Systems Optimization Lab

Department of Mechanical Engineering | McGill University

General research interests

Multidisciplinary design optimization of complex engineering systems; simulation-based engineering design; uncertainty quantification; optimization theory and algorithms; decomposition and coordination methods; design validation; platform-based product families, systems of systems and product-service systems; transportation (automotive and aerospace) and energy systems

Active investigations

Multidisciplinary design optimization of engineering systems and systems-of-systems

MDOThe motivation for this research is that engineering systems are becoming increasingly complex. In addition, challenging engineering problems may not be solvable by means of monolithic systems; novel design solutions that combine different systems together into systems-of-systems may be required to achieve functionalities that none of the individual systems can provide by themselves. It is widely accepted that the single most important cause of failures or unexpected system behavior is the inability to capture and understand all the interactions that exist among subsystems. This phenomenon is amplified when considering the integration of heterogeneous systems because synergy modes and common objectives are not well understood or defined. Our research so far has aimed at addressing the interaction and heterogeneity issues by developing hybrid methods for their coordination . Ongoing research focuses on dynamic and uncertainty aspects: the collective design objectives of the cooperative systems may be either unknown or vaguely defined at the individual system design stages, and they may change over time, especially in the operating phase. In recent work, we have applied both MDO and bio-inspired methods to air transportation design in the context of systems-of-systems. We have also conducted extensive numerical investigations of hon-hierarchical coordination methods and proposed a novel method for their implementation.

Surrogate-assisted, derivative-free optimization for robust simulation-based engineering design


Computer-aided engineering has revolutionized engineering design: computational models are now used to assess alternatives and conduct optimization studies. Challenges of this simulation-based design optimization paradigm include unavailable gradients or unreliable approximations thereof, high computational cost and inherent model uncertainty and noise. Derivative-free optimization (DFO) has been proposed for solving simulation-based design optimization problems. Our work so far has focused on developing a surrogate optimization framework that utilizes i) dynamic regression metamodels to reduce computational cost while handling uncertainty, ii) generalizd pattern search algorithms that have convergence properties and iii) different problem formulations for balancing global vs. local design space exploration and managing lack of information. We have also continued earlier work for conducting appropriate design validation. Our surrogate-assisted strategy exploits the unique features of the Mesh Adaptive Direct Search (MADS) algorithm, and emphasizes the use of surrogate models for acquiring information cost-effectrively while making decisions using the "true" models. Future research aims at developing robust optimization methods for minimizing the sensitivity of DFO design solutions with respect to uncertainties in design variables or model parameters.

Modeling and optimization of aerospace product-service systems


A product-service system (PSS) is a commodity overarching goods and services. An aerospace engineering example is a jet engine manufacturing selling propulsion power to an aircraft operator instead of the engine itself. PSSs are viewed increasingly as an attractive means to create additional revenue streams for manufacturers, add value to consumers and contribute to sustainability since life-cycle analysis and management is extremely important to their design, production and use. While the PSS concept is not new (utility companies sell power, vehicle manufacturers offer services such as extended warranties, etc.), the related engineering design literature is very limited. In recent years, this research area has attracted a lot of interest in the engineering design communities of Northern Europe, Korea and Japan, but not in North America. The majority of the literature is qualitative in nature, so our research aims at developing quantitative methods for model-based design optimization of PSSs. Specifically, we are developing methods to generate and assess PSS design alternatives by combining quantitative and qualitative techniques such as Quality Function Deployment (QFD), Value Engineering (VE) and Multidisciplinary Design Optimization (MDO) to identify critical PSS design variables and attributes, model the relationship between them and maximize added value of product-service offerings.

Multi-fidelity model management framework for multidisciplinary design analysis and optimization


Numerical engineering design optimization requires computational models to predict system behavior in large and multi- dimensional design spaces. But what constitutes an “adequate” model? How do we choose among different models during the optimization process depending on their fidelity level in different areas of the design and parameter spaces? How do we assess a model’s inadequacy? Fidelity is the degree to which a model reproduces the state and behavior of a real world object, feature or condition. Therefore, fidelity is a measure of the realism of a model or simulation. In the literature, the term “multi-fidelity” is used as an adjective for several terms: physics, surrogates, approximations, analysis, optimization, mapping and multidisciplinary design optimization (MDO). All these are pertinent to specific disciplines. Therefore, the semantics and usage of the term can differ substantially, which can lead to misconceptions and inappropriate methods for managing multi-fidelity models (MFMs). The objective of this research is to develop a framework to manage the use of models of varying fidelity regardless of their disciplinary structure. The proposed method for managing multi-fidelity models in engineering optimization supports decisions related to which model(s) should be used, and at what computational cost, during the design exploration of the optimization process. In summary, the research objectives are as follows:

  1. Developing a management framework of MFMs in MDO.
  2. Finding the relation between the errors of a set of models and a reference one in the aggregated error Euclidean space and the n-dimensional space.
  3. Implementing the developed framework in MDO, which will help in reducing the computational cost, allowing an efficient use of multiple black-boxes with multi-fidelity (MF) levels, preventing the search algorithms from reaching unattainable solutions and achieving concurrency between the analyses of different disciplines.
  4. Applying the proposed approach to the MDO of flexible wing structures of aircrafts, and flexible high-speed rotating blades of gas turbines.
  5. Utilizing the developed multi-fidelity analysis to consider critical off-design scenarios.

Integrating air systems in aircraft multidisciplinary design optimization


The complex nature of interaction between aircraft design and air systems design makes it a good candidate for integration into aircraft multidisciplinary design optimization (MDO). This research focuses on investigating methods to capture the sensitivities of air systems design on aircraft design. Air systems that are included in this research are environmental controls systems, ice protection systems, and fuel tank inerting systems. These systems consume pressurized bleed air from an aircraft’s engines to perform their respective functions. We are exploring methods to model the behavior of these systems, which are then incorporated into an MDO environment. This research investigates different techniques to integrate the developed models within the aircraft optimization loop where the interaction and sequencing with engine and wing design models can significantly vary the impact on the overall aircraft design. In addition, we are exploring methods for optimal engine bleed-port selection.

Composite stacking sequence optimization using mesh adaptive direct search


The use of composites has been increasing in land, aerospace, and marine applications due to their advantages over conventional isotropic materials. Most importantly, they provide the flexibility to tailor their properties by changing fiber orientation in the material. However, as advantageous as it may seem, this makes the design of laminated composite structures much more complex and tedious due to the large number of design variables (fiber orientation angles). This offers an opportunity to use optimization techniques to design the best suited structure as per the requirements of the specific application. The composite design guidelines and the manufacturing constraints limits the choice of ply orientation angles in a laminate to a set of discrete angles such as, [0◦, ±45◦, 90◦]. Moreover, the complexity exists because of the multi-modal and variable-dimensional design space with unattainable or costly derivatives. For instance, in engineering design optimization, the objective and constraint functions are often evaluated using black-box simulations and cannot be explicitly expressed analytically nor explicitly. Furthermore, it may be inappropriate to estimate the gradients due to costly evaluations and/or inherent noise in the model. This restricts the use of gradient-based optimization methods to solve such design problems. We use the Mesh Adaptive Direct Search (MADS) algorithm, and compare it to the Real-Coded Genetic Algorithm (RCGA) to optimize the helicopter rotor composite box-beam to achieve desired stiffness requirements determined from the aero-elastic analysis. The objective is to compare MADS, which has a proven convergence to the second-order stationary points, with RCGA, which generates solutions according to an arbitrarily chosen termination criterion and whose optimality cannot be characterized.

Completed projects

Multidisciplinary design optimization of vascular stents

Stent optimization

Vascular stents are tubular structures which are expanded inside an artery to provide structural support and to restore blood flow. Despite having a huge variety of stents in today's market, the adverse biological responses after stenting have not been completely addressed. In-stent restenosis, for instance, is a major problem of current stents. While the causes of restenosis are not completely understood, several studies have shown that low shear stress at the arterial wall is one of the culprits.
We developed a model for multidiscplinary (structural mechanics and fluid dynamics) design optimization of a vascular stent aiming at addressing these issues. A stent can be essentially considered a planar structure when unfolded. Modelling a stent as a lattice structure enables specific stent properties to be tailored by controlling the topology of the unit cell. The main structural properties to consider in stent design are: radial strength, flexibility, foreshortening and recoil. The model will also take into account the blood flow around the stent struts because the presence of the stent disturbs the flow and can create regions of low wall shear stress (critically low wall shear stresses can result in hyperplasia causing in-stent restenosis). These stent requirements were addressed by formulating and solving a multi-objective optimization problem. This approach generated a set of Pareto-optimal stent designs that can support medical doctors in making informed decision when choosing a stent.