The main pipes of reactor coolant systems (RCS) are usually long flexible structures that are connected to multiple key equipment and components of the nuclear system (e.g., reactor pressure vessel, steam generator, main pump, etc.). Mechanical analysis of pipe responses at key elbows and weld seams under static and dynamical load conditions is an essential step to ensure safety and reliability of the whole RCS. Common practice to keep the structural integrity of RCS piping under dynamical load (seismic or shock load) is to impose supporting devices at various locations so that the stiffness at weak spots can be improved. Nevertheless, the introduction of supporting devices, especially the mechanical stops, may cause significant increase of thermal stress due to the block of thermal expansion path of the piping. Hence, cooperative design and optimization of RCS piping supports by jointly considering the piping responses under static and dynamical load cases becomes quite a necessity. In this paper, such an optimal design task is formulated as a multi-objective optimization problem (MOP) with the stress level at key elbows and weld seams of the main pipes as objectives; and various parameters of each supporting device as design variables. The key feature of such MOP is that the number of design variables is unknown in prior. A single support sampling strategy is first proposed to observe the influence of one supporting device. Clustering algorithms are then applied to discover patterns from the single support sampling pool. A 3-snubber-3-stop main pipe support layout is determined via unsupervised clustering algorithms. We perform the surrogatemodel based parameter optimization once the optimization framework is fixed. Simulation results of the optimal piping support design show good satisfactions of stress level according to ASME boiler and pressure vessel code (BPVC) under both static and dynamical load cases. The data-driven design and optimization procedures presented in this paper suit the optimal design with conflicting objectives and unclear number of design variables.

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