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The general code described is capable of solving difficult nonlinear optimal control problems by using finite elements and a symbolic manipulator. Quick and accurate solutions are obtained with a minimum for user interaction. Since no user programming is required for most problems, there are tremendous savings to be gained in terms of time and money.
A new hybrid preconditioning algorithm will be presented which combines the favorable attributes of incomplete lower-upper (ILU) factorization with the favorable attributes of the approximate inverse method recently advocated by numerous researchers. The quality of the preconditioner is adjustable and can be increased at the cost of additional computation while at the same time the storage required is roughly constant and approximately equal to the storage required for the original matrix. In addition, the preconditioning algorithm suggests an efficient and natural parallel implementation with reduced communication. Sample calculations will be presented for the numerical solution of multi-dimensional advection-diffusion equations. The matrix solver has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The full paper will show numerous examples in CFD to demonstrate the efficiency and robustness of the method.
In the present Noisy Intermediate-Scale Quantum (NISQ), hybrid algorithms that leverage classical resources to reduce quantum costs are particularly appealing. We formulate and apply such a hybrid quantum-classical algorithm to a power system optimization problem called Unit Commitment, which aims to satisfy a target power load at minimal cost. Our algorithm extends the Quantum Approximation Optimization Algorithm (QAOA) with a classical minimizer in order to support mixed binary optimization. Using Qiskit, we simulate results for sample systems to validate the effectiveness of our approach. Here, we also compare to purely classical methods. Our results indicate that classical solvers are effective for our simulated Unit Commitment instances with fewer than 400 power generation units. However, for larger problem instances, the classical solvers either scale exponentially in runtime or must resort to coarse approximations. This opens the door to potential quantum advantage for systems with several hundred units, though quantum error correction may be necessary at this scale.
Random search algorithm for nonlinear orbital transfer problems applied to optimal control of satellite attitude acquisition
Abstract The hybrid hydraulic electric architecture (HHEA) seeks to combine the high power/torque/force density of hydraulics with the efficiency of electric machines. A set of common pressure rails is used to provide a majority of the power and this power is modulated by small electric machines to provide precise control for the operator. The HHEA has been studied in previous work using off-line dynamic programming optimization to determine energy efficient pressure rail selections, but this approach requires drive cycle information apriori. A Lagrange multiplier method has also been investigated where a set of gains (Lagrange multipliers) are optimized off-line with the idea the these gains, once determined, could be used for real-time operation. In this work, three new real-time pressure rail selection algorithms that do not require future drive cycle information are investigated; greedy, torque minimizing, and thresholding. The greedy control is found to only use 1% more energy than the globally optimal dynamic programming solution; but a model of energy loss is required.
Topics covered include: Optimal Tuner Selection for Kalman-Filter-Based Aircraft Engine Performance Estimation; Airborne Radar Interferometric Repeat-Pass Processing; Plug-and-Play Environmental Monitoring Spacecraft Subsystem; Power-Combined GaN Amplifier with 2.28-W Output Power at 87 GHz; Wallops Ship Surveillance System; Source Lines Counter (SLiC) Version 4.0; Guidance, Navigation, and Control Program; Single-Frame Terrain Mapping Software for Robotic Vehicles; Auto Draw from Excel Input Files; Observation Scheduling System; CFDP for Interplanetary Overlay Network; X-Windows Widget for Image Display; Binary-Signal Recovery; Volumetric 3D Display System with Static Screen; MMIC Replacement for Gunn Diode Oscillators; Feature Acquisition with Imbalanced Training Data; Mount Protects Thin-Walled Glass or Ceramic Tubes from Large Thermal and Vibration Loads; Carbon Nanotube-Based Structural Health Monitoring Sensors; Wireless Inductive Power Device Suppresses Blade Vibrations; Safe, Advanced, Adaptable Isolation System Eliminates the Need for Critical Lifts; Anti-Rotation Device Releasable by Insertion of a Tool; A Magnetically Coupled Cryogenic Pump; Single Piezo-Actuator Rotary-Hammering Drill; Fire-Retardant Polymeric Additives; Catalytic Generation of Lift Gases for Balloons; Ionic Liquids to Replace Hydrazine; Variable Emittance Electrochromics Using Ionic Electrolytes and Low Solar Absorptance Coatings; Spacecraft Radiator Freeze Protection Using a Regenerative Heat Exchanger; Multi-Mission Power Analysis Tool; Correction for Self-Heating When Using Thermometers as Heaters in Precision Control Applications; Gravitational Wave Detection with Single-Laser Atom Interferometers; Titanium Alloy Strong Back for IXO Mirror Segments; Improved Ambient Pressure Pyroelectric Ion Source; Multi-Modal Image Registration and Matching for Localization of a Balloon on Titan; Entanglement in Quantum-Classical Hybrid; Algorithm for Autonomous Landing; Quantum-Classical Hybrid for Information Processing; Small-Scale Dissipation in Binary-Species Transitional Mixing Layers; Superpixel-Augmented Endmember Detection for Hyperspectral Images; Coding for Parallel Links to Maximize the Expected Value of Decodable Messages; and Microwave Tissue Soldering for Immediate Wound Closure.
In this work, an innovative hybrid algorithm PAGOSA with FLIP + MPM is first presented by coupling PAGOSA with the particle FLIP + MPM, and applied to systematically exploring the 3D recompression of spall induced by double-shock waves in ductile materials as the few existing studies are currently limited to the pure longitudinal recompression of spall, and ignore the 3D effects. This algorithm solves the difficulties the grid-based methods encounter when applied to capturing the fracture in material. We first validate the capabilities of PAGOSA with FLIP + MPM to predict different fracture/fragmentation cases by solving two benchmark problems and comparing with the analytical solutions or the experiment results. The convergences and the infinity-norm errors are also investigated. Subsequently, the 3D effects are demonstrated by simulating the spallation in material using PAGOSA with FLIP + MPM and comparing with those in the longitudinal cases. Additionally, some factors that affect the spallation with 3D effects are also discussed. Finally, the recompressions of spall in material with/without 3D effects are systematically simulated and analyzed. The recompression of spall driven by a high explosive is also simulated to show the ability of PAGOSA with FLIP + MPM to handle this kind of problem. The conditions that can lead to a recompression of spall are explored. Also, numerical results show that PAGOSA with FLIP + MPM can accurately predict different fracture cases, that the 3D effects play an important role in fracture/fragmentation, and the recompression of spall is very sensitive to the occurrence conditions, shows great differences when considering 3D effects in real applications. Moreover, the present hybrid method can be easily extended to other grid-based techniques employed for fracture in materials.
Study focuses on obtaining efficient algorithm for estimation of confidence intervals of ML estimates. Four algorithms selected to solve associated constrained optimization problem. Hybrid algorithms, following search and gradient approaches, prove best.
In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.
The recent development of logical quantum processors marks a pivotal transition from the noisy intermediate-scale quantum (NISQ) era to the fault-tolerant quantum computing (FTQC) era. These devices have the potential to address classically challenging problems with polynomial computational time using quantum properties. However, they remain susceptible to noise, necessitating noise resilient algorithms. We introduce Quantum Zeno Monte Carlo (QZMC), a classical-quantum hybrid algorithm that demonstrates resilience to device noise and Trotter errors while showing polynomial computational cost for a gapped system. QZMC computes static and dynamic properties without requiring initial state overlap or variational parameters, offering reduced quantum circuit depth.
This paper addresses the problem of detecting and describing anomalies in large sets of high-dimensional symbol sequences. The approach taken uses unsupervised clustering of sequences using the normalized longest common subsequence (LCS) as a similarity measure, followed by detailed analysis of outliers to detect anomalies. As the LCS measure is expensive to compute, the first part of the paper discusses existing algorithms, such as the Hunt-Szymanski algorithm, that have low time-complexity. We then discuss why these algorithms often do not work well in practice and present a new hybrid algorithm for computing the LCS that, in our tests, outperforms the Hunt-Szymanski algorithm by a factor of five. The second part of the paper presents new algorithms for outlier analysis that provide comprehensible indicators as to why a particular sequence was deemed to be an outlier. The algorithms provide a coherent description to an analyst of the anomalies in the sequence, compared to more normal sequences. The algorithms we present are general and domain-independent, so we discuss applications in related areas such as anomaly detection.
Variational quantum algorithms (VQAs), which classically optimize a parametrized quantum circuit to solve a computational task, promise to advance our understanding of quantum many-body systems and improve machine learning algorithms using near-term quantum computers. Prominent challenges associated with this family of quantum-classical hybrid algorithms are the control of quantum entanglement and quantum gradients linked to their classical optimization. Known as the barren plateau phenomenon, these quantum gradients may rapidly vanish in the presence of volume-law entanglement growth, which poses a serious obstacle to the practical utility of VQAs. Inspired by recent studies of measurement-induced entanglement transition in random circuits, we investigate the entanglement transition in variational quantum circuits endowed with intermediate projective measurements. Considering the Hamiltonian Variational Ansatz (HVA) for the XXZ model and the Hardware Efficient Ansatz (HEA), we observe a measurement-induced entanglement transition from volume-law to area-law with increasing measurement rate. Moreover, we provide evidence that the transition belongs to the same universality class of random unitary circuits. Importantly, the transition coincides with a “landscape transition” from severe to mild/no barren plateaus in the classical optimization. Our work may provide an avenue for improving the trainability of quantum circuits by incorporating intermediate measurement protocols in currently available quantum hardware.
The polar decomposition of an m x n matrix A of full rank, where m is greater than or equal to n, can be computed using a quadratically convergent algorithm. The algorithm is based on a Newton iteration involving a matrix inverse. With the use of a preliminary complete orthogonal decomposition the algorithm can be extended to arbitrary A. How to use the algorithm to compute the positive semi-definite square root of a Hermitian positive semi-definite matrix is described. A hybrid algorithm which adaptively switches from the matrix inversion based iteration to a matrix multiplication based iteration due to Kovarik, and to Bjorck and Bowie is formulated. The decision when to switch is made using a condition estimator. This matrix multiplication rich algorithm is shown to be more efficient on machines for which matrix multiplication can be executed 1.5 times faster than matrix inversion.
A new hybrid-stress finite element algorithm, suitable for analyses of large, quasistatic, inelastic deformations, is presented. The algorithm is base upon a generalization of de Veubeke's complementary energy principle. The principal variables in the formulation are the nominal stress rate and spin, and thg resulting finite element equations are discrete versions of the equations of compatibility and angular momentum balance. The algorithm produces true rates, time derivatives, as opposed to 'increments'. There results a complete separation of the boundary value problem (for stress rate and velocity) and the initial value problem (for total stress and deformation); hence, their numerical treatments are essentially independent. After a fairly comprehensive discussion of the numerical treatment of the boundary value problem, we launch into a detailed examination of the numerical treatment of the initial value problem, covering the topics of efficiency, stability and objectivity. The paper is closed with a set of examples, finite homogeneous deformation problems, which serve to bring out important aspects of the algorithm.
GPS-based travel surveys are widely used in mobility studies to gather crucial qualitative data, like purpose, transportation mode and replaced mode. However, survey response still poses a burden to users, especially in long-term mobility studies, leading to response fatigue. We explore a survey-assist strategy to ease this burden by a novel, user-level modeling approach that leverages past responses from each user to predict responses for new trips, without relying on external data sources like GIS data. We investigate three main algorithms for predicting responses: (i) clustering trips and extrapolating responses for similar trips, (ii) using random forest classification, and (iii) clustering that uses a hybrid algorithm to determine spatial structure, which is then fed as input to a classic random forest classifier. The clustering approach can flexibly predict responses for even complex qualitative survey questions; it achieved F-scores of 65%. The random forest pipeline uses architecture that restricts it to predicting three predetermined survey questions: trip purpose, mode, and replaced mode. However, it achieved F-scores of 78%. While the survey-assist approach has been implemented by several proprietary systems, to our knowledge, this is the first exploration in the academic literature. It follows that this is also the first rigorous evaluation of multiple algorithms that can implement the approach. The evaluation uses a large scale, publicly available, longitudinal dataset consisting of ~ 92k trips from 235 users over a period of roughly one and a half years. With this approach, travel surveys can be pre-filled with the predicted responses for each trip, thus streamlining the survey process for users. Combined with an active learning system that requests user input on low-confidence predictions, models can be updated and improved over time to better support the long-term collection of longitudinal qualitative data.
An empirical study of the performance of the Viterbi decoders in bursty channels was carried out and an improved algebraic decoder for nonsystematic codes was developed. The hybrid algorithm was simulated for the (2,1), k = 7 code on a computer using 20 channels having various error statistics, ranging from pure random error to pure bursty channels. The hybrid system outperformed both the algebraic and the Viterbi decoders in every case, except the 1% random error channel where the Viterbi decoder had one bit less decoding error.
To facilitate and solve the prediction problem, awareness of the current state and health of the system is key, since it is necessary to perform condition-based system health predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditional. In case of next generation electric aircrafts, computing remaining flying time is safety-critical, since an aircraft that runs out of power (battery charge) while in the air will eventually lose control leading to catastrophe. In order to tackle and solve the prediction problem, it is essential to have awareness of the current health state of the system, especially since it is necessary to perform condition-based predictions. To be able to predict the future state of the system, it is also required to possess knowledge of the current and future operational conditions and flight profiles for accurate estimation of end-of-discharge (EOD) for the batteries. Similar framework can be implemented to other complex systems and subsystems. Our research approach is to develop a system level health monitoring safety indicator which runs estimation and prediction algorithms to estimate remaining useful life predictions at system, subsystem swell as component levels. Given models of the current and future system behavior, a general approach of model-based prognostics is discussed as a solution to the prediction problem and further for decision making. Data driven prognostics approaches have been equally used with good results in the past, where respective approaches have their own challenges to tackle. This limits their applicability to complex real-world domains: (a) high complexity or incompleteness of physics-based models and (b) limited representativeness of the training dataset for data-driven models. With the advent of internet of things for data collection and increased use of ML algorithms, hybrid approaches are the next avenue to reduce the challenges and achieve better results. An hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety critical systems is presented. In this framework, we use physics-based performance models to infer unobservable model parameters related to the system's components health solving a calibration problem.
The design of survivable algorithms requires a solid foundation for executing them. While hardware techniques for fault-tolerant computing are relatively well understood, fault-tolerant operating systems, as well as fault-tolerant applications (survivable algorithms), are, by contrast, little understood, and much more work in this field is required. We outline some of our work that contributes to the foundation of ultrareliable operating systems and fault-tolerant algorithm design. We introduce our consensus-based framework for fault-tolerant system design. This is followed by a description of a hierarchical partitioning method for efficient consensus. A scheduler for redundancy management is introduced, and application-specific fault tolerance is described. We give an overview of our hybrid algorithm technique, which is an alternative to the formal approach given.