Parametric CAD model based shape optimization using adjoint functions

Adjoint methods have proven to be an efficient way of calculating the gradient of an objective function with respect to a shape parameter for optimisation, with a computational cost nearly independent of the number of the design variables [1]. The approach in this paper links the adjoint surface sensitivities (gradient of objective function with respect to the surface movement) with the parametric design velocities (movement of the surface due to a CAD parameter perturbation) in order to compute the gradient of the objective function with respect to CAD variables.
For a successful implementation of shape optimization strategies in practical industrial cases, the choice of design variables or parameterisation scheme used for the model to be optimized plays a vital role. Where the goal is to base the optimization on a CAD model the choices are to use a NURBS geometry generated from CAD modelling software, where the position of the NURBS control points are the optimisation variables [2] or to use the feature based CAD model with all of the construction history to preserve the design intent [3]. The main advantage of using the feature based model is that the optimized model produced can be directly used for the downstream applications including manufacturing and process planning.
This paper presents an approach for optimization based on the feature based CAD model, which uses CAD parameters defining the features in the model geometry as the design variables. In order to capture the CAD surface movement with respect to the change in design variable, the “Parametric Design Velocity” is calculated, which is defined as the movement of the CAD model boundary in the normal direction due to a change in the parameter value.
The approach presented here for calculating the design velocities represents an advancement in terms of capability and robustness of that described by Robinson et al. [3]. The process can be easily integrated to most industrial optimisation workflows and is immune to the topology and labelling issues highlighted by other CAD based optimisation processes. It considers every continuous (“real value”) parameter type as an optimisation variable, and it can be adapted to work with any CAD modelling software, as long as it has an API which provides access to the values of the parameters which control the model shape and allows the model geometry to be exported. To calculate the movement of the boundary the methodology employs finite differences on the shape of the 3D CAD models before and after the parameter perturbation. The implementation procedure includes calculating the geometrical movement along a normal direction between two discrete representations of the original and perturbed geometry respectively. Parametric design velocities can then be directly linked with adjoint surface sensitivities to extract the gradients to use in a gradient-based optimization algorithm.
The optimisation of a flow optimisation problem is presented, in which the power dissipation of the flow in an automotive air duct is to be reduced by changing the parameters of the CAD geometry created in CATIA V5. The flow sensitivities are computed with the continuous adjoint method for a laminar and turbulent flow [4] and are combined with the parametric design velocities to compute the cost function gradients. A line-search algorithm is then used to update the design variables and proceed further with optimisation process.

Implementing a structural continuity constraint and a halting method for the topology optimization of energy absorbers

This study investigates topology optimization of energy absorbing structures in which material damage is accounted for in the optimization process. The optimization objective is to design the lightest structures that are able to absorb the required mechanical energy. A structural continuity constraint check is introduced that is able to detect when no feasible load path remains in the finite element model, usually as a result of large scale fracture. This assures that designs do not fail when loaded under the conditions prescribed in the design requirements. This continuity constraint check is automated and requires no intervention from the analyst once the optimization process is initiated. Consequently, the optimization algorithm proceeds towards evolving an energy absorbing structure with the minimum structural mass that is not susceptible to global structural failure. A method is also introduced to determine when the optimization process should halt. The method identifies when the optimization method has plateaued and is no longer likely to provide improved designs if continued for further iterations. This provides the designer with a rational method to determine the necessary time to run the optimization and avoid wasting computational resources on unnecessary iterations. A case study is presented to demonstrate the use of this method.

Time series wind power forecasting based on variant Gaussian process and TLBO

Due to the variability and stochastic nature of wind power system, accurate wind power forecasting has an important role in developing reliable and economic power system operation and control strategies. As wind variability is stochastic, Gaussian Process regression has recently been introduced to capture the randomness of wind energy. However, the disadvantages of Gaussian Process regression include its computation complexity and incapability to adapt to time varying time-series systems. A variant Gaussian Process for time series forecasting is introduced in this study to address these issues. This new method is shown to be capable of reducing computational complexity and increasing prediction accuracy. It is further proved that the forecasting result converges as the number of available data approaches innite. Further, a teaching learning based optimization (TLBO) method is used to train the model and to accelerate
the learning rate. The proposed modelling and optimization method is applied to forecast both the wind power generation of Ireland and that from a single wind farm to show the eectiveness of the proposed method.

Data-Driven Dynamic Modeling of Coupled Thermal and Electric Outputs of Microturbines

Microturbines are among the most successfully commercialized distributed energy resources, especially when they are used for combined heat and power generation. However, the interrelated thermal and electrical system dynamic behaviors have not been fully investigated. This is technically challenging due to the complex thermo-fluid-mechanical energy conversion processes which introduce multiple time-scale dynamics and strong nonlinearity into the analysis. To tackle this problem, this paper proposes a simplified model which can predict the coupled thermal and electric output dynamics of microturbines. Considering the time-scale difference of various dynamic processes occuring within microturbines, the electromechanical subsystem is treated as a fast quasi-linear process while the thermo-mechanical subsystem is treated as a slow process with high nonlinearity. A three-stage subspace identification method is utilized to capture the dominant dynamics and predict the electric power output. For the thermo-mechanical process, a radial basis function model trained by the particle swarm optimization method is employed to handle the strong nonlinear characteristics. Experimental tests on a Capstone C30 microturbine show that the proposed modeling method can well capture the system dynamics and produce a good prediction of the coupled thermal and electric outputs in various operating modes.

Optimal day-ahead scheduling of integrated urban energy systems

An optimal day-ahead scheduling method (ODSM) for the integrated urban energy system (IUES) is introduced, which considers the reconfigurable capability of an electric distribution network. The hourly topology of a distribution network, a natural gas network, the energy centers including the combined heat and power (CHP) units, different energy conversion devices and demand responsive loads (DRLs), are optimized to minimize the day-ahead operation cost of the IUES. The hourly reconfigurable capability of the electric distribution network utilizing remotely controlled switches (RCSs) is explored and discussed. The operational constraints from the unbalanced three-phase electric distribution network, the natural gas network, and the energy centers are considered. The interactions between the electric distribution network and the natural gas network take place through conversion of energy among different energy vectors in the energy centers. An energy conversion analysis model for the energy center was developed based on the energy hub model. A hybrid optimization method based on genetic algorithm (GA) and a nonlinear interior point method (IPM) is utilized to solve the ODSM model. Numerical studies demonstrate that the proposed ODSM is able to provide the IUES with an effective and economical day-ahead scheduling scheme and reduce the operational cost of the IUES.

Data-Driven Dynamic Prediction of Interrelated Heat and Electric Outputs of Microturbines

Microturbines are among the most successfully commercialized distributed energy resources, especially when they are used for combined heat and power generation. However, the interrelated thermal and electrical system dynamic behaviors have not been fully investigated. This is technically challenging due to the complex thermo-fluid-mechanical energy conversion processes which introduce multiple time-scale dynamics and strong nonlinearity into the analysis. To tackle this problem, this paper proposes a simplified model which can predict the coupled thermal and electric output dynamics of microturbines. Considering the time-scale difference of various dynamic processes occuring within microturbines, the electromechanical subsystem is treated as a fast quasi-linear process while the thermo-mechanical subsystem is treated as a slow process with high nonlinearity. A three-stage subspace identification method is utilized to capture the dominant dynamics and predict the electric power output. For the thermo-mechanical process, a radial basis function model trained by the particle swarm optimization method is employed to handle the strong nonlinear characteristics. Experimental tests on a Capstone C30 microturbine show that the proposed modeling method can well capture the system dynamics and produce a good prediction of the coupled thermal and electric outputs in various operating modes.

Improved Real-time State-of-Charge Estimation of LiFePO4 Battery Based on a Novel Thermoelectric Model

Li-ion batteries have been widely used in electric vehicles, and battery internal state estimation plays an important role in the battery management system. However, it is technically challenging, in particular, for the estimation of the battery internal temperature and state-ofcharge (SOC), which are two key state variables affecting the battery performance. In this paper, a novel method is proposed for realtime simultaneous estimation of these two internal states, thus leading to a significantly improved battery model for realtime SOC estimation. To achieve this, a simplified battery thermoelectric model is firstly built, which couples a thermal submodel and an electrical submodel. The interactions between the battery thermal and electrical behaviours are captured, thus offering a comprehensive description of the battery thermal and electrical behaviour. To achieve more accurate internal state estimations, the model is trained by the simulation error minimization method, and model parameters are optimized by a hybrid optimization method combining a meta-heuristic algorithm and the least square approach. Further, timevarying model parameters under different heat dissipation conditions are considered, and a joint extended Kalman filter is used to simultaneously estimate both the battery internal states and time-varying model parameters in realtime. Experimental results based on the testing data of LiFePO4 batteries confirm the efficacy of the proposed method.

Aerodynamic optimization using Adjoint methods and parametric CAD models

This paper describes an implementation of a method capable of integrating parametric, feature based, CAD models based on commercial software (CATIA) with the SU2 software framework. To exploit the adjoint based methods for aerodynamic optimisation within the SU2, a formulation to obtain geometric sensitivities directly from the commercial CAD parameterisation is introduced, enabling the calculation of gradients with respect to CAD based design variables. To assess the accuracy and efficiency of the alternative approach, two aerodynamic optimisation problems are investigated: an inviscid, 3D, problem with multiple constraints, and a 2D high-lift aerofoil, viscous problem without any constraints. Initial results show the new parameterisation obtaining reliable optimums, with similar levels of performance of the software native parameterisations. In the final paper, details of computing CAD sensitivities will be provided, including accuracy as well as linking geometric sensitivities to aerodynamic objective functions and constraints; the impact in the robustness of the overall method will be assessed and alternative parameterisations will be included.

New Method Based on the UNIFAC–VISCO Model for the Estimation of Ionic Liquids Viscosity Using the Experimental Data Recommended by Mathematical Gnostics

The viscosity of ionic liquids (ILs) has been modeled as a function of temperature and at atmospheric pressure using a new method based on the UNIFAC–VISCO method. This model extends the calculations previously reported by our group (see Zhao et al. J. Chem. Eng. Data 2016, 61, 2160–2169) which used 154 experimental viscosity data points of 25 ionic liquids for regression of a set of binary interaction parameters and ion Vogel–Fulcher–Tammann (VFT) parameters. Discrepancies in the experimental data of the same IL affect the quality of the correlation and thus the development of the predictive method. In this work, mathematical gnostics was used to analyze the experimental data from different sources and recommend one set of reliable data for each IL. These recommended data (totally 819 data points) for 70 ILs were correlated using this model to obtain an extended set of binary interaction parameters and ion VFT parameters, with a regression accuracy of 1.4%. In addition, 966 experimental viscosity data points for 11 binary mixtures of ILs were collected from literature to establish this model. All the binary data consist of 128 training data points used for the optimization of binary interaction parameters and 838 test data points used for the comparison of the pure evaluated values. The relative average absolute deviation (RAAD) for training and test is 2.9% and 3.9%, respectively.