Direct Parameter Optimization Research Articles

Influence of Steering Angle Profiles on the Orbit Transfer Trajectory

This paper considers a planar orbit transfer trajectory design problem using finite thrust modeling. In this problem, the steering angles associated with the thrust direction are calculated from the predetermined profile format, and the unknown parameters in the profile are directly optimized. Three profile formats that were implemented in previous lunar exploration missions are considered. In addition, a steering angle profile defined in the rotating frame and the optimal steering angle profile are newly studied to compare the performances. To this end, the direct parameter optimization problem and the indirect optimization problem are formulated, and the characteristics of the steering angle profile and its influence on the transfer trajectory are analyzed.

Modification‐based periodic gait planning for a 3‐D bipedal robot with two underactuated DOFs

AbstractThis work considers the periodic gait planning of a 3‐D bipedal robot with two underactuated DOFs. Instead of planning a periodic gait by a traditional direct parameter optimization search, which is usually time‐consuming, we present a novel modification‐based periodic motion planning method, which consists of two steps. Firstly, an initial gait is obtained by relaxing the periodicity constraints in the optimization search. Then, the initial gait is modified to be a periodic one. To achieve a successful gait modification, the gait modification theory is firstly presented, and a gait modification strategy is then proposed. Finally, the presented method is illustrated on the underactuated 3‐D biped, and a comparative simulation study is provided. It is shown that, compared with the traditional method, the time cost in the presented method is significantly reduced.

Technical Note: Optimization of spot and trimmer position during dynamically collimated proton therapy.

To demonstrate a novel theoretical optimization design which considers beam spot and trimmer positioning in addition to beamlet weighting for dynamically collimated proton therapy (DCPT) treatments. Prior to this, the previous methods of plan optimization used to study this emerging technology relied upon an intuitive selection criterion to fix the trimmers blades for a uniform grid of beam spots before determining the individual beamlet weights. To evaluate the potential benefit from this new optimization design, a treatment planning optimization study was performed in order to compare the algorithm's functionality against the existing methods of plan optimization. A direct parameter optimization (DPO) method was developed to determine beam spot and trimmer positions cohesively with beamlet weighting for DCPT treatment plans. Gradients were numerically determined from applying small adjustments to the aforementioned parameters and quantifying the resulting impact on an objective function. This technique was compared to the conventional trimmer selection algorithm (TSA) which does not optimize spot position concurrently with trimmer position. Both planning methods were used to optimize a set of brain treatment plans, and the resulting dose distributions were compared with dose-volume histogram quantities in addition to target coverage, homogeneity, and conformity metrics. An overall improvement to the target conformity and healthy tissue sparing was achieved with DPO over TSA while maintaining an equivalent planning target volume (PTV) coverage index for the three brain patients evaluated in this study. On average, the conformity index improved by 5.5% when utilizing DPO. A similar improvement in reducing the dose to several organs at risk was also noted. Both the TSA and DPO planning methods can achieve highly conformal treatments with the dynamic collimation system (DCS) technology. However, an improvement in the target conformity and healthy tissue sparing was achieved by simultaneously optimizing beam spot position, trimmer location, and beamlet weights using DPO in comparison to the TSA technique.

Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams

In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is composed of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly on the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces. To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized by the cantilever–surface mechanism. The optimization results show that the 2DOF nonlinear system presents the best average performance when the excitation signals have three possible forms. Moreover, we observe that while for the linear systems the optimal performance is obtained for small values of the electromagnetic damping, for the 2DOF nonlinear system optimal performance is achieved for large values of damping. This feature is of particular importance for the system׳s robustness to parasitic damping.

Optimal Low-Thrust Transfers to Lunar L1 Halo Orbit Using Variable Specific Impulse Engine

Given the advantages of variable specific impulse (VSI) engine, it is very likely that in the future there will be deep space missions that use this thrust as propulsion system. In this study, a design technique for a fuel optimal Earth-to-Halo transfer using VSI is proposed. The calculus of variations approach and direct parameter optimization are combined to formulate the trajectory optimization problem. The classic stable manifold, developed in dynamical systems theory, is employed to further reduce fuel consumption. Adjoint control transformation (ACT) and analytical gradients are incorporated to improve performance of the algorithm. Four transfer examples—direct transfers from 500 km low Earth orbit (LEO) and 3,629 km medium Earth orbit (MEO) to lunar L1 halo orbit—and indirect transfers with lunar flybys, are presented.

A Scour Depth Approach for Deriving Erodibility Parameters from Jet Erosion Tests

Abstract. Typically the erosion rate of cohesive soils is modeled using the excess shear stress equation, which includes two soil parameters: the erodibility coefficient (k d ) and the critical shear stress (I„ c ). A jet erosion test (JET) is a standardized method available for deriving the erodibility of cohesive soils. The JET data are typically analyzed using a Blaisdell solution approach. A second solution approach based on direct parameter optimization to the measured scour depth data has recently been proposed but with limited evaluation. Therefore, the objectives of this research were to: (1) develop a new spreadsheet tool that simultaneously solves for the erodibility parameters using both solution approaches, (2) evaluate the solutions in terms of their ability to predict the observed scour depth data, and (3) quantify differences in the predicted erodibility parameters from the two approaches. A series of JETs conducted across the Illinois River watershed in eastern Oklahoma were used to evaluate the performance of the spreadsheet and the solution methodologies. The new scour depth solution provided improved fits to the original scour depth data along with being more stable in converging to a solution as a function of the initial parameter estimates. The automated spreadsheet provides an easy-to-use tool for deriving erodibility parameters from JETs.

Surrogate-based optimization of climate model parameters using response correction

We present a computationally efficient methodology for the optimization of climate model parameters applied to a (one-dimensional) representative of a class of marine ecosystem models. We use a response correction technique to create a surrogate from a temporarily coarser discretized physics-based low-fidelity model. We demonstrate that replacing the direct parameter optimization of the high-fidelity ecosystem model by iteratively updating and re-optimizing the surrogate leads to a very satisfactory solution while yielding significant cost saving – about 84% when compared to the direct high-fidelity model optimization.

Relaxation of STO-3G and 6-31G* basis set functions in the series of LiF isoelectronic molecules of second row elements

The relaxation effect of functions of STO-3G and 6-31G* basis sets (BS) on their balance is considered in the series of LiF, BeO, BN, and C2 isoelectronic molecules. The values of parameters (exponential factors of basis functions, orbital exponents of Gaussian primitives, and contraction coefficients for the basis functions in molecules are found by the energy minimum criterion from unrestricted Hartree-Fock (UHF) calculations with a direct optimization of parameters: the simplex and Rosenbrock methods. Several optimization schemes differing in the number of parameters varied are performed. An important, from the practical viewpoint, relation between parameters of the basis functions of the sets in question is found through the mean values of Gaussian exponents. The relaxation effect on the variation of the total energy and relative errors in the calculations of interatomic distances, normal vibration frequencies, dissociation energies, and other properties of molecules are examined. The variation of the total energy upon the relaxation of STO-3G and 6-31G* basis functions (RBF) can achieve 1100 kJ/mole and 80 kJ/mole, respectively, and should be taken into account when evaluating energy characteristics, especially for the systems with high polar chemical bonds. The relaxation of STO-3G BS improves the description of molecular properties almost in all cases considered, whereas the relaxation of 6-31G* BS slightly affects its balance.

Optimal multirate control design for hard disk drive servo systems

This paper presents a multirate digital controller design for HDD servo systems via direct parameter optimization approach. In order to find a satisfactory multirate controller with good transient and steady state performance, a linear quadratic performance index with stability constraints is introduced. The controller parameters are selected based on the HDD servo system transient response data instead of a detailed plant model. The proposed method can improve the performance of LQG multirate servo designs without knowing the exact plant parameters or noise model. The effect of controller order on system performance is also studied. For a 4th order system studied, it is found that a 4th order controller is sufficient to achieve the optimal performance.