In the past decade, relevance vector machines have gained the attention of many researchers, and this machine learning technique is a Bayesian sparse kernel method, both for classification and regression problems. In general, the choice of appropriate learning hyperparameters is a crucial step in obtaining a well-tuned model. To overcome this issue, we apply a self-adaptive differential evolution algorithm. In this paper, we propose a relevance vector machine for regression combined with a novel self-adaptive differential evolution approach for predictive modelling of phosphorus concentration levels in a steelmaking process with real data. We compared the performance of proposed relevance vector machine (RVM) with other machine learning techniques, such as random forest (RF), artificial neural network (ANN), K-nearest neighbors (K-NN), and also with statistical learning techniques as, Beta regression model and multiple linear regression model. The RVM has performance better than RF, ANN, K-NN, and statistical techniques used. Our study indicates that RVM models are an adequate tool for the prediction of the phosphorus concentration levels in the steelmaking process.

在过去的十年中，相关性向量机引起了许多研究人员的关注，并且这种机器学习技术是贝叶斯稀疏核方法，用于分类和回归问题。通常，选择适当的学习超参数是获得良好模型的关键步骤。为了克服这个问题，我们应用了自适应差分进化算法。在本文中，我们提出了一种用于回归的关联向量机，结合一种新颖的自适应微分演化方法，可利用真实数据对炼钢过程中的磷浓度水平进行预测建模。我们将提议的相关向量机（RVM）与其他机器学习技术（例如随机森林（RF），人工神经网络（ANN），K近邻（K-NN），以及统计学习技术，例如Beta回归模型和多元线性回归模型。RVM的性能优于所使用的RF，ANN，K-NN和统计技术。我们的研究表明，RVM模型是预测炼钢过程中磷浓度水平的合适工具。