Journal: Scientific Reports

Article Title: Optimization of proton exchange membrane fuel cell design parameters using Tianji’s horse racing optimization

doi: 10.1038/s41598-026-35200-6

Figure Lengend Snippet: The schematic diagram of a PEMFC.

Article Snippet: In particular, THRO achieves the lowest sum of squared errors (SSE), with values of 2.06, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.12 \times 10^{-2}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.16 \times 10^{-2}$$\end{document} , 5.25, 1.056, and 0.813 for the NedStack PS6, Horizon 500W, BCS 500W, 250W, Avista SR-12 , and Ballard Mark V PEMFC stacks, respectively.

Techniques:

Journal: Scientific Reports

Article Title: Optimization of proton exchange membrane fuel cell design parameters using Tianji’s horse racing optimization

doi: 10.1038/s41598-026-35200-6

Figure Lengend Snippet: Electrical model of a PEMFC.

Article Snippet: In particular, THRO achieves the lowest sum of squared errors (SSE), with values of 2.06, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.12 \times 10^{-2}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.16 \times 10^{-2}$$\end{document} , 5.25, 1.056, and 0.813 for the NedStack PS6, Horizon 500W, BCS 500W, 250W, Avista SR-12 , and Ballard Mark V PEMFC stacks, respectively.

Techniques:

Journal: Scientific Reports

Article Title: Optimization of proton exchange membrane fuel cell design parameters using Tianji’s horse racing optimization

doi: 10.1038/s41598-026-35200-6

Figure Lengend Snippet: Objective function values obtained from each run of the THRO for: ( a ) NedStack PS6, ( b ) Horizon 500W, ( c ) BCS 500W, ( d ) 250W, ( e ) Avista SR-12, and ( f ) Ballard Mark V PEMFC stacks.

Article Snippet: In particular, THRO achieves the lowest sum of squared errors (SSE), with values of 2.06, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.12 \times 10^{-2}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.16 \times 10^{-2}$$\end{document} , 5.25, 1.056, and 0.813 for the NedStack PS6, Horizon 500W, BCS 500W, 250W, Avista SR-12 , and Ballard Mark V PEMFC stacks, respectively.

Techniques:

Journal: Scientific Reports

Article Title: Optimization of proton exchange membrane fuel cell design parameters using Tianji’s horse racing optimization

doi: 10.1038/s41598-026-35200-6

Figure Lengend Snippet: The convergence curves of different algorithms during the parameter extraction process of ( a ) NedStack PS6, ( b ) Horizon 500W, ( c ) BCS 500W, ( d ) 250W, ( e ) Avista SR-12, and ( f ) Ballard Mark V PEMFC stacks.

Article Snippet: In particular, THRO achieves the lowest sum of squared errors (SSE), with values of 2.06, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.12 \times 10^{-2}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.16 \times 10^{-2}$$\end{document} , 5.25, 1.056, and 0.813 for the NedStack PS6, Horizon 500W, BCS 500W, 250W, Avista SR-12 , and Ballard Mark V PEMFC stacks, respectively.

Techniques: Extraction

Journal: Scientific Reports

Article Title: Optimization of proton exchange membrane fuel cell design parameters using Tianji’s horse racing optimization

doi: 10.1038/s41598-026-35200-6

Figure Lengend Snippet: Box plot of different algorithms for ( a ) NedStack PS6, ( b ) Horizon 500W, ( c ) BCS 500W, ( d ) 250W PEMFC stacks, ( e ) Avista SR-12, and ( f ) Ballard Mark V stacks.

Article Snippet: In particular, THRO achieves the lowest sum of squared errors (SSE), with values of 2.06, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.12 \times 10^{-2}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.16 \times 10^{-2}$$\end{document} , 5.25, 1.056, and 0.813 for the NedStack PS6, Horizon 500W, BCS 500W, 250W, Avista SR-12 , and Ballard Mark V PEMFC stacks, respectively.

Techniques:

Journal: Scientific Reports

Article Title: Optimization of proton exchange membrane fuel cell design parameters using Tianji’s horse racing optimization

doi: 10.1038/s41598-026-35200-6

Figure Lengend Snippet: Mean rankings from Friedman test of ( a ) NedStack PS6, ( b ) Horizon 500W, ( c ) BCS 500W, ( d ) 250W, ( e ) Avista SR-12, and ( f ) Ballard Mark V PEMFC stacks.

Article Snippet: In particular, THRO achieves the lowest sum of squared errors (SSE), with values of 2.06, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.12 \times 10^{-2}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.16 \times 10^{-2}$$\end{document} , 5.25, 1.056, and 0.813 for the NedStack PS6, Horizon 500W, BCS 500W, 250W, Avista SR-12 , and Ballard Mark V PEMFC stacks, respectively.

Techniques:

Journal: Scientific Reports

Article Title: Optimization of proton exchange membrane fuel cell design parameters using Tianji’s horse racing optimization

doi: 10.1038/s41598-026-35200-6

Figure Lengend Snippet: Estimated I-V polarization curves using THRO and experimental curves of ( a ) NedStack PS6, ( b ) Horizon 500W, ( c ) BCS 500W, ( d ) 250W, ( e ) Avista SR-12, and ( f ) Ballard Mark V PEMFC stacks.

Article Snippet: In particular, THRO achieves the lowest sum of squared errors (SSE), with values of 2.06, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.12 \times 10^{-2}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.16 \times 10^{-2}$$\end{document} , 5.25, 1.056, and 0.813 for the NedStack PS6, Horizon 500W, BCS 500W, 250W, Avista SR-12 , and Ballard Mark V PEMFC stacks, respectively.

Techniques:

Journal: Scientific Reports

Article Title: Optimization of proton exchange membrane fuel cell design parameters using Tianji’s horse racing optimization

doi: 10.1038/s41598-026-35200-6

Figure Lengend Snippet: Model validation curves and experimental data of 250W PEMFC stacks.

Article Snippet: In particular, THRO achieves the lowest sum of squared errors (SSE), with values of 2.06, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.12 \times 10^{-2}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.16 \times 10^{-2}$$\end{document} , 5.25, 1.056, and 0.813 for the NedStack PS6, Horizon 500W, BCS 500W, 250W, Avista SR-12 , and Ballard Mark V PEMFC stacks, respectively.

Techniques: Biomarker Discovery

Journal: Scientific Reports

Article Title: Optimization of proton exchange membrane fuel cell design parameters using Tianji’s horse racing optimization

doi: 10.1038/s41598-026-35200-6

Figure Lengend Snippet: Variation of hydrogen and oxygen pressures, V–I curves for ( a ) NedStack PS6 ( b ) Horizon 500W ( c ) BCS 500W ( d ) Avista SR-12, and ( e ) Ballard Mark V PEMFC stacks.

Article Snippet: In particular, THRO achieves the lowest sum of squared errors (SSE), with values of 2.06, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.12 \times 10^{-2}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.16 \times 10^{-2}$$\end{document} , 5.25, 1.056, and 0.813 for the NedStack PS6, Horizon 500W, BCS 500W, 250W, Avista SR-12 , and Ballard Mark V PEMFC stacks, respectively.

Techniques:

Journal: Scientific Reports

Article Title: Optimization of proton exchange membrane fuel cell design parameters using Tianji’s horse racing optimization

doi: 10.1038/s41598-026-35200-6

Figure Lengend Snippet: Temperature variation, V–I curves for ( a ) NedStack PS6 ( b ) BCS 500W ( c ) Avista SR-12, and ( d ) Ballard Mark V PEMFC stacks.

Article Snippet: In particular, THRO achieves the lowest sum of squared errors (SSE), with values of 2.06, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.12 \times 10^{-2}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.16 \times 10^{-2}$$\end{document} , 5.25, 1.056, and 0.813 for the NedStack PS6, Horizon 500W, BCS 500W, 250W, Avista SR-12 , and Ballard Mark V PEMFC stacks, respectively.

Techniques: