1. **Case breach:** Local burning-through of the rocket case (see Figure 1 in Home section) which can result in catastrophic impact on the TVC system (see Figure 1, and Figure 2 (in Home section) for the test firing of TD31).

2. **Case burst:** Nozzle blocking or bore choking which results in overpressure in a combustion chamber.

3. **Nozzle Failure:** Deformations of the nozzle which, in particular, can reduce the thrust being generated. This effect can be induced by ablation process and abrupt breaking off of large pieces of the propellant. These pieces or a cloud of solid particles in the exhaust gases accumulating at the nozzle inlet can block temporarily the nozzle throat (transient nozzle blocking fault). A nonuniform failure of the nozzle (such as loosing a chunk of the aft exit cone, or partially failing a joint) will result in a non-axial component of thrust. A failure would also result in the plume moving closer to the aft skirt, causing increased heating and adversely affecting the TVC system.

4. **Bore choking:** Bore choking occurs when the propellant deforms (bulges) radially inward and disrupts the exhaust gas flow, causing a choked flow condition inside the motor. Bore choking can be most likely realized near radial slots and segment joints between two sections with a smaller radius of the aft section. This critical effect is typically caused by localized areas of low pressure arising near such inhomogeneous. Development testing has shown that this fault was observed, for example, in the primary construction of the Titan IV (see Figure 3). Bore choking has the potential of causing booster over-pressure and catastrophic failure.

5. **Debonding:** Potentially large parts of the propellant debond from the liner and become loose. They can bend and stick inside the bore. In the large rocket with the large aspect ratio of the bore volume the depleted propellant can significantly obscure the bore volume leading to chocking.

6. **Propellant structural failure:** Critical defects are cracks and voids in solid propellant and slots of booster joint segments. These defects can stimulate the increase of local burning rate that can result in abruption of lager enough piece of the propellant. This piece can stick to a narrow place of the burning propellant or choke minimum cross section of the nozzle. This can cause a sharp catastrophic jump of the booster trust and overpressure in the chamber head.

7. **Combustion instabilities:** Instabilities of combustion in the system.

8. **GN&C Failure:** an unexpected or no response to given commands.

9. **Structural Failure:** Large-scale buckling in the case or first to second stage coupling could result in a non-linear vehicle causing excessive aerodynamic drag. Small-scale buckling may alter stress/strain levels in the case.

10. **PLI bond-line failure:** Material properties degradation or contamination

11. **Ignition failure:** Failure of ignition in system.

ATK Courtesy

ATK Courtesy

SRB early warning system: we used the direct detection sensor data and provided a real-time learning of the parameters of the set of low-order physics models for onset and progression of system faults and autonomously generate the robust prediction of fault evolution for a possible decision support. Models include prior knowledge of thermal, fluid dynamics, and material processes in SRB

Synthetic Data

Synthetic Data

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DIAGNOSTICS & PROGNOSTIC

We used sensor pressure data in the nominal regime (sensors P1, P2, and P for test #1) to reconstruct parameters of the internal ballistics of the test firing of TD31. This data is used for the fault diagnostics from the sensor pressure data in tests #2 and #3. We reconstructed dynamics of the fault (area of the hole in the forward pressure) and thrust dynamics

Figure 3. Titan IV overpressure fault

Clearly the development of the FD&P that incorporates physics models of the faults has to verified and validated in a multi-stage procedure involving high-fidelity modeling, ground, and flying tests. We have developed a novel Bayesian framework that can infer parameters of nonlinear stochastic dynamical models. We have derived a low-dimensional performance model (LDPM) of the SRBs and demonstrated that our Bayesian framework can infer and track parameters of the LDPM in real time. In particular, we developed detailed models of the nozzle choking fault and the case breach fault that accurately reproduce characteristic dynamical features of the fault observed in the ground tests and incorporate it into the Bayesian inferential framework. The essential modifications of the model include (i) the dynamics of the nozzle ablation; (ii) a given propellant geometry and the relation between burn distance and burning area; (iii) the dynamics of heating of the metal walls in the hole through the metal case; (iv) the dynamics of silicon melting in the nozzle walls; and (v) the geometry of the fault. These modifications are also included in a high-fidelity model of the case breach fault built in FLUENT. Using the results of the theoretical analysis of the case breach fault and FLUENT simulations we derive and verify corresponding LDPM and incorporate it into a Bayesian inferential framework as a part of on-board FD&P system for SRBs. We used synthetic data generated by the LDPM to verify the accuracy and the time resolution of the diagnostics and prognostics of the case breach fault.

We showed that the method developed of us to improve the performance of the standard algorithm in the situations of possible misses and false alarms. To model the miss we consider a situation when small pressure deviation from the nominal value persists for a few second prior to the crossing the alarm level. In this case the time window between the alarm and catastrophe becomes too short [see Figure 4(a)]. To model the false alarm we consider a situation, in which the pressure crosses the alarm level, but then returns to its nominal value [see Figure 1(b)]. Such situation can be realized e.g. in case of the temporarily nozzle blocking fault.

We also showed that our Bayesian framework provides additional information ahead of the alarm time about the most likely course of the pressure dynamics and reduces the probability of the misses and false alarms. The novel approach is based on the combination of the effective models of nominal and off-nominal SRB operation, learned from high-fidelity simulations and a Bayesian sensor-fusion framework for estimating and tracking the state of a nonlinear stochastic dynamical system.

Synthetic Data

Figure 4. (a) Example of an overpressure fault (black line) representing a possible miss situation. The blue dashed and red solid lines indicate the alarm and the catastrophe levels respectively. (b) Example of an overpressure fault representing a possible false alarm situation. The blue dashed and red solid lines are the same as in (a).

To simulate faults we introduce a system of stochastic partial differential equations (SPDEs) for momentum, energy, and mass of combustion products averaged over a cross-section area that takes into account fluctuations of the burning rate and a graded propellant performance. For analysis of time-series data we derive a low-dimensional model by averaging the SPDEs along the booster length. The parameters of the gas flow are estimated on the basis of an effective Bayesian framework developed by us, including applications to the inference of the SRBs parameters. The estimated parameters are used to predict the probability of the fault at a given time. In the simulations presented below we illustrate our approach with two main faults: (i) case breach fault which is modeled as a burning-through of a hole in a rocket case and (ii) nozzle blocking fault which is modeled as an efficient reduction of the nozzle throat area. The proposed method can be extended to encompass other faults, including the propellant structural failure, bore choking, and case burst faults.

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