Ravindra Patankar

Fatigue crack growth under variable-amplitude loading: Part I – Model formulation in state-space setting☆

Abstract This two-part paper presents formulation and validation of a non-linear dynamical model of fatigue crack growth in ductile alloys under variable-amplitude loading including single-cycle overloads, irregular sequences, and random loads. The model is formulated in the state-space setting based on the crack closure concept and captures the effects of stress overload and reverse plastic flow. The state variables of the model are crack length and crack opening stress. This paper, which is the first part, presents formulation of the state-space model that can be restructured as an autoregressive moving average (ARMA) model for real-time applications such as health monitoring and life extending control. The second part is the companion paper that is dedicated to model validation with fatigue test data under different types of variable-amplitude and spectrum loading.

Fatigue crack growth under variable-amplitude loading: Part II – Code development and model validation

Abstract A state-space model of fatigue crack growth has been formulated based on the crack closure concept in the first part of the two-part paper. The unique feature of this state-space model is that the constitutive equation for crack-opening stress is governed by a low-order non-linear difference equation without the need for storage of a long load history. Therefore, savings in the computation time and memory requirements are significant. This paper, which is the second part, provides information for code development and validates the state-space model with fatigue test data for different types of variable-amplitude and spectrum loading in 7075-T6 and 2024-T3 aluminum alloys, respectively. Predictions of the state-space model are compared with those of the FASTRAN and AFGROW codes.

A State-Space Model of Fatigue Crack Growth

This paper proposes a nonlinear dynamic model of fatigue crack growth in the state-space setting based on the crack closure concept under cyclic stress excitation of variable amplitude and random loading. The model state variables are the crack length and the crack opening stress. The state-space model is capable of capturing the effects of stress overload and underload on crack retardation and acceleration, and the model predictions are in fair agreement with experimental data on the 7075-T6 aluminum alloy. Furthermore, the state-space model recursively computes the crack opening stress via a simple functional relationship and does not require a stacked array of peaks and valleys of stress history for its execution; therefore, savings in both computation time and memory requirement are significant. As such, the state space model is suitable for real-time damage monitoring and control in operating machinery.

State-space modeling of fatigue crack growth in ductile alloys ☆

Abstract This paper presents a nonlinear dynamical model of fatigue crack growth in ductile alloys under variable-amplitude loading. The model equations are formulated in the state-space setting based on the crack closure concept and capture the effects of stress overload and reverse plastic flow. The state variables of the model are crack length and crack opening stress. The constitutive equation of crack-opening stress in the state-space model is governed by a low-order nonlinear difference equation that does not require storage of a long load history. The state-space model can be restructured as an autoregressive moving average (ARMA) model for real-time applications such as health monitoring and life extending control. The model is validated with fatigue test data for different types of variable-amplitude and spectrum loading including single-cycle overloads, irregular sequences, and random loads in 7075-T6 and 2024-T3 alloys. Predictions of the state-space model are also compared with those of the FASTRAN-II model.

Failure precursor detection in complex electrical systems using symbolic dynamics

Failures in a plants electrical components are a major source of performance degradation and plant unavailability. In order to detect and monitor failure precursors and anomalies early in electrical systems, we have developed a signal processing method that can detect and map patterns to an anomaly measure. Application of this technique for failure precursor detection in electronic circuits resulted in robust detection. This technique was observed to be superior to conventional pattern recognition techniques such as neural networks and principal component analysis for anomaly detection. Moreover, this technique based on symbolic dynamics offers superior robustness due to averaging associated with experimental probability calculations. It also provided a monotonically increasing smooth anomaly plot which was experimentally repeatable to a remarkable accuracy.

Damage mitigating controller design for structural durability

Synthesis of a damage-mitigating control law requires additional information on damage states beyond what is needed for the design of a conventional output feedback controller. In this context, the paper establishes the necessity of a fatigue damage model that must account for the impact of variable-amplitude stress excitation on crack growth rate (e.g., crack retardation and sequence effects). It is shown that predicted structural durability and the damage-mitigating controller design could be grossly inaccurate if the fatigue crack damage model does not represent the effects of variable-amplitude cyclic stress. A specific example is given based on the design of output-feedback damage-mitigating controllers for a reusable rocket engine that was reported in an earlier publication. Simulation results are presented to compare the predicted structural durability and closed-loop performance of the rocket engine under the same controllers for two different damage models, with and without consideration of the effects of variable-amplitude stress.

Damage-Mitigating Control With Overload Injection: Experimental Validation of the Concept

The goal of damage-mitigating control is to enhance structural durability of mechanical systems (e.g., advanced aircraft, spacecraft, and power plants) while retaining high performance. So far the reported work in damage-mitigating control has focused on reduction of peak stresses to increase structural durability. This paper presents a novel concept that takes advantage of the physical phenomenon of fatigue crack retardation. Overload pulses are intermittently injected into the plant as a feedforward signal through the actuator(s) in addition to robust feedback control. A feedforward sequence of limited overload pulses and a robust feedback control law are designed based on state-space models of fatigue-crack damage and plant dynamics. A series of experiments have been conducted on a laboratory test apparatus to demonstrate feasibility of the overload injection concept for robust damage-mitigating control.

Prognosis of Failure Precursor in Complex Electrical Systems Using Symbolic Dynamics

Failures in a plants electrical components are a major source of performance degradation and plant unavailability. In order to detect and monitor failure precursors and anomalies early in electrical systems, we have developed signal processing capabilities that can detect and map patterns in already existing and available signals to an anomaly measure. Toward this end, the language measure theory based on real analysis, finite state automaton, symbolic dynamics and information theory has been deployed. Application of this theory for electronic circuit failure precursor detection resulted in a robust statistical pattern recognition technique. This technique was observed to be superior to conventional pattern recognition techniques such as neural networks and principal component analysis for anomaly detection because it exploits a common physical fact underling most anomalies which conventional techniques do not. Symbolic dynamic technique resulted in a monotonically increasing smooth anomaly plot which was experimentally repeatable to a remarkable accuracy. For the Van der Pol oscillator circuit board experiment, this lead to consistently accurate predictions for the anomaly parameter and its range.

Damage mitigating control of a reusable rocket engine for structural durability

The goal of damage mitigating control is to achieve a desired level of trade-off between structural durability of critical component(s) and overall dynamic performance of the plant (e.g., aircraft, spacecraft, and energy conversion systems). The paper presents the synthesis of damage-mitigating output feedback controllers and applies this method to a reusable rocket engine by taking fatigue crack damage of turbine blades into consideration. The effects of crack growth retardation due to overload are included in the fatigue damage model which is formulated in the state-space setting. Simulation results are presented to demonstrate the effectiveness of the damage-mitigating control concept.

Damage-mitigating control with overload injection: experimental validation of the concept

The goal of damage-mitigating control is to enhance structural durability of operating machinery while retaining high performance. So far the reported work in damage-mitigating control has focused on reduction of peak stresses to increase structural durability. The paper presents a novel concept that takes advantage of the physical phenomenon of fatigue crack retardation. Overload pulses are intermittently injected into the plant as a feedforward signal through the actuator(s) in addition to robust feedback control. The feedforward sequence of overload pulses and the robust feedback control law are designed based on state-space models of fatigue-crack damage and plant dynamics. A series of experiments have been conducted on a laboratory test apparatus to demonstrate feasibility of the overload injection concept for robust damage-mitigating control.