Sekhar Tangirala

Stochastic modeling of fatigue crack dynamics for on-line failure prognostics

This paper presents a nonlinear stochastic model of fatigue crack dynamics for real-time computation of the time-dependent damage rate and accumulation in mechanical structures. The model configuration allows construction of a filter for estimation of the current damage state and prediction of the remaining service life based on the underlying principle of extended Kalman filtering instead of solving the Kolmogorov forward equation. This approach is suitable for online damage sensing, failure prognosis, life prediction, reliability analysis, decision-making for condition-based maintenance and operation planning, and life extending control in complex dynamical systems. The model results have been verified by comparison with experimentally generated statistical data of time-dependent fatigue cracks in specimens made of 2024-T3 aluminum alloy.

A Variable Buoyancy Control System for a Large AUV

A large autonomous undersea vehicle (AUV), the Seahorse, has been designed, constructed, and tested by the Applied Research Laboratory at Pennsylvania State University (ARL/PSU, University Park, PA) for the U.S. Naval Oceanographic Office (NAVOCEANO, Stennis Space Center, MS). The vehicle is required to launch in shallow water (<10 m) and to hover without propulsion. Additionally, due to the very large size of the vehicle, low operating speeds and very long missions, small changes in vehicle trim resulting from battery replacement, sensor exchanges, and water temperature variations can result in significant drag-induced energy penalties over the duration of a mission. It is, therefore, important to continually maintain the AUV in fore-aft trim over the course of the mission. The vehicle is equipped with a two tank variable buoyancy system (VBS) to meet these requirements. The resulting control problem is one where the control variable, pump rate, is proportional to the third derivative of the sensed variable, depth; there are significant delays, and forces are nonlinear (including discontinuous) and highly uncertain. This paper describes the design of the VBS and the control software operating in two modes: depth control mode and trim control mode. In-water test data and simulation results are presented to illustrate the performance of the VBS controller. The benefits of the presented approach lie in the intuitiveness and simplicity of the design and the robustness as evidenced by the performance in both fresh and salt water. This paper provides practical insight into the operation of a VBS with an AUV and discusses actual operational experience. To our knowledge, no previous work considers the significance of an observed surface capture phenomenon to the design of a VBS control system, especially in very shallow water.

Controlled Markov chains with safety upper bound

In this note, we introduce and study the notion of safety control of stochastic discrete-event systems (DESs), modeled as controlled Markov chains. For nonstochastic DESs modeled by state machines or automata, safety is specified as a set of forbidden states, or equivalently by a binary valued vector that imposes an upper bound on the set of states permitted to be visited. We generalize this notion of safety to the setting of stochastic DESs by specifying it as an unit-interval valued vector that imposes an upper bound on the state probability distribution vector. Under the assumption of complete state observation, we identify: 1) the set of all state feedback controllers that satisfy the safety requirement for any given safe initial state probability distribution, and 2) the set of all safe initial state probability distributions for a given state feedback controller.

A nonlinear stochastic model of fatigue crack dynamics

This paper presents a nonlinear stochastic model for prediction of fatigue crack damage in metallic materials. The model structure allows estimation of the current damage state and prediction of the remaining service life based on the underlying principle of Gauss-Markov processes without solving the extended Kalman filter equation in the Wiener integral setting or the Kolmogorov forward equation in the Ito integral setting. The model results have been verified with experimentally-generated statistical data of time-dependent fatigue cracks for 2024-T3 and 7075-T6 aluminum alloys.

Life-extending control of mechanical structures: experimental verification of the concept

The concept of life-extending control is built upon the two disciplines of Systems Science and Mechanics of Materials, and its goal is to achieve an optimized trade-off between dynamic performance and structural durability of the plant under control. Experimental and simulation results reported in recent publications show that a life extending control system can substantially reduce the structural damage accumulated in critical components with no significant loss of plant performance. This enhancement of structural durability is accomplished via nonlinear optimization to generate a sequence of open-loop commands that maneuver the plant from a known initial state, along a prescribed trajectory, close to the final desired-state subject to constraints on the damage rate and accumulation in critical components. This paper presents a methodology for analytical development of a robust feedforward-feedback control policy for life extension and high performance of mechanical structures. The concept of life-extending control is experimentally verified in a laboratory testbed which is a two-degree-of-freedom (2DOF) mechanical system excited by a computer-controlled shaker table. Test results demonstrate that the fatigue life of test specimens can be substantially extended with no appreciable degradation in the dynamic performance of the mechanical system.

Hybrid-model based hierarchical mission control architecture for autonomous underwater vehicles

We present a hybrid, hierarchical architecture for mission control of autonomous underwater vehicles (AUVs). The architecture is model based and is designed with semiautomatic verification of safety and performance specifications as a primary capability in addition to the usual requirements such as real-time constraints, scheduling, shared-data integrity, etc. The architecture is realized using a commercially available graphical hybrid systems design and code generation tool. While the tool facilitates rapid redesign and deployment, it is crucial to include safety and performance verification into each step of the (re)design process. A formal model of the interacting hybrid automata in the design tool is outlined, and a tool is presented to automatically convert hybrid automata descriptions from the design tool into a format required by two hybrid verification tools. The application of this mission control architecture to a survey AUV is described and the procedures for verification outlined.

A bottom-up approach to verification of hybrid model-based hierarchical controllers with application to underwater vehicles

We present a systematic method of verification for a hierarchical hybrid system which is developed using a bottom-up approach. The bottom level of the hybrid system hierarchy is verified first, and each higher-level is subsequently verified with the assumption that all lower levels are correct. At each step in the verification process, lower and higher levels than the one currently being verified may be abstracted, thus reducing the complexity of verification. This method is algorithmically developed and integrated into the design of a hierarchical hybrid mission-level controller for an autonomous underwater vehicle

Damage-mitigating control of mechanical structures: experimental verification of the concept

The concept of damage-mitigating control is built upon the two disciplines of control systems and mechanics of materials, and its goal is to achieve optimized trade-off between the system performance and structural durability of the plant under control. Simulation studies have shown a substantial reduction in the damage accumulation in the critical components of a rocket engine with no significant loss of performance. This paper reports experimental verification of the damage-mitigating control concept on a laboratory testbed which is a two-degree-of-freedom mechanical system excited by a computer-controlled shaker table. Test results demonstrate: (i) the important feature of optimized damage-mitigating control by extending fatigue life up to three and one half times with no significant performance degradation; and (ii) close agreement between the analytical prediction of damage and experimental observations.

Life extending control of gas turbine engines

This paper presents a concept of life extending control for application to air-breathing gas turbine engines in continuation of similar work, reported earlier, on bipropellant rocket engines. As an example, a life extending control policy is formulated for reduction of stresses at the root of the fan and compressor blades with the primary modes of damage being fatigue cracks. An outline of the overall damage mitigating system is described, showing the interaction between the structural models, damage models, and the controller. As a preliminary proof-of-concept, a test case is presented where the stress profile and the rate of stresses are considered as indicators of structural damage in the fan and compressor blades.

Stochastic Modeling of Fatigue Crack Dynamics for On-line Damage Estimation and Life Prediction

Abstract This paper presents a nonlinear stochastic model of fatigue damage dynamics for real-time computation of the time-dependent rate and accumulation of fatigue crack damage in metallic materials. The model structure allows construction of a filter for estimation of the current damage state and prediction of the remaining service life based on the underlying principle of the Gauss-Markov processes in the Wiener integral setting instead of solving the Kolmogorov forward equation in the Ito integral setting. The model results have been verified with experimentally generated statistical data of time-dependent fatigue crack damage for the 2024-T3 and 7075-T6 Aluminum alloys.