Fast Bayesian identification of a class of elastic weakly nonlinear systems using backbone curves

This paper introduces a method for the identification of the parameters of nonlinear structures using a probabilistic Bayesian framework, employing a Markov chain Monte Carlo algorithm. This approach uses analytical models to describe the unforced, undamped dynamic responses of structures in the frequency–amplitude domain, known as the backbone curves. The analytical models describing these backbone curves are then fitted to measured responses, found using the resonant-decay method. To investigate the proposed identification method, a nonlinear two-degree-of-freedom example structure is simulated numerically and analytical expressions describing the backbone curves are found. These expressions are then used, in conjunction with the backbone curve data found through simulated experiment, to estimate the system parameters. It is shown that the use of these computationally-cheap analytical expressions allows for an extremely efficient method for modelling the dynamic behaviour, providing an identification procedure that is both fast and accurate. Furthermore, for the example structure, it is shown that the estimated parameters may be used to accurately predict the existence of dynamic behaviours that are well-away from the backbone curve data provided; specifically the existence of an isola is predicted

Emulator-Based Control for Actuator-Based Hardware-in-the-Loop Testing, Control Engineering Practice

Abstract Hardware-in-the-loop (HWiL) is a form of component testing where hardware components a linked with software models. In order to test mechanical components an additional transfer system is required to link the software and hardware subsystems. The transfer system typically comprises of sensors and actuators and the dynamic effects of these components need to be eliminated to give accurate results. In this paper an emulator-based control strategy is presented for actuator based HWiL. Emulator-based control can solve the twin problems of stability and fidelity caused by the unwanted transfer system (actuator) dynamics. Significantly EBC can emulate the inverse of a transfer system which is not causally invertible, allowing a wider range of more complex transfer systems to be controlled. A robustness analysis is given and experimental results presented

Numerical continuation analysis of a dual-sidestay main landing gear mechanism

A model of a three-dimensional dual-sidestay landing gear mechanism is presented and employed in an investigation of the sensitivity of the downlocking mechanism to attachment point deflections. A motivation for this study is the desire to understand the underlying nonlinear behavior, which may prevent a dual-sidestay landing gear from downlocking under certain conditions. The model formulates the mechanism as a set of steady-state constraint equations. Solutions to these equations are then continued numerically in state and parameter space, providing all state parameter dependencies within the model from a single computation. The capability of this analysis approach is demonstrated with an investigation into the effects of the aft sidestay angle on retraction actuator loads. It was found that the retraction loads are not significantly affected by the sidestay plane angle, but the landing gear’s ability to be retracted fully is impeded at certain sidestay plane angles. This result is attributed to the landing gear’s geometry, as the locklinks are placed under tension and cause the mechanism to lock. Sidestay flexibilities and attachment point deflections are then introduced to enable the downlock loads to be investigated. The investigation into the dual sidestay’s downlock sensitivity to attachment point deflections yields an underlying double-hysteresis loop, which is highly sensitive to these deflections. Attachment point deflections of a few millimeters were found to prevent the locklinks from automatically downlocking under their own weight, hence requiring some external force to downlock the landing gear. Sidestay stiffness was also found to influence the downlock loads, although not to the extent of attachment point deflection

Frequency-Domain Bifurcation Analysis of a Nonlinear Flight Dynamics Model

This paper presents a methodology for systematically studying the nonlinear frequency responses of an aircraft model using numerical continuation with periodic forcing, thereby presenting an extension of conventional bifurcation analysis in flight dynamics applications. The motivation is to identify nonlinear phenomena in the frequency domain that are absent in linearized models - upon which many control law designs are based - and which therefore risks degrading the performance or robustness of the linear-model based controllers. Since the aerospace industry typically uses linearizations in controller design, both open and closed loop behaviors are considered. When the example aircraft considered here is forced with small control surface deflections, highly nonlinear responses are observed. This includes period doubling bifurcations, fold bifurcations leading to existence of multiple solutions, quasi periodic motions, and formation of isolas. Closed-loop responses of a proportional stability augmentation controller for this aircraft become out of phase with the linear prediction at low forcing frequencies when the aircraft operates at high angle of attack. To address these behaviors, the methodology is extended by employing two-parameter continuation of the controller gain to assess its effectiveness in those nonlinear regions, where linear controller design techniques cannot be used. Time histories are used to verify the results

Inverse dynamics modelling of upper-limb tremor, with cross-correlation analysis

A method to characterise upper-limb tremor using inverse dynamics modelling in combination with cross-correlation analyses is presented. A 15 degree-of-freedom inverse dynamics model is used to estimate the joint torques required to produce the measured limb motion, given a set of estimated inertial properties for the body segments. The magnitudes of the estimated torques are useful when assessing patients or evaluating possible intervention methods. The cross-correlation of the estimated joint torques is proposed to gain insight into how tremor in one limb segment interacts with tremor in another. The method is demonstrated using data from a single patient presenting intention tremor because of multiple sclerosis. It is shown that the inertial properties of the body segments can be estimated with sufficient accuracy using only the patient's height and weight as a priori knowledge, which ensures the method's practicality and transferability to clinical use. By providing a more detailed, objective characterisation of patient-specific tremor properties, the method is expected to improve the selection, design and assessment of treatment options on an individual basis

A novel COL4A1 frameshift mutation in familial kidney disease: the importance of the C-terminal NC1 domain of type IV collagen.

BACKGROUND: Hereditary microscopic haematuria often segregates with mutations of COL4A3, COL4A4 or COL4A5 but in half of families a gene is not identified. We investigated a Cypriot family with autosomal dominant microscopic haematuria with renal failure and kidney cysts. METHODS: We used genome-wide linkage analysis, whole exome sequencing and cosegregation analyses. RESULTS: We identified a novel frameshift mutation, c.4611_4612insG:p.T1537fs, in exon 49 of COL4A1. This mutation predicts truncation of the protein with disruption of the C-terminal part of the NC1 domain. We confirmed its presence in 20 family members, 17 with confirmed haematuria, 5 of whom also had stage 4 or 5 chronic kidney disease. Eleven family members exhibited kidney cysts (55% of those with the mutation), but muscle cramps or cerebral aneurysms were not observed and serum creatine kinase was normal in all individuals tested. CONCLUSIONS: Missense mutations of COL4A1 that encode the CB3 [IV] segment of the triple helical domain (exons 24 and 25) are associated with HANAC syndrome (hereditary angiopathy, nephropathy, aneurysms and cramps). Missense mutations of COL4A1 that disrupt the NC1 domain are associated with antenatal cerebral haemorrhage and porencephaly, but not kidney disease. Our findings extend the spectrum of COL4A1 mutations linked with renal disease and demonstrate that the highly conserved C-terminal part of the NC1 domain of the α1 chain of type IV collagen is important in the integrity of glomerular basement membrane in humans

Simplifying transformations for nonlinear systems: Part I, an optimisation-based variant of normal form analysis

This paper introduces the idea of a ‘simplifying transformation’ for nonlinear structural dynamic systems. The idea simply stated; is to bring under one heading, those transformations which ‘simplify’ structural dynamic systems or responses in some sense. The equations of motion may be cast in a simpler form or decoupled (and in this sense, nonlinear modal analysis is encompassed) or the responses may be modified in order to isolate and remove certain components. It is the latter sense of simplification which is considered in this paper. One can regard normal form analysis in a way as the removal of superharmonic content from nonlinear system response. In the current paper, this problem is cast in an optimisation form and the differential evolution algorithm is used

Low Order Model for the Dynamics of Bi-Stable Composite Plates

This article presents the derivation and validation of a low order model for the non-linear dynamics of cross-ply bi-stable composite plates focusing on the response of one stable state. The Rayleigh–Ritz method is used to solve the associated linear problem to obtain valuable theoretical insight into how to formulate an approximate non-linear dynamic model. This allows us to follow a Galerkin approach projecting the solution of the non-linear problem onto the mode shapes of the linear problem. The order of the non-linear model is reduced using theoretical results from the linear solution yielding a low order model. The dynamic response of a bi-stable plate specimen is studied to simplify the model further by only keeping the non-linear terms leading to observed oscillations. Simulations for the dynamic response using the derived model are presented showing excellent agreement with the experimentally observed behaviour. Additionally, deflection shapes are measured and compared with the calculated mode shapes, showing good agreement