Iterative solution of nonlinear optimal control problems.
Mathematical programming methods for solving nonlinear state-constrained discrete optimal control problems
DYNAMIC PROGRAMMING↗
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Critical composite joint subcomponents: Analysis and test results
This program has been conducted to develop the technology for critical structural joints of a composite wing structure meeting design requirements for a 1990 commercial transport aircraft. A prime objective of the program was to demonstrate the ability to reliably predict the strength of large bolted composite joints. Load sharing between bolts in multirow joints was computed by a nonlinear analysis program (A4FJ) which was used both to assess the efficiency of different joint design concepts and to predict the strengths of large test articles representing a section from a wing root chord-wise splice. In most cases, the predictions were accurate to within a few percent of the test results. A highlight of these tests was the consistent ability to achieve gross-section failure strains on the order of 0.005 which represents a considerable improvement over the state of the art. The improvement was attained largely as the result of the better understanding of the load sharing in multirow joints provided by the analysis. The typical load intensity on the structural joints was about 40 to 45 thousand pound per inch in laminates having interspersed 37 1/2-percent 0-degree plies, 50-percent + or - 45-degrees plies and 12 1/2-percent 90-degrees plies. The composite material was Toray 300 fiber and Ciba-Geigy 914 resin, in the form of 0.010-inch thick unidirectional tape.
Bunin, B. L.↗
A 6 degree-of-freedom Lorentz force vibration isolator with nonlinear controller
This program demonstrated the technical feasibility of constructing large-stroke magnetic suspensions that can meet the active vibration isolation requirements of Space Station. These requirements include: (1) strokes over 1 cm in all directions, (2) actuator bandwidths over 100 Hz, (3) isolator roll-off frequencies below 10(exp -2) Hertz, and (4) force capability over 1 Newton in all axes. The 100 Hz actuator bandwidth allows the suspension to reject any direct force disturbances that act on the microgravity experiment, for example forces created by cable connections. The low isolator roll-off frequency and large stroke allow the magnetic suspension to isolate the microgravity experiment from Space Station vibrations above the roll-off frequency. The capability to meet these requirements was demonstrated by designing, constructing and testing a six-degree-of-freedom, prototype magnetic suspension system that featured high-performance, Lorentz-force actuators and full multi-input, multi-output control. This prototype suspension is designed to isolate large orbiter locker experiments under typical spacecraft constraints of size, weight, and power. Suspension in the full six-degrees-of-freedom was successfully demonstrated in this program while using a gravity-force unload mechanism to simulate a space environment. The prototype isolator is capable of space-based isolation service with relatively minor modification. The use of advanced, nonlinear control algorithms were investigated on a specially designed single-degree-of-freedom testbed. This low acceleration test facility simulates the Space Station vibration isolation problem in a single horizontal axis with low-friction, air-slide support. This allowed testing at the desired microgravity levels, without the gravity bias effects that are seen in a full six-degrees-of-freedom suspension. Precision components were used to reduce residual accelerations to microgravity levels so that the effects of sensor, actuator, and electronic noise could be evaluated. During the Phase 2 program, this testbed was used to demonstrate the advantages of nonlinear control algorithms to provide increased vibration isolation performance.
Fenn, Ralph↗
Two Programs for Supersonic Wing Design and Analysis
COREL and W12SC3 useful in aerodynamic design and analysis of wings for supersonic speeds. COREL (Conical Relaxation) program solves nonlinear full potential equation for spanwise section of wing in crossflow plane, and option exists to correct result for nonconical geometry. W12SC3 applies lineartheory panel methods to compute solutions for wing/body configuration. Programs restricted to supersonic flows and useful for many design, analysis, and optimization applications. COREL and W12SC3 written in FORTRAN IV for batch execution.
Mason, W. H.↗
Structural/control system optimization with variable actuator masses
A method is presented to integrate the design space for structural/control system optimization problems in the case of linear state feedback control. Nonstructural lumped masses and control system design variables as well as structural sizing variables are all treated equally as independent design variables in the optimization process. Structural and control design variable linking schemes are used in order to avoid a prohibitively large increase in the total number of independent design variables. When actuator masses are treated as nonstructural lumped mass design variables, special consideration is given to the relation between the transient peak responses and the required actuator masses which is formulated as a behavior constraint form. The original nonlinear mathematical programming problem based on a finite element formulation and linear state feedback is replaced by a sequence of explicit approximate problems exploiting various approximation concepts such as design variable linkings, temporary constraint deletion and first order Taylor series expansion of nonlinear behavior constraints in terms of intermediate design variables. Examples which involve a variety of dynamic behavior constraints (including constraints on closed-loop eigenvalues, peak transient displacements, peak actuator forces, and relations between the peak responses and the actuator masses) are effectively solved by using the method presented.
Jin, Ik M.↗
Critical joints in large composite aircraft structure
A program was conducted at Douglas Aircraft Company to develop the technology for critical structural joints of composite wing structure that meets design requirements for a 1990 commercial transport aircraft. The prime objective of the program was to demonstrate the ability to reliably predict the strength of large bolted composite joints. Ancillary testing of 180 specimens generated data on strength and load-deflection characteristics which provided input to the joint analysis. Load-sharing between fasteners in multirow bolted joints was computed by the nonlinear analysis program A4EJ. This program was used to predict strengths of 20 additional large subcomponents representing strips from a wing root chordwise splice. In most cases, the predictions were accurate to within a few percent of the test results. In some cases, the observed mode of failure was different than anticipated. The highlight of the subcomponent testing was the consistent ability to achieve gross-section failure strains close to 0.005. That represents a considerable improvement over the state of the art.
Nelson, W. D.↗
Application and implementation of transient algorithms in computer programs
A brief introduction is given to the nonlinear finite element programs developed at Lawrence Livermore National Laboratory. The four programs are DYNA3D and DYNA2D, which are explicit hydrocodes, and NIKE3D and NIKE2D, which are implicit programs. The main emphasis is on DYNA3D with asides about the other programs. During the past year several new features were added to DYNA3D, and major improvements were made in the computational efficiency of the shell and beam elements. Most of these new features and improvements will eventually make their way into the other programs. The emphasis in the computational mechanics effort was always, and continues to be, efficiency. To get the most out of the supercomputers, all Crays, the programs were vectorized where possible. Several of the more interesting capabilities of DYNA3D will be described and the impact on efficiency will be discussed. Some of the recent work on NIKE3D and NIKE2D will also be presented. In the belief that a single example is worth a thousand equations, the theory is skipped entirely and the examples presented.
Benson, David J.↗
Efficient proximal subproblem solvers for a nonsmooth trust-region method
In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition—a bound that ensures the trial iterate produces sufficient decrease of the subproblem model. In this paper, we expound on various proximal trust-region subproblem solvers that generalize traditional trust-region methods for smooth unconstrained and convex-constrained problems. We introduce a simplified spectral proximal gradient solver, a truncated nonlinear conjugate gradient solver, and a dogleg method. Finally, we compare algorithm performance on examples from data science and PDE-constrained optimization.
97 MATHEMATICS AND COMPUTING↗
AEDNET - A simulator for nonlinear networks.
AEDNET system of digital computer programs for on-line simulation of nonlinear networks and oscilloscope display
ON-LINE PROGRAMMING↗
Development of computer program NAS3D using Vector processing for geometric nonlinear analysis of structures
An algorithm for vectorized computation of stiffness matrices of an 8 noded isoparametric hexahedron element for geometric nonlinear analysis was developed. This was used in conjunction with the earlier 2-D program GAMNAS to develop the new program NAS3D for geometric nonlinear analysis. A conventional, modified Newton-Raphson process is used for the nonlinear analysis. New schemes for the computation of stiffness and strain energy release rates is presented. The organization the program is explained and some results on four sample problems are given. The study of CPU times showed that savings by a factor of 11 to 13 were achieved when vectorized computation was used for the stiffness instead of the conventional scalar one. Finally, the scheme of inputting data is explained.
Mangalgiri, P. D.↗
A mixed-integer PDE-constrained optimization formulation for constructing electromagnetic cloaks with multiple materials
We study the design of an electromagnetic cloak from multiple materials with an additional constraint on the mass of the cloak. Our problem is an example of a topology optimization problem, and we formulate this problem as a mixed-integer partial-differential equation constrained optimization (MIPDECO) problem, where Maxwell’s equation models the propagation of the wave through the cloak and surrounding medium. We use binary variables to model the assignment of the different materials, and their relevant properties (permittivity and density). The mass constraint adds a nontrivial constraint to this problem. We propose a two-phase strategy to solve this problem. In the first phase, we solve a continuous relaxation, and then propose a new variant of the feasibility pump that exploits the structure of the PDE to obtain an initial integral solution candidate. In the second phase, we use a trust-region approach to improve this incumbent. We also consider a continuation or mesh-sequencing approach to find better solutions faster on consecutively finer meshes. We present detailed numerical results to illustrate the effectiveness of our approaches for constructing multi-material cloaks with a mass constraint.
Calculus of Variations and Optimization↗
Multistage economic MPC for systems with a cyclic steady state: A gas network case study
Multistage model predictive control (MPC) provides a robust control strategy for dynamic systems with uncertainties and a setpoint tracking objective. Moreover, extending MPC to minimize an economic cost instead of tracking a pre-calculated optimal setpoint improves controller performance. This paper presents a novel multistage economic nonlinear model predictive control (E-NMPC) framework for dynamic systems operating under uncertainty, with specific application to natural gas transmission networks. A key innovation lies in the integration of cyclic steady-state (CSS) constraints within the multistage MPC formulation, enabling the controller to manage periodic operating conditions commonly observed in energy systems. A Lyapunov-based descent condition is enforced to ensure robust stability of the controller. The multistage economic MPC framework is validated on two gas pipeline case studies, where it successfully minimizes net energy consumption, respects operational constraints under uncertain demand profiles, and guides the network to optimal cyclic operation. The Lyapunov function remains bounded in both case studies, validating the robust stability of multistage E-NMPC.
03 NATURAL GAS↗
SYNTHESIS IN A MULTIDIMENSIONAL SPACE WITH AUTOMATED MATERIAL SELECTION
Design synthesis in a multidimensional space with automated material selection
EXPERIMENT DESIGN↗
A nonlinear encoder Technical report no. 1, 9 May - 9 Sep. 1964
Nonlinear encoder - sinusoidal reference voltage, comparator, nonlinear counter, and clock inhibit circuit
ENCODER↗
Constrained minimization problems in finite- dimensional spaces.
Constrained minimization problems in finite- dimensional spaces in unified approach
OPTIMAL CONTROL↗
Constrained minimization under vector-valued criteria in finite dimensional spaces.
Constrained minimization problem extended to necessary conditions for characterizing noninferior points to determine vector-valued criteria in finite dimensional spaces
OPTIMIZATION↗
Optimization of a corrugated stiffened composite panel under uniaxial compression
An approach of structural optimization has been used to optimize the weight of a simply supported, corrugated hat stiffened composite panel under uniaxial compression. The approach consists of the employment of nonlinear mathematical programming techniques to reach an optimum solution. Some simplifying assumptions are made in the stress analysis to obtain faster convergence to an optimum solution. With these simplifying assumptions the number of unknown design parameters is reduced to twelve.
Agarwal, B. L.↗
Dynamic Discharge Arc Driver
A computer program using nonlinear RLC circuit analysis was developed to accurately model the electrical discharge performance of the Ames 1-MJ energy storage and arc-driver system. Solutions of circuit parameters are compared with experimental circuit data and related to shock speed measurements. Computer analysis led to the concept of a Dynamic Discharge Arc Driver (DDAD) capable of increasing the range of operation of shock-driven facilities. Utilization of mass addition of the driver gas offers a unique means of improving driver performance. Mass addition acts to increase the arc resistance, which results in better electrical circuit damping with more efficient Joule heating, producing stronger shock waves. Preliminary tests resulted in an increase in shock Mach number from 34 to 39 in air at an initial pressure of 2.5 torr.
Dannenberg, R. E.↗