Browse Topic: Statistical analysis
This paper deals with the uncertainty estimation of identified frequency and damping trends of whirl flutter modes, obtained by applying system identification methods on experimental data. In particular, two different identification approaches are considered, namely the free-decay analysis by using Matrix Pencil algorithm and the Data-Driven Stochastic Subspace Identification method (SSI), applied to system response to stochastic input. The two approaches lead to as many uncertainty estimation methodologies, both leveraging the bootstrapping statistical process. A full validation procedure is then set up to assess the accuracy of such methods in correctly quantifying the uncertainty of the estimated statistics. To do so, a wing-rotor state-space linear numerical model is used to simulate system response to both dwell and stochastic inputs. The state space numerical system aims to replicate the ATTILA wing-rotor wind-tunnel model, which falls in the framework of Clean Sky 2 European program to investigate the possible occurrence of whirl-flutter instability in tiltrotor configurations. Hence, one of the proposed methodologies is applied to ATTILA experimental data for both modal identification and uncertainty estimation, and the processed flutter trends are reported in a few conditions of particular interest due to the progressive approaching of whirl-flutter condition.
This study investigates Reynolds number effects on rotor wake vortex development using a hyperbaric rotor facility capable of pressurizing air up to 100 bar. Background-oriented schlieren (BOS) and hot-wire anemometry (HWA) were applied to characterize vortex trajectories, core growth, and circumferential velocity distribution. BOS measurements revealed consistent blade-to-blade trajectory deviations and vortex pairing across all operating conditions, despite that the investigated three-bladed rotor was milled from a single piece of aluminum, ensuring precise manufacturing and a highly symmetric geometry. A statistical scheme was developed to analyze the radial structure of fluctuating tip vortices, which traverse the pointwise fiber-film sensor in a fixed position. With increasing vortex Reynolds number, the tip vortices are more compact with a reduction in core growth. The circulation in the vortices grows with the vortex radial coordinate, and converges at a radial position basically independent of the vortex core size. Observed asymmetries in young vortices at low Reynolds numbers indicate enhanced roll-up dynamics. The results demonstrate the facility’s ability to isolate Reynolds number effects in rotor wake dynamics.
Bench-level tribological experiments were utilized to evaluate material, coating, and lubricant formulation effects on the loss-of-lubricant survivability of tapered roller end and cone rib contacts. Cone rib and roller end contacts were simulated using a single rotating roller and rotating flat disk. The applied load and rotational speeds of the roller and disk were controlled to simulate representative rotorcraft gearbox bearing operating conditions. The contacts were lubricated for an initial period before the lubricant supply was shut off, and the supply tube was then removed. Tests continued to run, without additional oil, until the measured friction force reached a predetermined cutoff value. Weibull-based statistical analysis was used to compare the loss-of-lubrication runtimes.
Launch, recovery, and deck handling operational performance on smaller ship platforms like Corvettes, Frigates and Destroyers are qualified as the most challenging tasks in the UAS ship-deployment of a VTOL Uncrewed Air System (UAS). One of the main hurdles is the random nature of seaway-created deck motions coupled with ship structure disturbed air wake patterns. The MoD has supported a range of work aimed at bringing Quiescent Period Prediction (QPP) technology to fruition. QPP firstly requires Wave Profiling RADAR to measure the sea wave system out to approximately 2km in the region around a vessel. Secondly these measurements are employed in a wave propagation model to predict the actual wave forces acting on a vessel. Using the wave predictions as inputs to a vessel model makes possible to predict the actual (deterministic as opposed to statistical) motions of a vessel. Wave systems naturally alternate groups of large waves with smaller waves, this property, combined with the predictive ability, allows to identify the quietest (most quiescent) periods in which to conduct wave limited naval operations. Naval mission planners in the Royal Navy, and elsewhere in the World, appreciate the need to maintain rapid, but safe, deck tempo. The fundamental concept is to measure remote sea surface profiles to predict the future wave forces acting upon a vessel. The objective is to expand ship operating deck limits to approximately Sea State 6+. The deck definitions generally empirically measured by using standard rating scales, are replaced by instrumented devices reporting the status of the deck prior to touch-down. In this paper, a thorough discussion describing the QPP deck measuring devices designed to replace piloted cueing is provided. Theory, previous simulation studies and current at-sea testing along with data results, are also discussed. To conclude, the interface of the deck measuring device into the next version of the UK UAS system, is provided. The results of the RADAR trial indicated that the RADAR data was reliable, with the RADAR images matching the physical map. The two-dimensional surface plot showed both the RADAR blocking fence along with an additional target. An additional observation concerning the operation over the deck whilst the ship is experiencing a quiescent ship motion period. The coupled secondary effect documents minimized air wake confusion. This is owing to fewer ship structure excursions into and out of the air flow. To better define deck airflow around the ship the integration of a Doppler LIDAR instrumented federate is proposed. This is meant to predict the future vessel air wake and look for quiescent periods in this paralleling the vessel motion QPP technique.
In the context of Rotorcraft Pilot Couplings, the biomechanics of the pilot body play a fundamental role in determining the stability of the pilot-vehicle closed loop system. The response of the pilot body is, in turn, inherently stochastic, being a function of pilot biometrics and muscular activation. Coupling the statistical distribution of pilot biomechanical behavior determined in specialized experimental campaign with linear models of the helicopter heave dynamics, an uncertainty propagation procedure is developed, with the aim of estimating the statistical distribution of the stability margins of the closed loop pilot-vehicle system. Results obtained varying the collective lever characteristics, as well as the helicopter model parameters, align well with results obtained previously in deterministic settings. However, the new scheme allows to define quantitative robustness indices.
A framework for statistical comparison between analytical and experimental structural loads has been developed and applied to approximately 100 counters within the UH-60A Airloads test program. This framework relies on established structural load variability methods with novel applications to analytical structural load development maneuver time transient analysis. The analytical results are from Rotorcraft Comprehensive Analysis System (RCAS) spanwise structural loads developed with hub load and spanwise aerodynamic loads prescribed. RCAS consistently under predicted the Coefficient of Variation (COV) associated with spanwise Normal bending when compared to flight data. This resulted in significant scale factors required to achieve a μ+2σ reliability for structural load development. RCAS results for Edgewise bending scale factors proved slightly better than Normal bending in addition to more even over / under prediction of COV when compared to flight data.
This study presents a statistical approach for detecting and estimating damage to multicopter propellers through a comprehensive probabilistic model. The methodology is derived from model-based analysis and applied within the time series statistical techniques. This research accounts for uncertainties in the estimation process and offers confidence intervals for assessing the extent of damage to the propellers. The framework employs functionally pooled (FP) models characterized by parameters that depend on damage sizes, proper statistical estimation, and decision-making schemes. The validation and assessment are assessed via a hexacopter flying in circles with a constant velocity and altitude under turbulence. The damage size ranges from healthy to 10 mm. The method achieves fast damage detection and precise magnitude estimation based on a segment of a single measured signal obtained from aircraft sensors during flight.
When the target value of functional geometrical specification is too tight, its cascade of tolerances is at the feasibility limit of production. In this case, the geometrical Tolerancing method loses its benefits and generates an excessive level of non-Conformity which induces additional costs that are not acceptable. The aim of this paper is first to introduce the background concerning chain of dimension method and tolerances capabilities based on test specimen results. Secondly, demonstrate ability to apply statistical calculation. Thirdly extend conventional chain of dimension in one dimension to multi-holes system installation. And, then analyze potential effect by stress evaluation. And confirm the demonstration of improvement on Tolerancing installation calculations, by onboarding all stakeholder (design, manufacturing, stress) early in design phase (interfaces maturation) and by analyzing more in detail installations constraints. This method should be applied first on "non-critical" junction, because it needs to be further matured and so it is not yet mature enough for primary structure and associated quality checks. In conclusion, as a result, it is possible to increase tolerance specification of parts and manage risks of non-assembly. In conclusion, tolerances for holes localization could be approximatively multiplied by two compared to basic calculation method.
Rotor blade optimization presents a multifaceted challenge as traditional design methodologies rely on computationally exhaustive high-fidelity computational fluid dynamics (CFD). Conversely, low-fidelity techniques such as potential flow based codes are inaccurate, especially in the regions of flow separation. This paper proposes leveraging artificial neural networks (ANNs) to predict the performance polar of a given airfoil geometry, and to facilitate the inverse design of airfoil, a modified form of ANNs (known as Tandem Neural Networks (T-NNs)) is implemented. The airfoil inverse design is a multi-point optimization problem (at multiple angles of attack) and therefore, the T-NNs are trained on the vectors of performance polar instead of individual angles of attack. The paper also delves into a comprehensive analysis of data wrangling, airfoil parametrization and design of experiments to cover a wide range of rotorcraft airfoils. A novel way of including practical design constraints for airfoil geometry is also included. Finally, this work demonstrates the application of the proposed methodology for airfoil inverse design, statistical analysis for generating a family of airfoils and optimization of HART-II rotor using T-NNs and Genetic Algorithm (GA).
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A robust framework for fault detection and identification of rotor degradation in multicopters while effectively rejecting the effects of gusts is introduced. The rotor fault detection and identification methods employed in this study are based on excitation-response signals of the aircraft under ambient turbulence to distinguish between an aircraft response to gusts and rotor faults. A concise overview of the development of statistical time series model for healthy aircraft using the aircraft attitudes as the output and controller commands as the input is presented. This model is utilized to extract quality features for training a simple neural network to perform effective online rotor fault detection and identification in a hexacopter exceptional speed of making a decision and accuracy of fault classification. It is shown that using a statistical time series model assisted neural network employed for online monitoring is capable of rejecting gusts, sensitive to even 20% rotor degradation and achieves fault detection and identification in less than 2 s after the fault with an accuracy over 99%.
This work introduces the use of "global" stochastic models to detect and identify rotor failures in multicopters under different operating conditions, turbulence, and uncertainty. The identification of an extended class of time-series models known as Vector-dependent Functionally Pooled AutoRegressive models, which are characterized by parameters that depend on both forward velocity and gross weight, using scalar or vector aircraft response signals under white noise excitation has been described. A concise overview of the residual based statistical decision making schemes for fault detection and identification of rotor failures is provided. The scalar and vector statistical models, along with residual variance and residual uncorrelatedness methods were validated and their effectiveness was assessed by a proof-of-concept application to aircraft flight for healthy and faulty states under severe turbulence and intermediate operating conditions. The results of this study demonstrate the effectiveness of all the proposed residual-based time series methods in terms of prompt rotor fault detection, although the methods based on Vector AutoRegressive models exhibit improved performance compared to their scalar counterparts with respect to their performance in identifying rotor failures in the post-failure controller compensated state.
Sikorsky has developed a specification outlining the use of three casting technologies: simulation, additive manufacturing of the mold and low pressure casting. This specification has been used in the past on new development projects with positive results, reducing lead times and number of pours to produce a useable part. When the S-92 program needed to develop a second source for a casting, they worked with Magellan Aerospace to implement the specification. The project proceeded on time with all castings able to be used. Some elements of the specification were modified to work with a legacy part design, including the use of statistical process controls to reduce variability in crucible pouring.
This article introduces a probabilistic model-based programming language called AURA-Sim that enables the quantification, propagation, and analysis of arbitrary random distributions through nonlinear systems. Probabilistic programming languages are a relatively recent innovation that are intended to automate much of the low-level programming required to implement common statistical computations. Model-based programming languages are designed to simplify the specification of complex dynamical systems, having many separate components that interact over time, and are widely used for developing complex systems in numerous disciplines. This articles explains the harmonious combination of these two programming concepts into a unified programming language that enables system designers to directly solve many of the most important problems of uncertainty management for dynamical systems. The resulting language is developed as a set of C++ libraries and exposed to the user in the model-based language of SIMULINK and MATLAB. AURA-Sim allows system designers to model essentially arbitrary random processes and to propagate them through a wide variety of nonlinear dynamical systems. This capability is not currently available in any model-based programming language. The AURA-Sim library is based on generalized polynomial chaos (gPC) theory which is reviewed in the following. Traditionally, uncertainty quantification, propagation, and analysis has been conducted using Monte Carlo simulation; however, Monte Carlo simulations often incur a high computational cost, are time consuming, and slow to converge. Even after dedicating the time and computational resources to perform exhaustive Monte Carlo analysis, comprehensive coverage of the uncertainty space is not assured and reasoning over the simulation results requires additional cost. The AURA-Sim approach offers the potential to provide comprehensive coverage with a single simulation run, drastically reducing the required cost. Reasoning and calculating inferential statistics from the results does not required large data sets because the simulation signals are represented as random quantities.
Existing Structural Health Monitoring (SHM) techniques generally depend on deterministic parameters in order to detect, localize, and quantify damage. This limits the applicability of such systems in real-life situations, where stochastic, time-varying structural response, as well as complex damage types immersed in operational/environmental uncertainties are almost always encountered. Thus, there lies a need for the proposal of statistical quantities and methods for assessing structural health. That is, a holistic probabilistic SHM framework involving damage detection, localization, and quantification, is due if such systems are to become standard on VTOL platforms. In this work, a novel probabilistic approach for active-sensing acousto-ultrasound SHM targeting damage detection and quantification is proposed based on stochastic non-parametric time series representations. Statistical signal processing techniques are used to formulate statistical hypothesis tests, based on which a decision can be made to whether a component is healthy or damaged within pre-defined confidence bounds. The methods presented herein can also be used for damage quantification. The proposed framework is first applied to a notched Aluminum coupon with different damage sizes within an active-sensing, local "hot-spot" monitoring framework. After that, experimental data collected over a stiffened Aluminum panel, representing a sub-scale fuselage component, is analyzed using the probabilistic framework for validation of the proposed methods on more real-life structures. Results show the advantage of the proposed techniques in citing confidence to the decision-making process when compared with state-of-the-art damage indicators. In addition, insights into damage localization within a probabilistic framework are also presented, which may be used as a preliminary step to damage localization
Guided-wave-based acousto-ultrasound structural health monitoring (SHM) methods have attracted the interest of the SHM community as guided waves can travel long distances without significant dissipation and are capable of detecting small damage sizes of several types. However, when subject to changing environmental and operational conditions (EOC), guided-wave-based methods may give false indications of damage as they exhibit increased sensitivity to varying EOC. In order to improve the reliability and enable the large-scale applicability of these methods, and to build a robust SHM system, it is necessary to quantify the uncertainty in guided wave propagation due to changing EOC. In this paper, a rigorous investigation on the uncertainty involved in the propagation of Lamb waves due to the variation in temperature and material properties of nominally-identical structures has been performed both numerically and experimentally. A high fidelity finite element model is established to study the effect of small temperature perturbation on the S0 and A0 modes of Lamb waves and the associated uncertainty is quantified. Then experiments are performed under ambient laboratory temperature variations during an eleven day period. The experimental results have indicated that temperature variations as small as 0.5°C may result variations in the amplitude of Lamb waves and affect the damage index. Then uncertainty due to the variation in material properties has been considered by taking into account the statistical Gamma distributed dependency between Young's modulus and Poisson ratio jointly and the associated variation in the damage index is also investigated.
This work introduces the use of statistical time series methods to detect rotor failures in multicopters. A concise overview of the development of various time series models using scalar or vector signals, statistics, and fault detection methods is provided. The fault detection methods employed in this study are based on parametric time series representations and response-only signals of the aircraft state, as the external excitation is non-observable. The comparative assessment of the effectiveness of scalar and vector statistical models and several residual-based fault detection methods are presented in the presence of external disturbances, such as various levels of turbulence and uncertainty, and for different rotor failure scenarios. The results of this study demonstrate the effectiveness of all the proposed residual-based time series methods in terms of prompt rotor fault detection, although the methods based on Vector AutoRegressive (VAR) models exhibit improved performance compared to their scalar counterparts with respect to their robustness and effectiveness for different turbulence levels and ability to distinguish between healthy and fault compensated condition after rotor failure.
Pitching airfoil measurements are known to exhibit significant scatter at near- and post-stall angles of attack. Applying data-driven algorithms revealed the presence of bimodal distribution within the data scatter, suggesting that the statistical mean and standard deviation often used to represent cycle-to-cycle variations are incorrect. Considering the historical significance of dynamic stall measurements, a thorough assessment was undertaken to ascertain that the observed furcation in the data is not a result of facility or post processing error. Once confirmed, cluster-averages, associated variances, and group probability were identified as the best alternative to represent groups in the data. Several existing clustering techniques were tested, however, their shortcomings led to the development of two new data-driven algorithms. A uniqueness that is common to both of the new algorithms is that the clustering process is based on the flow phenomena that contribute the most energy to the overall flow variations. By operating in the optimal basis that maximizes the variance in the measurements, separation of clusters became efficient. When applied to several test cases, the clusters revealed the causes for such grouping, such as the variations in the separation location, occurrence of LE/TE stall, presence/absence of a dynamic stall vortex (or vortices), reattachment angle, etc. In all the cases, the physical processes and their effects were obscured by the phase-average curves. Further analyses to study the effects of Mach number, reduced frequency, mean angle and amplitude of oscillation revealed trends in the group probability. Aerodynamic damping, peak values of pitching moment and lift were substantially different between the clusters, as well as with the phase-average. Considering future semi-empirical models that need to account for cycle switching from one group to another, Markov process (and chain) was studied.
ABSTRACT An analytical approach to identify manufacturing span reduction opportunities is presented. Span and variation reduction are key elements in operations management that lead directly to improved inventory turns. Generic solutions (such as implementing one type of corrective action across all gates of a production line) is a conventional approach that can lead to poor long term decisions. Statistical measures, such as coefficient of variation, standard deviation, and average span, are calculated and compared against target values to identify span and variation reduction opportunities. The focus is on gated areas of the production flow, where improved targets need to be achieved. This approach identifies Lean, Variation Reduction and Design Improvement opportunities and was used to implement corrective actions that resulted in 29.3% reduction in the average span for a production Bell main rotor blade in 2017.
ABSTRACT This article describes an approach to learning gearbox operating conditions, defined by torque, rotational speed, and power, from acceleration data. Learning operating conditions paves the way to learning gearbox state-of-health because health indicators have to be normalized with respect to operating conditions to avoid false alarms. Moreover, because operational data is vastly larger than data associated with faults, representation learning is easier (and often only possible) from the operational data. The article compares two different solutions, one based on a multi-layer perceptron and the other on a recurrent network using the first four statistical moments as input features. The decision process, including heuristics and domain knowledge, used for selection of the network topology is described in detail. Models were found most effective in estimating the mechanical power transmitted through the gearbox and provided improvements over the second moment (RMS) alone.
ABSTRACT Major challenges of high quality requirements are associated with internal statistical variability, i.e., too severe gap between "as-designed" vs. "as-built" composite micro-structures. Therefore, the objective of this work is development of general physics-based methodology to correlate structural performance of RCS with inevitable variability of internal designs and demonstrate it on examples of representative composite sub-elements. Generated results can be used to provide guidance for simplifications and relaxation of existing quality requirements with obvious cost and availability improvement. Demonstration of implementation is shown on quantification of damage initiation in laminated structures under conditions of tension and bending.
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