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DOE OSTI2020

Applying Information Theory to Design Optimal Filters for Photometric Redshifts

In this paper we apply ideas from information theory to create a method for the design of optimal filters for photometric redshift estimation. We show the method applied to a series of simple example filters in order to motivate an intuition for how photometric redshift estimators respond to the properties of photometric passbands. We then design a realistic set of six filters covering optical wavelengths that optimize photometric redshifts for z <= 2.3 and i < 25.3. We create a simulated catalog for these optimal filters and use our filters with a photometric redshift estimation code to show that we can improve the standard deviation of the photometric redshift error by 7.1% overall and improve outliers 9.9% over the standard filters proposed for the Large Synoptic Survey Telescope (LSST). We compare features of our optimal filters to the LSST and find that the LSST filters incorporate key features for optimal photometric redshift estimation. Finally, we describe how information theory can be applied to a range of optimization problems in astronomy.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Domain Knowledge Guided Bayesian Optimization For Autonomous Alignment Of Complex Scientific Instruments

Bayesian Optimization (BO) is a powerful tool for optimizing complex non-linear systems. However, its performance degrades in high-dimensional problems with tightly coupled parameters and highly asymmetric objective landscapes, where rewards are sparse. In such needle-in-a-haystack scenarios, even advanced methods like trust-region BO (TurBO) often lead to unsatisfactory results. We propose a domain knowledge guided Bayesian Optimization approach, which leverages physical insight to fundamentally simplify the search problem by transforming coordinates to decouple input features and align the active subspaces with the primary search axes. We demonstrate this approach's efficacy on a challenging 12-dimensional, 6-crystal Split-and-Delay optical system, where conventional approaches, including standard BO, TuRBO and multi-objective BO, consistently led to unsatisfactory results. When combined with an reverse annealing exploration strategy, this approach reliably converges to the global optimum. The coordinate transformation itself is the key to this success, significantly accelerating the search by aligning input co-ordinate axes with the problem's active subspaces. As increasingly complex scientific instruments, from large telescopes to new spectrometers at X-ray Free Electron Lasers are deployed, the demand for robust high-dimensional optimization grows. Our results demonstrate a generalizable paradigm: leveraging physical insight to transform high-dimensional, coupled optimization problems into simpler representations can enable rapid and robust automated tuning for consistent high performance while still retaining current optimization algorithms.

FOS: Computer and information sciences↗

DOE OSTI2019

Optimization of process models for determining volatility distribution and viscosity of organic aerosols from isothermal particle evaporation data

The composition of organic aerosol under different ambient conditions as well as their phase state have been a subject of intense study in recent years. One way to study particle properties is to measure the particle size shrinkage in a diluted environment at isothermal conditions. From these measurements it is possible to separate the fraction of low-volatility compounds from high-volatility compounds. In this work, we analyse and evaluate a method for obtaining particle composition and viscosity from measurements using process models coupled with input optimization algorithms. Two optimization methods, the Monte Carlo genetic algorithm and Bayesian inference, are used together with process models describing the dynamics of particle evaporation. The process model optimization scheme in inferring particle composition in a volatility-basis-set sense and composition-dependent particle viscosity is tested with artificially generated data sets and real experimental data. Optimizing model input so that the output matches these data yields a good match for the estimated quantities. Both optimization methods give equally good results when they are used to estimate particle composition to artificially test data. Finally, the timescale of the experiments and the initial particle size are found to be important in defining the range of values that can be identified for the properties from the optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Neural Networks for Prediction of Complex Chemistry in Water Treatment Process Optimization

Water chemistry plays a critical role in the design and operation of water treatment processes. Detailed chemistry modeling tools use a combination of advanced thermodynamic models and extensive databases to predict phase equilibria and reaction phenomena. The complexity and formulation of these models preclude their direct integration in equation-oriented modeling platforms, making it difficult to use their capabilities for rigorous water treatment process optimization. Neural networks (NN) can provide a pathway for integrating the predictive capability of chemistry software into equation-oriented models and enable optimization of complex water treatment processes across a broad range of conditions and process designs. Herein, we assess how NN architecture and training data impact their accuracy and use in equation-oriented water treatment models. We generate training data using PhreeqC software and determine how data generation and sample size impact the accuracy of trained NNs. The effect of NN architecture on optimization is evaluated by optimizing hypothetical black-box desalination processes using a range of feed compositions from USGS brackish water data set, tracking the number of successful optimizations, and testing the impact of initial guess on the final solution. Our results clearly demonstrate that data generation and architecture impact NN accuracy and viability for use in equation-oriented optimization problems.

Dudchenko, Alexander V↗

NASA NTRS1972

An engineering optimization method with application to STOL-aircraft approach and landing trajectories

An optimization method has been developed that computes the optimal open loop inputs for a dynamical system by observing only its output. The method reduces to static optimization by expressing the inputs as series of functions with parameters to be optimized. Since the method is not concerned with the details of the dynamical system to be optimized, it works for both linear and nonlinear systems. The method and the application to optimizing longitudinal landing paths for a STOL aircraft with an augmented wing are discussed. Noise, fuel, time, and path deviation minimizations are considered with and without angle of attack, acceleration excursion, flight path, endpoint, and other constraints.

Jacob, H. G.↗

NASA NTRS1972

Computerized optimal control system design for reusable and expendable boost vehicles.

An optimization technique has been developed which combines the practical features of hybrid simulation of the dynamic system under study with the systematic approach of modern control theory where a mathematically formulated design criterion is optimized by functional minimization. Standard hybrid computer optimization methods using high-speed repetitive simulations and gradient minimization schemes have been extended to obtain time-varying optimal gain schedules and reduce the sensitivity of the optimized system to parameter and disturbance uncertainties. In this approach the performance index is expressed in meaningful engineering terms that reflect the interactions among all major disciplines, structures, control/actuation system design, aerodynamics and performance. The basic optimization technique is developed and its application to current aerospace control problems including the space shuttle is presented in detail. In the discussion of the application, the controllers resulting from the technique are compared with controllers developed by conventional methods. The paper concludes with a review of the advantages and disadvantages of the technique and plans for future applications.

Connor, C. L.↗

NASA NTRS1971

Design of optimal probing signals for vector parameter estimation.

In the design of optimal inputs or probing signals for parameter estimation, it is more natural to consider functions of the Fisher information matrix as the criterion of optimality instead of some function of the error covariance matrix. The input which maximizes the Fisher information measure for efficient estimation of a scalar parameter also provides the minimum error variance. The information is thus a logical choice for the optimality criterion in scalar problems. No such obvious choice is apparent for vector parameter estimation. A number of performance measures are examined and compared in the present study, and a useful criterion is selected. The design of an optimal probing signal using this criterion is shown to be equivalent to an optimal control problem in which certain equality constraints must be satisfied. This problem may be solved by conventional techniques of deterministic or stochastic optimal control.

Nahi, N. E.↗

NASA NTRS1972

On the determination of optimal costly measurement strategies for linear stochastic systems.

This paper presents the formulation of a class of optimization problems dealing with selecting, at each instant of time, one measurement provided by one out of many sensors. Each measurement has an associated measurement cost. The basic problem is then to select an optimal measurement policy, during a specified observation time interval, so that a weighted combination of prediction accuracy and accumulated observation cost is optimized. The current analysis is limited to the class of linear stochastic dynamic systems and measurement subsystems. The problem of selecting the optimal measurement strategy can be transformed into a deterministic optimal control problem. It is shown that the optimal measurement policy and the associated matched Kalman-type filter can be precomputed.

Athans, M.↗

NASA NTRS1974

Four-body trajectory optimization

A comprehensive optimization program has been developed for computing fuel-optimal trajectories between the earth and a point in the sun-earth-moon system. It presents methods for generating fuel optimal two-impulse trajectories which may originate at the earth or a point in space and fuel optimal three-impulse trajectories between two points in space. The extrapolation of the state vector and the computation of the state transition matrix are accomplished by the Stumpff-Weiss method. The cost and constraint gradients are computed analytically in terms of the terminal state and the state transition matrix. The 4-body Lambert problem is solved by using the Newton-Raphson method. An accelerated gradient projection method is used to optimize a 2-impulse trajectory with terminal constraint. The Davidon's Variance Method is used both in the accelerated gradient projection method and the outer loop of a 3-impulse trajectory optimization problem.

Pu, C. L.↗

NASA NTRS1973

Optimality of incompletely measurable active and passive attitude control systems

Passive attitude control systems and active systems with incomplete state measurements are only suboptimal systems in the sense of optimal control theory, since optimal systems require complete state measurements or state estimations. An optimal system, then, requires additional hardware (especially in the case of flexible spacecraft) which results in higher costs. Therefore, it is a real engineering problem to determine how much an optimal system exceeds the suboptimal system, or in other words, what is the suboptimal system's degree of optimality. The problem will be treated in three steps: (1) definition of the degree of optimality for linear, time-invariant systems; (2) a computation method using the quadratic cost functional; (3) application to a gravity-gradient stabilized three-body satellite and a spinning flexible satellite.

Schiehlen, W.↗

NASA NTRS1975

On optimal soft-decision demodulation

Wozencraft and Kennedy have suggested that the appropriate demodulator criterion of goodness is the cut-off rate of the discrete memoryless channel created by the modulation system; the criterion of goodness adopted in this note is the symmetric cut-off rate which differs from the former criterion only in that the signals are assumed equally likely. Massey's necessary condition for optimal demodulation of binary signals is generalized to M-ary signals. It is shown that the optimal demodulator decision regions in likelihood space are bounded by hyperplanes. An iterative method is formulated for finding these optimal decision regions from an initial good quess. For additive white Gaussian noise, the corresponding optimal decision regions in signal space are bounded by hypersurfaces with hyperplane asymptotes; these asymptotes themselves bound the decision regions of a demodulator which, in several examples, is shown to be virtually optimal. In many cases, the necessary condition for demodulator optimality is also sufficient, but a counter example to its general sufficiency is given.

Lee, L. N.↗

NASA NTRS1976

On optimal soft-decision demodulation

A necessary condition is derived for optimal J-ary coherent demodulation of M-ary (M greater than 2) signals. Optimality is defined as maximality of the symmetric cutoff rate of the resulting discrete memoryless channel. Using a counterexample, it is shown that the condition derived is generally not sufficient for optimality. This condition is employed as the basis for an iterative optimization method to find the optimal demodulator decision regions from an initial 'good guess'. In general, these regions are found to be bounded by hyperplanes in likelihood space; the corresponding regions in signal space are found to have hyperplane asymptotes for the important case of additive white Gaussian noise. Some examples are presented, showing that the regions in signal space bounded by these asymptotic hyperplanes define demodulator decision regions that are virtually optimal.

Lee, L.-N.↗

NASA NTRS1982

Combining analysis with optimization at Langley Research Center. An evolutionary process

The evolutionary process of combining analysis and optimization codes was traced with a view toward providing insight into the long term goal of developing the methodology for an integrated, multidisciplinary software system for the concurrent analysis and optimization of aerospace structures. It was traced along the lines of strength sizing, concurrent strength and flutter sizing, and general optimization to define a near-term goal for combining analysis and optimization codes. Development of a modular software system combining general-purpose, state-of-the-art, production-level analysis computer programs for structures, aerodynamics, and aeroelasticity with a state-of-the-art optimization program is required. Incorporation of a modular and flexible structural optimization software system into a state-of-the-art finite element analysis computer program will facilitate this effort. This effort results in the software system used that is controlled with a special-purpose language, communicates with a data management system, and is easily modified for adding new programs and capabilities. A 337 degree-of-freedom finite element model is used in verifying the accuracy of this system.

Rogers, J. L., Jr.↗

NASA NTRS1981

Optimal maneuvers at supersonic speeds in a vertical plane

This paper presents several optimal maneuvers of supersonic aircraft in a vertical plane. The general dimensionless equations of motion are derived and the computation of the optimal trajectories are carried out using the aerodynamics and engine characteristics of a light-weight fighter called the supercruiser. Because of the normalizing of the control variables, namely, the load factor and the thrust-to-weight ratio, the results applied to any supersonic aircraft. The optimality of the singular thrust control and the optimal junction of different subarcs are discussed. The proposed method of computing the optimal trajectory is very efficient and makes explicit the selection of the optimal control. The technique should be useful for performance assessment of supersonic aircraft with potential for implementation of onboard flight control system.

Vinh, N. X.↗

NASA NTRS1983

Structural optimization by multilevel decomposition

The application of formal optimization techniques to the design of large engineering structures such as aircraft is presently hindered in connection with the large number of design variables involved. According to an approach which attempts to overcome the difficulties, the problem is broken up into several smaller subproblems. This approach has, however, weaknesses which may prevent a determination of the minimum structural weight. Schmit and Ramanathan (1973) have developed a method, which is designed to incorporate control of the material distribution among the finite elements of an assembled structure for a two-level optimization. However, the optimization schemes considered would not be suitable to optimization schemes considered would not be suitable to multidisciplinary optimization of large engineering systems. Sobieszczanski-Sobieski (1982) proposed a method for decomposing a large multidisciplinary optimization problem into a number of small subproblems. The present investigation is concerned with the implementation of this method.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1983

Large-scale structural optimization

Problems encountered by aerospace designers in attempting to optimize whole aircraft are discussed, along with possible solutions. Large scale optimization, as opposed to component-by-component optimization, is hindered by computational costs, software inflexibility, concentration on a single, rather than trade-off, design methodology and the incompatibility of large-scale optimization with single program, single computer methods. The software problem can be approached by placing the full analysis outside of the optimization loop. Full analysis is then performed only periodically. Problem-dependent software can be removed from the generic code using a systems programming technique, and then embody the definitions of design variables, objective function and design constraints. Trade-off algorithms can be used at the design points to obtain quantitative answers. Finally, decomposing the large-scale problem into independent subproblems allows systematic optimization of the problems by an organization of people and machines.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1984

Application of optimization techniques to vehicle design: A review

The work that has been done in the last decade or so in the application of optimization techniques to vehicle design is discussed. Much of the work reviewed deals with the design of body or suspension (chassis) components for reduced weight. Also reviewed are studies dealing with system optimization problems for improved functional performance, such as ride or handling. In reviewing the work on the use of optimization techniques, one notes the transition from the rare mention of the methods in the 70's to an increased effort in the early 80's. Efficient and convenient optimization and analysis tools still need to be developed so that they can be regularly applied in the early design stage of the vehicle development cycle to be most effective. Based on the reported applications, an attempt is made to assess the potential for automotive application of optimization techniques. The major issue involved remains the creation of quantifiable means of analysis to be used in vehicle design. The conventional process of vehicle design still contains much experience-based input because it has not yet proven possible to quantify all important constraints. This restraint on the part of the analysis will continue to be a major limiting factor in application of optimization to vehicle design.

Prasad, B.↗

NASA NTRS1986

Optimization methods and silicon solar cell numerical models

An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.

Girardini, K.↗