Abstract

Abstract

Abstract
In this paper, we explore the use of reference values (predictors) for the optimal objective function value of hard combinatorial optimization problems, instead of bounds, obtained by data mining techniques, and that may be used to assess the quality of heuristic solutions for the problem. With this purpose, we resort to the rectangular two-dimensional strip-packing problem (2D-SPP), which can be found in many industrial contexts. Mostly this problem is solved by heuristic methods, which provide good solutions. However, heuristic approaches do not guarantee optimality, and lower bounds are generally used to give information on the solution quality, in particular, the area lower bound. But this bound has a severe accuracy problem. Therefore, we propose a data mining-based framework capable of assessing the quality of heuristic solutions for the 2D-SPP. A regression model was fitted by comparing the strip height solutions obtained with the bottom-left-fill heuristic and 19 predictors provided by problem characteristics. Random forest was selected as the data mining technique with the best level of generalisation for the problem, and 30,000 problem instances were generated to represent different 2D-SPP variations found in real-world applications. Height predictions for new problem instances can be found in the regression model fitted. In the computational experimentation, we demonstrate that the data mining-based framework proposed is consistent, opening the doors for its application to finding predictions for other combinatorial optimisation problems, in particular, other cutting and packing problems. However, how to use a reference value instead of a bound, has still a large room for discussion and innovative ideas. Some directions for the use of reference values as a stopping criterion in search algorithms are also provided. © 2018 Elsevier Ltd

Abstract

Abstract

Abstract
This paper proposes the linear frequency cepstral coefficients as highly discriminative features for anomaly detection in ball bearings using vibration sensor data. These features are based on cepstral analysis and are capable of encoding the patterns of a spectral magnitude profile. Incipient damages on bearings can grow rapidly under normal use resulting in vibration and harsh noise. If left undetected, this damage will worsen, leading to high maintenance costs or even injury. Multiple interferences in an industrial environment contaminate the signal, making it a challenge to correctly identify the bearings’ condition. Many studies have attempted to overcome this issue at the signal level. However, the discriminative capacity of the current vibration signal features is still vulnerable to interference, which motivates this work. In order to demonstrate the benefits of these features, we (1) show that they are computationally efficient and suitable for real-time incremental training; (2) conduct discriminative analysis by evaluating the separability performance and comparing it with the state of the art; and (3) test the robustness of the proposed features under noise interference, which is ideal for use in the harsh operating conditions of industrial machinery. The data was obtained from a laboratory workbench setting that reproduces bearing fault scenarios. Results show that the proposed features are fast, competitive when compared to state-of-the-art features, and resilient to high levels of interference. Despite the higher performance when using the quadratic model, the proposed features remain highly discriminative when used with several other discriminant function. © 2019, Springer-Verlag London Ltd., part of Springer Nature.