![Kohonen SOM training The training f the Kohonen Network is done by a specific algorithm. The goal is to obtain a map where 2 points which are nearby in the input space are also closed in the map. Step1: Initialize weights (randomly or with sample from the input space) Step2: Update each node in the map in proportion with the distance from its weight vector to the input vector: mi = mi + η(t) * hci(t) * [x(t)-mi(t)] Where: mi is the weight vector of the ith node η (t) is the learning rate h ci (t) is the neighborhood function (the more a node is far from the BMU the smaller value is returned by this function)](https://image.slidesharecdn.com/system-monitoring4160/85/System-Monitoring-14-320.jpg)
System Monitoring
- 1. S Y S T E M M O N I T O R I N G The use of machine learning techniques in structural and motor monitoring…
- 2. I N T R O D U C T I O N What is system monitoring ? Why doing system monitoring: financial and technical challenges. Machine learning techniques: why are they so popular? The goal of machine learning in system monitoring: Pattern Recognition
- 3. Structural Health Monitoring Information that needs to be extracted from a structure: damage location and size. Different methods of analyzing a structure: Vibration-based damage detection Electric potential-based damage detection Impedance-based damage detection sensor
- 4. Fault Detection In Motor Measurement of current , voltage… Relevant information that needs to be extracted from a motor: bearing faults, broken bars, friction… Pertinent measurements to perform the diagnosis of a motor
- 5. From Sensor Data to the Training set Why is it impossible to use raw data from sensor to perform machine learning algorithm (over-fitting, environmental noise, changes over the life-time) The importance of domain expertise Common method that have been applied to compute a training set. Time x 1 ………x n y 1 …….y m … ...…………… … ...…………… … ...…………… … ...…………… … ...…………… Feature Extraction
- 6. Feature Extraction in the time-domain Comparison with a known sensor signal (undamaged) Computationally easy. Ideal for methods which are not based on a frequency theory. Known signal Unknown sensor signal Area Between the 2 Root Mean Square of each curve Root Mean Square of the difference Correlation Coefficient x 1 x n Input vector
- 7. Switching from time to frequency Domain Noise is attenuated Significant information are more easy to find Damage or faults are often directly related to specific frequencies and their harmonics Time Fourier Transformation x 1 x n Input vector Principal Component Analysis
- 8. Machine Learning techniques Neural Networks are the most common learning tool used in system monitoring: Easy to implement and to train Ability to perform pattern recognition and therefore to detect damages or defaults Two kind of networks are used in system monitoring: Feed-Forward Neural Network Kohonen Self Organizing Map
- 9. Feed Forward Neural Networks 1 1 Input Layer Hidden Layer Output Layer x 1 x n Input vector y 1 y m Output vector The size of the network is usually small: Input vector: 3-20 nodes
- 10. Back-Propagation algorithm To train the feed forward neural Networks the most common algorithm is the back propagation algorithm Step1: Initialize weights. Step2: Present Inputs vector and desired outputs Present training vectors from the training set to the network; calculate the output of every node by propagating inputs through the network using the activation function selected (sigmoid, step…) Step3: Update Weights Adapt weight starting at the output nodes and working back to the first hidden layer by: Wij(t+1)=Wij(t) + ηδjX’i δj = yj(1-yj)(oj-yj) for output node δj=X’j (1-X’j) Σ δk Wjk for hidden node Step4: Repeat by going to step 2 until weights do not change.
- 11. Real-world distribution. 0 for class A 1 for class B t=50 t=100 t=150 t=200 Training Architecture of the network Back-Propagation algorithm B A
- 12. Kohonen Self Organizing Map (SOM) Kohonen network can be viewed as a clustering method so that similar data samples tend to be mapped to nearby neurons. Kohonen SOM is also a projection method which maps high-dimensional data space into low-dimensional space. Thanks to its clustering ability, Kohonen networks are used in system monitoring, to perform a preliminary organization of the input space. Because it is an unsupervised learning technique, it needs to be associated with another intelligent tool.
- 13. Kohonen Self Organizing Map (SOM) x 1 x n Input vector To each node of the network is associated a vector in the input space mi 1 mi n When the input vector is presented to the map, its distance to the weight vector of each node is computed. The map returns the closest node which is called the Best Matching Unit. BMU The output of the map is usually sent to another learning machine which will finish the process of pattern recognition.
- 14. Kohonen SOM training The training f the Kohonen Network is done by a specific algorithm. The goal is to obtain a map where 2 points which are nearby in the input space are also closed in the map. Step1: Initialize weights (randomly or with sample from the input space) Step2: Update each node in the map in proportion with the distance from its weight vector to the input vector: mi = mi + η(t) * hci(t) * [x(t)-mi(t)] Where: mi is the weight vector of the ith node η (t) is the learning rate h ci (t) is the neighborhood function (the more a node is far from the BMU the smaller value is returned by this function)
- 15. Kohonen SOM training (example) 10x10 Kohonen Map X 1 X2 X3 Y … ...…………… … ...…………… … ...…………… 0 1 33 Training Set Where Y is the number of short-circuit terms and x1,x2,x3 are the amplitude of specific frequency in the spectrum
- 16. Kohonen SOM training (example) 10x10 Kohonen Map 0 4 5 6 7 8 9 10 11 13 15 18 19 21 25 23 28 29 29 31 33 X 1 X2 X3 Y … ...…………… … ...…………… … ...…………… 0 1 33 Training Set
- 17. Results Results are characterize by: Very good accuracy; usually about 90% of good tests Good results have to be associated with good domain expertise. Very specific results; Because there are many types of faults and damages in a system, usually a network is dedicated to only one. Depending on the fault the input vector will be different. Better results are obtained with very particular network. Monitoring systems are often composed of several networks.
- 18. Conclusion Despite good results more research needs to be done in system monitoring especially in the case where several faults or damages occur at the same time.