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At least 163 records · Page 9

Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer

This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.

Pai, P. F.↗

Non-linear controls influence functions in an aircraft dynamics simulator

In the development and testing of novel structural and controls concepts, such as morphing aircraft wings, appropriate models are needed for proper system characterization. In most instances, available system models do not provide the required additional degrees of freedom for morphing structures but may be modified to some extent to achieve a compatible system. The objective of this study is to apply wind tunnel data collected for an Unmanned Air Vehicle (UAV), that implements trailing edge morphing, to create a non-linear dynamics simulator, using well defined rigid body equations of motion, where the aircraft stability derivatives change with control deflection. An analysis of this wind tunnel data, using data extraction algorithms, was performed to determine the reference aerodynamic force and moment coefficients for the aircraft. Further, non-linear influence functions were obtained for each of the aircraft s control surfaces, including the sixteen trailing edge flap segments. These non-linear controls influence functions are applied to the aircraft dynamics to produce deflection-dependent aircraft stability derivatives in a non-linear dynamics simulator. Time domain analysis of the aircraft motion, trajectory, and state histories can be performed using these nonlinear dynamics and may be visualized using a 3-dimensional aircraft model. Linear system models can be extracted to facilitate frequency domain analysis of the system and for control law development. The results of this study are useful in similar projects where trailing edge morphing is employed and will be instrumental in the University of Maryland s continuing study of active wing load control.

Guerreiro, Nelson M.↗

High Velocity Linear Induction Launcher with Exit-Edge Compensation for Testing of Aerospace Components

Advances in ultra high speed linear induction electromagnetic launchers over the past decade have focused on magnetic compensation of the exit and entry-edge transient flux wave to produce efficient and compact linear electric machinery. The paper discusses two approaches to edge compensation in long-stator induction catapults with typical end speeds of 150 to 1,500 m/s. In classical linear induction machines, the exit-edge effect is manifest as two auxiliary traveling waves that produce a magnetic drag on the projectile and a loss of magnetic flux over the main surface of the machine. In the new design for the Stator Compensated Induction Machine (SCIM) high velocity launcher, the exit-edge effect is nulled by a dual wavelength machine or alternately the airgap flux is peaked at a location prior to the exit edge. A four (4) stage LIM catapult is presently being constructed for 180 m/s end speed operation using double-sided longitudinal flux machines. Advanced exit and entry edge compensation is being used to maximize system efficiency, and minimize stray heating of the reaction armature. Each stage will output approximately 60 kN of force and produce over 500 G s of acceleration on the armature. The advantage of this design is there is no ablation to the projectile and no sliding contacts, allowing repeated firing of the launcher without maintenance of any sort. The paper shows results of a parametric study for 500 m/s and 1,500 m/s linear induction launchers incorporating two of the latest compensation techniques for an air-core stator primary and an iron-core primary winding. Typical thrust densities for these machines are in the range of 150 kN/sq.m. to 225 kN/sq.m. and these compete favorably with permanent magnet linear synchronous machines. The operational advantages of the high speed SCIM launcher are shown by eliminating the need for pole-angle position sensors as would be required by synchronous systems. The stator power factor is also improved.

Kuznetsov, Stephen↗

Linear Actuator Has Long Stroke and High Resolution

The term precision linear actuator, direct drive ( PLADD ) refers to a robust linear actuator designed to be capable of repeatedly performing, over a lifetime of the order of 5 to 10 years, positioning maneuvers that include, variously, submicron increments or slews of the order of a centimeter. The PLADD is capable of both long stroke (120 mm) and high resolution (repeatable increments of 20 nm). Unlike precise linear actuators of prior design, the PLADD contains no gears, levers, or hydraulic converters. The PLADD, now at the prototype stage of development, is intended for original use as a coarse-positioning actuator in a spaceborne interferometer. The PLADD could also be adapted to terrestrial applications in which there are requirements for long stroke and high resolution: potential applications include medical imaging and fabrication of semiconductor devices. The PLADD (see figure) includes a commercially available ball-screw actuator driven directly by a commercially available three-phase brushless DC motor. The ball-screw actuator comprises a spring-preloaded ball nut on a ball screw that is restrained against rotation as described below. The motor is coupled directly (that is, without an intervening gear train) to a drive link that, in turn, is coupled to the ball nut. By eliminating the gear train, the direct-drive design eliminates the complexity, backlash, and potential for misalignment associated with a gear train. To prevent inadvertent movement, there is a brake that includes flexured levers compressed against the drive link by preload springs. This is a power-off brake: There are also piezoelectric stacks that can be activated to oppose the springs and push the levers away from the drive link. Hence, power must be applied to the piezoelectric stacks to release the drive link from braking. To help ensure long operational life, all of the mechanical drive components are immersed in an oil bath within hermetically sealed bellows. The outer end of the bellows holds the outer end of the ball screw, thereby preventing rotation of the ball screw. Positioning is controlled by an electronic control system that includes digital and analog subsystems that interact with the motor and brake and with two sensor/encoder units: a Hall-effect-sensor rotation encoder and a linear glass-scale encoder. This system implements a proportional + integral + derivative control algorithm that results in variation of voltage commands to each of the three pairs of windings of the brushless DC motor. In one of two alternative control modes, the voltages are applied to the windings in a trapezoidal commutation scheme on the basis of timing signals obtained from the Hall-effect sensors; this scheme yields relatively coarse positioning - 24 steps per motor revolution. The second control mode involves a sinusoidal commutation scheme in which the output of the linear glass-scale encoder is transposed to rotational increments to yield much finer position feedback - more than 400,000 steps per revolution.

Cook, Brant T.↗

Adjustment of Adaptive Gain with Bounded Linear Stability Analysis to Improve Time-Delay Margin for Metrics-Driven Adaptive Control

This paper presents the application of Bounded Linear Stability Analysis (BLSA) method for metrics driven adaptive control. The bounded linear stability analysis method is used for analyzing stability of adaptive control models, without linearizing the adaptive laws. Metrics-driven adaptive control introduces a notion that adaptation should be driven by some stability metrics to achieve robustness. By the application of bounded linear stability analysis method the adaptive gain is adjusted during the adaptation in order to meet certain phase margin requirements. Analysis of metrics-driven adaptive control is evaluated for a linear damaged twin-engine generic transport model of aircraft. The analysis shows that the system with the adjusted adaptive gain becomes more robust to unmodeled dynamics or time delay.

Bakhtiari-Nejad, Maryam↗

Bounded Linear Stability Analysis - A Time Delay Margin Estimation Approach for Adaptive Control

This paper presents a method for estimating time delay margin for model-reference adaptive control of systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent the conventional model-reference adaptive law by a locally bounded linear approximation within a small time window using the comparison lemma. The locally bounded linear approximation of the combined adaptive system is cast in a form of an input-time-delay differential equation over a small time window. The time delay margin of this system represents a local stability measure and is computed analytically by a matrix measure method, which provides a simple analytical technique for estimating an upper bound of time delay margin. Based on simulation results for a scalar model-reference adaptive control system, both the bounded linear stability method and the matrix measure method are seen to provide a reasonably accurate and yet not too conservative time delay margin estimation.

Nguyen, Nhan T.↗

Preprocessing Inconsistent Linear System for a Meaningful Least Squares Solution

Mathematical models of many physical/statistical problems are systems of linear equations. Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Sen, Syamal K.↗

Preprocessing in Matlab Inconsistent Linear System for a Meaningful Least Squares Solution

Mathematical models of many physical/statistical problems are systems of linear equations~ Due to measurement and possible human errors/mistakes in modeling/data, as well as due to certain assumptions to reduce complexity, inconsistency (contradiction) is injected into the model, viz. the linear system. While any inconsistent system irrespective of the degree of inconsistency has always a least-squares solution, one needs to check whether an equation is too much inconsistent or, equivalently too much contradictory. Such an equation will affect/distort the least-squares solution to such an extent that renders it unacceptable/unfit to be used in a real-world application. We propose an algorithm which (i) prunes numerically redundant linear equations from the system as these do not add any new information to the model, (ii) detects contradictory linear equations along with their degree of contradiction (inconsistency index), (iii) removes those equations presumed to be too contradictory, and then (iv) obtain the . minimum norm least-squares solution of the acceptably inconsistent reduced linear system. The algorithm presented in Matlab reduces the computational and storage complexities and also improves the accuracy of the solution. It also provides the necessary warning about the existence of too much contradiction in the model. In addition, we suggest a thorough relook into the mathematical modeling to determine the reason why unacceptable contradiction has occurred thus prompting us to make necessary corrections/modifications to the models - both mathematical and, if necessary, physical.

Sen, Symal K.↗

Compact, Low-Force, Low-Noise Linear Actuator

Actuators are critical to all the robotic and manipulation mechanisms that are used in current and future NASA missions, and are also needed for many other industrial, aeronautical, and space activities. There are many types of actuators that were designed to operate as linear or rotary motors, but there is still a need for low-force, low-noise linear actuators for specialized applications, and the disclosed mechanism addresses this need. A simpler implementation of a rotary actuator was developed where the end effector controls the motion of a brush for cleaning a thermal sensor. The mechanism uses a SMA (shape-memory alloy) wire for low force, and low noise. The linear implementation of the actuator incorporates a set of springs and mechanical hard-stops for resetting and fault tolerance to mechanical resistance. The actuator can be designed to work in a pull or push mode, or both. Depending on the volume envelope criteria, the actuator can be configured for scaling its volume down to 4 2 1 cm3. The actuator design has an inherent fault tolerance to mechanical resistance. The actuator has the flexibility of being designed for both linear and rotary motion. A specific configuration was designed and analyzed where fault-tolerant features have been implemented. In this configuration, an externally applied force larger than the design force does not damage the active components of the actuator. The actuator housing can be configured and produced using cost-effective methods such as injection molding, or alternatively, its components can be mounted directly on a small circuit board. The actuator is driven by a SMA -NiTi as a primary active element, and it requires energy on the order of 20 Ws(J) per cycle. Electrical connections to points A and B are used to apply electrical power in the resistive NiTi wire, causing a phase change that contracts the wire on the order of 5%. The actuation period is of the order of a second for generating the stroke, and 4 to 10 seconds for resetting. Thus, this design allows the actuator to work at a frequency of up to 0.1 Hz. The actuator does not make use of the whole range of motion of the SMA material, allowing for large margins on the mechanical parameters of the design. The efficiency of the actuator is of the order of 10%, including the margins. The average dissipated power while driving at full speed is of the order of 1 W, and can be scaled down linearly if the rate of cycling is reduced. This design produces an extremely quiet actuator; it can generate a force greater than 2 N and a stroke greater than 1 cm. The operational duration of SMA materials is of the order of millions of cycles with some reduced stroke over a wide temperature range up to 150 C.

Badescu, Mircea↗

Compact, Low-Force, Low-Noise Linear Actuator

Actuators are critical to all the robotic and manipulation mechanisms that are used in current and future NASA missions, and are also needed for many other industrial, aeronautical, and space activities. There are many types of actuators that were designed to operate as linear or rotary motors, but there is still a need for low-force, low-noise linear actuators for specialized applications, and the disclosed mechanism addresses this need. A simpler implementation of a rotary actuator was developed where the end effector controls the motion of a brush for cleaning a thermal sensor. The mechanism uses a SMA (shape-memory alloy) wire for low force, and low noise. The linear implementation of the actuator incorporates a set of springs and mechanical hard-stops for resetting and fault tolerance to mechanical resistance. The actuator can be designed to work in a pull or push mode, or both. Depending on the volume envelope criteria, the actuator can be configured for scaling its volume down to 4x2x1 cu cm. The actuator design has an inherent fault tolerance to mechanical resistance. The actuator has the flexibility of being designed for both linear and rotary motion. A specific configuration was designed and analyzed where fault-tolerant features have been implemented. In this configuration, an externally applied force larger than the design force does not damage the active components of the actuator. The actuator housing can be configured and produced using cost-effective methods such as injection molding, or alternatively, its components can be mounted directly on a small circuit board. The actuator is driven by a SMA -NiTi as a primary active element, and it requires energy on the order of 20 Ws(J) per cycle. Electrical connections to points A and B are used to apply electrical power in the resistive NiTi wire, causing a phase change that contracts the wire on the order of 5%. The actuation period is of the order of a second for generating the stroke, and 4 to 10 seconds for resetting. Thus, this design allows the actuator to work at a frequency of up to 0.1 Hz. The actuator does not make use of the whole range of motion of the SMA material, allowing for large margins on the mechanical parameters of the design. The efficiency of the actuator is of the order of 10%, including the margins. The average dissipated power while driving at full speed is of the order of 1 W, and can be scaled down linearly if the rate of cycling is reduced. This design produces an extremely quiet actuator; it can generate a force greater than 2 N and a stroke greater than 1 cm. The operational duration of SMA materials is of the order of millions of cycles with some reduced stroke over a wide temperature range up to 150 C.

Badescu, Mircea↗

Development of a Low Inductance Linear Alternator for Stirling Power Convertors

The free-piston Stirling power convertor is a promising technology for high efficiency heat-to-electricity power conversion in space. Stirling power convertors typically utilize linear alternators for converting mechanical motion into electricity. The linear alternator is one of the heaviest components of modern Stirling power convertors. In addition, state-of-art Stirling linear alternators usually require the use of tuning capacitors or active power factor correction controllers to maximize convertor output power. The linear alternator to be discussed in this paper, eliminates the need for tuning capacitors and delivers electrical power output in which current is inherently in phase with voltage. No power factor correction is needed. In addition, the linear alternator concept requires very little iron, so core loss has been virtually eliminated. This concept is a unique moving coil design where the magnetic flux path is defined by the magnets themselves. This paper presents computational predictions for two different low inductance alternator configurations, and compares the predictions with experimental data for one of the configurations that has been built and is currently being tested.

Stirling↗

Development of a Low-Inductance Linear Alternator for Stirling Power Convertors

The free-piston Stirling power convertor is a promising technology for high-efficiency heat-to-electricity power conversion in space. Stirling power convertors typically utilize linear alternators for converting mechanical motion into electricity. The linear alternator is one of the heaviest components of modern Stirling power convertors. In addition, state-of-the-art Stirling linear alternators usually require the use of tuning capacitors or active power factor correction controllers to maximize convertor output power. The linear alternator to be discussed in this paper eliminates the need for tuning capacitors and delivers electrical power output in which current is inherently in phase with voltage. No power factor correction is needed. In addition, the linear alternator concept requires very little iron, so core loss has been virtually eliminated. This concept is a unique moving coil design where the magnetic flux path is defined by the magnets themselves. This paper presents computational predictions for two different low inductance alternator configurations. Additionally, one of the configurations was built and tested at GRC, and the experimental data is compared with the predictions.

Stirling↗

Studies in Astronomical Time Series Analysis: VII. An Enquiry Concerning Non-Linearity, the RMS-Mean Flux Relation, and log-Normal Flux Distributions

A broad and widely used class of stationary, linear, additive time series models can have statistical properties which many authors have asserted imply that the underlying process must be non-linear, non-stationary, multiplicative, or inconsistent with shot noise. This result is demonstrated with exact and numerical evaluation of the model flux distribution function and dependence of flux standard deviation on mean flux (here and in the literature called the rms-flux relation). These models can: (1) exhibit normal, log-normal or other flux distributions; (2) show linear or slightly non-linear rms-mean flux dependencies; as well as (3) match arbitrary second order statistics of the time series data. Accordingly the above assertions cannot be made on the basis of statistical time series analysis alone. Also idscussed are ambiguities in the meaning of terms relevant to this study – linear, stationary and multiplicative – and functions that can transform observed fluxes to a normal distribution as well or better than the logarithm.

Jeffrey D Scargle↗

Linear and Nonlinear Trend Analyzes in Global Satellite‐Based Precipitation, 1998–2017

Precipitation varies spatio‐temporally in amount, intensity, and frequency. Although, much research has been conducted on analyzing precipitation patterns and variation at the global scale, trend types have still not received much attention. This study developed a new polynomial‐based model for detecting nonlinear and linear trends in a satellite precipitation product (TRMM 3B43) for the 1998–2017 period at a near‐global scale. We used an automated trend classification method that detects significant trends and classifies them into linear and nonlinear (cubic, quadratic, and concealed) trend types in satellite‐based precipitation at near‐global, continental, and climate zone scales. We found that 12.3% of pixel‐based precipitation time series across the globe have significant trend at 0.05 significance level (50% positive and 50% negative trends). In all continents except Asia, decreasing trends were found to cover larger areas than corresponding increasing trends. Regarding climate zone and precipitation trend change, our results indicate that a linear trend is dominant in the warm temperate (77.7%) and equatorial climates (80.4%) while the least linear change was detected in the polar climate (68.9%). The combined results of continental and climate zone scales indicate significant increasing trends in Asia and arid climate over the last 20 yr. Furthermore, positive trends were found to be more significant at the continental scale, particularly, in Asia relative to the climate zone scale. Linear change in precipitation (80%) was the most dominant trend observed as opposed to nonlinear (quadratic [11%] and cubic [9%]) trend types at the global scale.

Majid Kazemzadeh↗

Demonstration of Linear Covariance Analysis Techniques to Evaluate Entry Descent and Landing Guidance Algorithms, Vehicle Configurations, Analysis Techniques, and Trajectory Profiles

Linear covariance analysis techniques have been previously developed to analyze closed-loop entry, descent, and landing (EDL) scenarios and the initial validation efforts are under-way confirming the generated GN&C system performance results. Given both the theoretical foundation and previous conceptual demonstration, this work begins to flex the potential of linear covariance analysis for atmospheric flight and highlight its versatility and reliability by evaluating multiple entry guidance algorithms, vehicle configurations, trajectory profiles, environment conditions, and analysis techniques for a variety of trade studies. To demonstrate the benefit linear covariance analysis can provide in producing rapid yet accurate performance data, two entry profiles are adopted including the NASA Mars Science Laboratory (MSL) and Exploration Flight Test-1 (EFT-1) while utilizing two different guidance algorithms, the Apollo Final Phase (AFP) and the Fully Numeric Predictor-Corrector Entry Guidance (FNPEG) with different navigation sensor suites in a 6 degree-of-freedom (6-DOF) simulation environment. Results are shown using both linear covariance and Monte Carlo analysis techniques to high-light the consistency between the two methodologies and continue the validation maturation of linear covariance analysis for entry, descent, and landing.

EDL↗

Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.

Applied Dynamical Systems↗

Iterative methods in GPU-resident linear solvers for nonlinear constrained optimization

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra methods are often inefficient. For example, methods for solving ill-conditioned linear systems have relied on conditional branching, which degrades performance on hardware accelerators such as graphical processing units (GPUs). To improve the efficiency of solving ill-conditioned systems, our computational strategy separates computations that are efficient on GPUs from those that need to run on traditional central processing units (CPUs). Our strategy maximizes the reuse of expensive CPU computations. Iterative methods, which thus far have not been broadly used for ill-conditioned linear systems, play an important role in our approach. In particular, we extend ideas from Arioli et al., (2007) to implement iterative refinement using inexact LU factors and flexible generalized minimal residual (FGMRES), with the aim of efficient performance on GPUs. In conclusion, we focus on solutions that are effective within broader application contexts, and discuss how early performance tests could be improved to be more predictive of the performance in a realistic environment.

97 MATHEMATICS AND COMPUTING↗

Energy recovery proton linear accelerator

High-power proton linear accelerators have important applications in both scientific research and industry. However, the operation of such accelerators with megawatt-level beam power is expensive and limits the broad availability of these facilities. In this Letter, we propose a novel energy recovery proton linear accelerator in which the final GeV-level proton beam is reinjected into the linear accelerator from the accelerator exit and is decelerated in the same accelerator down to about 2 MeV, close to the initial beam energy. This substantially reduces the power consumption of the proton linear accelerator and also avoids the need for a high-power beam dump. We demonstrate this concept through self-consistent simulations and show that the beam-beam effect between the forward-accelerating beam and the backward-decelerating beam would not be a limiting factor for the proposed concept. A potential application of this concept to an electron-ion collider based on energy recovery electron and ion accelerators is discussed.

Energy recovery linacs↗