In engineering fields, computational models provide a tool that can simulate a real world response and enhance our understanding of physical phenomenas. However, such models are often computationally expensive with multiple sources of uncertainty related to the model’s input/assumptions. For example, the literature indicates that ligament’s material properties and its insertion site locations have a significant effect on the performance of knee joint models, which makes addressing uncertainty related to them a crucial step to make the computational model more representative of reality. However, previous sensitivity studies were limited due to the computational expense of the models.

The high computational expense of sensitivity analysis can be addressed by performing the analysis with a reduced number of model runs or by creating an inexpensive surrogate model. Both approaches are addressed in this work by the use of Polynomial chaos expansion (PCE)-based surrogate models and design of experiments (DoE). Therefore, the objectives of this dissertation were:​ 1- provide guidelines for the use of PCE-based models and investigate their efficiency in case of non-linear problems. 2- utilize PCE and DoE-based tools to introduce efficient sensitivity analysis approaches to the field of knee mechanics.

To achieve these objectives, a frame structure was used for the first aim, and a rigid body computational model for two knee specimens was used for the second aim. Our results showed that, for PCE-based surrogate models, once the recommended number of samples is used, increasing the PCE order produced more accurate surrogate models. This conclusion was reflected in the R² values realized for three highly non-linear functions ( 0.9998, 0.9996 and 0.9125, respectively). Our results also showed that the use of PCE and DoE-based sensitivity analyses resulted in practically identical results with significant savings in the computational cost of sensitivity analysis when compared to a traditional quasi-Monte Carlo (MC) approach (95% and 98% reductions in model evaluations for analyses with 10 and 6 uncertain variables, respectively). Finally, the use of D-optimal DoE resulted in a reduction in the number of samples required to perform sensitivity analysis by 64.4%, which reduced the computational burden by 1018 hours.