Karan Bhatia

A case study on Naval Ship’s gas turbine propulsion system:

For part 1 of this article, I will use a publicly available dataset so that you can follow along the steps. The data is provided by the Center for Machine Learning and Intelligent Systems at the University of California. This is the link to the original data.

The data contains sensor readings of a simulated Naval Ship, frigate type, using Gas Turbine (GT) propulsion plant. The data is presented in vectors of 18 dimensions containing 16 sensor readings, which are shown below.

Lever position (lp) Ship speed (v) [knots] Gas Turbine (GT) shaft torque (GTT) [kN m] GT rate of revolutions (GTn) [rpm] Gas Generator rate of revolutions (GGn) [rpm] Starboard Propeller Torque (Ts) [kN] Port Propeller Torque (Tp) [kN] Hight Pressure (HP) Turbine exit temperature (T48) [C]

GT Compressor inlet air temperature (T1) [C] GT Compressor outlet air temperature (T2) [C] HP Turbine exit pressure (P48) [bar] GT Compressor inlet air pressure (P1) [bar] GT Compressor outlet air pressure (P2) [bar] GT exhaust gas pressure (Pexh) [bar] Turbine Injecton Control (TIC) [%] Fuel flow (mf) [kg/s]

The top five vectors out of 11934 are shown in figure 1. Here we will use 16 sensor data to predict the Compressor decay state coefficient, the last-second variable in the column of the data frame as shown in the figure 1.

• Step 1: Identify the goals you want to achieve from your IoT system.

First, we need to clearly define our goal, what we hope to achieve from our IIoT system. Here we will use 16 sensor data to predict the compressor's efficiency using the Compressor decay state coefficient, the last-second variable in the column of the data frame. And of course, another goal is that we want to be able to use it for digital twin's capabilities like what-if scenarios, fault identifications etc. Our goal will drive what models we use in our next steps.

• Step 2: Analyze your system, gather available data and make a rough draft design.

The data source doesn't provide any information on how the existing system looks like. From my experience of a gas-power plant, I believe the system should look somewhat similar to this.

Identify all the system's sensors and Factors that will feed our prediction model. I have assigned our potential candidates for IoT sensors in the pink circles in the schematic. I define the factors as the static parameters that are specific to the equipment, location, material type, model number etc. One thing is to note is we will not eliminate any potential sensors. We will see why in the next step. For this case study, we can generate a location as one static variable. We won't be able to use it in this case study as we only have one unique system, although it's nice to have in case we want to transfer learnings from this system to other systems in the plant. Ultimately, this will help us quickly answer questions like 'why equipment in a certain location is failing more often than another location?', or 'how the degradations like microbiologically influenced corrosion (MIC) are spreading across our plant' etc.

Consider the following questions about our potential IoT candidates before we move to the next step:

Which IoT Sensors will provide the best prediction for the Compressor efficiency?
This is an important question. You may design an accurate IoT system with hundreds of sensors but tracking them all will create a bigger maintenance problem than the one we are trying to solve. We need to know which IoT sensors are absolutely essential for accurate prediction, in rank-wise order.

Can we remove any IoT Sensor without affecting the prediction accuracy?
If accuracy is decreased marginally, is the trade-off worth it?

Are any IoT sensors effectively redundant with each other?
For example, if vibrations on a motor increase linearly with its RPM, we don’t need to measure both.

• Step 3: Design and optimize the IoT logic architecture

In this step, we will try to answer the questions using some simple machine learning tools. Although it is possible to calculate this in excel, I strongly recommend using statistical computing software like Matlab, R packages, or Python libraries.

There is no single cookie-cutter solution for all systems, so we will explore several statistical and machine learning models in this section and use whichever gives us the best result for our model. The first thing we need to do is calculate the significance of each sensor on the compressor efficiency. Basically, we need to find variance and co-variance within each of the sensor's data. You can use several methods for this; some of the popular ones are K Nearest Neighbors, Partial Least Squares, Decision tree, or probabilistic methods like Bayesian clustering. I choose to use a Decision tree since the data we have is relatively simple, and it's easy to visualize a decision tree. We won't detail what a decision tree is. A quick google search will land you dozens of great tutorials. Here is a wikipedia link to get started.

For this case study, I was able to make a decision tree of about 281 nodes. The best way to understand the results is by plotting them in the graph as we go along. Since 281 nodes are too big to put in the article, here are the top four nodes for the decision tree in figure 3. Using the same parameters, Figure 4 presents the actual distribution using a random sampling method. At each node, we are asking a question and breaking down our data into two subsets. The first one is 'compressor_outlet_temp<787?' for the condition that is false; the log of compressor efficiency is very close to –0.04. (why log? Because it helps keep data on the same scale. Do this if you are unsure about the range/distributions of your data). And similarly, if the condition is true, we ask the next question and so on.

Visualization gives us great insights that we often miss out on in our regression analysis; always lay out your data in the form of graphs, whenever possible.

Next, we want to know how a particular sensor affects the efficiency of the Compressor. We can perform a chi-squared (chi²) statistical test on this and then normalize the p-value of each sensor such that they all add to 1 (it is essential to do this so that we can compare the importance of each sensor on the same scale). Here is how the final result should look like.

In this graph, each bar represents the relative significance of each sensor on the Compressor efficiency. As we can see, Compressor_outlet_temp has the highest significance on compressor efficiency. Interestingly, the first three sensors have almost no effect on the compressor’s efficiency (less than 0.001 relative significance). We don’t need those sensors for prediction, so we will remove these three sensors from our IoT architecture. This is how it would look like if we remove those three sensors from our IoT architecture.

Almost the same. So we can proceed.

Next, we calculate the correlation between each of the sensors. We can do this in many ways: one way is by using regression analysis for each sensor readings to calculate the coefficient of determination, also called R2. The most similar pairs of sensors are found by calculating the rank correlation, which means that all the values are replaced with their rank (i.e., first, second, third, etc. ), and then the correlation is calculated. We can also combine this with decision tree regression analysis to visualize the similar pairs of our IoT sensor candidates. This is shown in the plot: figure 7.

Interestingly, the pair of { starboard propeller torque and portside propeller torque}, {lever position and ship speed}, {fuel flow and hp turbine temperature} both are merged far from the root in our decision tree regression. Meaning they are so highly correlated that they are practically the same. This makes sense if you think about it; the lever position directly governs the speed, both propellers are probably driven by a same power-train, hence the differential torque is same and so on. Hence, we can say that they are redundant. We will remove one from each redundant pairs: Portside propeller torque, ship speed, hp turbine temperature.

Outlier sensor data: Sometimes, you may come across a sensor in your system that gives random data. Instead of helping with prediction, these sensor’s data create un-necessary complications or noise in your data. We should try to identify this before we design our prediction model. We can use a simple technique called one-class classification (OCC). It involves fitting a model on the distributed data and predicting whether new data is normal or an outlier/anomaly. Performing OCC analysis on all sensor data individually, it was found that turbine injection control sensor data had some anomalies. However, use some practical judgement before eliminating the sensor from IoT architecture.

Ok, let us summarize: we started with 16 sensors, we found three of them had no effect at all on the compressor efficiency. Pairs of three sensors were redundant, and one sensor had many anomalies that probably won’t contribute positively to data prediction. We can remove these seven sensors from our IoT architecture.

So out of 16 sensors, we have selected only nine sensors for our IoT architecture. We also have detailed information on how each sensor will contribute to our prediction goal. We are now ready to create a prediction model.

• Step 4. Make a prediction model.

We have nine sensors to detect compressor efficiency with 11934 unique data instances. Since we have moderate size data, we can use one of many available deep learning algorithms to solve this. I am using a simple neural network model with two hidden layers for this step. There are better techniques out there, which I am not discussing here; I recommend exploring and try them out.