# A Review on Vibration-Based Condition Monitoring of Rotating Machinery
## 4 Analytical Review
### Category p3: Diagnostics
[PERSON] and [PERSON] in 2020 [227] present a vibration-based ML model (VML), with a multi-layered perceptron (MLP) network, four hidden layers and each of them with a variable quantity of nonlinear neuron, applied to the fault diagnosis of a test rig, demonstrating the robustness in the prediction capabilities of the method, even when blindly applied to machine data from the different operating condition. ANNs have shown, in a varied number of works in the past and even today, their effectiveness for carrying out classification tasks aimed at diagnostics; however, recently, the attention has shifted more towards DNNs techniques, as the performed analysis (Table 4) demonstrated. It is also noted that the work relating to DNNs is mainly concentrated in the last three years and principally applied to rolling bearings diagnostics. A more flexible structure, better adaptability, and stronger learning ability are the main advantages of DNNs compared with ANNs, and the high number of hidden layers with non-linear transformation allows a powerful ability in vibration signals features learning. A variety of models are proposed for fault diagnosis and, among these, convolutional models (CNNs) have become one of the most popular deep learning methods because they support diverse input data, not only vectors, e.g., images. Some examples applied to rolling bearing diagnostics are: MIMNTet, a CNN with multi-dimensional signal inputs and multi-dimensional task outputs, proposed by [PERSON] et al. in 2021 [233]; the CNN and transfer learning (TL) based fault diagnosis method proposed by [PERSON] et al. in 2021 [234]; a one-dimensional-CNN and a dilated CNN, obtained through the combination between a CNN and an automatic hyper-parametric optimization, proposed by [PERSON] et al. in 2020 [238]. The deep morphological CNN (DMCNet), where a morphological filter is used to implement noise reduction and impulsive component extraction, and the multiscale CNN (MSCNN), with a novel morphological layer is smoothly embedded in DNN as a signal processing layer to extract impulses and filter out the noise, were presented by [PERSON] and [PERSON] in 2021, in [244,245], respectively; a multi-channels DCNN (MC-DCNN) was described by [PERSON] et al. [246], with a high definition 1D image of raw three axes accelerometer signals as input, and the deep capsule network with stochastic delta rule (DCN-SDR) was presented by [PERSON] et al. in 2019 [269]. Support vector machines (SVMs) form another significant class of ML methods often used in fault detection, to perform regression or classification, based on the identification of support vectors, which maximize the distance between decision hyperplanes and closest data points [27]. They can be used even in presence of data that cannot be linearly separated; in these cases, SVMs use kernel transformations to make data linearly separable. Different kernels can be used, such as linear, polynomial, and Gaussian kernels. The hypersphere support vector machine, used in the case of linear indivisibility, is based on a nonlinear mapping of training samples from the original space to a high-dimension feature space [220]. In addition to the models that fall into these three main classes, there are ML models based on the methods K-nearest-neighbor (KNN), decision trees (DTs), fuzzy predictive models, random forest. Hybrid solutions, e.g., classifier based on SVMs and ANNs [25] or neuro-fuzzy models have been investigated. Furthermore, in some studies, multi-sensor-based approaches are used (for example by combining vibration and sound measurements),using data fusion methods. [PERSON] et al. in [259] examine the fusion of the SVMs, ANNs, and D-S evidence theory classifiers. A classification accuracy comparison among four different models afferent to the classes ANNs, KNN, DTs and SVMs was developed by [PERSON] and [PERSON] in 2019 [217], and SVM reports the best classification outcomes.