OBJECTIVE: Develop reliability-based design optimization (RBDO) techniques and software package for simulation-based designs to improve military ground vehicle systems and subsystems. These techniques are intended to be used for new vehicle designs and for changes to existing designs. The techniques should be able to determine effect on vehicle life that a particular change would cause. In addition, the techniques are expected to go beyond durability into other areas of vehicle design assessment, such as mobility and survivability. DESCRIPTION: This SBIR project will define, determine, and develop innovative numerical methods and computational tools for assessing uncertainty, risk and tradeoffs in vehicle designs and will implement a reliability-based design optimization (RBDO) of ground vehicle systems and subsystems for diverse physical applications including survivability, durability, mobility, fuel efficiency, etc. To extend RBDO, which traditionally has focused solely on durability, to broader applications such as survivability and mobility, it will be necessary to develop both sensitivity-based and sampling-based RBDO methods. Because the focus of this work is the optimization methodology itself, and not the solvers for the different disciplines, the expected RBDO solution is one that will allow for the user to modularly plug in their own solver (referred to here as a"black box") for the discipline being studied. We will focus initially on a crash safety/survivability problem. RBDO problems exhibit a strong parallel nature which requires large computations, so the proposed RBDO methods need to be mapped to a multiple core environment in High Performance Computing (HPC) to increase computational efficiency. For input random variables such as material strength parameters or duty cycle roughness, various input marginal distributions and correlated variables need to be supported. Also, both random and interval variables need to be supported. Methods for modeling input Probability Density Functions (PDFs) and Cumulative Density Functions (CDFs) from experimental data are necessary for both marginal and joint distributions. These new techniques should be able to handle interval distributions as well as the more traditional probability distributions. For sampling based RBDO, accuracy of the proposed surrogate model must be demonstrated. Since it is very expensive to run tests or full physics-based simulations of vehicle system and subsystems, it is important to minimize the number of samples needed by the RBDO solution process, so an efficient sequential sampling strategy should be implemented. Also, user generated surrogate models need to be supported for reliability analysis and RBDO. For sensitivity-based RBDO, in addition to the first-order reliability method (FORM), a higher-order method (similar to second-order reliability method (SORM)) needs to be developed for highly nonlinear RBDO problems. The proposed RBDO code needs to be easy to integrate with available commercial/non-commercial M & S codes via interfaces for broader multidisciplinary applications. For problems with a large number of potential design variables, to effectively use surrogate models, a variable screening method should be developed by mathematically determining the effect of variables on the output variances and automatically selecting variables that have the most significant affect on output. Lack of input model information and surrogate model uncertainty should be considered for confidence (i.e., assure reliability) of optimized designs. For prediction and evaluation of output distributions, a multi-dimensional visualization capability would be desirable, to allow for human users to appreciate the variability of the problem and its solution. PHASE I: The contractor shall research, design, and develop a reliability-based design optimization method and software package for multidisciplinary ground vehicle applications under input uncertainty. The contractor shall demonstrate integration of the RBDO code with commercial/non-commercial codes. The design methodology shall have the ability to be mapped on to multiple processors for speedy optimization process using such standard parallel techniques. The contractor shall show a plan for how to integrate the RBDO solver with various"black box"physics-based simulations in areas such as survivability, mobility and fuel-efficiency. The key focus for this stage will be crash safety/survivability optimization, using a"black box"for the objective and constraint functions in the optimization. The contractor shall discuss with the contracting officer"s representative (COR) a case study to work in Phase II. Feasibility of key capabilities: independent and correlated input variables, both sensitivity-based and sampling-based RBDO methods, random and interval variables, accuracy of surrogate models, and efficient sequential sampling strategy will be evaluated to help determine transition to Phase II. In addition, the contractor is expected to provide an assessment of the scalability of the algorithms to larger problems and more processors. PHASE II: The contractor shall extend the research and development of the robust optimization methodology from Phase I into a working"user friendly"software package. Tests on various necessary capabilities shall be conducted to demonstrate the accuracy, robustness, and performance of the methodology in a variety of conditions. The contractor shall show successful integration with"black box"simulations in crash safety/survivability, an area not normally accommodated by RBDO techniques. In addition to survivability, it is desired that both mobility and fuel-efficiency can be handled, but to keep the scope manageable, only the survivability portion will be demonstrated at this phase. The contractor shall perform a case study as agreed to with the COR before the start of this phase. By the end of Phase II, the software package must be ready to progress to full commercialization in Phase III. To improve the chances for successful commercialization, the user interface will be critical at this stage, and it is expected that a significant portion of the investment will go to this. PHASE III DUAL USE APPLICATIONS: The RBDO design methodology and software package developed above in the description can be used in a broad range of military and civilian applications. For potential military applications, the RBDO techniques and software package developed can be used by US Army, USMC, Air Force, Navy, as well as vehicle OEM"s and DOD suppliers to analyze performances and optimize systems of vehicle components for reliability and RBDO of systems. Also, via commercialization, civilian applications need to be promoted. Potential exists for use in the civilian automotive industry and for other applications. A good user interface and demonstrated integration with a variety of"black box"simulations are critical metrics for success in the marketplace.