An Expert System-Driven Method for Parametric Trajectory Optimization During Conceptual Design

The objective of this paper is to investigate a reliable method to generate optimal ascent trajectory for hypersonic air-breathing vehicles. When solving optimal trajectories in endo-atmospheric flight, most of traditional indirect methods suffer from difficulties in finding an appropriate initial guess and getting a convergent solution for the two point boundary value problem (TPBVP). With improvements on on-board computer performance, direct methods such as pseudospectral method show promising potential for real-time optimal guidance. It removes the need for computing analytical gradients of aerodynamic coefficients, and remains high accurate solution similar to indirect methods. In this work, optimal ascent trajectory generation problem was formulated as a fuel-optimal control problem. Gauss pseudospectral method (GPM) was presented to generate the optimal ascent trajectories. Optimal solutions from GPM were compared with an indirect method based on finite difference method (FDM). Numerical simulations were studied with various initial conditions to investigate the optimal trajectory characteristics for hypersonic air-breathing vehicles. The results verified the validity and accuracy of GPM for ascent trajectory optimization.

This paper presents a methodology for the concurrent first-stage preliminary design and ascent trajectory optimization, with application to a Vega-derived light launch vehicle. The reuse as first stage of an existing upper-stage (Zefiro 40) requires a redesign of the propellant grain geometry, in order to account for the mutated operating conditions. An optimization code based on the parallel running of several differential evolution algorithms is used to find the optimal law of the internal pressure during first-stage operation, together with the optimal thrust direction and other relevant flight parameters of the entire ascent trajectory. The payload injected into a target orbit is maximized, while meeting multiple design constraints, either involving the alone solid rocket motor or dependent on the actual flight trajectory. Numerical results for sun-synchronous orbit injection are presented.

Ascent trajectory optimization in the atmospheric phase is challenging since nonlinear aerodynamic forces and strict path constraints exist. Traditional convex optimization approaches mostly rely on linearization to convexify the problem, but their convergence is sensitive to user-provided initial state and control profiles. In this article, we decompose the problem into three subproblems for optimizing the flight-path angle, the heading angle, and the speed. The first two subproblems are convexified mainly by successive approximation while the theoretical analysis is conducted to equivalently transform the third subproblem into an initial value problem. The proposed approach can keep most nonlinearity of the original problem. This brings a unique benefit in that an iterative algorithm for solving the subproblems can quickly converge in a few iterations even when rough initial state and control profiles are provided and no trust region is used. Additionally, linking constraints with the exoatmospheric phase are properly formulated and convexified so that an integrated iterative algorithm can be developed to obtain an ascent trajectory from lift-off to orbit. Numerical results are provided to demonstrate the effectiveness and efficiency of the proposed approach.

Multistage launch vehicles are employed to place spacecraft and satellites in their operational orbits. If the rocket aerodynamics and propulsion are modeled appropriately, optimization of their ascent trajectory consists in determining the coast duration and the thrust time history that maximize the final mass at injection. This research derives all the necessary conditions for ascent path optimization of a multistage launch vehicle. With reference to an existing rocket, the indirect heuristic method is then applied, for the numerical determination of the overall ascent trajectory. An effective approach is used with the intent of satisfying the path constraint related to the maximum dynamical pressure in the atmospheric phase. Then, the recently introduced, implicit-type variable-time-domain neighboring optimal guidance is applied to the upper stage powered arc, for the purpose of obtaining the corrective control actions in the presence of nonnominal flight conditions. The guidance approach at hand, based on the second-order analytical conditions for optimality, proves to be rather effective (in terms of propellant budget), and guarantees very accurate orbit injection in spite of perturbations.

This paper is concerned with theoretical and algorithmic development for fast generation of optimal launch ascent trajectories through the atmosphere and guidance, particularly in highly constrained missions. The theoretical investigation oers an insight into what may be called atmospheric primer vector theory, in which the critical roles of the primer vector in the determination of optimal endo-atmospheric ascent trajectories are explored in some detail. The algorithmic development focuses on ascent missions tightly constrained by aerodynamic bending moment limit. The expansion of algorithm capability aims at rapid and automated generation of such highly constrained optimal ascent trajectories. When carried on-board, this process realizes optimal closed-loop ascent guidance. An in-depth application of the theoretical and algorithmic developments in this paper is conducted using the vehicle model and mission profile of the Ares I Crew Launch Vehicle. Extensive simulations are conducted to compare optimal closed-loop with conventional open-loop ascent guidance approaches. The tests oer some rich and revealing comparisons on how each approach performs on inequality constraint observance and injected mass in the presence of winds and dispersions.

Launch vehicle trajectory optimization has gained enormous significance in the recent past. Constraints handling and accuracy of launch vehicle system, are challenging factors, on account of their high degree of non-linearity. This paper brings in the application of thetaparticle swarm optimization (TH-PSO), which is a recently emerged variant of particle swarm optimization (PSO), for launch vehicle trajectory optimization, which can efficiently handle the constraints and drive the system towards optimality. TH–PSO approach is implemented on a multistage liquid propellant rocket, taking angle of attack as the control parameter. Single and dual thrust cases were solved using TH-PSO technique, and a comparative study was made with classical PSO in terms of terminal error, IE consistency of solutions. Based on the statistics, it can be confirmed that in both single and dual thrust cases TH-PSO outperformed, classical PSO. Copyright © 2016 Praise Worthy Prize S.r.l. - All rights reserved

Selecting composite materials considering cost and environmental impact in the early phases of aircraft structure design

Ascent trajectory optimization and explicit guidance problems for a satellite launch vehicle with yaw maneuver in a 3-dimension are considered. The trajectory optimization problem with boundary conditions is formulated as a nonlinear programming problem by parameterizing the inertial pitch and yaw attitude control variables, and is solved by using the SQP algorithm. The flight constraints such as gravity-turn and range safety conditions are imposed. An explicit inertial guidance algorithm in the exoatmospheric phase is also presented. The guidance algorithm provides steering command and time-to-go value directly using the current states of the vehicle and the desired orbit insertion conditions. The liquid propelled Delta 2910 launch vehicle is used as a numerical model.

Due to the growing threat of climate change, we are challenged to find improved assessment practises to recognize solutions for sustainable urban development. The focus of the study is on the life cycle design of a district energy system for a new residential development in Finland. This study analyses LCC (life cycle costs) and carbon emissions (LCA (life cycle assessment)), i.e., the “viability” of different energy systems through a methodological life cycle framework. By combining LCC and LCA, a LCM (life cycle management) perspective is portrayed to support decision-making on a long-term basis. The comparable energy design options analysed are (1) district heating (reference design), (2) district heating with building integrated photovoltaic panels, (3) ground source heat pump, and (4) ground source heat pump with building-integrated photovoltaic panels. The results show that the design option with the highest initial investment (4) is in fact the most viable from a life cycle perspective. This study further strengthens the connection between cost savings and carbon emissions reduction in a life cycle context. Thus, by implementing LCC and LCA analysis in an early design phase, justified economic and environmental design decisions can be identified to develop more sustainable urban areas.

Numerical solutions of multi-phase optimal control problems are considered, where a phase is defined as a subinterval in which the right-hand sides of the differential equations are continuous. At the phase boundaries, the state, control, and design vectors may have jumps; in addition, the dimension of these vectors as well as the dimension of the right-hand sides may change. Two direct methods for solving such problems are presented : a multiple-shooting approach and a collocation method. Both methods avoid the adjoint differential equations. By these transcriptions, the optimal control problem is converted into a nonlinear programming problem (NLP), which is solved using standard sequential quadratic programming (SQP) algorithms. The methods are applied to determine optimal ascent and reentry trajectories of a two-stage-to-orbit vehicle. Both methods are embedded into an advanced user interface which allows a user to edit most of the necessary input in a simple way. This utility is described briefly.

A fixed-point formulation and the associated algorithms for rapid generation of optimal ascent trajectories of launch vehicles through the atmosphere are presented. The complete ascent trajectory is tacitly divided into an endo-atmospheric and an exo-atmospheric portion. Since the exo-atmospheric trajectory can be obtained reliably and rapidly, a special form of two-point boundary value problem (TPBVP) is formulated in the endo-atmospheric portion. This special TPBVP leads to a sequence of nested fixed-point problems. Several algorithmic options to solve these problems using modified fixed-point iterations are discussed. The main advantages of the fixed-point formulation and algorithm are software simplicity and more robust convergence. Numerical results, both in open-loop trajectory generation and closed-loop simulations, are presented to demonstrate the discussions. The algorithm is validated and verified by comparing the results with the results obtained from existing method.

Considering the current trend oil and gas corporations are facing, they are continuously focusing on increasing their operational efficiency. Declining oil and gas prices lead their operational departments to reduce the cost of drilling and producing hydrocarbons, which ultimately results in streamlining the operational cost of their drilling tools. Oilfield service companies with hybrid business models must take all life cycle cost into account. To influence these costs and to optimize capital and operational efficiency as well as service availability, comprehensive cost models are used in the product development process. For the consecutive development stages from feasibility through detailed design, models with increasing level of detail are required. Cost modeling within the development process is typical in the petroleum industry. Currently, models are available for specific applications in single development phases. This paper describes a holistic approach to analyze and optimize life cycle cost and service availabilities of drilling systems from the early concept phase through deployment. The result is a fast, secure and easy usable software tool as well as a standardized process to develop competitive, high-technology drilling systems. To identify requirements for these models, a stakeholder analysis is performed and described. Based on the analysis results, information flows are defined: Who provides and needs which information at what point of time within the process? With this foundation, new models are created or existing models extended to meet the requirements. In this context, best practices from different industries are also reviewed and implemented where applicable. A parallel use of the models during the respective development stage enables an iterative improvement. The development of the models and current results are detailed in this paper. In early conceptual design phases, it is challenging to calculate life cycle cost with sparse information about the complex future drilling system, so cost-estimating relationships must be devised. Maintenance times and intervals, which are one of the main operational cost triggers, must be assessed by concurrent high level tool performance and reliability. Cost efficiency, tool performance and reliability must be balanced to achieve high customer expectations and high margins. During the detailed design phase, system costs, such as alternative costs, e.g., through non-availability of tools, in addition to bottom-up models on the component level, must be considered. These modular models are connected to each other to exchange data via standard interfaces. They calculate future cost projections and identify key cost drivers. This enables continuous cost optimization through the whole development process. Results to support decision-making as well as cost saving potentials are shown with an exemplary development process of a drilling tool by using the life cycle costing approach.

Optimization of launch vehicle ascent trajectories with path constraints and coast arcs

Although the product life cycle cost (LCC) is mainly committed by early design stages, designers do not consider the costs caused in subsequent phases of life cycle. The estimating method for the product life cycle cost in early design processes has been required because of both the lack of detailed information and time for a detailed LCC for a various range of design concepts. This paper suggests an approximate LCC method that allows the designer to make comparative LCC estimation between the different product concepts. The product attributes at the conceptual design phase and LCC factors are introduced and the significant product attributes are determined by statistical analysis. Neural network algorithms are applied to estimate LCC by considering the identified product attributes as inputs and the LCC as output. Trained learning algorithms for the known characteristics of existing products will quickly give the estimation of LCC for new product concepts. The estimation for maintenance and energy costs of electronic appliances is shown as an example. The proposed method provides the good estimation for the LCC and gives the guidelines leading to cost-effective design decision-making at the early design stage.

<div class="section abstract"><div class="htmlview paragraph">Current transport aircraft are mature systems, thus require increased fidelity at the beginning of the design process to allow further optimization. Furthermore, a desire exists to explore unconventional aircraft configurations at the conceptual level. This has motivated the development of a tool which effectively manages the trade-off between high-fidelity levels, flexibility and short turn-around times. This paper presents a CATIA V5-based parametric aircraft geometry modeler developed by Bombardier Aerospace. The aim of the tool is to provide consistent high-fidelity geometric data early in the conceptual aircraft design process.</div><div class="htmlview paragraph">The intended near-term use of the modeler is two-fold: during the early design phase, the modeler computes geometric data such as areas, volumes, ESDU aircraft parameters, etc. In the competitive analysis domain, the tool provides a high-quality three-dimensional model with manageable effort. In both cases, the engineer is presented with a fully parametric three-dimensional CATIA V5 aircraft model. In the medium-term, use by expert departments is envisioned. </div><div class="htmlview paragraph">Moreover, the geometrical data extracted from CATALIST can be saved into a standard database and fed to various analysis codes to compute aircraft performance characteristics. As aircraft models are in native CATIA V5 format, this fits seamlessly into the established design process at Bombardier Aerospace. Additionally, this approach allows critical analyses to be performed earlier in the conceptual design phase.</div><div class="htmlview paragraph">Aircraft exterior and interior modules are in use today along with systems modules and a basic structural representation. An overview of the key features of the tool is presented along with sample applications. Tool usability and modeling quality have been extensively validated with selected regional aircraft and business jets from Bombardier.</div></div>