{"id":7546,"date":"2025-12-15T11:44:23","date_gmt":"2025-12-15T02:44:23","guid":{"rendered":"https:\/\/aizoth.com\/?post_type=use_case&#038;p=7546"},"modified":"2025-12-15T11:44:23","modified_gmt":"2025-12-15T02:44:23","slug":"contents-e022","status":"publish","type":"use_case","link":"https:\/\/aizoth.com\/en\/use_case\/contents-e022\/","title":{"rendered":"Exploring Robust Optimal Molding Conditionsfor PET Containers Using Multi-Sigma\u00ae"},"content":{"rendered":"\n<p class=\"has-medium-font-size wp-block-paragraph\"><strong>This case study developed a high-accuracy AI surrogate model from injection-molding simulation results for PET containers and successfully identified robust optimal solutions while accounting for noise factors.<\/strong><\/p>\n\n\n\n<div style=\"height:60px\" 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><strong>1. Building a Surrogate Model with 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>, this case study developed a high-accuracy surrogate model from PET injection-molding simulations and identified noise-robust optimal molding conditions.<br><\/p>\n\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=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"868\" height=\"606\" src=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_1_1.png\" alt=\"1. Building a Surrogate Model with Multi-Sigma\u00ae\" class=\"wp-image-7548\" style=\"width:619px;height:auto\" srcset=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_1_1.png 868w, https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_1_1-300x209.png 300w\" sizes=\"auto, (max-width: 868px) 100vw, 868px\" \/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"191\" src=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_1_2-1.png\" alt=\"1. Building a Surrogate Model with Multi-Sigma\u00ae\" class=\"wp-image-7650\" style=\"width:333px;height:auto\"\/><\/figure>\n<\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"911\" height=\"499\" src=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_1_3-1.png\" alt=\"1. Building a Surrogate Model with Multi-Sigma\u00ae\" class=\"wp-image-7649\" style=\"width:753px;height:auto\" srcset=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_1_3-1.png 911w, https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_1_3-1-300x164.png 300w\" sizes=\"auto, (max-width: 911px) 100vw, 911px\" \/><\/figure>\n<\/div>\n\n\n<div style=\"height:60px\" 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><strong>2. Contribution Analysis of Molding Conditions Using Multi-Sigma<sup>\u00ae<\/sup><\/strong><\/strong><\/h2>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Using the contribution-analysis feature, we quantitatively evaluated how each molding condition impacts warpage and strength, yielding the following findings:<\/p>\n\n\n\n<div class=\"kv\">\n  <div class=\"k\">Warpage:<\/div>\n  <div class=\"v\">increases with higher melt temperature\/<\/div>\n  <div class=\"k\"><\/div>\n  <div class=\"v\">decreases with higher ambient temperature.<\/div>\n<\/div>\n\n<style>\n  \/* \u3053\u306e<style>\u306f\u540c\u3058\u30ab\u30b9\u30bf\u30e0HTML\u30d6\u30ed\u30c3\u30af\u306b\u5165\u308c\u3066OK *\/\n  .kv{\n    display:grid;\n    grid-template-columns:max-content 1fr;\n    column-gap:.5em;\n    row-gap:.2em;\n    font-size:20px; \n  }\n  .k{white-space:nowrap}\n  .v{margin:0}\n<\/style>\n\n\n\n<div class=\"kv\">\n  <div class=\"k\">Strength:<\/div>\n  <div class=\"v\">increases with higher mold temperature\/<\/div>\n  <div class=\"k\"><\/div>\n  <div class=\"v\">decreases with higher melt temperature.<\/div>\n<\/div>\n\n<style>\n  \/* \u3053\u306e<style>\u306f\u540c\u3058\u30ab\u30b9\u30bf\u30e0HTML\u30d6\u30ed\u30c3\u30af\u306b\u5165\u308c\u3066OK *\/\n  .kv{\n    display:grid;\n    grid-template-columns:max-content 1fr;\n    column-gap:.5em;\n    row-gap:.2em;\n    font-size:20px; \n  }\n  .k{white-space:nowrap}\n  .v{margin:0}\n<\/style>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Notably, melt temperature emerged as the primary factor mediating the trade-off between these two properties, providing important insights for balanced design of molding conditions.<\/p>\n\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=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"516\" src=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_2.png\" alt=\"2. Contribution Analysis of Molding Conditions Using Multi-Sigma\u00ae\" class=\"wp-image-7551\" style=\"width:816px;height:auto\" srcset=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_2.png 960w, https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_2-300x161.png 300w\" sizes=\"auto, (max-width: 960px) 100vw, 960px\" \/><\/figure>\n<\/div>\n\n\n<div style=\"height:60px\" 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><strong>3. Exploration of Robust Optimal Solutions Using Multi-Sigma<sup>\u00ae<\/sup><\/strong><\/strong><\/h2>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Multi-Sigma<sup>\u00ae<\/sup> supports robust optimization by explicitly accounting for noise-factor variability. In this case study, because ambient temperature is hard to control, we model it as a noise factor, sweep 25\u201335 \u00b0C, and identify settings that satisfy the following performance criteria:<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Worst-case warpage \u2264 1.37 [mm]<br>Worst-case strength \u2265 71 [MPa]<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">These robust optimal molding conditions were derived by rapidly evaluating large numbers of scenarios using the Multi-Sigma<sup>\u00ae<\/sup> surrogate model.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"934\" height=\"805\" src=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_3-1.png\" alt=\"3. Exploration of Robust Optimal Solutions Using Multi-Sigma\u00ae\" class=\"wp-image-7553\" style=\"width:489px;height:auto\" srcset=\"https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_3-1.png 934w, https:\/\/aizoth.com\/wp-content\/uploads\/2025\/12\/E022_3-1-300x259.png 300w\" sizes=\"auto, (max-width: 934px) 100vw, 934px\" \/><\/figure>\n<\/div>\n\n\n<div style=\"height:60px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-small-font-size wp-block-paragraph\">Note 1\uff1a Note: The data used in this analysis is processed and edited based on the data published in the article below, under Creative Commons Attribution 4.0 International (CC BY 4.0) license.<br>Data source: Chen <em>et al.<\/em> (2023), <em>Processes<\/em>, 11:414. <a href=\"https:\/\/doi.org\/10.3390\/pr11020414\">https:\/\/doi.org\/10.3390\/pr11020414<\/a><br>Note 2: The strength data are synthetic, modeled on real world data.<\/p>\n\n\n\n<div style=\"height:100px\" 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