Establishing a prediction model is a key step for the implementation of prognostic and health management. The prediction model can be used to forecast the change trend of the characteristics of the vibration signal and analyze the potential failure in the future. Taking the vibration of power plant steam turbine as an example, the full vector fusion and fault prediction were studied. Due to the fact that the evaluation of the machine fault with only one transducer may result in a fault judgement with partiality, an information fusion method based on the theory of full vector spectrum was adopted to extract the vibration feature. An autoregressive prediction model was established. The collected vibration signals with pairing channels were fused. The time sequence of the fused vectors and spectrums were used to build the prediction model. The amplitude of main vector of rotating frequency and spectrum order structure were analyzed and predicted. The uncertainty of the spectrum structure can be eliminated by the information fusion. The reliability of the fault prediction was improved. The study on vibration prediction model system laid a technical foundation for the fault prognostic research.
By the techniques of prediction, equipment status deterioration laws can be drawn out from the machine historical state parameters and thus potential faults can be predicted. The maintenance plan can be arranged reasonably to ensure the safe operation of the equipment [
When a fault prediction model was established, fault signature was obtained from vibration transducers. Although multiple transducers were used in the monitoring system, fault signature was still extracted from one of them. Based on the change of eigenvalues or characteristic vector, possible failures could be predicted. According to the theory of full spectrum and holographic and full vector spectrum [
The structure of the full vector fault prediction and diagnosis system is shown in Figure
Diagram of prediction system based on full vector spectrum.
Since, in the same measurement section, vibration obtained by a single transducer has certain one-sidedness, information fusion is needed to extract the vibration vector. The vibration vector is the fused signal of the two transducers installed in different directions. It can reflect the actual circumstances of the machine vibration. It is a feasible way to judge the trend of equipment operating status by vibration vector.
Assuming that the two transducers of
The motion equations in
After some trigonometric function calculations, (
As shown in Figure
Ellipse orbit.
In Figure
If the ellipse was drawn in the same coordinate system, the running state of the rotor can be understood directly [
The maximum displacement of the rotor is at the vertex point of the major axis of the ellipse. The major axis of the ellipse is the biggest displacement of the vibration. It can stand for the size of the rotor vibration. Here the ellipse’s long half axis was called the main vibration vector, and the short half axis was called the assistant vibration vector.
According to the theory of full vector spectrum, the main vector of vibration harmonic can be simplified as a simple calculation by FFT [
In (
Prediction method of vibration vector was based on autoregressive (AR) model. Autoregressive model is a common form of time series [
For a stationary time sequence
Here
When
The parameter estimation of AR model is linear estimation, which is fast and robust, and it is easy to be used in practical engineering. ARMA(
The establishment of the model is shown in Figure
Process of prediction model establishment.
The order of the model is an important factor that affects the accuracy of the prediction results. Once the order number is selected, the prediction model structure is determined. At present, the commonly used order selection criteria were information criterion [
For the AR(
Mean value was estimated by
Self-covariance was estimated by
For the sample
Replace
The AR prediction model is established according to the historical data. In the process of using, as the data is updated, the number of order of the AR model remains unchanged, but the coefficients of each order are revised. A relational database based on Microsoft SQL Server was built in the monitoring system for the purpose of facilitating the trend analysis and fault prediction. There are real-time data tables and historical data tables in the database. Every two seconds the acquisition system collects a set of data for real-time monitoring. The prediction system reads the data from the historical data table and sends it into the established AR model for the trend analysis and numerical prediction. Historical data is divided into seven levels. The first level stores the data of the last 8 hours; the second level stores the data of the last day; the third level stores the data of the last week; the fourth level stores the data of the last month; the fifth level stores the data of the last three months; the sixth level stores the data for the last six months; and the seventh level stores the data for the last year. Historical data older than one year is no longer used for fault prediction. When the number of predicted steps was determined, the time span of prediction results was different with the different time data series.
In order to verify the correctness of the method for data fusion and prediction, an online monitoring system was installed in a power plant in China, and the vibration data were collected. The steam turbine of the power plant drives the feed water pump to supply water for the boiler. The rotor structure of the steam turbine feed pump group is composed of a steam turbine rotor, a feed water pump shaft, and a flexible coupling which is used for connecting the rotor and the feed pump shaft. The steam turbine feed pump on-site photo is shown in Figure
Photo of the steam turbine feed pump.
Internal structure of the steam turbine feed pump.
Layout of vibration measuring point.
The sampling frequency is 1600 Sa/s; sampling length is 1024 points; the rotor speed is 3000 r/min. The vibration waveforms of S5 and S6 are shown in Figure
Vibration wave of
Wave of
Wave of
Spectrum of
Spectrum of
Spectrum of
Figure
Full vector spectrum and shaft orbit.
Full vector spectrum
Shaft orbit
The fault severity can be determined by analyzing the vibration amplitude. Full vector data fusion was carried out based on the collected vibration signals to extract the full vector amplitude of rotating frequency. The AR(
Comparison between predicted and measured values.
The fault position and property can be determined in accordance with the machine structure by analysis the spectrum structure [
Obtaining signal with one single transducer, whether the transducer mounts in
Full vector spectrum prediction with AR(
Vibration analysis is one of the important methods for fault diagnosis of rotating machinery. By collecting the vibration signal and extracting the eigenvector, the established vibration analysis and prediction system can be used as an important support for equipment health management. By analyzing and predicting the vibration feature, it is possible to evaluate the operating status of the equipment, predict deterioration trends, and identify potential failures that may occur.
The established AR prediction model can predict the changes of vibration amplitude and full vector spectrum. By predicting the change of the amplitude, it is possible to determine the deterioration tendency of the equipment and to predict how long the alarm will occur. When the alarm is predicted to occur in the near future, the full vector spectrum prediction model is called to check the amplitude changes at different characteristic frequencies. The characteristic frequency is related to the corresponding equipment failure; for example, rotating frequency is related to the failure of dynamic unbalance. By examining the changes of the amplitude of the characteristic frequency in the spectrum, it is possible to judge out the possible fault to occur. The vibration feature prediction can provide a decision-making basis for the equipment management and maintenance department.
In the machine condition monitoring system, the AR model is an effective prediction method. It can be used to predict the change value of the vibration. The structure of the prediction model can be determined by the order number of the AR model. The order of the model was fixed. The coefficients of each order can be determined by the calculation of the sample data. In the actual condition monitoring system, the sampling data was changed as time goes on. The coefficients of each order can be modified to fit in with the latest running state by calculating the sample data in the latest period of time.
For the data feature extraction, since the full vector amplitude can reflect the maximum vibration amplitude of the equipment, the prediction model was constructed based on the full vector amplitude. The AR amplitude prediction model can forecast the change trend of the equipment effectively. By analyzing the structure characteristics and the change of full vector spectrum, the fault property and failure position can be predicted. Compared with signals with a single transducer, the full vector spectrum is more effective to reflect the fault condition of the equipment.
Signal feature extraction and prediction model establishment were two important aspects in the process of the fault prediction. The full vector fusion and fault prediction were studied with the turbine as the research object. The construction of the AR prediction model can effectively solve the problem of vibration data prediction. Since the signal of a single transducer has shortage of one-sidedness for the machine fault diagnosis, the information fusion was accomplished based on the theory of full vector spectrum. The full vector amplitude was extracted to reflect the strength of the equipment. The full vector spectrum was figured out to analyze the fault property. The amplitude and spectrum of fused signal can overcome the shortage of one-sidedness.
The established AR prediction model based on the time series full vector amplitude can determine the change of vibration intensity effectively. The established AR spectrum prediction model based on the time series full vector spectrum can predict the change of the structure of the vibration spectrum effectively. According to the failure mechanism of the machine equipment, it is possible to determine the nature and location of the fault by analyzing the predicted frequency spectrum. The study on signal feature extraction based on the theory of full vector spectrum and the construction of prediction model based on the theory of AR model lays a technical foundation for the further research of prognostic and health management.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This project is supported by the Guidance Program of the Key Projects of Scientific and Technical Research of Department of Education of Henan Province (13B603970.0), Natural Science Research Program of Department of Education of Henan Province (2010B460015), and the Opening Project of Key Laboratory of Precision Manufacturing Technology and Engineering, Henan Polytechnic University (PMTE201302A).