An optimizer smoothes out the measurements in order to make them fit the available model as well as possible. The design of the Kalman filter depends upon the available measurements, the process conditions to be estimated and the amount of noise in the measurements.Ī technique that smoothes the available measurements based on a mathematical model is data reconciliation. These states represent the estimated values of the unmeasured process variables as well as the filtered values of the measured variables. It utilizes data available from previous measurements and estimates the current states of the process. One technique that finds the values of unmeasured process variables that can be inferred from the measured variables is called Kalman filtering ( Lewis and Syrmos, 1995). The value of λ is typically correlated with the accuracy of the measurement. The values of λ can be chosen between zero and one, where a value of one results in no filtering and a value of zero does not take any measurements into account. The parameter λ determines the effect of previous measurements on the filtered values. Where y k represents the current measurement and y ˆ is the filtered measurement. Note that the streaming data recording process needs to be done continuously in real time, while the detection process can be run in the background executing only once every interval (e.g., every second or minute) with more memory (DRAM). Finally, we use the key characteristics of the culprit flows revealed by the reversible sketches to mitigate the attacks. We also apply other false-positive reduction techniques as discussed later. Moreover, we aggregate the 2D sketches in the same way and adopt them to further distinguish different types of attacks. Intuitively, a large forecast error implies there is an anomaly, thus, the forecast error is the key metric for detection in our system. By subtracting the forecast sketch from the current one, we obtain the forecast error sketches.
#Moving average matlab 2008 series#
The forecast time series analysis method (e.g., EWMA, or exponentially weighted moving average) can help remove noise. Based on linearity of the sketches, we summarize the sketches over multiple routers into an aggregate sketch and apply time series analysis methods for aggregate sketches to obtain the forecast sketches for change detection. First, we record the network traffic with sketches in each router.
![moving average matlab 2008 moving average matlab 2008](https://www.mathworks.com/help/examples/matlab/win64/SmoothDataWithSamplePointsMATLABExample_01.png)
It signifies a noticeable change in process dynamics due to major disturbance or fault is detected.ĮWMA Chart: Exponential Weighted Moving Average (EWMA) chart is a weighted plot of statistics of process variable, usually the process variable x itself or the sample mean x ¯, by placing a weight w, 0 ≤ w ≤ 1 on the most recent data point and a forgetting factor 1 – w on the last statistics.įigure 16.8 shows the architecture of the HiFIND system.
![moving average matlab 2008 moving average matlab 2008](https://ww2.mathworks.cn/help/examples/signal/win64/SignalSmoothingExample_03.png)
If the previous points fall out of the mask, the process is said to be not in statistical control. It determines the maximum statistically allowable deviation of the previous data points.
![moving average matlab 2008 moving average matlab 2008](https://ars.els-cdn.com/content/image/1-s2.0-S0360544220303078-egi10HRTGQRK62.jpg)
The control limit of CUSUM is expressed as an overlay mask. Due to this nature, the definition of control limits of CUSUM is not UCL and LCL. The real concern is the slope or the deviation between successive data points. Therefore, in using CUSUM charts, it is not our concern whether or not the cumulated sum of the statistics falls over a fixed UCL and LCL. The objective of using CUSUM is to detect changes in monitoring statistics.