. The fluctuating pressure in DT will make the flow system oscillate and the pipe wall crack and even the steel plate will be lost. Abnormal noise generated by unit unstable operation will be harmful to the workers’ physical and mental health. Existing recommendations in Chinese National Standards regarding stability parameters of hydropower units, GB/T 11348.52008 [
It is an effective way to understand the stability characteristics of a unit by field test under different working conditions. To determine a machine’s mechanical condition, Nässelqvist et al. [
For the task of stability parameters identification of a hydropower turbine, it is possible to define a regression vector from a set of inputs and nonlinear mapping in order to finally estimate a model suitable for prediction. There are some typical methods for regression applied in many areas of engineering research [
In this paper, a method based on LSSVM model is presented for prediction and regression of hydropower unit stability parameters. The data are obtained from a field test of a 200 MW Francis unit under different working conditions. The results show good performance of the model, which is of great significance to the unit condition monitoring and fault detection.
The rest of the paper is organized as follows: in Section
LSSVM is a modification to SVM regression formulation, proposed by Rubio et al. The main idea is to transform the problem from quadratic programs to solving a set of linear equations. The LSSVM regression framework can be formulated as follows [
The formulation includes a bias term, as in most standard SVM formulations, which is usually not the case in the other methods. The relative importance between the smoothness of the solution and data fitting is governed by the scalar,
By applying the kernel trick
The resulting LSSVM model can be evaluated at new point
In (
The feedforward NNBP is a very popular model in neural networks. It does not have feedback connections, but errors are backpropagated during model training. Least mean squared error is used. Many applications can be formulated when using a feedforward NNBP and the methodology is used as the model for most multilayered neural networks. Errors in the output determine measures of hidden layer output errors, which are used as a basis to adjust the connection weights between the pairs of layers. Recalculating the outputs is an iterative process that is carried out until the errors fall below a certain tolerance level. Learning rate parameters scale the adjustments to weights. A momentum parameter can also be used in scaling the adjustments from a previous iteration and adding to the adjustments in the current iteration [
How well the developing models will make predictions for cases that are not in the training set should be put into consideration. LSSVM and NNBP, like other nonlinear parametric models, can suffer from overfitting problem. The models that are too complex may fit the noise, not just the signal, leading to overfitting. Overfitting is dangerous because it can lead to predictions that are far beyond the range of the training data with LSSVM and NNBP. When the training data include enough information, overfitting can be avoided effectively. In the model applications, the data sets applied in LSSVM and NNBP models are selected from four field tests, ranging from 0 MW to 200 MW of the whole load. So the training data of the vibration and pressure have covered all the information of the unit, which can deal with overfitting problem of LSSVM and NNBP models.
LSSVM is based on the structural risk minimization principle, while NNBP is based on the empirical risk minimization principle. LSSVM includes two structural parts: the error term
In addition, the selection of the kernel function should satisfy the Mercer condition. The radial basis function (RBF) kernel is selected in this paper. LSSVM with RBF kernel yields a good generalization performance. And using LSSVM with an RBF kernel does not risk too much overfitting, which can be explained by looking to the optimal values of the kernel parameter [
The data sets for the LSSVM models were selected from field tests of a 200 MW Francis turbine unit in China. The test unit located near the load center of China Eastern Power Grid is mainly used to do the peak and frequency regulation. It was put into power generation on August 16, 2008. Table
Specifications.
Equipment  Type  Parameters 

Turbine  HLK333CLJ485  Rated power: 204.1 MW 


Generator  SF200/40/10800  Rated voltage: 13.8 kV 
The test will mainly measure the following parameters including frame vibration, guide bearing displacement, and pressure fluctuation in DT. Figure
Testing components in a hydropower unit.
Part of the sensor installation of LGB.
For a Francis turbine, it is significantly meaningful to solve the problem of pressure fluctuation influenced by the lowfrequency vortex in DT. Francis turbine works well under the optimal conditions, that is, rated head and wicker gate opening. There is less pressure in DT when the water in runner outlet flows along the axial direction, while, in deviation from the optimal operating conditions, there will be a certain circumferential velocity component for the water flow which will form vortex phenomenon under the action of centrifugal force.
As [
When
According to the test results, Figure
Pressure of DT changes with power and head.
Figure
Time series plot in access door of DT.
The vibration data related with power and head were collected on August 16, 2012, September 26, 2012, June 6, 2013, and October 15, 2013, respectively. The LGB is the main loadbearing part of the whole unit. As stated in Chinese National Standards GB/T11348.52008 and GB/T171892007, there are allowable values for LGB. For example, the radial vibration (
Vibration in
Time series plot of LGB vibration.
Figure
The vibration of LGB can be mainly affected by hydraulic, mechanical, and electrical factors. Under different working head, the vibration varies with rotation speed and power. As shown in Figure
The data set was divided into two groups: a training set and a testing set. The training and testing sets were applied for the making of the models and to evaluate the predictive authority of the constructed models, respectively. The free LSSVM toolbox (LSSVM v1.8) was applied with MATLAB version R2010a to gather all the LSSVM models.
The statistical means of the mean absolute error (MAE), the root mean square error (RMSE), and the coefficient of determination (
Data from the field tests on August 16, 2012, September 26, 2012, and June 6, 2013, under different working conditions were used for training the LSSVM model. The testing set including 400 pieces of data selected from the test on October 15, 2013, was used to validate the performance of the presented model. In this study, the Gaussian radial basis function was used as the kernel function of LSSVM. The parameters
Figure
LSSVM forecasting performance.
Models  Performance evaluation  

MAE  RMSE 
 
LSSVM  2.013  2.783  0.98 
NNBP  2.154  3.012  0.93 
Vibration forecasting results in
The testing criteria of MAE, RMSE, and
Data of pressure in DT from the field tests on August 16, 2012, June 6, 2013, and October 15, 2013, under different working conditions were used for training the LSSVM model. The testing set including 340 pieces of data selected from the test on September 26, 2012, was used to validate the performance of the presented model. The results of forecasting by LSSVM were compared with that by NNBP. The optimized obtained values of
Figure
LSSVM forecasting performance.
Models  Performance evaluation  

MAE  RMSE 
 
LSSVM  3.926  7.425  0.95 
NNBP  4.261  7.920  0.89 
Pressure forecasting results of LGB.
The test criteria parameters achieved for LSSVM and NNBP in Table
This paper has presented an LSSVM approach for forecasting stability parameters of a 200 MW Francis turbine unit. The objective of this paper was to examine the feasibility of using LSSVM in forecasting the vibration in
The authors declare that there is no conflict of interests regarding the publication of this paper.
Chen Qijuan planned the work and field tests. Qiao Liangliang drafted the main part of the paper and implemented the different forecasting methods, NNBP and LSSVM. Chen Qijuan contributed to the error analysis.
This research is funded by the National Natural Science Foundation of China (no. 51379160).