Fault Diagnosis of Induction Motors with Dynamical Neural Networks Jarmo Lehtonen Department of Automation and Systems Technology Helsinki University of Technology Espoo, Finland
Heikki N. Koivo Department of Automation and Systems Technology Helsinki University of Technology Espoo, Finland
[email protected]
[email protected]
Abstract –The paper studies the fault diagnosis of induction motors using neural network time-series models. The problem has been widely discussed in the literature and neural networks have been used in the fault diagnosis of induction motors. However, the neural network models have been mostly static - dynamical neural networks have been overlooked and have not received enough attention in this context. Here neural network time-series models are created for the normal and faulty motor. A filter bank of the models is formed and a Bayesian classifier is used to determine the correct classification of the motor condition, when tested with different types of FEM simulated data for different degrees of load. Keywords: Fault diagnosis, induction motor, neural networks, time-series, Bayesian classifier.
1
Introduction
The study of induction motor fault detection and identification has been of increasing interest during the last 20 years and a great amount of research has been done on the topic, e.g. [1] lists 365 books, papers and articles related to induction motor fault diagnosis. It is preferable to find faults before complete motor failure. This is called incipient fault detection. Often the motor can run with incipient faults, but eventually it will lead to motor failure causing downtime and large losses. Methods of induction motor fault diagnosis and detection are various. Most methods are based on stator current spectra (motor current signature analysis, MCSA) e.g. [ 2 ], neural/fuzzy inference systems e.g. [3], vibration analysis e.g. [4] or higher order current spectra e.g. [5]. Different faults often require different mechanisms for their detection. A model based method using time-series prediction for fault detection and identification in induction motors is less common. Most methods use fault diagnosis based on data directly through some means of limit checking or classification and not through application of models of the motor itself. Some papers advocate physical model-based systems, e.g. [6]. These models have the advantage of containing meaningful physical variables, but what the
models gain in physical relevance they often lose in accuracy. For example when feeding a physical-based model with converter fed voltages the results are inaccurate. For purposes of fault diagnosis from the stator current the simple physical-based models do not give enough accuracy when applied to rotor and stator faults. This problem is also noted in research literature. Empirical coefficients are used for phenomena that cannot be accurately modeled, so that proper results are achieved for motors of standard design. Problems arise when motors are studied that are of new design, that are in transient states or are fed by nonsinusoidal voltages [Arkkio 1991]. A reason for why a physical-based model cannot model the motor adequately is that it cannot properly take into account all the mechanical, structural and operational details, which differ from motor to motor. As physical model-based systems have their limitations, this study focuses on the use of time-series modeling for creating induction motor models for the purposes of fault diagnosis. The tool used for modeling in this work is a neural network based time-series model. This research focuses on three different motor conditions: healthy motor, rotor faulty motor and stator faulty motor condition. The motor is susceptible to several other faults than the ones modeled here, including different combinations of faults and faults of different severity. In the study rotor faults of different degree are tested on the system. The motor studied here is a 35 kW asynchronous machine with a squirrel cage rotor. The study is limited to the neural network approach to fault identification using a model-based structure. The data is provided by FEM (Finite Element Model) simulation of a real induction motor with different fault and load conditions. First the inputs and outputs for the system are chosen at a general level. Then the behavior of the chosen variables is studied in different fault and load conditions. After this the neural network models are constructed between the inputs and the outputs. The models are then used as a model bank for different fault cases and a Bayesian classifier is used as a decision making tool for choosing which model represents the given condition most accurately.
2
Faults in induction motor
Of all the electrical machines, induction motors are the most common in industry due to their simplicity, rugged structure, cheapness and easy maintainability. A threephase induction motor is the most popular polyphase induction motor. There are several different types of faults that can manifest themselves in an induction motor. Faults are often classified according to where they occur in the motor. The most common faults are stator faults, rotor faults, bearing faults and eccentricity faults. These faults are mechanical in nature, but they have varying effect on the electrical signatures of the motor. The most common faults can be further classified according to [7] as follows: 1) Stator faults resulting in the opening of the phase winding 2) Rotor faults due to broken rotor bars or broken endrings. 3) Static or dynamic air-gap irregularities (eccentricity faults) 4) Bent shaft (dynamic eccentricity) 5) Misalignment 6) Bearing and gear box failures Eccentricity faults can be static or dynamic in nature. Static eccentricity is such that the rotor has uneven air-gaps with respect to the stator but the positions and sizes of the air-gaps remain the same, i.e. the axes of the stator and rotor do not coincide. In case of dynamic eccentricity the rotational axis of the rotor is not in the centre of the rotor. Thus the air-gaps vary dynamically as the rotor rotates in the case of dynamic eccentricity. Faults can occur due to external effects, mistakes in production or assembly, or due to bad operating habits. Frequently faults occur due to several factors. For example, motor faults are frequently internal, such as bearing or winding faults, but the reason can be external, such as overheating caused by excessive dirt.
3
Modeling
The motor studied here is a 35 kW asynchronous machine with a squirrel cage rotor. The FEM models were constructed and simulated in the Laboratory of Electromechanics at Helsinki University of Technology. Models were built for different faults and load conditions. This research studies the data for healthy, rotor faulted and a stator faulted motor. Each condition is studied under three different loads: no load, half of the rated load, and full rated load. The rotor-fault is studied with two different cases: 1) A motor with three broken rotor bars and an end ring 2) A motor with one broken rotor bar.
A stator fault is a motor with a turn to turn short circuit in the stator windings. The FEM models were simulated with measured and simulated converter voltages. The measured converter voltages were taken from runs of a similar motor described by the models. The degree to which the stator current can be used for fault diagnosis is questionable. In general faults do not cause large deviations in the stator current, but some higher harmonics do arise, which can be detected from the data to some degree. The induction motor is fed with a supply voltage of 400V, which is divided into three phases. All of these voltages are used as inputs. Each voltage gives rise to a stator current with the same fundamental frequency and the same phase shift as the corresponding voltage. Thus each phase is considered here to represent a separate I/O relationship in the following manner: i1 (t ) = M (Φ1 , u1 (t -1),..., u1 (t - n ), i1 (t -1),..., i1 (t - n )), i2 (t ) = M (Φ 2 , u2 (t -1),..., u2 (t - n ), i2 (t -1),..., i2 (t - n )), (1) i3 (t ) = M (Φ 3 , u3 (t -1),..., u3 (t - n ), i3 (t -1),..., i3 (t - n )),
where 1, 2 and 3 represent the different phases, uj(k) is the voltage, ij(k) the current and Φj a set of model parameters for phase j at time k. Function M is a neural network function, specifically a Multilayer Perceptron Network. After some experimenting, a three layer neural network model was chosen as the basic neural network structure. The regressor structure was chosen to be nonlinear autoregressive with exogeneous inputs (NARX). This is because the error in the electrical measurement of the voltage inputted to the FEM-models is thought to be very small. The number of nodes for the hidden layer was determined empirically. The fault detection and identification (FDI) scheme is based on a model bank of different models, each of which represents a given motor operating condition (Fig. 1). The models are built using neural network based time-series models, which are constructed for the motor based on the data of the motor in a given condition. Measured input is given to the models from the motor and the model outputs are then compared to the measured motor output signal. A residual is formed from these differences between the system and model outputs. The residual is then used by some form of classifier to obtain a motor condition classification. The classifier chooses a model, which represents the data most accurately. Assuming valid and accurate model, this model should then be the model for the condition in which the system is operating at that moment. This is then used as the system fault classification result. Here a Bayesian classifier for classifying the motor condition from the residuals is used.
amplitude of the stator current increases as the load increases. In no-load condition the amplitude maximum is 50 A, for half a load 60A and for full load 100A, approximately. The figures also indicate that the form of the stator current changes with respect to load. Hence it is suitable to model the different load conditions separately.
4.2
Motor with rotor fault
Fig. 1. The structure of the model-based FDI system used.
4
Data
The next step is to look at the data and see if any regularity can be noted under different load and fault conditions. The data used in the study is generated using a FEM (Finite Element Method) model of a 35kW induction motor. The data is generated for three different load conditions: no load, half load and full load. The load is determined with respect to the nominal load present in the motor nameplate. The voltages used to feed the motor are obtained from a voltage converter. In some cases the motor can be fed with sinusoidal input voltage, but this study centers on motors with converter feed.
4.1
Healthy motor
Fig. 3. Stator current i1 of a rotor faulty motor with no load, half load and full load. Again the figures show that the amplitude increases with respect to the load. A rotor fault causes low frequency oscillation in the stator current which is more apparent in the higher load conditions. This can be seen from the figure on the left hand side. The amplitudes of the data are at the same level as in the healthy case, i.e. a rotor fault does not seem to cause an increase in amplitude by itself. There are, however, subtle changes in the shape of the data but no obvious characteristics of faults can be seen by eye.
4.3
Fig. 2. Healthy stator current i1 with no load, half load and full load. The figures above show the stator current (i1) when a healthy motor is under different load conditions. The right hand side picture on each figure is an up close zoom of the data on the left hand side. The figures show clearly that the
Motor with a stator turn fault
The analysis of currents shows that load is a significant factor in the shape of the stator current, hence it is necessary to obtain measurements in a steady state with a known load. The load can be estimated using the slip, because it is known that slip increases as a function of load. The figures also show that adequate data for fault diagnosis can be obtained in a short time interval.
1) Create the model structures for the different phases in under different fault and load conditions (3 phases, 3 loads and 3 faults means a total of 27 models). 2) Calculate the neural networks weights for each model using a suitable algorithm. Check that the optimization routine successfully avoids local minima in the process and that the models are accurate when tested with validation data. 3) The residuals of the models are calculated with respect to the data from different operation conditions. The residuals are calculated separately for each load, assuming that the estimate for the load can be obtained e.g. from the slip. 4) The necessary covariance matrices for the Bayesian classifier are calculated from the data. The a priori probabilities for the different fault conditions are chosen for the classifier. 5) The conditional probabilities can now be calculated from residual values corresponding to the given data, which is assumed to come from the motor in operation.
4.5
Fig. 4. Stator current i1 of a motor with a stator turn fault, with no load, half load and full load. A data set from a time interval of 0.25s to 0.5s is enough to capture the low frequency oscillations. Most of the fault information is present in the higher order harmonics of the currents, thus it is necessary to have a high enough sampling frequency. Here sampling frequency of 40 kHz is used.
Fig. 5. NN - model output (blue) and the testing data set (red) for a healthy motor under half load. Figure 5 shows that the neural network model corresponds with the validation data with good accuracy also by visual inspection.
4.4
Using a Bayesian classifier for 3-phase input and output with non-linear neural network models
The fault diagnostics scheme is tested by comparing it against a validation data, which was not used in neural network training. The results of the test are presented in the following tables (Table 1, The Bayesian probabilities for the different motor conditions with no load, Table 2 and Table 3). The structure of the tables is such that the data which is input to the models is in the columns. The rows represent probabilities given by the classifier for how well the model describes the given data. For example, consider Table 2. The Bayesian probabilities for the different motor conditions with no load, when the data to the models is from a motor with a healthy condition (the second column) the Bayesian probability that the data is from a model describing a healthy condition is 0.41. The highest probability for the operating condition corresponding to each input data is presented bolded, and in practise this would be the fault classification of the system for a given data. For this validation data set it can be seen that the system performs correct classification. The highest probabilities are on the diagonal of the tables, which means that the model representing the same data as the input to the fault diagnosis system has the highest probability for representing that data. The results indicate that the higher the load the more evident are the fault characteristics in the stator current i.e. the amplitude of the fault harmonics increases.
Results
The procedure for using the method is listed below as a reminder for the reader for how the results are obtained:
Table 1. The Bayesian probabilities for the different motor conditions with no load.
The condition for Data from which the classifier healthy probability is given motor 0.41 Healthy condition Rotor faulty condition with 3 broken bars & end ring 0.37 Stator faulty condition 0.22
Data from rotor Data from faulty motor with 1 stator broken bar faulty motor 0.38 0.28
0.44 0.18
0.21 0.51
Table 2. The Bayesian probabilities for the different motor conditions with half load. The condition for Data from which the classifier healthy probability is given motor 0.59 Healthy condition Rotor faulty condition with 3 broken bars & end ring 0.18 Stator faulty condition 0.22
Data from rotor Data from faulty motor with 1 stator broken bar faulty motor 0.26 0.26
0.71 0.03
0.0 0.74
Table 3. The Bayesian probabilities for the different motor conditions with full load. The condition for Data from which the classifier healthy probability is given motor 0.64 Healthy condition Rotor faulty condition with 3 broken bars & end ring 0.08 Stator faulty condition 0.28
Data from rotor Data from faulty motor with 1 stator broken bar faulty motor 0.02 0.28
0.98 0.00
0.03 0.70
Next, independent data was used in testing the models. The neural network models were not taught again. Table 4. The Bayesian probabilities for the different motor conditions with no load. Data from The condition for healthy which the classifier motor probability is given Healthy condition 0.36 Rotor faulty condition with 3 broken bars & end ring 0.37 Stator faulty condition 0.27
Data from Data from rotor faulty motor with 1 stator faulty motor broken bar 0.35 0.10
0.36 0.28
0.10 0.80
Table 5. The Bayesian probabilities for the different motor conditions with half load.
Data from The condition for healthy which the classifier motor probability is given 0.65 Healthy condition Rotor faulty condition with 3 broken bars & end ring 0.01 Stator faulty condition 0.34
Data from Data from rotor faulty motor with 1 stator faulty motor broken bar 0.64 0.06
0.04 0.32
0.0 0.94
Table 3. The Bayesian probabilities for the different motor conditions with full load. The condition for Data from which the classifier healthy probability is given motor 0.59 Healthy condition Rotor faulty condition with 3 broken bars & end ring 0.09 Stator faulty condition 0.31
Data from rotor Data from faulty motor with 1 stator broken bar faulty motor 0.12 0.05
0.70 0.18
0.02 0.98
The results show that a mild rotor fault cannot be diagnosed properly under no-load and half-load operation. The fault diagnosis system cannot make a distinction between the mild rotor fault and the healthy condition. The stator fault is diagnosed properly for the no load and half load conditions with good probability. For full load the classification results are proper. This is probably due to the fact that load amplifies the fault harmonics in the stator current, and therefore the fault indicator is stronger. When tested with validation data the rotor fault was diagnosed with a 0.98 probability in the full load condition and for the independent testing data the rotor fault is diagnosed with a 0.70 probability. The result is good, as it shows that the rotor fault can be detected gradually to some degree even when the model for the fault is created for a fault of different severity. This only applies for the full load conditions, however.
5
Conclusions
This paper studied the use of neural networks for modelbased fault diagnostics of induction motors. The idea was to use data provided by accurate FEM simulations of motor operation under different fault and load conditions to create identification based neural network model models which can be used for online fault diagnosis. The neural network models are created for each phase of the three phase induction motor, and each load condition is handled separately. Most of the faults cases have to be left out due to the unavailability of data for different fault conditions. The data is often a restriction for data-based models, because each different situation would require its own set of data, along with data for validation and testing. For this work a FEM model of a 35 kW induction motor was simulated for cases of a healthy, rotor faulted and stator faulted motor.
The parameters for the model were obtained from a real operational motor. No real measurement data was used in the thesis, but studies with FEM simulations of induction motors show that the data is very realistic with respect to the data obtained from real motor measurements, see e.g. [Arkkio 1990]. Measurement data from a real motor was, however, used as an input to the FEM models in the data group that was used to build the time series models. Use of real measurement data includes some measurement error into the data and hence makes it more suitable for testing the method. FEM simulations are not appropriate for online fault detection because of excessive computational time, but they can be easily used to simulate vast amounts of data for different motor operating conditions and faults. Models were built separately for the data using methods of identification in order to get necessary computational speed for a possible on-line implementation. A few notes about what has to be taken into consideration if the method were to be implemented on a real machine: • In a practical application an estimate of the motor load would be needed in order to use the correct models for that particular load condition. This can be obtained e.g. by estimating the slip. Also the models here are made for and tested only for three discrete load conditions. It was not tested how the method works for “in-between” values of load. • The validity of the method taught using FEM data would have to be proven to work on real machine data as well. • The models could also be taught using real machine data from a machine on which different faults are imposed in different load conditions. The feasibility of FEM data is that it can be used to relatively easily generate great amounts of motor data for different operational states (different faults and load conditions) • Lots of descriptive data is needed for the implementation and tuning of a neural network model based FDI scheme, if it is to be robust under harsh conditions. This is a common factor for all data-based methods. • Steady-state operation is assumed. Hence an algorithm should be implemented for steady-state operation. The algorithm should also decide when the motor is in steadystate. One possibility is to deduct this from the slip and motor speed. The model construction, testing, simulation and fault classification were implemented in a Matlabenvironment. For the creation of neural network based identification models a special Matlab-toolbox called NNSYSID was used. The fault classification was implemented using a classical Bayes classifier, which calculates the conditional probability for how well a given model represents the data which is inputted to the FDI system. The results indicate that for most of the load cases the classification was successful. The highest probability given by the classifier for a model to present the data inputted to the fault diagnosis system was the criteria for the classification. The fault characteristics inflicted on the stator current were reasonably small and hard to see by
simple visual inspection. The classifier results are not completely unanimous, because the probability was divided between the different models in each condition and load. The results indicate that as the load increases the faults characteristics are more evident in the data. The correct conditional classification probabilities increase with the load. It should be noted that the performance of a fault detection algorithm is proportional to the effectiveness of the fault indicator. Stator current, although being a noninvasive indicator, is not a very clear indicator. Effectiveness of different fault indicators is studied for example in [Negrea 2004]. It is clear that if measured data is available from some other fault indicator then the presented FDI method can be applied in a similar way and the better the indicator the better the results. Better indicators for common induction motor faults than stator current are e.g. circulating currents and fluxes. Preliminary studies show forces to be good fault indicators also, but they are problematic to measure directly. The faults in the stator current are manifested by certain harmonic frequencies and hence it is important that the models are accurate enough. Especially when using nonlinear neural network models there is a risk that the neural network parameter estimation algorithm converges to a local minimum and the model is not the best possible one. Hence it is important to retrain the neural network models until the model achieves the necessary accuracy.
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