Probabilistic Modeling and Reliability-based Design Optimization of a Ground Source Heat Pump System

Zilong Zhao, Yanwen Xu, Yu-Feng Lin, Xinlei Wang, Pingfeng Wang


  • Addressed reliability problem of a Ground Source Heat Pump (GSHP) system.•
  • Probabilistic Uncertainty Indexes were integrated into design and random variables.•
  • Constraint functions were determined to ensure the GSHP system performance.•
  • Uncertainties’ effects were summarized through comprehensive case studies.


The optimization design of a ground source heat pump (GSHP) system can be crucial in improving its performance and economic competitiveness. The effect of probabilistic uncertainties of design variables in a GSHP system was analyzed using reliability-based design optimization (RBDO) method. An analytical borehole heat transfer model was selected as the frame of energy simulation in this work. With the goal to minimize the cumulative costs over a 20-year lifespan of the GSHP system, a non-linear optimization was carried out under three constraint factors imposed on the internal flow in ground heat exchanger: The inlet water temperature, water pressure losses and Reynolds number to ensure turbulent flow. Three design variables including depth of boreholes, ground pipe radius and mass flow rate, and two random variables at the installation site, including the groundwater velocity and ground thermal conductivity were considered in this investigation. Different uncertainty levels were assigned into the probability indexes of all five variables, which were studied under multiple reliability levels of all three constraints. Results showed that uncertainties of variables can strongly affect the system reliability and total cost determination. The compromised increment of system cost to ensure the reliability was discussed, and the optimal combinations of design variables (borehole depth, pipe radius and mass flow rate) were also given under different designing scenarios.

Zhao, Z., Y. Xu, Y-F. Lin, X. Wang, and P. Wang. 2021. Probabilistic Modeling and Reliability-based Design Optimization of a Ground Source Heat Pump System. Applied Thermal Engineering. 197.

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