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All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions

The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local and represents a small change in the stiffness matrix compared to the baseline (undamaged) structure. The exact solution to a slightly modified set of equations can be obtained from the baseline solution economically without actually solving the modified system.. Shennan-Morrison-Woodbury (SMW) formulas are matrix update formulas that allow this (Akgun et al., 1998b). SMW formulas were therefore used here to compute adjoint displacements for sensitivity computation and structural displacements in damaged configurations.

Akgun, Mehmet A.↗
NASA NTRS1999

Optimization of Aerospace Structure Subject to Damage Tolerance Criteria

The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers. It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages. A common method for topology optimization is that of compliance minimization which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local and represents a small change in the stiffness matrix compared to the baseline (undamaged) structure. The exact solution to a slightly modified set of equations can be obtained from the baseline solution economically without actually solving the modified system. Sherrnan-Morrison-Woodbury (SMW) formulas are matrix update formulas that allow this. SMW formulas were therefore used here to compute adjoint displacements for sensitivity computation and structural displacements in damaged configurations.

Akgun, Mehmet A.↗
NASA NTRS2001

Shape Optimization of Supersonic Turbines Using Response Surface and Neural Network Methods

Turbine performance directly affects engine specific impulse, thrust-to-weight ratio, and cost in a rocket propulsion system. A global optimization framework combining the radial basis neural network (RBNN) and the polynomial-based response surface method (RSM) is constructed for shape optimization of a supersonic turbine. Based on the optimized preliminary design, shape optimization is performed for the first vane and blade of a 2-stage supersonic turbine, involving O(10) design variables. The design of experiment approach is adopted to reduce the data size needed by the optimization task. It is demonstrated that a major merit of the global optimization approach is that it enables one to adaptively revise the design space to perform multiple optimization cycles. This benefit is realized when an optimal design approaches the boundary of a pre-defined design space. Furthermore, by inspecting the influence of each design variable, one can also gain insight into the existence of multiple design choices and select the optimum design based on other factors such as stress and materials considerations.

Papila, Nilay↗
NASA NTRS2001

Free-form Airfoil Shape Optimization Under Uncertainty Using Maximum Expected Value and Second-order Second-moment Strategies

Free-form shape optimization of airfoils poses unexpected difficulties. Practical experience has indicated that a deterministic optimization for discrete operating conditions can result in dramatically inferior performance when the actual operating conditions are different from the - somewhat arbitrary - design values used for the optimization. Extensions to multi-point optimization have proven unable to adequately remedy this problem of "localized optimization" near the sampled operating conditions. This paper presents an intrinsically statistical approach and demonstrates how the shortcomings of multi-point optimization with respect to "localized optimization" can be overcome. The practical examples also reveal how the relative likelihood of each of the operating conditions is automatically taken into consideration during the optimization process. This is a key advantage over the use of multipoint methods.

Huyse, Luc↗
NASA NTRS2001

Discrete-State Simulated Annealing For Traveling-Wave Tube Slow-Wave Circuit Optimization

Algorithms based on the global optimization technique of simulated annealing (SA) have proven useful in designing traveling-wave tube (TWT) slow-wave circuits for high RF power efficiency. The characteristic of SA that enables it to determine a globally optimized solution is its ability to accept non-improving moves in a controlled manner. In the initial stages of the optimization, the algorithm moves freely through configuration space, accepting most of the proposed designs. This freedom of movement allows non-intuitive designs to be explored rather than restricting the optimization to local improvement upon the initial configuration. As the optimization proceeds, the rate of acceptance of non-improving moves is gradually reduced until the algorithm converges to the optimized solution. The rate at which the freedom of movement is decreased is known as the annealing or cooling schedule of the SA algorithm. The main disadvantage of SA is that there is not a rigorous theoretical foundation for determining the parameters of the cooling schedule. The choice of these parameters is highly problem dependent and the designer needs to experiment in order to determine values that will provide a good optimization in a reasonable amount of computational time. This experimentation can absorb a large amount of time especially when the algorithm is being applied to a new type of design. In order to eliminate this disadvantage, a variation of SA known as discrete-state simulated annealing (DSSA), was recently developed. DSSA provides the theoretical foundation for a generic cooling schedule which is problem independent, Results of similar quality to SA can be obtained, but without the extra computational time required to tune the cooling parameters. Two algorithm variations based on DSSA were developed and programmed into a Microsoft Excel spreadsheet graphical user interface (GUI) to the two-dimensional nonlinear multisignal helix traveling-wave amplifier analysis program TWA3. The algorithms were used to optimize the computed RF efficiency of a TWT by determining the phase velocity profile of the slow-wave circuit. The mathematical theory and computational details of the DSSA algorithms will be presented and results will be compared to those obtained with a SA algorithm.

Wilson, Jeffrey D.↗
NASA NTRS1996

DCTune Perceptual Optimization of Compressed Dental X-Rays

In current dental practice, x-rays of completed dental work are often sent to the insurer for verification. It is faster and cheaper to transmit instead digital scans of the x-rays. Further economies result if the images are sent in compressed form. DCTune is a technology for optimizing DCT (digital communication technology) quantization matrices to yield maximum perceptual quality for a given bit-rate, or minimum bit-rate for a given perceptual quality. Perceptual optimization of DCT color quantization matrices. In addition, the technology provides a means of setting the perceptual quality of compressed imagery in a systematic way. The purpose of this research was, with respect to dental x-rays, 1) to verify the advantage of DCTune over standard JPEG (Joint Photographic Experts Group), 2) to verify the quality control feature of DCTune, and 3) to discover regularities in the optimized matrices of a set of images. We optimized matrices for a total of 20 images at two resolutions (150 and 300 dpi) and four bit-rates (0.25, 0.5, 0.75, 1.0 bits/pixel), and examined structural regularities in the resulting matrices. We also conducted psychophysical studies (1) to discover the DCTune quality level at which the images became 'visually lossless,' and (2) to rate the relative quality of DCTune and standard JPEG images at various bitrates. Results include: (1) At both resolutions, DCTune quality is a linear function of bit-rate. (2) DCTune quantization matrices for all images at all bitrates and resolutions are modeled well by an inverse Gaussian, with parameters of amplitude and width. (3) As bit-rate is varied, optimal values of both amplitude and width covary in an approximately linear fashion. (4) Both amplitude and width vary in systematic and orderly fashion with either bit-rate or DCTune quality; simple mathematical functions serve to describe these relationships. (5) In going from 150 to 300 dpi, amplitude parameters are substantially lower and widths larger at corresponding bit-rates or qualities. (6) Visually lossless compression occurs at a DCTune quality value of about 1. (7) At 0.25 bits/pixel, comparative ratings give DCTune a substantial advantage over standard JPEG. As visually lossless bit-rates are approached, this advantage of necessity diminishes. We have concluded that DCTune optimized quantization matrices provide better visual quality than standard JPEG. Meaningful quality levels may be specified by means of the DCTune metric. Optimized matrices are very similar across the class of dental x-rays, suggesting the possibility of a 'class-optimal' matrix. DCTune technology appears to provide some value in the context of compressed dental x-rays.

Watson, Andrew B.↗
NASA NTRS1998

High-Lift Optimization Design Using Neural Networks on a Multi-Element Airfoil

The high-lift performance of a multi-element airfoil was optimized by using neural-net predictions that were trained using a computational data set. The numerical data was generated using a two-dimensional, incompressible, Navier-Stokes algorithm with the Spalart-Allmaras turbulence model. Because it is difficult to predict maximum lift for high-lift systems, an empirically-based maximum lift criteria was used in this study to determine both the maximum lift and the angle at which it occurs. Multiple input, single output networks were trained using the NASA Ames variation of the Levenberg-Marquardt algorithm for each of the aerodynamic coefficients (lift, drag, and moment). The artificial neural networks were integrated with a gradient-based optimizer. Using independent numerical simulations and experimental data for this high-lift configuration, it was shown that this design process successfully optimized flap deflection, gap, overlap, and angle of attack to maximize lift. Once the neural networks were trained and integrated with the optimizer, minimal additional computer resources were required to perform optimization runs with different initial conditions and parameters. Applying the neural networks within the high-lift rigging optimization process reduced the amount of computational time and resources by 83% compared with traditional gradient-based optimization procedures for multiple optimization runs.

Greenman, Roxana M.↗
NASA NTRS2003

Coupled Multi-Disciplinary Optimization for Structural Reliability and Affordability

A computational simulation method is presented for Non-Deterministic Multidisciplinary Optimization of engine composite materials and structures. A hypothetical engine duct made with ceramic matrix composites (CMC) is evaluated probabilistically in the presence of combined thermo-mechanical loading. The structure is tailored by quantifying the uncertainties in all relevant design variables such as fabrication, material, and loading parameters. The probabilistic sensitivities are used to select critical design variables for optimization. In this paper, two approaches for non-deterministic optimization are presented. The non-deterministic minimization of combined failure stress criterion is carried out by: (1) performing probabilistic evaluation first and then optimization and (2) performing optimization first and then probabilistic evaluation. The first approach shows that the optimization feasible region can be bounded by a set of prescribed probability limits and that the optimization follows the cumulative distribution function between those limits. The second approach shows that the optimization feasible region is bounded by 0.50 and 0.999 probabilities.

Abumeri, Galib H.↗
NASA NTRS2004

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Nemec, Marian↗
NASA NTRS2002

Overall Traveling-Wave-Tube Efficiency Improved By Optimized Multistage Depressed Collector Design

Depressed Collector Design The microwave traveling wave tube (TWT) is used widely for space communications and high-power airborne transmitting sources. One of the most important features in designing a TWT is overall efficiency. Yet, overall TWT efficiency is strongly dependent on the efficiency of the electron beam collector, particularly for high values of collector efficiency. For these reasons, the NASA Glenn Research Center developed an optimization algorithm based on simulated annealing to quickly design highly efficient multistage depressed collectors (MDC's). Simulated annealing is a strategy for solving highly nonlinear combinatorial optimization problems. Its major advantage over other methods is its ability to avoid becoming trapped in local minima. Simulated annealing is based on an analogy to statistical thermodynamics, specifically the physical process of annealing: heating a material to a temperature that permits many atomic rearrangements and then cooling it carefully and slowly, until it freezes into a strong, minimum-energy crystalline structure. This minimum energy crystal corresponds to the optimal solution of a mathematical optimization problem. The TWT used as a baseline for optimization was the 32-GHz, 10-W, helical TWT developed for the Cassini mission to Saturn. The method of collector analysis and design used was a 2-1/2-dimensional computational procedure that employs two types of codes, a large signal analysis code and an electron trajectory code. The large signal analysis code produces the spatial, energetic, and temporal distributions of the spent beam entering the MDC. An electron trajectory code uses the resultant data to perform the actual collector analysis. The MDC was optimized for maximum MDC efficiency and minimum final kinetic energy of all collected electrons (to reduce heat transfer). The preceding figure shows the geometric and electrical configuration of an optimized collector with an efficiency of 93.8 percent. The results show the improvement in collector efficiency from 89.7 to 93.8 percent, resulting in an increase of three overall efficiency points. In addition, the time to design a highly efficient MDC was reduced from a month to a few days. All work was done in-house at Glenn for the High Rate Data Delivery Program. Future plans include optimizing the MDC and TWT interaction circuit in tandem to further improve overall TWT efficiency.

Vaden, Karl R.↗
NASA NTRS2006

Optimal Design of Passive Flow Control for a Boundary-Layer-Ingesting Offset Inlet Using Design-of-Experiments

This research will investigate the use of Design-of-Experiments (DOE) in the development of an optimal passive flow control vane design for a boundary-layer-ingesting (BLI) offset inlet in transonic flow. This inlet flow control is designed to minimize the engine fan-face distortion levels and first five Fourier harmonic half amplitudes while maximizing the inlet pressure recovery. Numerical simulations of the BLI inlet are computed using the Reynolds-averaged Navier-Stokes (RANS) flow solver, OVERFLOW, developed at NASA. These simulations are used to generate the numerical experiments for the DOE response surface model. In this investigation, two DOE optimizations were performed using a D-Optimal Response Surface model. The first DOE optimization was performed using four design factors which were vane height and angles-of-attack for two groups of vanes. One group of vanes was placed at the bottom of the inlet and a second group symmetrically on the sides. The DOE design was performed for a BLI inlet with a free-stream Mach number of 0.85 and a Reynolds number of 2 million, based on the length of the fan-face diameter, matching an experimental wind tunnel BLI inlet test. The first DOE optimization required a fifth order model having 173 numerical simulation experiments and was able to reduce the DC60 baseline distortion from 64% down to 4.4%, while holding the pressure recovery constant. A second DOE optimization was performed holding the vanes heights at a constant value from the first DOE optimization with the two vane angles-of-attack as design factors. This DOE only required a second order model fit with 15 numerical simulation experiments and reduced DC60 to 3.5% with small decreases in the fourth and fifth harmonic amplitudes. The second optimal vane design was tested at the NASA Langley 0.3- Meter Transonic Cryogenic Tunnel in a BLI inlet experiment. The experimental results showed a 80% reduction of DPCP(sub avg), the circumferential distortion level at the engine fan-face.

Allan, Brian G.↗
NASA NTRS2006

Optimal Design of Passive Flow Control for a Boundary-Layer-Ingesting Offset Inlet Using Design-of-Experiments

This research will investigate the use of Design-of-Experiments (DOE) in the development of an optimal passive flow control vane design for a boundary-layer-ingesting (BLI) offset inlet in transonic flow. This inlet flow control is designed to minimize the engine fan face distortion levels and first five Fourier harmonic half amplitudes while maximizing the inlet pressure recovery. Numerical simulations of the BLI inlet are computed using the Reynolds-averaged Navier-Stokes (RANS) flow solver, OVERFLOW, developed at NASA. These simulations are used to generate the numerical experiments for the DOE response surface model. In this investigation, two DOE optimizations were performed using a D-Optimal Response Surface model. The first DOE optimization was performed using four design factors which were vane height and angles-of-attack for two groups of vanes. One group of vanes was placed at the bottom of the inlet and a second group symmetrically on the sides. The DOE design was performed for a BLI inlet with a free-stream Mach number of 0.85 and a Reynolds number of 2 million, based on the length of the fan face diameter, matching an experimental wind tunnel BLI inlet test. The first DOE optimization required a fifth order model having 173 numerical simulation experiments and was able to reduce the DC60 baseline distortion from 64% down to 4.4%, while holding the pressure recovery constant. A second DOE optimization was performed holding the vanes heights at a constant value from the first DOE optimization with the two vane angles-of-attack as design factors. This DOE only required a second order model fit with 15 numerical simulation experiments and reduced DC60 to 3.5% with small decreases in the fourth and fifth harmonic amplitudes. The second optimal vane design was tested at the NASA Langley 0.3-Meter Transonic Cryogenic Tunnel in a BLI inlet experiment. The experimental results showed a 80% reduction of DPCPavg, the circumferential distortion level at the engine fan face.

Allan, Brian G.↗
NASA NTRS2007

Efficient Optimization of Low-Thrust Spacecraft Trajectories

A paper describes a computationally efficient method of optimizing trajectories of spacecraft driven by propulsion systems that generate low thrusts and, hence, must be operated for long times. A common goal in trajectory-optimization problems is to find minimum-time, minimum-fuel, or Pareto-optimal trajectories (here, Pareto-optimality signifies that no other solutions are superior with respect to both flight time and fuel consumption). The present method utilizes genetic and simulated-annealing algorithms to search for globally Pareto-optimal solutions. These algorithms are implemented in parallel form to reduce computation time. These algorithms are coupled with either of two traditional trajectory- design approaches called "direct" and "indirect." In the direct approach, thrust control is discretized in either arc time or arc length, and the resulting discrete thrust vectors are optimized. The indirect approach involves the primer-vector theory (introduced in 1963), in which the thrust control problem is transformed into a co-state control problem and the initial values of the co-state vector are optimized. In application to two example orbit-transfer problems, this method was found to generate solutions comparable to those of other state-of-the-art trajectory-optimization methods while requiring much less computation time.

Lee, Seungwon↗
NASA NTRS2012

Direct Method Transcription for a Human-Class Translunar Injection Trajectory Optimization

This paper presents a new trajectory optimization software package developed in the framework of a low-to-high fidelity 3 degrees-of-freedom (DOF)/6-DOF vehicle simulation program named Mission Analysis Simulation Tool in Fortran (MASTIF) and its application to a translunar trajectory optimization problem. The functionality of the developed optimization package is implemented as a new "mode" in generalized settings to make it applicable for a general trajectory optimization problem. In doing so, a direct optimization method using collocation is employed for solving the problem. Trajectory optimization problems in MASTIF are transcribed to a constrained nonlinear programming (NLP) problem and solved with SNOPT, a commercially available NLP solver. A detailed description of the optimization software developed is provided as well as the transcription specifics for the translunar injection (TLI) problem. The analysis includes a 3-DOF trajectory TLI optimization and a 3-DOF vehicle TLI simulation using closed-loop guidance.

Witzberger, Kevin E.↗
NASA NTRS2012

Optimal Force Control of Vibro-Impact Systems for Autonomous Drilling Applications

The need to maintain optimal energy efficiency is critical during the drilling operations performed on future and current planetary rover missions (see figure). Specifically, this innovation seeks to solve the following problem. Given a spring-loaded percussive drill driven by a voice-coil motor, one needs to determine the optimal input voltage waveform (periodic function) and the optimal hammering period that minimizes the dissipated energy, while ensuring that the hammer-to-rock impacts are made with sufficient (user-defined) impact velocity (or impact energy). To solve this problem, it was first observed that when voice-coil-actuated percussive drills are driven at high power, it is of paramount importance to ensure that the electrical current of the device remains in phase with the velocity of the hammer. Otherwise, negative work is performed and the drill experiences a loss of performance (i.e., reduced impact energy) and an increase in Joule heating (i.e., reduction in energy efficiency). This observation has motivated many drilling products to incorporate the standard bang-bang control approach for driving their percussive drills. However, the bang-bang control approach is significantly less efficient than the optimal energy-efficient control approach solved herein. To obtain this solution, the standard tools of classical optimal control theory were applied. It is worth noting that these tools inherently require the solution of a two-point boundary value problem (TPBVP), i.e., a system of differential equations where half the equations have unknown boundary conditions. Typically, the TPBVP is impossible to solve analytically for high-dimensional dynamic systems. However, for the case of the spring-loaded vibro-impactor, this approach yields the exact optimal control solution as the sum of four analytic functions whose coefficients are determined using a simple, easy-to-implement algorithm. Once the optimal control waveform is determined, it can be used optimally in the context of both open-loop and closed-loop control modes (using standard realtime control hardware).

Aldrich, Jack B.↗
NASA NTRS2012

Computational Optimization of a Natural Laminar Flow Experimental Wing Glove

Computational optimization of a natural laminar flow experimental wing glove that is mounted on a business jet is presented and discussed. The process of designing a laminar flow wing glove starts with creating a two-dimensional optimized airfoil and then lofting it into a three-dimensional wing glove section. The airfoil design process does not consider the three dimensional flow effects such as cross flow due wing sweep as well as engine and body interference. Therefore, once an initial glove geometry is created from the airfoil, the three dimensional wing glove has to be optimized to ensure that the desired extent of laminar flow is maintained over the entire glove. TRANAIR, a non-linear full potential solver with a coupled boundary layer code was used as the main tool in the design and optimization process of the three-dimensional glove shape. The optimization process uses the Class-Shape-Transformation method to perturb the geometry with geometric constraints that allow for a 2-in clearance from the main wing. The three-dimensional glove shape was optimized with the objective of having a spanwise uniform pressure distribution that matches the optimized two-dimensional pressure distribution as closely as possible. Results show that with the appropriate inputs, the optimizer is able to match the two dimensional pressure distributions practically across the entire span of the wing glove. This allows for the experiment to have a much higher probability of having a large extent of natural laminar flow in flight.

Hartshom, Fletcher↗
NASA NTRS2016

Integrated Medical Model (IMM) Optimization Version 4.0 Functional Improvements

The IMMs ability to assess mission outcome risk levels relative to available resources provides a unique capability to provide guidance on optimal operational medical kit and vehicle resources. Post-processing optimization allows IMM to optimize essential resources to improve a specific model outcome such as maximization of the Crew Health Index (CHI), or minimization of the probability of evacuation (EVAC) or the loss of crew life (LOCL). Mass and or volume constrain the optimized resource set. The IMMs probabilistic simulation uses input data on one hundred medical conditions to simulate medical events that may occur in spaceflight, the resources required to treat those events, and the resulting impact to the mission based on specific crew and mission characteristics. Because IMM version 4.0 provides for partial treatment for medical events, IMM Optimization 4.0 scores resources at the individual resource unit increment level as opposed to the full condition-specific treatment set level, as done in version 3.0. This allows the inclusion of as many resources as possible in the event that an entire set of resources called out for treatment cannot satisfy the constraints. IMM Optimization version 4.0 adds capabilities that increase efficiency by creating multiple resource sets based on differing constraints and priorities, CHI, EVAC, or LOCL. It also provides sets of resources that improve mission-related IMM v4.0 outputs with improved performance compared to the prior optimization. The new optimization represents much improved fidelity that will improve the utility of the IMM 4.0 for decision support.

risk assessment↗
NASA NTRS2017

Low-Thrust Trajectory Optimization with Simplified SQP Algorithm

The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.

Parrish, Nathan L.↗