Timothy A. Doughty

Investigating Nonlinear Models for Health Monitoring in Vibrating Structures

This paper investigates a method of nondestructive health monitoring based on mapping variations in a system’s estimated nonlinear parametric model. The studied system is a slender cantilever beam harmonically excited around its second natural frequency. Known significant nonlinear parameters for this system including quadratic damping and terms due to bending and inertia are considered. This study uses the Continuous Time based nonlinear system identification technique. The method used here has advantages over mappings of the system’s linear parameters, such as natural frequency whose apparent value is shown to change as the amplitude of excitation is increased for physical systems behaving nonlinearly. Crack initiation and growth was effectively identified, but the effectiveness of the method was shown to be a function of the number and nature of the terms included in the model, and the number of records used in the identification process. The use of a simple nonlinear stiffness term and frequency records near resonance produced the best results. This method is shown to identify changes in the system’s behavior well before the failure of the system being studied, suggesting the method may lead users to avoid catastrophic failure in practice.© 2009 ASME

Effect of Nonlinear Parametric Model Accuracy in Crack Prediction and Detection

The use of nonlinear system identification has been applied to predicting and tracking cracks as they form and propagate through a vibrating cantilevered beam. Continuous Time based nonlinear system identification is used in application to the harmonically excited system. Model parameters are shown to vary as the beam transitions to failure, though no attention has been given to the accuracy of the parameters identified. In this application the effects of fixing sets of model parameters to their known, accurate values is explored as a method to enhance the health monitoring technique.

Nonlinear Model Tracking for Varying System Geometries

Although linear models can successfully explain many behaviors for physical systems, they are unable to describe the complexities of nonlinear systems. Therefore, health monitoring methods based on linear models run the risk of misidentifying nonlinear behavior as failing. Nonlinear Model Tracking (NMT), a health monitoring technique, is used here on a slender cantilevered beam subject to harmonic excitation near the beams second natural frequency, and the fatigue due to excitation. A second order nonlinear differential equation model has been assumed with cubic stiffness. This method uses the Continuous Time based nonlinear system identification technique allowing for model parameter estimation based on stimulus and response. The robustness of this method is demonstrated in its implementation and application to differing system geometries. These geometries studied here illustrate the reliability of this methodology indifferent to the system under observation. This method has shown, with repeatability, the onset of crack initiation and growth, well in advance of catastrophic failure, and has also been shown to work when the healthy system behaves with distinct nonlinearities, where linear techniques fail. The results indicate that NMT can be used for many different systems.

Numerical Enhancement of Nonlinear Model Tracking for Health Monitoring

Crack formation in a vibrating cantilever beam has been identified with the in situ nondestructive health monitoring Nonlinear Model Tracking (NMT) technique. The nonlinear cubic stiffness parameter has been chosen as the system’s dominant nonlinearity and has been tracked until catastrophic failure using a Continuous Time based system identification. The use of a nonlinear model allows for a range of healthy but complex system dynamics, such as changing natural frequency, which indicates a change in system health in traditional linear system health monitoring. Previous research has shown that significant change in the nonlinear parameter indicates a transition from a healthy to unhealthy system. The purpose of this study is to improve the robustness of the NMT method by investigating new data processing techniques. Numerical integration, regression fit with linear FRF, and strain gage sensors were introduced. The results of these new techniques were then compared with results from previous techniques to highlight effectiveness in determining change in a system’s health.

Nonlinear Model Tracking in Application to Failed Nondestructive Evaluations

The nondestructive health monitoring method of Nonlinear Model Tracking (NMT) is introduced and tested under various conditions. The study involves the fatigue and failure of a slender cantilevered beam subject to harmonic nonstationary base excitation around the beam’s second natural frequency. A nonlinear differential equation model for the system is assumed and parameters for the model are estimated using Continuous Time System Identification populated with healthy system stimulus and response data. Updated with real time data sets from the system in operation, the method tracks changes in parameter estimates. The NMT method indicates with repeatability the onset of plasticity, crack initiation and growth well in advance of system failure. Additionally, the NMT method is shown to not give false alarms when system behavior varies in a way that is associated with nonlinear phenomena. Linear methods based on tracking the system’s natural frequency are shown to misidentify the onset of failure for fully healthy systems.Copyright

Experimental Validation of Nonlinear Model Tracking with Varying Conditions

Mechanical systems can be described with models involving mass, damping, stiffness and nonlinear parameters, albeit with varying complexity. With known healthy model values, investigation of beam failure by crack initiation and propagation can be approached through monitoring model values while the system is excited. This approach uses harmonic excitation and focusses on the nonlinear model value. This experimental testing is performed near the system’s second natural frequency in a thin cantilever beam. Holding continuous sinusoidal forcing, significant shifts in the beam’s nonlinear parameter serve as an early warning of the system’s failure. This study is a continuation of iterative research [Song et al.: Mech. Syst. Sig. Process. 49(1–2), 13–23 (2014)] to verify the integrity and robustness of this particular type of health monitoring in cantilevered beams. This study explores how varying beam geometry, material, excitation frequency, and introducing an additional mass to the system will affect the expected change in the nonlinear parameter as well as how standard beams excited by discretely changing frequencies will give rise to these changes. Results indicate these variables alter the nature of the model, yet still provide significant warning of system failure. In practice, the scope of applicability becomes apparent in both the type of systems and excitations to prevent catastrophic failure.

Implementing Noise, Multi-Frequency Stimulus, and Realtime Analysis to Nonlinear Model Tracking

Crack initiation in a cantilevered beam subject to harmonic excitation near the beam’s second natural frequency has been determined using Nonlinear Model Tracking (NMT), a health monitoring technique. This method assumes a second order nonlinear differential equation model with cubic stiffness; the nonlinear parameter is tracked until catastrophic failure using a Continuous Time based System Identification. Previous research has shown that significant change in the value of the nonlinear parameter indicates the system’s transition from healthy to unhealthy. This study introduced Gaussian noise into the raw stimulus and response data at various signal-to-noise ratios. The results were compared with those of the original data to highlight the technique’s effectiveness in determining a change in the system’s health. The model’s robustness was also investigated by exciting the system at a range of frequencies near resonance, and the results of this test were compared to results from excitation at a single frequency. New methods of identifying crack formation in the beam were also implemented. The raw acceleration response data was plotted next to the nonlinear parameter in real time, and the system’s natural frequency was recorded before and after crack initiation.

Monitoring the Health of a Cantilever Beam Using Nonlinear Modal Tracking

Cantilever beams can often be used as representative models for more complex systems and can accurately display the expected behavior of these systems under different loads. The health of a cantilever beam after being subjected to harmonic excitation at its second resonance frequency is determined using a nondestructive health monitoring technique. Nonlinear Modal Tracking assumes a second order differential equation that factors in mass, stiffness, and damping of the beam with a cubic nonlinearity parameter. Research so far has confirmed that a drastic shift in this nonlinear term is a result of crack initiation and an indicator of the beam’s transition from healthy to unhealthy. Application of this Nonlinear Modal Tracking can be beneficial in monitoring the health of structures in order to predict catastrophic failure. The purpose of this study was to investigate several new techniques and conditions to verify the robustness of the model.

Building Inclusive Undergraduate Teams

This paper describes a research project to encourage and enhance formation of undergraduate project teams with a focus on inclusivity. The project was developed by a team of undergraduate students working with a pair of engineering faculty. A survey including questions about team study groups was prepared and used to gather data about how engineering student teams are formed and how students perceive teams at different points as they progress through the curriculum. Interviews with junior/senior level students were filmed and the footage was used to build a composite video to serve as motivation to first and second year students. The video was presented in a second year dynamics class and the students were surveyed to understand the effectiveness of the intervention.The survey results indicate that nearly half of all junior/senior engineering students feel ethically charged to include other students in a study group, while only 32% of second year students feel ethically charged. This research is part of a larger effort to develop methods for merging engineering ethics and professionalism in the mechanical engineering curriculum.Copyright

Varied System Geometry and Noise Implementation Applied to Nonlinear Model Tracking

The following is a study in nondestructive health monitoring wherein the physical system being studied is excited near resonance and mapped through its transition from health to failure. The system studied is a slender cantilever beam excited near its second natural frequency. For this study, no damage is initiated and so it comes in contrast to the more common techniques where the damage type and location allow for an element of control in instrumentation and analysis. The method implemented allows for health monitoring in situ, so it does not require stopping the event to do system testing, as is the case for many common approaches. Moreover, this method, implements a nonlinear model of the physical system, avoiding false flags that can be problematic for linear-based methods when applied to systems demonstrating healthy nonlinear behavior. The method, known as Nonlinear Model Tracking (NMT) uses a theoretical model of the system that includes a cubic nonlinear stiffness term. Experimentally, stimulus and response data are collected and used in Continuous Time-based system identification to estimate the system’s nonlinear stiffness coefficient. Harmonic fitting to the two recorded data sets allow for robust performance in the presence of noise and variations in the system geometry show that, even in cases where the nonlinear model is not accurate for the system being studied, the method works consistently. In many of the tests the method gives premonition of failure hours in advance, which would in many real world scenarios, gives users time to react safely. This study focusses particularly on varying inputs to the system and attempting to map changes in parameter estimation to stages of damage.Copyright