Jonathan Hong

Introduction to State Estimation of High-Rate System Dynamics

Engineering systems experiencing high-rate dynamic events, including airbags, debris detection, and active blast protection systems, could benefit from real-time observability for enhanced performance. However, the task of high-rate state estimation is challenging, in particular for real-time applications where the rate of the observer’s convergence needs to be in the microsecond range. This paper identifies the challenges of state estimation of high-rate systems and discusses the fundamental characteristics of high-rate systems. A survey of applications and methods for estimators that have the potential to produce accurate estimations for a complex system experiencing highly dynamic events is presented. It is argued that adaptive observers are important to this research. In particular, adaptive data-driven observers are advantageous due to their adaptability and lack of dependence on the system model.

Variable Input Space Observer for Structural Health Monitoring of High-Rate Systems

The development of high-rate structural health monitoring methods is intended to provide damage detection on timescales of 10 µs -10ms where speed of detection is critical to maintain structural integrity. Here, a novel Variable Input Observer (VIO) coupled with an adaptive observer is proposed as a potential solution for complex high-rate problems. The VIO is designed to adapt its input space based on real-time identification of the system’s essential dynamics. By selecting appropriate time-delayed coordinates defined by both a time delay and an embedding dimension, the proper input space is chosen which allows more accurate estimations of the current state and a reduction of the convergence rate. The optimal time-delay is estimated based on mutual information, and the embedding dimension is based on false nearest neighbors. A simulation of the VIO is conducted on a two degree-of-freedom system with simulated damage. Results are compared with an adaptive Luenberger observer, a fixed time-delay observer, and a Kalman Filter. Under its preliminary design, the VIO converges significantly faster than the Luenberger and fixed observer. It performed similarly to the Kalman Filter in terms of convergence, but with greater accuracy.The development of high-rate structural health monitoring methods is intended to provide damage detection on timescales of 10 µs -10ms where speed of detection is critical to maintain structural integrity. Here, a novel Variable Input Observer (VIO) coupled with an adaptive observer is proposed as a potential solution for complex high-rate problems. The VIO is designed to adapt its input space based on real-time identification of the system’s essential dynamics. By selecting appropriate time-delayed coordinates defined by both a time delay and an embedding dimension, the proper input space is chosen which allows more accurate estimations of the current state and a reduction of the convergence rate. The optimal time-delay is estimated based on mutual information, and the embedding dimension is based on false nearest neighbors. A simulation of the VIO is conducted on a two degree-of-freedom system with simulated damage. Results are compared with an adaptive Luenberger observer, a fixed time-delay observer, ...

An Experimental Test Bed for Developing High-Rate Structural Health Monitoring Methods

Complex, high-rate dynamic structures, such as hypersonic air vehicles, space structures, and weapon systems, require structural health monitoring (SHM) methods that can detect and characterize damage or a change in the system’s configuration on the order of microseconds. While high-rate SHM methods are an area of current research, there are no benchmark experiments for validating these algorithms. This paper outlines the design of an experimental test bed with user-selectable parameters that can change rapidly during the system’s response to external forces. The test bed consists of a cantilever beam with electronically detachable added masses and roller constrains that move along the beam. Both controllable system changes can simulate system damage. Experimental results from the test bed are shown in both fixed and changing configurations. A sliding mode observer with a recursive least squares parameter estimator is demonstrated that can track the system’s states and changes in its first natural frequency.

Variable input observer for state estimation of high-rate dynamics

High-rate systems operating in the 10 μs to 10 ms timescale are likely to experience damaging effects due to rapid environmental changes (e.g., turbulence, ballistic impact). Some of these systems could benefit from real-time state estimation to enable their full potential. Examples of such systems include blast mitigation strategies, automotive airbag technologies, and hypersonic vehicles. Particular challenges in high-rate state estimation include: 1) complex time varying nonlinearities of system (e.g. noise, uncertainty, and disturbance); 2) rapid environmental changes; 3) requirement of high convergence rate. Here, we propose using a Variable Input Observer (VIO) concept to vary the input space as the event unfolds. When systems experience high-rate dynamics, rapid changes in the system occur. To investigate the VIO’s potential, a VIO-based neuro-observer is constructed and studied using experimental data collected from a laboratory impact test. Results demonstrate that the input space is unique to different impact conditions, and that adjusting the input space throughout the dynamic event produces better estimations than using a traditional fixed input space strategy.

Experimental Round Robin for Predicting Electronic Component Response from High-G Loads

The Air Force Research Laboratory led an experimental Round Robin with members of the Department of Defense and Department of Energy to validate capabilities to predict the response of electrical assemblies due to mechanical shock. Specifically, high-g shock that has peak accelerations in the 10,000–20,000 g range with durations of 0.1–0.5 ms. These accelerations were generated through the use of a Very High-G machine and a MTS Drop Tower. The test article contained an array of accelerometers placed on each of the four printed circuit boards within the unit. Input data was collected for the computational performers by mounting accelerometers to the top and bottom of a test fixture while simultaneously capturing the response of the item under test inside of the fixture. The input data was provided to the different performers, then the performers’ prediction results of the test articles accelerometer data were compared to the experimental data. This paper will present the experimental techniques that were utilized for the MTS Drop Tower series, the input data, and a discussion of the evaluation metrics used for the comparison of the models to the experimental data.

Development of a Mapping Function for a Low- to High-Amplitude Input

The Air Force Research Laboratory is continuing research to design a controllable pyroshock test to excite a test item over the entire frequency spectrum from low (10 Hz) to high (10 kHz) at different forcing levels. When a linear Frequency Response Function exists we would expect that we can design a multiple input test to achieve a desired output response based on superposition of the single input modal response of the test structure. Experimental modal analysis is performed to evaluate the differences in FRF’s for the different input force levels generated by a modal hammer and a detonator. The final outcome of this research endeavor is to be able to perform a modal analysis on the test platform and use that information to define the input force location, magnitude, and time delay to achieve a desired output response. Initial studies at the output location will focus on utilizing the Shock Response Spectrum as the Figure of Merit, however, energy methods and other criteria may be considered. This paper will present progress in the development of the Design-a-Shock method and the difficulties that were encountered in trying to capture the input response of a detonator, the lessons learned from the testing, and a discussion on the characterization of the system response.

Effect of Radial Confinement on Wave Propagation and Vibrational Response in Bars

It is currently beyond the state-of-the art to accurately predict the instantaneous dynamic response of a structure with rapidly changing boundary conditions. In order to establish a basic understanding of changing boundary conditions, we examine the wave propagation through a bar subject to mechanical confinement. The Air Force Research Laboratory has conducted several experiments investigating the effect of non-traditional boundary conditions, such as mid-structure confinement, on the local and global dynamic response of rods using a modified Hopkinson Bar configuration with radial clamping. We have shown that the wave velocity in the mechanically clamped area is significantly lower than that in a stress free bar. This paper presents the experimental results and analytical modeling of the effect of radial confinement on dynamic response in bars.