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Results for “Quadratic Optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Interface models for three-dimensional Rayleigh–Taylor instability

We derive interface models for three-dimensional Rayleigh–Taylor instability (RTI), making use of a novel asymptotic expansion in the non-locality of the fluid flow. These interface models are derived for the purpose of studying universal features associated with RTI such as the Froude number in single-mode RTI, the predicted quadratic growth of the interface amplitude under multi-mode random perturbations, the optimal (viscous) mixing rates induced by the RTI and the self-similarity of horizontally averaged density profiles and the remarkable stabilization of the mixing layer growth rate which arises for the three-fluid two-interface heavy–light–heavy configuration, in which the addition of a third fluid bulk slows the growth of the mixing layer to a linear rate. Our interface models can capture the formation of small-scale structures induced by severe interface roll-up, reproduce experimental data in a number of different regimes and study the effects of multiple interface interactions even as the interface separation distance becomes exceedingly small. Compared with traditional numerical schemes used to study such phenomena, our models provide a computational speed-up of at least two orders of magnitude.

Mechanics↗

DOE OSTI2018

Quantum Annealing for Prime Factorization

We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function then transforming the k-bit coupling (k ≥ 3) terms to quadratic terms using ancillary variables. Our resource-efficient method uses O (log 2 ( N )) binary variables (qubits) for finding the factors of an integer N. We present how to factorize 15, 143, 59989, and 376289 using 4, 12, 59, and 94 logical qubits, respectively. This method was tested using the D-Wave 2000Q for finding an embedding and determining the prime factors for a given composite number. The method is general and could be used to factor larger integers as the number of available qubits increases, or combined with other ad hoc methods to achieve better performances for specific numbers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Weak lensing of intensity mapping: The cosmic infrared background

Gravitational lensing deflects the paths of cosmic infrared background (CIB) photons, leaving a measurable imprint on CIB maps. The resulting statistical anisotropy can be utilized to reconstruct the matter distribution out to the redshifts of CIB sources. To this end, we generalize the cosmic microwave background (CMB) lensing quadratic estimator to any weakly non-Gaussian source field, by deriving the optimal lensing weights. We point out the additional noise and bias caused by the non-Gaussianity and the “self-lensing” of the source field. We propose methods to reduce, subtract, or model these non-Gaussianities. We demonstrate that CIB lensing should be detectable with Planck data and detectable at high significance for future CMB experiments like CCAT-Prime. The CIB thus constitutes a novel source image for lensing studies, providing constraints on the amplitude of structure at intermediate redshifts between galaxies and the CMB. CIB lensing measurements will also give valuable information on the star-formation history in the Universe, constraining CIB halo models beyond the CIB power spectrum. By laying out a detailed treatment of lens reconstruction from a weakly non-Gaussian source field, this report constitutes a stepping stone toward lens reconstruction from continuum or line intensity mapping data, such as the Lyman-alpha emission, absorption, and the 21 cm radiation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

First Constraints on the Epoch of Reionization Using the Non-Gaussianity of the Kinematic Sunyaev-Zel’dovich Effect from the South Pole Telescope and Herschel-SPIRE Observations

We report results from an analysis aimed at detecting the trispectrum of the kinematic Sunyaev-Zel’dovich (kSZ) effect by combining data from the South Pole Telescope (SPT) and Herschel-SPIRE experiments over a 100 deg 2 field. The SPT observations combine data from the previous and current surveys, namely SPTpol and SPT-3G, to achieve depths of 4.5, 3, and 16 μ K - arcmin in bands centered at 95, 150, and 220 GHz. For SPIRE, we include data from the 600 and 857 GHz bands. We reconstruct the velocity-induced large-scale correlation of the small-scale kSZ signal with a quadratic estimator that uses two cosmic microwave background (CMB) temperature maps, constructed by optimally combining data from all the frequency bands. We reject the null hypothesis of a zero trispectrum at 10.3 σ level. However, the measured trispectrum contains contributions from both the kSZ and other undesired components, such as CMB lensing and astrophysical foregrounds, with kSZ being sub-dominant. We use the agora simulations to estimate the expected signal from CMB lensing and astrophysical foregrounds. After accounting for the contributions from CMB lensing and foreground signals, we do not detect an excess kSZ-only trispectrum and use this nondetection to set constraints on reionization. By applying a prior based on observations of the Gunn-Peterson trough, we obtain an upper limit on the duration of reionization of Δ z re , 50 < 4.5 (95% confidence level). We find these constraints are fairly robust to foregrounds assumptions. This trispectrum measurement is independent of, but consistent with, Planck’s optical depth measurement. This result is the first constraint on the epoch of reionization using the non-Gaussian nature of the kSZ signal.

79 ASTRONOMY AND ASTROPHYSICS↗

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.↗

DOE OSTI2023

Quantum Search Approaches to Sampling-Based Motion Planning

In this paper, we present a novel formulation of traditional sampling-based motion planners as database-oracle structures that can be solved via quantum search algorithms. We consider two complementary scenarios: for simpler sparse environments, we formulate the Quantum Full Path Search Algorithm (q-FPS), which creates a superposition of full random path solutions, manipulates probability amplitudes with Quantum Amplitude Amplification (QAA), and quantum measures a single obstacle free full path solution. For dense unstructured environments, we formulate the Quantum Rapidly Exploring Random Tree algorithm, q-RRT, that creates quantum superpositions of possible parent-child connections, manipulates probability amplitudes with QAA, and quantum measures a single reachable state, which is added to a tree. As performance depends on the number of oracle calls and the probability of measuring good quantum states, we quantify how these errors factor into the probabilistic completeness properties of the algorithm. We then numerically estimate the expected number of database solutions to provide an approximation of the optimal number of oracle calls in the algorithm. We compare the q-RRT algorithm with a classical implementation and verify quadratic run-time speedup in the largest connected component of a 2D dense random lattice. We conclude by evaluating a proposed approach to limit the expected number of database solutions and thus limit the optimal number of oracle calls to a given number.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1979

Flexible space structure model reduction by modal cost analysis

It is noted that reduced models and reduced controllers for flexible space structures are obtained by retaining those modes which make the greatest contribution to quadratic control objectives. Attention is given to the relative importance of damping, frequency and mode shapes in the mode truncation decisions for the following control objectives: attitude control, vibration suppression and figure control. It is also shown that using Modal Cost Analysis (MCA) on the closed loop modes of the optimally controlled system allows the construction of reduced control policies which feedback only those closed loop coordinates which are most critical to the quadratic control performance criterion. In this manner, the modes which need to be controlled are deduced from truncations of the optimal controller.

Skelton, R. E.↗

DOE OSTI2015

A Bound-Plus-Equality Constrained Quadratic Minimization Algorithm for Inverse Problems

Explore the source record for details and available documents.

optimization, inverse problems↗

NASA NTRSDate not supplied

A Convex Optimization Approach to Improving Suboptimal Hyperparameters of Sliced Normal Distributions

Sliced Normal (SN) distributions are a generalization of Gaussian distributions where the quadratic argument of the exponential is replaced with a sum of squares polynomial. SNs may be used to represent the distribution of a diverse set of random variables including multi-modal, non-symmetric, and skewed distributions. Unfortunately, the likelihood function of a SN includes a normalization constant and the inclusion of this normalization constant makes the likelihood a non-convex function of the hyperparameters which define the SN. In previous work, suboptimal fitting of the hyperparameters was performed by transforming the given data into a higher dimensional monomial basis and selecting the optimal hyperparameters of a Gaussian fit in this space. However, this approach did not account for the effect of lifting on the normalization constant. Indeed, it was observed that as the number of monomials is increased the likelihood of the Sliced Normal can decrease. In this paper, we increase the likelihood of Sliced Normals found using the previous method by developing a convex formulation which scales the covariance matrix of the Gaussian fit such that the likelihood of the Sliced Normal is maximized. The result is significant improvements of the log likelihood of fitted SN distributions, including a significant increase, especially for problems with 500+ monomials.

Convex optimization approach to improving suboptim↗

DOE OSTI2022

Qualitative trend analysis based on a mixed-integer representation

Shape constrained spline fitting is a useful method to impose prior knowledge onto flexible semi-parametric models during parameter estimation. Most typically, the function shape is imposed through order restrictions on the regression coefficients. The intended shape is considered known or selected based on heuristic rules. In this study, we present a method to estimate the optimal set of order restrictions to segment a univariate data series into episodes with distinct shapes. This is also known as the qualitative trend analysis (QTA) problem. The obtained solution uses a trade-off between lack-of-fit and model complexity. Further, our practical implementation takes inspiration from the generalized order restricted information criterion (GORIC) for inequality-constrained model selection. From this, one learns (a) that QTA can be formulated as a mixed-integer quadratic program (MIQP) and (b) that the newly proposed mixed order restricted information criterion (MORIC) enables optimal segmentation. This is illustrated through didactic case studies.

42 ENGINEERING↗

NASA NTRS1973

Real-time optimal guidance for orbital maneuvering.

A new formulation for soft-constraint trajectory optimization is presented as a real-time optimal feedback guidance method for multiburn orbital maneuvers. Control is always chosen to minimize burn time plus a quadratic penalty for end condition errors, weighted so that early in the mission (when controllability is greatest) terminal errors are held negligible. Eventually, as controllability diminishes, the method partially relaxes but effectively still compensates perturbations in whatever subspace remains controllable. Although the soft-constraint concept is well-known in optimal control, the present formulation is novel in addressing the loss of controllability inherent in multiple burn orbital maneuvers. Moreover the necessary conditions usually obtained from a Bolza formulation are modified in this case so that the fully hard constraint formulation is a numerically well behaved subcase. As a result convergence properties have been greatly improved.

Cohen, A. O.↗

NASA NTRS1992

Reliable design of H-2 optimal reduced-order controllers via a homotopy algorithm

Due to control processor limitations, the design of reduced-order controllers is an active area of research. Suboptimal methods based on truncating the order of the corresponding linear-quadratic-Gaussian (LQG) compensator tend to fail if the requested controller dimension is sufficiently small and/or the requested controller authority is sufficiently high. Also, traditional parameter optimization approaches have only local convergence properties. This paper discusses a homotopy algorithm for optimal reduced-order control that has global convergence properties. The exposition is for discrete-time systems. The algorithm has been implemented in MATLAB and is applied to a benchmark problem.

Collins, Emmanuel G.↗

NASA NTRSDate not supplied

Modified Cascading Generalized Inverse Control Allocation

The current aviation revolution towards electric propulsion aircraft (e.g., electric vertical takeoff-and-landing) brings unique control challenges. These vehicles are typically over-actuated (more effectors than desired control outcomes), may require control strategies for the three phases of flight (hover, transition and cruise), and currently have limited electric power availability. These vehicle challenges bring the need for optimal control allocation to the forefront of research. A leading control allocation algorithm, used in current flight vehicles, is the Cascading Generalized Inverse (CGI). Unfortunately, the Cascading Generalized Inverse algorithm is unable to achieve some desired outcomes, it intermittently provides non-optimal allocations, and it may fail to preserve moment direction near maximal achievable outcomes. In this research, the shortcomings of the Cascading Generalized Inverse algorithm are addressed by augmenting the algorithm with Scalar Difference Quadratic unsaturation identification and location at each iteration. Rigorous theory is shown that the Modified Cascading Generalized Inverse performs better at obtaining optimal allocations for all attainable outcomes. Numerical case studies for over-actuated vehicles demonstrate resolution to the aforementioned deficiencies.

Control Allocation↗

NASA NTRSDate not supplied

Modified Cascading Generalized Inverse Control Allocation

Control Allocation↗

DOE OSTI2018

Modeling error PDF optimization based wavelet neural network modeling of dynamic system and its application in blast furnace ironmaking

In general, the modeling errors of dynamic system model are a set of random variables. The traditional performance index of modeling such as means square error (MSE) and root means square error (RMSE) can not fully express the connotation of modeling errors with stochastic characteristics both in the dimension of time domain and space domain. Therefore, the probability density function (PDF) is introduced to completely describe the modeling errors in both time scales and space scales. Based on it, a novel wavelet neural network (WNN) modeling method is proposed by minimizing the two-dimensional (2D) PDF shaping of modeling errors. First, the modeling error PDF by the tradional WNN is estimated using data-driven kernel density estimation (KDE) technique. Then, the quadratic sum of 2D deviation between the modeling error PDF and the target PDF is utilized as performance index to optimize the WNN model parameters by gradient descent method. Since the WNN has strong nonlinear approximation and adaptive capability, and all the parameters are well optimized by the proposed method, the developed WNN model can make the modeling error PDF track the target PDF, eventually. Simulation example and application in a blast furnace ironmaking process show that the proposed method has a higher modeling precision and better generalization ability compared with the conventional WNN modeling based on MSE criteria. Furthermore, the proposed method has more desirable estimation for modeling error PDF that approximates to a Gaussian distribution whose shape is high and narrow.

Modelling↗

DOE OSTI2024

Optimizing dietary rumen-degradable starch to rumen-degradable protein ratio improves lactation performance and nitrogen utilization efficiency in mid-lactating Holstein dairy cows

The dietary rumen-degradable starch (RDS) to rumen-degradable protein (RDP) ratio, denoted as the RDS-to-RDP ratio (SPR), has been proven to enhance in vitro rumen fermentation. However, the effects of dietary SPR in vivo remain largely unexplored. This study was conducted to investigate the effect of dietary SPR on lactation performance, nutrient digestibility, rumen fermentation patterns, blood indicators, and nitrogen (N) partitioning in mid-lactating Holstein cows. Seventy-two Holstein dairy cows were randomly assigned to three groups (24 head/group), balanced for (mean ± standard deviation) days in milk (116 ± 21.5), parity (2.1 ± 0.8), milk production (42 ± 2.1 kg/d), and body weight (705 ± 52.5 kg). The cows were fed diets with low (2.1, control), medium (2.3), or high (2.5) SPR, formulated to be isoenergetic, isonitrogenous, and iso-starch. The study consisted of a one-week adaptation phase followed by an eight-week experimental period. The results indicated that the high SPR group had a lower dry matter intake compared to the other groups ( p < 0.05). A quadratic increase in milk yield and feed efficiency was observed with increasing dietary SPR ( p < 0.05), peaking in the medium SPR group. The medium SPR group exhibited a lower milk somatic cell count and a higher blood total antioxidant capacity compared to other groups ( p < 0.05). With increasing dietary SPR, there was a quadratic improvement ( p < 0.05) in the total tract apparent digestibility of crude protein, ether extract, starch, neutral detergent fiber, and acid detergent fiber. Although no treatment effect was observed in rumen pH, the rumen total volatile fatty acids concentration and microbial crude protein synthesis increased quadratically ( p < 0.05) as dietary SPR increased. The molar proportion of propionate linearly increased ( p = 0.01), while branched-chain volatile fatty acids linearly decreased ( p = 0.01) with increasing dietary SPR. The low SPR group (control) exhibited higher concentration of milk urea N, rumen ammonia N, and blood urea N than other groups ( p < 0.05). Despite a linear decrease ( p < 0.05) in the proportion of urinary N to N intake, increasing dietary SPR led to a quadratic increase ( p = 0.01) in N utilization efficiency and a quadratic decrease ( p < 0.05) in the proportion of fecal N to N intake. In conclusion, optimizing dietary SPR has the potential to enhance lactation performance and N utilization efficiency. Based on our findings, a medium dietary SPR (with SPR = 2.3) is recommended for mid-lactating Holstein dairy cows. Nevertheless, further research on rumen microbial composition and metabolites is warranted to elucidate the underlying mechanisms of the observed effects.

Chen, Panliang↗

NASA NTRS1983

Active flutter control using discrete optimal constrained dynamic compensators

A method for synthesizing digital active flutter suppression controllers using the concept of optimal output feedback is presented. A recently developd convergent algorithm is employed to determine constrained control law parameters that minimize an infinite-time discrete quadratic performance index. Low-order compensator dynamics are included in the control law and the compensator parameters are computed along with the output feedback gain as part of the optimization process. An input noise adjustment procedure is used to improve the stability margins of the digital active flutter controller. Results from investigations into sample rate variation, prefilter pole variation, and effects of varying flight condtions are discussed. The study indicates that a digital control law which accommodates computation delay can stabilize the wing with reasonable rms performance and adequate stability margins.

Broussard, J. R.↗

DOE OSTI2024

Small-correlated-against-large estimator for the lensing of the cosmic microwave background

Weak gravitational lensing of the cosmic microwave background (CMB) carries imprints of the physics operating at redshifts much lower than that of recombination and serves as an important probe of cosmological structure formation, dark matter physics, and the mass of neutrinos. Reconstruction of the CMB lensing deflection field through use of quadratic estimators has proven successful with existing data but is known to be sub-optimal on small angular scales ($\ell > 3000$) for experiments with low noise levels. Future experiments will provide better observations in this regime, but these techniques will remain statistically limited by their approximations. We show that correlations between fluctuations of the large-scale temperature gradient power of the CMB sourced by $\ell < 2000$, and fluctuations of the local small-scale temperature power reveal a lensing signal which is prominent in even the real-space pixel statistics across a CMB temperature map. We present the development of the Small Correlated Against Large Estimator (SCALE), a novel estimator for the CMB lensing spectrum which offers promising complementary analysis alongside other reconstruction techniques in this regime. The SCALE method computes correlations between both the large/small-scale temperature gradient power in harmonic space, and it is able to quantitatively recover unbiased statistics of the CMB lensing field without the need for map-level reconstruction. SCALE can outperform quadratic estimator signal-to-noise by a factor of up to 1.5 in current and upcoming experiments for CMB lensing power spectra $C_{6000 < L < 8000}^{\phi\phi}$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗