{"id":6083,"date":"2025-07-17T14:55:08","date_gmt":"2025-07-17T05:55:08","guid":{"rendered":"https:\/\/aizoth.com\/?post_type=use_case&#038;p=6083"},"modified":"2025-12-05T15:45:20","modified_gmt":"2025-12-05T06:45:20","slug":"contents-e013","status":"publish","type":"use_case","link":"https:\/\/aizoth.com\/en\/use_case\/contents-e013\/","title":{"rendered":"Multi-objective optimization of an advanced Lorenz cycle (ALC) using a surrogate model based on Multi-Sigma\u00ae"},"content":{"rendered":"\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>In pursuit of a carbon-neutral society, the development of highly efficient thermal energy conversion technologies for both heating and cooling is becoming increasingly important. Currently, to improve the energy efficiency of next-generation industrial complexes\u2014such as cold chains, data centers, and direct air capture (DAC) systems\u2014there is a pressing need for thermal management systems capable of operating under large temperature glides, ranging approximately from -30\u2103 to 150\u2103. To address this challenge, an advanced Lorenz cycle (ALC) utilizing the organic Rankine cycle has been proposed. In this study, we constructed a surrogate model for a heat pump based on the ALC and explored high-efficiency operating conditions through multi-objective optimization.<\/strong><\/p>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" style=\"font-size:30px;text-decoration:underline\"><strong>1. <strong>Prediction of Temperature and Coefficient of Performance (COP) Using Multi-Sigma<sup>\u00ae<\/sup><\/strong><\/strong><\/h2>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Using Multi-Sigma<sup>\u00ae<\/sup>, a surrogate model was constructed based on cycle simulation data of a heat pump for water heating. This surrogate model demonstrated high prediction accuracy, with correlation coefficients of 0.925 for temperature and 0.888 for the coefficient of performance (COP), which represents energy efficiency.<\/p>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:600px\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Explanatory Variables:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>(A)<\/strong> Alternative refrigerant composition ratio<\/li>\n\n\n\n<li><strong>(B)<\/strong> Heat source flow rate [ton\/h], <strong>(C)<\/strong> Cooling source flow rate [ton\/h]<\/li>\n\n\n\n<li><strong>(D)<\/strong> Heat source temperature [\u2103], <strong>(E)<\/strong> Compressor pressure [MPa]<\/li>\n\n\n\n<li><strong>(F)<\/strong> Refrigerant flow rate [ton\/h]<\/li>\n<\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>Target Variables:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Temperature [\u2103]<\/li>\n\n\n\n<li>COP<\/li>\n<\/ul>\n<\/div>\n<\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"927\" height=\"511\" src=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_1.png\" alt=\"Prediction of Temperature and Coefficient of Performance (COP) Using Multi-Sigma\u00ae Temperature COP\" class=\"wp-image-6084\" style=\"width:717px;height:auto\" srcset=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_1.png 927w, https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_1-300x165.png 300w\" sizes=\"auto, (max-width: 927px) 100vw, 927px\" \/><\/figure>\n<\/div>\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" style=\"font-size:30px;text-decoration:underline\"><strong>2. Contribution analysis of Temperature and Coefficient of Performance (COP) Using Multi-Sigma<sup>\u00ae<\/sup><\/strong><\/h2>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">The temperature was positively influenced by the heat source temperature and negatively influenced by the cooling source flow rate.<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">The COP was positively influenced by the cooling source flow rate and negatively influenced by the refrigerant composition ratio.<\/p>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"329\" src=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_2-1024x329.png\" alt=\"Factor Analysis of Temperature and Coefficient of Performance (COP) Using Multi-Sigma\u00ae Temperature COP\" class=\"wp-image-6085\" srcset=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_2-1024x329.png 1024w, https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_2-300x96.png 300w, https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_2.png 1254w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" style=\"font-size:30px;text-decoration:underline\"><strong>3. Tailor-Made Optimization Using Multi-Sigma<sup>\u00ae<\/sup><\/strong><\/h2>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Under the specified conditions of the target system (see note), multi-objective optimization was conducted with the aim of maximizing the COP at a temperature of 110\u2103 (\u00b10.1\u2103), resulting in the following optimal operating conditions: Under these conditions, a temperature of 110.03\u2103 and a COP of 6.22 were achieved.<\/p>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-right has-small-font-size wp-block-paragraph\">Note: Heat source flow rate: 344.1 ton\/h, Cooling source flow rate: 113.1 ton\/h,<br>Heat source temperature: 75\u00b0C                                                                   <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"203\" src=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_3-1024x203.png\" alt=\"Tailor-Made Optimization Using Multi-Sigma\u00ae Heat transfer\" class=\"wp-image-6086\" srcset=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_3-1024x203.png 1024w, https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_3-300x60.png 300w, https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_3.png 1681w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"alignright size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"783\" height=\"621\" src=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_4.png\" alt=\"Tailor-Made Optimization Using Multi-Sigma\u00ae Multi-objestive optimization\" class=\"wp-image-6087\" style=\"width:512px;height:auto\" srcset=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_4.png 783w, https:\/\/aizoth.com\/wp-content\/uploads\/2025\/07\/E013_4-300x238.png 300w\" sizes=\"auto, (max-width: 783px) 100vw, 783px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-text-align-left has-medium-font-size wp-block-paragraph\"><strong>A surrogate model capable of accurately predicting the behavior of complex heat pump systems was efficiently constructed by utilizing Multi-Sigma<sup>\u00ae<\/sup>, enabling easy implementation of factor analysis and multi-objective optimization. These results are expected to contribute to energy conservation and CO\u2082 reduction in both industrial and residential sectors.<\/strong><\/p>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-right wp-block-paragraph\">This usecase is based on results obtained from a project, JPNP14004, commissioned by the New Energy and Industrial Technology Development Organization (NEDO).<\/p>\n\n\n\n<p class=\"has-text-align-right has-small-font-size wp-block-paragraph\">Reference Material: NEDO Leading Research Program \/ Advanced Lorenz Cycle (ALC) Thermal Management Technology<br>(NEDO: New Energy and Industrial Technology Development Organization, a Japanese national R&amp;D agency under the Ministry of Economy, <br>Trade and Industry)<br>(1) <a href=\"https:\/\/www.nedo.go.jp\/content\/800019340.pdf\">https:\/\/www.nedo.go.jp\/content\/800019340.pdf<\/a><br>(2) <a href=\"https:\/\/www.nedo.go.jp\/content\/100974246.pdf\">https:\/\/www.nedo.go.jp\/content\/100974246.pdf<\/a><\/p>\n\n\n\n<div style=\"height:40px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-fe48e5de wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button has-custom-width wp-block-button__width-50 is-style-outline is-style-outline--1\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color has-medium-font-size has-custom-font-size wp-element-button\" href=\"https:\/\/aizoth.com\/en\/contact\/\" style=\"border-radius:100px;background-color:#ffe200\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Contact Us<\/strong><\/a><\/div>\n<\/div>\n\n\n\n<p class=\"has-text-align-center has-large-font-size 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