Quadtree SBFEM and optimization based forward and inverse interval analysis for PCM-integrated walls

References

• Y.-Z. Wang et al., “A polyethylene glycol/hydroxyapatite composite phase change material for thermal energy storage,” Appl. Therm. Eng., vol. 113, pp. 1475–1482, Feb. 2017. DOI: 10.1016/j.applthermaleng.2016.11.159.
   Web of Science ®Google Scholar
• S.-H. Wi et al., “Dynamic heat transfer and thermal performance evaluation of PCM-doped hybrid hollow plaster panels for buildings,” J. Hazard. Mater., vol. 374, pp. 428–436, Jul. 2019. DOI: 10.1016/j.jhazmat.2019.03.136.
   PubMed Web of Science ®Google Scholar
• F. Kuznik et al., “A review on phase change materials integrated in building walls,” Renew. Sustain. Energy Rev., vol. 15, no. 1, pp. 379–391, Jan. 2011. DOI: 10.1016/j.rser.2010.08.019.
   Web of Science ®Google Scholar
• T. Yan et al., “Performance evaluation of a PCM-embedded wall integrated with a nocturnal sky radiator,” Energy, vol. 210, pp. 118412, Nov. 2020. DOI: 10.1016/j.energy.2020.118412.
   Web of Science ®Google Scholar
• S. B. Sadineni, S. Madala, and R. F. Boehm, “Passive building energy savings: a review of building envelope components,” Renew. Sustain. Energy Rev., vol. 15, no. 8, pp. 3617–3631, Oct. 2011. DOI: 10.1016/j.rser.2011.07.014.
   Web of Science ®Google Scholar
• U. Stritih et al., “Integration of passive PCM technologies for net-zero energy buildings,” Sustain. Cities Soc., vol. 41, pp. 286–295, Aug. 2018. DOI: 10.1016/j.scs.2018.04.036.
   Web of Science ®Google Scholar
• W. Y. Lin et al., “Optimal design of a thermal energy storage system using phase change materials for a netzero energy solar decathlon house,” Energy Build., vol. 208, pp. 109626, Feb. 2020. DOI: 10.1016/j.enbuild.2019.109626.
   Web of Science ®Google Scholar
• P. K. S. Rathore and S. K. Shukla, “Enhanced thermophysical properties of organic PCM through shape stabilization for thermal energy storage in buildings: a state of the art review,” Energy Build., vol. 236, pp. 110799, Apr. 2021. DOI: 10.1016/j.enbuild.2021.110799.
   Web of Science ®Google Scholar
• B. Lamrani, K. Johannes, and F. Kuznik, “Phase change materials integrated into building walls: an updated review,” Renew. Sustain. Energy Rev., vol. 140, pp. 110751, Apr. 2021. DOI: 10.1016/j.rser.2021.110751.
   Web of Science ®Google Scholar
• Y. Gao and X. Meng, “A comprehensive review of integrating phase change materials in building bricks: methods, performance and applications,” J. Energy Storage, vol. 62, pp. 106913, Jun. 2023. DOI: 10.1016/j.est.2023.106913.
   Web of Science ®Google Scholar
• X. N. Wang et al., “A critical review on phase change materials (PCM) for sustainable and energy efficient building: design, characteristic, performance and application,” Energy Build., vol. 260, pp. 111923, Apr. 2022. DOI: 10.1016/j.enbuild.2022.111923.
   Web of Science ®Google Scholar
• Y. Zhang et al., “Application of latent heat thermal energy storage in buildings: state-of-the-art and outlook,” Build. Environ., vol. 42, no. 6, pp. 2197–2209, Jun. 2007. DOI: 10.1016/j.buildenv.2006.07.023.
   Web of Science ®Google Scholar
• Y. K. Zhou, “Demand response flexibility with synergies on passive PCM walls, BIPVs, and active air-conditioning system in a subtropical climate,” Renew. Energy, vol. 199, pp. 204–225, Nov. 2022. DOI: 10.1016/j.renene.2022.08.128.
   Web of Science ®Google Scholar
• W. W. Sun et al., “Numerical modeling and optimization of annual thermal characteristics of an office room with PCM active–passive coupling system,” Energy Build., vol. 254, pp. 111629, Jan. 2022. DOI: 10.1016/j.enbuild.2021.111629.
   Web of Science ®Google Scholar
• Y.-P. Zhang et al., “Influence of additives on thermal conductivity of shape-stabilized phase change material,” Sol. Energy Mater. Sol. Cells, vol. 90, no. 11, pp. 1692–1702, Jul. 2006. DOI: 10.1016/j.solmat.2005.09.007.
   Web of Science ®Google Scholar
• X. Y. Zheng and Y. K. Zhou, “A three-dimensional unsteady numerical model on a novel aerogel-based PV/T-PCM system with dynamic heat-transfer mechanism and solar energy harvesting analysis,” Appl. Energy, vol. 338, pp. 120899, May 2023. DOI: 10.1016/j.apenergy.2023.120899.
   Web of Science ®Google Scholar
• M. Alam et al., “Energy saving potential of phase change materials in major Australian cities,” Energy Build., vol. 78, pp. 192–201, Aug. 2014. DOI: 10.1016/j.enbuild.2014.04.027.
   Web of Science ®Google Scholar
• W. Xiao, X. Wang, and Y.-P. Zhang, “Thermal analysis of lightweight wall with shape-stabilized PCM panel for summer insulation,” J. Eng. Thermophys., vol. 30, pp. 1561–1563, Sep. 2009. DOI: 10.3321/j.issn:0253-231X.2009.09.036.
   Google Scholar
• Y. P. Zhang et al., “ Preparation, thermal performance and application of shape-stabilized PCM in energy efficient buildings,” Energy Build., vol. 38, no. 10, pp. 1262–1269, Oct. 2006. DOI: 10.1016/j.enbuild.2006.02.009.
   Web of Science ®Google Scholar
• A. C. Evers, M. A. Medina, and Y. Fang, “Evaluation of the thermal performance of frame walls enhanced with paraffin and hydrated salt phase change materials using a dynamic wall simulator,” Build. Environ., vol. 45, no. 8, pp. 1762–1768, Aug. 2010. DOI: 10.1016/j.buildenv.2010.02.002.
   Web of Science ®Google Scholar
• R. Cai et al., “Review on optimization of phase change parameters in phase change material building envelopes,” J. Build. Eng., vol. 35, pp. 101979, Mar. 2021. DOI: 10.1016/j.jobe.2020.101979.
   Web of Science ®Google Scholar
• M. Saffari et al., “Simulation-based optimization of PCM melting temperature to improve the energy performance in buildings,” Appl. Energy, vol. 202, pp. 420–434, Sep. 2017. DOI: 10.1016/j.apenergy.2017.05.107.
   Web of Science ®Google Scholar
• X.-Q. Sun et al., “Energy and economic analysis of a building enclosure outfitted with a phase change material board (PCMB),” Energy Convers. Manage., vol. 83, pp. 73–78, Jul. 2014. DOI: 10.1016/j.enconman.2014.03.035.
   Web of Science ®Google Scholar
• E. Markarian and F. Fazelpour, “Multi-objective optimization of energy performance of a building considering different configurations and types of PCM,” Sol. Energy, vol. 191, pp. 481–496, Oct. 2019. DOI: 10.1016/j.solener.2019.09.003.
   Web of Science ®Google Scholar
• R. A. Kishore et al., “Optimizing PCM-integrated walls for potential energy savings in U.S. Buildings,” Energy Build., vol. 226, pp. 110355, Nov. 2020. DOI: 10.1016/j.enbuild.2020.110355.
   Web of Science ®Google Scholar
• Y. K. Zhou, S. Q. Zheng, and G. Q. Zhang, “Artificial neural network based multivariable optimization of a hybrid system integrated with phase change materials, active cooling and hybrid ventilations,” Energy Convers. Manage., vol. 197, pp. 111859, Oct. 2019. DOI: 10.1016/j.enconman.2019.111859.
   Web of Science ®Google Scholar
• Y. K. Zhou, S. Q. Zheng, and G. Q. Zhang, “Machine learning-based optimal design of a phase change material integrated renewable system with on-site PV, radiative cooling and hybrid ventilations–study of modelling and application in five climatic regions,” Energy, vol. 192, pp. 116608, Feb. 2020. DOI: 10.1016/j.energy.2019.116608.
   Web of Science ®Google Scholar
• Z. Y. Li, Y. Q. Zhao, and X. Zou, “The research for uncertainty heat transfer process of phase change thermal storage based on Monte Carlo method,” AMM, vol. 291–294, pp. 632–635, Feb. 2013. DOI: 10.4028/www.scientific.net/AMM.291-294.632.
   Google Scholar
• Y. Zhou et al., “Passive and active phase change materials integrated building energy systems with advanced machine-learning based climate-adaptive designs, intelligent operations, uncertainty-based analysis and optimisations: a state-of-the-art review,” Renew. Sustain. Energy Rev., vol. 130, pp. 109889, Sep. 2020. DOI: 10.1016/j.rser.2020.109889.
   Web of Science ®Google Scholar
• Y. K. Zhou, S. Q. Zheng, and G. Q. Zhang, “A state-of-the-art-review on phase change materials integrated cooling systems for deterministic parametrical analysis, stochastic uncertainty-based design, single and multi-objective optimisations with machine learning applications,” Energy Build., vol. 220, pp. 110013, Aug. 2020. DOI: 10.1016/j.enbuild.2020.110013.
   Web of Science ®Google Scholar
• Y. K. Zhou, S. Q. Zheng, and G. Q. Zhang, “Machine-learning based study on the on-site renewable electrical performance of an optimal hybrid PCMs integrated renewable system with high-level parameters’ uncertainties,” Renew. Energy, vol. 151, pp. 403–418, May 2020. DOI: 10.1016/j.renene.2019.11.037.
   Web of Science ®Google Scholar
• Y. K. Zhou and S. Q. Zheng, “Multi-level uncertainty optimisation on phase change materials integrated renewable systems with hybrid ventilations and active cooling,” Energy, vol. 202, pp. 117747, Jul. 2020. DOI: 10.1016/j.energy.2020.117747.
   Web of Science ®Google Scholar
• J. Mazo et al., “Uncertainty propagation and sensitivity analysis of thermo-physical properties of phase change materials (PCM) in the energy demand calculations of a test cell with passive latent thermal storage,” Appl. Therm. Eng., vol. 90, pp. 596–608, Nov. 2015. DOI: 10.1016/j.applthermaleng.2015.07.047.
   Web of Science ®Google Scholar
• R. Peng, H. Yang, and Y. Xue, “Full-scale bounds estimation for the nonlinear transient heat transfer problems with interval uncertainties,” Int. J. Comput. Methods, vol. 18, no. 08, pp. 2150026, Apr. 2021. DOI: 10.1142/S0219876221500262.
   Web of Science ®Google Scholar
• W. Tian et al., “Transient response bounds analysis of heat transfer problems based on interval process model,” Int. J. Heat Mass Transf., vol. 148, pp. 119027, Feb. 2020. DOI: 10.1016/j.ijheatmasstransfer.2019.119027.
   Web of Science ®Google Scholar
• C. Wang and H. G. Matthies, “Non-probabilistic interval process model and method for uncertainty analysis of transient heat transfer problem,” Int. J. Therm. Sci., vol. 144, pp. 147–157, Oct. 2019. DOI: 10.1016/j.ijthermalsci.2019.06.002.
   Web of Science ®Google Scholar
• X. Du, Z. Tang, and Q. Xue, “Interval inverse analysis of hyperbolic heat conduction problem,” Int. Commun. Heat Mass Transf., vol. 54, pp. 75–80, May 2014. DOI: 10.1016/j.icheatmasstransfer.2014.03.014.
   Web of Science ®Google Scholar
• Y. Xue and H. Yang, “A numerical method to estimate temperature intervals for transient convection–diffusion heat transfer problems,” Int. Commun. Heat Mass Transf., vol. 47, pp. 56–61, Oct. 2013. DOI: 10.1016/j.icheatmasstransfer.2013.07.005.
   Web of Science ®Google Scholar
• W. Chong and Z. Qiu, “Interval analysis of steady-state heat convection–diffusion problem with uncertain-but-bounded parameters,” Int. J. Heat Mass Transf., vol. 91, pp. 355–362, Dec. 2015. DOI: 10.1016/j.ijheatmasstransfer.2015.07.115.
   Web of Science ®Google Scholar
• C. Wang and H. G. Matthies, “Novel interval theory-based parameter identification method for engineering heat transfer systems with epistemic uncertainty,” Int. J. Numer. Methods Eng., vol. 115, no. 6, pp. 756–770, Apr. 2018. DOI: 10.1002/nme.5824.
   Web of Science ®Google Scholar
• H. Ouyang et al., “Correlation propagation for uncertainty analysis of structures based on non-probabilistic ellipsoidal model,” Appl. Math. Modell., vol. 88, pp. 190–207, Dec. 2020. DOI: 10.1016/j.apm.2020.06.009.
   Web of Science ®Google Scholar
• Z. Y. Wang et al., “The interval analysis for uncertainty heat transfer process of phase change thermal storage based on perturbation method,” AMR, vol. 838–841, pp. 1939–1943, Nov. 2013. DOI: 10.4028/www.scientific.net/AMR.838-841.1939.
   Google Scholar
• Y. He, X. Dong, and H. Yang, “A new adaptive algorithm for phase change heat transfer problems based on quadtree SBFEM and smoothed effective heat capacity method,” Numer. Heat Transf. Part B, vol. 75, no. 2, pp. 111–126, May 2019. DOI: 10.1080/10407790.2019.1607116.
   Web of Science ®Google Scholar
• Y. He, H. Yang, and A. J. Deeks, “An element-free Galerkin scaled boundary method for steady-state heat transfer problems,” Numer. Heat Transf. Part B, vol. 64, no. 3, pp. 199–217, Jun. 2013. DOI: 10.1080/10407790.2013.791777.
   Web of Science ®Google Scholar
• E. T. Ooi, C. Song, F. Tin-Loi, and Z. Yang, “Polygon scaled boundary finite elements for crack propagation modelling: scaled boundary polygon finite elements for crack propagation,” Int. J. Numer. Meth. Eng., vol. 91, no. 3, pp. 319–342, Mar. 2012. DOI: 10.1002/nme.4284.
   Web of Science ®Google Scholar
• A. Saputra, H. Talebi, D. Tran, C. Birk, and C. Song, “Automatic image‐based stress analysis by the scaled boundary finite element method,” Int. J. Numer. Meth. Eng., vol. 109, no. 5, pp. 697–738, 2017. May 2016. DOI: 10.1002/nme.5304.
   Web of Science ®Google Scholar
• X. Chen, T. Luo, E. T. Ooi, E. H. Ooi, and C. Song, “A quadtree-polygon-based scaled boundary finite element method for crack propagation modeling in functionally graded materials,” Theor. Appl. Fract. Mech., vol. 94, pp. 120–133, Apr. 2018. DOI: 10.1016/j.tafmec.2018.01.008.
   Web of Science ®Google Scholar
• C. Ran and H. Yang, “Sensitivity analysis-based full-scale bounds estimation for 2-D interval bi-modular problems,” Arch. Appl. Mech., vol. 91, no. 7, pp. 3011–3034, Apr. 2021. DOI: 10.1007/s00419-021-01945-x.
   Web of Science ®Google Scholar
• H. Guo et al., “A quadtree-polygon based scaled boundary finite element method for image-based mesoscale fracture modelling in concrete,” Eng. Fract. Mech., vol. 211, pp. 420–441, Apr. 2019. DOI: 10.1016/j.engfracmech.2019.02.021.
   Web of Science ®Google Scholar
• C. Song and J. P. Wolf, “The scaled boundary finite-element method—alias consistent infinitesimal finite-element cell method—for elastodynamics,” Comput. Methods Appl. Mech. Eng., vol. 147, no. 3–4, pp. 329–355, Aug. 1997. DOI: 10.1016/S0045-7825(97)00021-2.
   Web of Science ®Google Scholar
• C. Wang, Z. Qiu, and Z. Y. Yang, “Collocation methods for uncertain heat convection-diffusion problem with interval input parameters,” Int. J. Therm. Sci., vol. 107, pp. 230–236, Sep. 2016. DOI: 10.1016/j.ijthermalsci.2016.04.012.
   Web of Science ®Google Scholar
• S. Chen, B. Merriman, S. Osher, and P. Smereka, “A simple level set method for solving Stefan problems,” J. Comput. Phys., vol. 135, no. 1, pp. 8–29, Sep. 1997. DOI: 10.1006/jcph.1997.5721.
   Web of Science ®Google Scholar
• H. Yang and Y. He, “Solving heat transfer problems with phase change via smoothed effective heat capacity and element-free Galerkin methods,” Int. Commun. Heat Mass Transf., vol. 37, no. 4, pp. 385–392, Apr. 2010. DOI: 10.1016/j.icheatmasstransfer.2009.12.002.
   Web of Science ®Google Scholar
• R. W. Lewis and K. Ravindran, “Finite element simulation of metal casting,” Int. J. Numer. Meth. Eng., vol. 47, no. 1–3, pp. 29–59, Feb. 2000. DOI: 10.1002/(SICI)1097-0207(20000110/30)47:1/3<29::AID-NME760>3.0.CO;2-X.
   Web of Science ®Google Scholar
• B. Spalding, “The finite element method in heat-transfer analysis,” Int. J. Heat Mass Transf., vol. 41, no. 16, pp. 2563–2564, Aug. 1998. DOI: 10.1016/S0017-9310(96)00312-2.
   Google Scholar
• C. R. Dyer, “Computing the Euler number of an image from its quadtree,” Comput. Graph. Image Process., vol. 13, no. 3, pp. 270–276, Jul. 1980. DOI: 10.1016/0146-664X(80)90050-7.
   Google Scholar
• H. Sundar, R. S. Sampath, and G. Biros, “Bottom-up construction and 2:1 balance refinement of linear octrees in parallel,” SIAM J. Sci. Comput., vol. 30, no. 5, pp. 2675–2708, Jul. 2008. DOI: 10.1137/070681727.
   Web of Science ®Google Scholar
• Y. He, J. Guo, H. Yang, and C. R. Dyer, “Image-based numerical prediction for effective thermal conductivity of heterogeneous materials: a quadtree based scaled boundary finite element method,” Int. J. Heat Mass Transf., vol. 128, pp. 335–343, Jan. 2019. DOI: 10.1016/j.ijheatmasstransfer.2018.08.099.
   Web of Science ®Google Scholar
• N. Provatas, N. Goldenfeld, and J. Dantzig, “Adaptive mesh refinement computation of solidification microstructures using dynamic data structures,” J. Comput. Phys., vol. 148, no. 1, pp. 265–290, Jan. 1999. DOI: 10.1006/jcph.1998.6122.
   Web of Science ®Google Scholar
• Z. Liu et al., “Influence of phase change material (PCM) parameters on the thermal performance of lightweight building walls with different thermal resistances,” Case Stud. Therm. Eng., vol. 31, pp. 101844, Feb. 2022. DOI: 10.1016/j.csite.2022.101844.
   Web of Science ®Google Scholar
• The MathWorks, Inc., Matlab Optimization Toolbox User’s Guide (R2018A), 2018.
   Google Scholar
• Y. Q. He and H. T. Yang, “Solving inverse couple-stress problems via an element-free Galerkin (EFG) method and Gauss–Newton algorithm,” Finite Elem. Anal. Des., vol. 46, no. 3, pp. 257–264, Mar. 2010. DOI: 10.1016/j.finel.2009.09.009.
   Web of Science ®Google Scholar
• H. Wang and S. Xiang S, “On the convergence rates of Legendre approximation,” Math. Comp., vol. 81, no. 278, pp. 861–877, Apr. 2011. DOI: 10.1090/S0025-5718-2011-02549-4.
   Web of Science ®Google Scholar
• C. Ran and H. Yang, H., “A new numerical technique for interval analysis of convection-diffusion heat transfer problems using LSE and optimization algorithm,” Numer. Heat Transf. Part B, vol. 77, no. 3, pp. 195–214, Nov. 2020. DOI: 10.1080/10407790.2019.1693188.
   Web of Science ®Google Scholar
• B. Ganapathysubramanian and N. Zabaras, “Sparse grid collocation schemes for stochastic natural convection problems,” J. Comput. Phys., vol. 225, no. 1, pp. 652–685, Jul. 2007. DOI: 10.1016/j.jcp.2006.12.014.
   Web of Science ®Google Scholar
• A. Klimke and B. Wohlmuth, “Computing expensive multivariate functions of fuzzy numbers using sparse grids,” Fuzzy Sets Syst., vol. 154, no. 3, pp. 432–453, Sep. 2005. DOI: 10.1016/j.fss.2005.02.017.
   Web of Science ®Google Scholar
• S. Smolyak, “Computing expensive multivariate functions of fuzzy numbers using sparse grids,” Dokl. Akad. Nauk SSSR Syst., vol. 148, no. 5, pp. 1042–1045, Jan. 1963.
   Google Scholar
• K. L. Judd, L. Maliar, S. Maliar, and R. Valero, “Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain,” J. Econ. Dyn. Control, vol. 44, pp. 92–123, Jul. 2014. DOI: 10.1016/j.jedc.2014.03.003.
   Web of Science ®Google Scholar
• A. J. Deeks and J. P. Wolf, “A virtual work derivation of the scaled boundary finite-element method for elastostatics,” Comput. Mech., vol. 28, no. 6, pp. 489–504, Jun. 2002. DOI: 10.1007/s00466-002-0314-2.
   Web of Science ®Google Scholar