{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T05:02:37Z","timestamp":1779253357826,"version":"3.51.4"},"reference-count":22,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,15]],"date-time":"2022-01-15T00:00:00Z","timestamp":1642204800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["Grant 2017YFB0304100"],"award-info":[{"award-number":["Grant 2017YFB0304100"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Grant 71672032"],"award-info":[{"award-number":["Grant 71672032"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for Central University","award":["Grant N2005011"],"award-info":[{"award-number":["Grant N2005011"]}]},{"name":"Scientific Research Funds of Educational Department of Liaoning Province","award":["Grant LT2020008"],"award-info":[{"award-number":["Grant LT2020008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>With the improvement of industrial requirements for the quality of cold rolled strips, flatness has become one of the most important indicators for measuring the quality of cold rolled strips. In this paper, the strip production data of a 1250 mm tandem cold mill in a steel plant is modeled by an improved deep neural network (the improved DNN) to improve the accuracy of strip shape prediction. Firstly, the type of activation function is analyzed, and the monotonicity of the activation function is deemed independent of the convexity of the loss function in the deep network. Regardless of whether the activation function is monotonic, the loss function is not strictly convex. Secondly, the non-convex optimization of the loss functionextended from the deep linear network to the deep nonlinear network, is discussed, and the critical point of the deep nonlinear network is identified as the global minimum point. Finally, an improved Swish activation function based on batch normalization is proposed, and its performance is evaluated on the MNIST dataset. The experimental results show that the loss of an improved Swish function is lower than that of other activation functions. The prediction accuracy of a deep neural network (DNN) with an improved Swish function is 0.38% more than that of a deep neural network (DNN) with a regular Swish function. For the DNN with the improved Swish function, the mean square error of the prediction for the flatness of cold rolled strip is reduced to 65% of the regular DNN. The accuracy of the improved DNN is up to and higher than the industrial requirements. The shape prediction of the improved DNN will assist and guide the industrial production process, reducing the scrap yield and industrial cost.<\/jats:p>","DOI":"10.3390\/s22020656","type":"journal-article","created":{"date-parts":[[2022,1,16]],"date-time":"2022-01-16T20:45:21Z","timestamp":1642365921000},"page":"656","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Flatness Prediction of Cold Rolled Strip Based on Deep Neural Network with Improved Activation Function"],"prefix":"10.3390","volume":"22","author":[{"given":"Jingyi","family":"Liu","sequence":"first","affiliation":[{"name":"College of Sciences, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuni","family":"Song","sequence":"additional","affiliation":[{"name":"College of Sciences, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiayi","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Sciences, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4546-818X","authenticated-orcid":false,"given":"Maimutimin","family":"Balaiti","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nina","family":"Song","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sen","family":"Li","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,15]]},"reference":[{"key":"ref_1","unstructured":"Wang, P. 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