Closed-form Mathematical Models Research Articles

Fundamental limits to learning closed-form mathematical models from data

Given a finite and noisy dataset generated with a closed-form mathematical model, when is it possible to learn the true generating model from the data alone? This is the question we investigate here. We show that this model-learning problem displays a transition from a low-noise phase in which the true model can be learned, to a phase in which the observation noise is too high for the true model to be learned by any method. Both in the low-noise phase and in the high-noise phase, probabilistic model selection leads to optimal generalization to unseen data. This is in contrast to standard machine learning approaches, including artificial neural networks, which in this particular problem are limited, in the low-noise phase, by their ability to interpolate. In the transition region between the learnable and unlearnable phases, generalization is hard for all approaches including probabilistic model selection.

Remaining Useful Life Prediction of Bearings Using Ensemble Learning: The Impact of Diversity in Base Learners and Features

Abstract Prognostics and health management (PHM) of bearings is crucial for reducing the risk of failure and the cost of maintenance for rotating machinery. Model-based prognostic methods develop closed-form mathematical models based on underlying physics. However, the physics of complex bearing failures under varying operating conditions is not well understood yet. To complement model-based prognostics, data-driven methods have been increasingly used to predict the remaining useful life (RUL) of bearings. As opposed to other machine learning methods, ensemble learning methods can achieve higher prediction accuracy by combining multiple learning algorithms of different types. The rationale behind ensemble learning is that higher performance can be achieved by combining base learners that overestimate and underestimate the RUL of bearings. However, building an effective ensemble remains a challenge. To address this issue, the impact of diversity in base learners and extracted features in different degradation stages on the performance of ensemble learning is investigated. The degradation process of bearings is classified into three stages, including normal wear, smooth wear, and severe wear, based on the root-mean-square (RMS) of vibration signals. To evaluate the impact of diversity on prediction performance, vibration data collected from rolling element bearings was used to train predictive models. Experimental results have shown that the performance of the proposed ensemble learning method is significantly improved by selecting diverse features and base learners in different degradation stages.

Decision-facilitating information in hidden-action setups: an agent-based approach

The hidden-action model captures a fundamental problem of principal-agent theory and provides an optimal sharing rule when only the outcome but not the effort can be observed (Holmström in Bell J Econ 10(1):74, 1979). However, the hidden-action model builds on various explicit and also implicit assumptions about the information of the contracting parties. This paper relaxes key assumptions regarding the availability of information included in the hidden-action model in order to study whether and, if so, how fast the optimal sharing rule is achieved and how this is affected by the various types of information employed in the principal-agent relation. Our analysis particularly focuses on information about the environment and about feasible actions for the agent. We follow an approach to transfer closed-form mathematical models into agent-based computational models and show that the extent of information about feasible options to carry out a task only has an impact on performance if decision makers are well informed about the environment, and that the decision whether to perform exploration or exploitation when searching for new feasible options only affects performance in specific situations. Having good information about the environment, on the contrary, appears to be crucial in almost all situations.

A Comparative Study on Machine Learning Algorithms for Smart Manufacturing: Tool Wear Prediction Using Random Forests

Manufacturers have faced an increasing need for the development of predictive models that predict mechanical failures and the remaining useful life (RUL) of manufacturing systems or components. Classical model-based or physics-based prognostics often require an in-depth physical understanding of the system of interest to develop closed-form mathematical models. However, prior knowledge of system behavior is not always available, especially for complex manufacturing systems and processes. To complement model-based prognostics, data-driven methods have been increasingly applied to machinery prognostics and maintenance management, transforming legacy manufacturing systems into smart manufacturing systems with artificial intelligence. While previous research has demonstrated the effectiveness of data-driven methods, most of these prognostic methods are based on classical machine learning techniques, such as artificial neural networks (ANNs) and support vector regression (SVR). With the rapid advancement in artificial intelligence, various machine learning algorithms have been developed and widely applied in many engineering fields. The objective of this research is to introduce a random forests (RFs)-based prognostic method for tool wear prediction as well as compare the performance of RFs with feed-forward back propagation (FFBP) ANNs and SVR. Specifically, the performance of FFBP ANNs, SVR, and RFs are compared using an experimental data collected from 315 milling tests. Experimental results have shown that RFs can generate more accurate predictions than FFBP ANNs with a single hidden layer and SVR.

Design and Calibration of a Soft Multiple Degree of Freedom Motion Sensor System Based On Dielectric Elastomers

Abstract Soft robots use active deformable structures to provide highly capable yet simple and robust robotic systems. Motion sensors for soft robots must, therefore, be able to provide joint position sensing on deformable, multiple degrees of freedom (DOFs) joints often found in soft robot architectures and whose kinematics are not accurately described by closed-form mathematical models. This article proposes a method for designing dielectric elastomer sensor systems for such soft robots. The method is presented as a case study of a soft sensor system for an existing robotic manipulator designed for magnetic resonance image-guided surgery to the prostate. A calibration method based on support vector regression (SVR) is proposed to calibrate the coupled, multi-DOFs sensor system without a model. A prototype sensor system is built and is shown to reach a precision of 0.3 mm root mean square/1.2 mm maximum when calibrated with SVR. These results show sufficient precision for many applications and suggest th...

A Precise Indoor Localization Approach based on Particle Filter and Dynamic Exclusion Techniques

Indoor localization with a significant degree of precision is extremely challenging. In this paper, we present a precise indoor localization approach based on novel particle filter and dynamic exclusion techniques. The approach is compared with the Euclidean Distance probabilistic methods used for localization. The novelty of the proposed approach stems from its ability to fuse data collected from different sensor technologies to converge to more accurate distance estimation. Furthermore, the proposed approach is a pattern-based one that relies on empirical training data as opposed to closed-form mathematical models.

Investigation into the Response of Fully Clamped Circular Steel, Copper, and Aluminum Plates Subjected to Shock Loading

The plastic responses of clamped mild steel, copper, and aluminum circular plates subjected to blast loads are investigated. In this way, extensive experimental results concerning the variations of central deflection and natural strain distributions are presented. The effects of plate thickness, stand-off distance, and material properties on the mid-point deflection, on the deformation profile and on the natural strain distributions are considered. Moreover, the influence of impulse on the mid-point deflection and strain distribution are demonstrated. The applied impulse imparted to the plate was obtained from the recorded motion of the ballistic pendulum. Using the obtained experimental input-output data, closed form mathematical models based on nondimensional analysis and Singular Value Decomposition method have been found. The comparisons of the closed form mathematical models of this work with those in literature illustrate the robustness and the efficacy of this approach.

The use of metamodeling for VoIP over WiFi capacity evaluation [Transactions Letters

The increasing popularity of wireless fidelity (Wi-Fi) networks at home, in public areas and in the enterprise motivates extensive modeling and analysis of their performance measures, such as network capacity and quality of service (QoS) capabilities. Some of the easier performance problems can be solved by analytical modeling methods, but most of the complicated ones, involving several design parameters from multiple layers, can only be answered through simulation studies that are typically implicit and less suitable for design and optimization. Hence, we believe it is crucial to obtain explicit mathematic models, that are effective in representing system behavior and a basis for performance optimization. Here, we first advocate the application of formal empirical modeling techniques to performance studies of Wi-Fi networks, in order to find usable, if approximate, closed-form mathematical models. Subsequently, by applying these metamodeling techniques, we perform a case study with very useful results: our VoWiFi (voice over Wi-Fi) admission capacity metamodel gives a much tighter bound than those existing in the literature and leads to a more effective admission control scheme. Our work, therefore, points out a new direction for future performance studies of Wi-Fi networks.

Modeling and Control of Acoustic Ducts

This paper presents closed-form mathematical models for an acoustic duct with general boundary conditions. These infinite-dimensional models are derived using symbolic computations. A new method to obtain finite dimensional approximations of infinite-dimensional models using quartic functions is presented. The theoretical models are compared with the experimental data obtained for the KSU duct. The experimental results of a new robust broadband feedback controller, designed using passivity-based techniques, are presented. The controller design is shown to be robust to the unmodeled dynamics and parametric uncertainty.