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.

Functional expression of a novel Kunitz type protease inhibitor from the human blood fluke Schistosoma mansoni

BACKGROUND: Schistosomes are able to survive for prolonged periods in the blood system, despite continuous contact with coagulatory factors and mediators of the host immune system. Protease inhibitors likely play a critical role in host immune modulation thereby promoting parasite survival in this extremely hostile environment. Even though Kunitz type serine protease inhibitors have been shown to play important physiological functions in a range of organisms these proteins are less well characterised in parasitic helminths.

METHODS: We have cloned one gene sequence from S. mansoni, Smp_147730 (SmKI-1) which is coded for single domain Kunitz type protease inhibitor, E. coli-expressed and purified. Immunolocalisation and western blotting was carried out using affinity purified polyclonal anti-SmKI-1 murine antibodies to determine SmKI-1 expression in the parasite. Protease inhibitor assays and coagulation assays were performed to evaluate the functional roles of SmKI-1.

RESULTS: SmKI-1 is localised in the tegument of adult worms and the sub-shell region of eggs. Furthermore, this Kunitz protein is secreted into the host in the ES products of the adult worm. Recombinant SmKI-1 inhibited mammalian trypsin, chymotrypsin, neutrophil elastase, FXa and plasma kallikrein with IC50 values of 35 nM, 61 nM, 56 nM, 142 nM and 112 nM, respectively. However, no inhibition was detected for pancreatic elastase or cathepsin G. SmKI-1 (4 μM) delayed blood clot formation, reflected in an approximately three fold increase in activated partial thromboplastin time and prothrombin time.

CONCLUSIONS: We have functionally characterised the first Kunitz type protease inhibitor (SmKI-1) from S. mansoni and show that it has anti-inflammatory and anti-coagulant properties. SmKI-1 is one of a number of putative Kunitz proteins in schistosomes that have presumably evolved as an adaptation to protect these parasites from the defence mechanisms of their mammalian hosts. As such they may represent novel vaccine candidates and/or drug targets for schistosomiasis control.