# A Robust Conformal Framework for IoT-Based Predictive Maintenance
## 4 Commercial Modular Aeropropulsion Simulation System (CMAPSS) Dataset  
The CMAPSS simulated datasets [21], courtesy of the NASA Center of Excellence, represent a typical ensemble of a jet engine (turbofan) that operates with a faulty and complex wear system. This dataset presents a pivotal and trusted data source for diagnostic and prognostic analysis, allowing the RUL prediction of each separate unit, thereby modeling their specific and progressive failure processes. Generally, engine failure refers to mechanical degradation resulting from variations in output sensor parameters caused by damage or wear, with its pattern following a typical evolutionary trajectory, which can be depicted by the curve shown in Figure 3. This curve illustrates the gradual decline in jet performance over time, supporting the analysis and prediction of engine RUL. Particularly, the CMAPSS software involves the simultaneous failures of up to five rotating sub-components, which are presented in Figure 4: fan, low-pressure compressor (LPC), high-pressure compressor (HPC), low-pressure turbine (LPT), and high-pressure turbine (HPT). In addition to component-level failures, the CMAPSS simulation environment incorporates various flight conditions that can significantly influence engine performance, including parameters such as altitude, Mach number, and throttle resolve angle (TRA), which permit more realistic modeling of a wide range of operational scenarios. Other relevant variants of the CMAPSS have been proposed by [PERSON] et al. [36], leveraging a more tailored and structured approach intended to represent a small fleet of aircraft better by taking advantage of the CMAPSS tool, which presents an extension of the original dataset but captures similar patterns and trends in the data, de facto incorporating its predecessor. The generation process adopted by the authors is presented in Algorithm 1. Specifically, FD001 and FD002 consist of 100 engine units each, whereas FD003 and FD004 consist of 260 and 249 units, respectively. The specific measurements present various operational parameters, such as fuel flow, fan speed, and various temperatures and pressures throughout the turbofan engine system. These datasets could be mainly grouped into two classes, as presented in Table 1:  
* Single operational condition: FD1-FD3 presents a single working condition, indicating that the data were captured at specific flight settings (Mach, TRA, Altitude). * Multiple operational condition: FD2-FD4 presents six working conditions, indicating that the data were captured at different flight settings (Mach, TRA, Altitude). Figure 4: Turbofan Engine System, [PERSON] et al. [21]. Figure 3: Visualization of a typical turbofan degradation pattern. ```
Input: Initial deterioration values \((f_{0},e_{0})\) chosen from \([0.99,1]\). Output: Time series data of observables (e.g., \(N_{f}\), \(N_{c}\), \(w_{f},\dots\)). Initialize: Set initial conditions \((f_{0},e_{0})\). Loop until Failure: while\(H(t)>0\)do
1. Apply Degradation: Using an exponential decay model, update flow \(f(t)\) and efficiency \(e(t)\). 2. Simulate Fault Evolution: Randomly evolve fault parameters within predefined constraints. 3. Compute Health Index: Calculate \(H(t)=g\big{(}e(t),f(t)\big{)}\). Post-processing: Superimpose measurement noise onto the data. return Output time series of observables for each operational cycle (hours) [21]. ```  
**Algorithm 1**Generate Degradation Data  
The main differences between these two classes of datasets can also be visually inspected through Figure 5. The FD1 dataset represents a singular failure modality and operational condition, while the FD2 dataset presents the same failure condition through different operational settings. In the above-mentioned figure of the RUL, presented on the axis, it is calculated following Equation (20). Basically, it represents the reverse of the number of cycles as hours [21], which is a known parameter that sets the granularity of the sensor series from the beginning till the EoL.