C-MAPSS Simulation and Datasets

The Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) is a NASA developed tool used to simulate a realistic large commercial turbo- fan engine. The software was coded in MATLAB (The MathWorks, Inc.) and Simulink (The MathWorks, Inc.) environments with a number of ed- itable input parameters that allow the users to enter values specific to their own applications regarding environmental conditions, operational profile, etc. (Frederick et al., 2007).

C-MAPSS programme was used to implement the simulation of the PHM08 Challenge Data Set and Turbofan Engine Degradation Simulations (Saxena and Goebel, 2008a,b). All data sets differ from each other and were simulated under various combinations of regimes, operational conditions and fault modes. It is recorded that several sensor channels characterise fault evolution during operation. The data sets are made publicly available for the model training and the validation of results (Saxena and Goebel, 2008b).

Figure 4.1: A simplified diagram of an engine sim- ulation modelled in C-MAPSS (Frederick et al., 2007)

Figure 4.2: Subroutines of a model (Frederick et al., 2007; Saxena et al., 2008b)

The engine diagram in Figure 4.1 demonstrates the fundamental parts of an engine simulation, and the flow chart in Figure 4.2 demonstrates how the different subroutines are assembled in the simulation. The comprehensive con- trol systems illustrated in these figures are formed of the following fragments (Frederick et al., 2007):

- A fan-speed controller for the specification of throttle-resolver angle - Three high-limit regulators to avoid the engine from exceeding its own

design limits of engine-pressure ratio, core speed, and high-pressure tur- bine exit temperature

- Four limiting regulators to avoid static pressure at the high-pressure compressor exit from going off too low

- Core speed acceleration and deceleration limiters

- A comprehensive logic structure integrating the control-system frag- ments in a similar manner to real engine controllers

- A power-management system allowing engine operation over a wide range of thrust levels covering the full range of flight conditions.

- In addition to the engine model, an atmospheric model is included with the capability of operation at

– altitudes from sea level to 40,000 ft

– Mach numbers from 0 to 0.90

– temperatures from 60 to 103 ◦F

C-MAPSS aero engine degradation simulations possess the following characteristic features that make them both convenient and suitable for the development of prognostic algorithms on multi step ahead RUL estimations (Ramasso and Saxena, 2014; Saxena and Goebel, 2008a,b):

- Each data set contains multivariate and multidimensional time series representing sensor magnitudes over time and three operational settings that have a significant effect on engine performance and variations within opera- tional regimes. Therefore, the data sets can closely imitate real systems by exemplifying multidimensional operations of complex non-linear systems.

- Data sets are divided into training and test trajectories, the latter being individual subsets. In the training trajectories, operational cases of complete run-to-failure data are formed, which are supposed to be used to train multi step ahead life prediction algorithms. The test trajectories, on the other hand, can only set up via shorter instances with data up to a certain time prior to adopting system failure.

- The sensors are contaminated with operational regimes and noise to simulate instability within parameter readings during operation. Also, each trajectory is assigned a distinct degree of initial wear and manufacturing vari- ation, which is considered normal and unknown to the user.

-The fault effects are hidden on account of operational conditions and regimes, which is yet another common feature of most real-life operational systems.

-Raw values at each time point in data are regarded as a snapshot of the parameters taken during a single cycle, and each column corresponds to a different variable (see Table 4.1).

Table 4.1: PHM08 challenge data set parameters available to participants as sensor data Saxena et al. (2008b)

Parameters Symbol Description Unit

Unit — — —

Time — — t

Setting 1 — Altitude ft

Setting 2 — Mach Number M

Setting 3 — Sea-level Temperature ◦F

Sensor 1 T2 Total temperature at fan inlet ◦R

Sensor 2 T24 Total temperature at LPC outlet ◦R

Sensor 3 T30 Total temperature at HPC outlet ◦R

Sensor 4 T50 Total temperature at LPT outlet ◦R

Sensor 5 P2 Pressure at fan inlet psia

Sensor 6 P15 Total pressure in bypass-duct psia

Sensor 7 P30 Total pressure at HPC outlet psia

Sensor 8 Nf Physical fan speed rpm

Sensor 9 Nc Physical core speed rpm

Sensor 10 epr Engine pressure ratio —

Sensor 11 Ps30 Static pressure at HPC outlet psia

Sensor 12 phi Ratio of fuel flow to Ps30 pps/psi

Sensor 13 NRf Corrected fan speed rpm

Sensor 14 NRc Corrected core speed rpm

Sensor 15 BPR Bypass Ratio —

Sensor 16 farB Burner fuel-air ratio —

Sensor 17 htBleed Bleed Enthalpy —

Sensor 18 Nf dmd Demanded fan speed rpm

Sensor 19 PCNfR dmd Demanded corrected fan speed rpm

Sensor 20 W31 HPT coolant bleed lbm/s

Sensor 21 W32 LPT coolant bleed lbm/s

LPC/HPC=Low/High Pressure Compressor - LPT/HPT= Low/High Pressure Turbine

Each trajectory in a dataset is from a different operational instance of a complex aero engine system under dynamic operating regimes. The data

sets can be regarded as a fleet of the same type of aircraft. Since data can be collected from numerous samples, it is possible for algorithms to extract the behaviours of each trajectory and make collaborative calculations for the different courses of system actions.

Table 4.2: Number of trajectories and regimes in C-MAPSS data sets

Dataset: Training Trajectories Test Trajectories Regimes

FD001 100 100 1 (sea level) FD002 260 259 6 FD003 100 100 1 FD004 248 249 1 (sea level) PHM08 Test 218 218 6 PHM08 Final Test 435 6

Table 4.2 summarises the fundamental differences between datasets. In all subsets, the test sets have a corresponding training set. FD002 and FD004 are formed of six different operational regimes, while FD001 and FD003 in- clude only one operational condition. FD003 and FD004 also include an extra fault mode (fan degradation). Since each data set has a particular number of operational conditions and fault modes that can have a direct impact on their performance, only the trajectories in the same data set can be regarded being from an identical system. On the other hand, PHM08 Challenge Data Set only includes one corresponding training set for two different test sets. The devel- opers are expected to model their algorithms using this single set of training data for both ’test’ and ’final test’ sets provided in the same package. Also, unlike the Turbofan Engine Degradation Simulation, the true RUL values are not provided for the challenge participants. Instead, users are asked to upload their “test” results on the repository page to receive their scoring function re- sults (Saxena and Goebel, 2008a). Since the true RULs are not given, it is not

possible to validate the results with any other prognostic metrics. For the “fi- nal test”, the users can only send their results once, and therefore this subset does not allow a test-and-trial type of submission and can only be validated by a third party.

The validation uses the taxonomy of RUL performance measures and prognostic metrics presented in the Literature chapter (section 2.4). In Ap- pendix A, a comparison of the well-known publications is provided. The met- ric results obtained by particular works are summarised in table A.1 and the leader board for the PHM08 data challenge is presented in table A.2.