The Log-Asset Dynamic with Euler–Maruyama Scheme under Wishart Processes

This article deals with Wishart process which is defined as matrix generalization of a squared Bessel process. We consider a single risky asset pricing model whose volatility is described by Wishart affine diffusion processes. The multifactor volatility specification enables this model to be flexible enough to describe the market prices for short or long maturities. The aim of the study is to derive the log-asset returns dynamic under the double Wishart stochastic volatility model. The corrected Euler–Maruyama discretization technique is applied in order to obtain the numerical solution of the log-asset return dynamic under Bi-Wishart processes. The numerical examples show the effect of the model parameters on the asset returns under the double Wishart volatility model.

Bayesian network-based root cause analysis and fault pathway identification in complex industrial processes

Real-time root cause identification (RCI) of faults or abnormal events in industries gives plant personnel the opportunity to address the faults before they progress and lead to failure. RCI in industrial systems must deal with their complex behavior, variable interactions, corrective actions of control systems and variability in faulty behavior. Bayesian networks (BNs) is a data-driven graph-based method that utilizes multivariate sensor data generated during industrial operations for RCI. Bayesian networks, however, require data discretization if data contains both discrete and continuous variables. Traditional discretization techniques such as equal width (EW) or equal frequency (EF) discretization result in loss of dynamic information and often lead to erroneous RCI. To deal with this limitation, we propose the use of a dynamic discretization technique called Bayesian Blocks (BB) which adapts the bin sizes based on the properties of data itself. In this work, we compare the effectiveness of three discretization techniques, namely EW, EF and BB coupled with Bayesian Networks on generation of fault propagation (causal) maps and root cause identification in complex industrial systems. We demonstrate the performance of the three methods on the industrial benchmark Tennessee-Eastman (TE) process. For two complex faults in the TE process, the BB with BN method successfully diagnosed correct root causes of the faults, and reduced redundancy (up to 50%) and improved the propagation paths in causal maps compared to other two techniques.

An Approach to Acquire the Constraints Using Panel Big Data Hybrid Association Rule and Discretization Process for Breast Cancer Prediction

In recent years, big data has become an important branch of computer science. However, without AI, it is difficult to dive into the context of data as a prediction term, relying on a large feature of improving the process of prediction is connected with big data modelling, which appears to be a significant aspect of improving the process of prediction. Accordingly, one of the basic constructions of the big data model is the rule-based method. Rule-based method is used to discover and utilize a set of association rules that collectively represent the relationships identified by the system. This work focused on the use of the Apriori algorithm for the investigations of constraints from panel data using the discretization preprocess technique. The statistical outcomes are associated with the improved preprocess that can be applied over the transaction and it can illustrate interesting rules with confidence approximately equal to one. The minimum support provided to the present rule considers constraint as a milestone for the prediction model. The model makes an effective and accurate decision. In nowadays business, several guidelines have been produced. Moreover, the generation method was upgraded because of an association data algorithm that works for dissimilar principles of the structures compared with fewer breaks that are delivered by the discretization technique.

Coupled topology and shape optimization using an embedding domain discretization method

Density-based topology optimization and node-based shape optimization are often used sequentially to generate production-ready designs. In this work, we address the challenge to couple density-based topology optimization and node-based shape optimization into a single optimization problem by using an embedding domain discretization technique. In our approach, a variable shape is explicitly represented by the boundary of an embedded body. Furthermore, the embedding domain in form of a structured mesh allows us to introduce a variable, pseudo-density field. In this way, we attempt to bring the advantages of both topology and shape optimization methods together and to provide an efficient way to design fine-tuned structures without predefined topological features.

An Improved Algorithm to Predict the Pose-dependent Cutting Stability in Robot Milling

Chattering is one of the most important factors affecting productivity of robot machining. This paper investigates the pose-dependent cutting stability of a 5-DOF hybrid robot. By merging the complete robot structural dynamics with the cutting force at TCP, an effective approach for stability analysis of the robot milling process is proposed using the full-discretization technique. The proposed method enables the computational efficiency to be significantly improved because the system transition matrix can be simply generated using a sparse matrix multiplication. Both simulation and experimental results on a full size prototype machine show that the stability lobes are highly pose-dependent and primarily dominated by the lower-order structural modes.

Two Efficient Time-Marching Explicit Procedures Considering Spatially/Temporally-Defined Adaptive Time-Integrators

In this paper, two explicit time-marching techniques are discussed for the solution of hyperbolic models, which are based on adaptively computed parameters. In both these techniques, time integrators are locally and automatically evaluated, taking into account the properties of the spatially/temporally discretized model and the evolution of the computed responses. Thus, very versatile solution techniques are enabled, which allows computing highly accurate responses. Here, the so-called adaptive [Formula: see text] method is formulated based on the elements of the adopted spatial discretization (elemental formulation), whereas the so-called adaptive [Formula: see text] method is formulated based on the degrees of freedom of the discretized model (nodal formulation). In this context, each adaptive procedure can be better applied according to the specific features of the focused spatial discretization technique. At the end of the paper, numerical results are presented, illustrating the excellent performance of the discussed adaptive formulations.

Weak entropy solutions to a model in induction hardening, existence and weak-strong uniqueness

In this paper, we investigate a model describing induction hardening of steel. The related system consists of an energy balance, an ordinary differential equation (ODE) for the different phases of steel, and Maxwell’s equations in a potential formulation. The existence of weak entropy solutions is shown by a suitable regularization and discretization technique. Moreover, we prove the weak-strong uniqueness of these solutions, i.e. that a weak entropy solutions coincides with a classical solution emanating form the same initial data as long as the classical one exists. The weak entropy solution concept has advantages in comparison to the previously introduced weak solutions, e.g. it allows to include free energy functions with low regularity properties corresponding to phase transitions.

Optimal State Control of Fractional Order Differential Systems: The Infinite State Approach

Optimal control of fractional order systems is a long established domain of fractional calculus. Nevertheless, it relies on equations expressed in terms of pseudo-state variables which raise fundamental questions. So in order remedy these problems, the authors propose in this paper a new and original approach to fractional optimal control based on a frequency distributed representation of fractional differential equations called the infinite state approach, associated with an original formulation of fractional energy, which is intended to really control the internal system state. In the first step, the fractional calculus of variations is revisited to express appropriate Euler Lagrange equations. Then, the quadratic optimal control of fractional linear systems is formulated. Thanks to a frequency discretization technique, the previous theoretical equations are converted into an equivalent large dimension integer order system which permits the implementation of a feasible optimal solution. A numerical example illustrates the validity of this new approach.