Theoretical investigation of intrinsic point defects and the oxygen migration behavior in rare earth hafnates

In this work, the composition-dependent point defect types and formation energies of RE₂Hf₂O₇ (RE = La, Ce, Pr, Nd, Pm, Sm, Eu and Gd) as well as the oxygen diffusion behavior are systematically investigated by first-principles calculations. The possible defect reactions and dominant defect complexes under stoichiometric and non-stoichiometric conditions are revealed. It is found that O Frenkel pairs are the predominant defect in stoichiometric pyrochlore hafnates. Hf-RE cation anti-site defects, accompanied by RE vacancies and/or oxygen interstitials, are stable in the non-stoichiometric case of HfO₂ excess. On the other hand, RE-Hf anti-site defects together with oxygen vacancies and/or RE interstitials are preferable in the case of RE₂O₃ excess. The energy barriers for the migration along the V_O48f - V_O48f pathway of pyrochlore hafnates were calculated to be between 0.81 eV and 0.89 eV. Based on these results, a defect engineering strategy is proposed and the pyrochlore hafnates investigated here are predicted to exhibit potential oxygen ionic conductivity.     

Machine fault diagnosis with small sample based on variational information constrained generative adversarial network

In actual engineering scenarios, limited fault data leads to insufficient model training and over-fitting, which negatively affects the diagnostic performance of intelligent diagnostic models. To solve the problem, this paper proposes a variational information constrained generative adversarial network (VICGAN) for effective machine fault diagnosis. Firstly, by incorporating the encoder into the discriminator to map the deep features, an improved generative adversarial network with stronger data synthesis capability is established. Secondly, to promote the stable training of the model and guarantee better convergence, a variational information constraint technique is utilized, which constrains the input signals and deep features of the discriminator using the information bottleneck method. In addition, a representation matching module is added to impose restrictions on the generator, avoiding the mode collapse problem and boosting the sample diversity. Two rolling bearing datasets are utilized to verify the effectiveness and stability of the presented network, which demonstrates that the presented network has an admirable ability in processing fault diagnosis with few samples, and performs better than state-of-the-art approaches.     

Output-relevant Variational autoencoder for Just-in-time soft sensor modeling with missing data

Main challenges for developing data-based models lie in the existence of high-dimensional and possibly missing observations that exist in stored data from industry process. Variational autoencoder (VAE) as one of the deep learning methods has been applied for extracting useful information or features from high-dimensional dataset. Considering that existing VAE is unsupervised, an output-relevant VAE is proposed for extracting output-relevant features in this work. By using correlation between process variables, different weight is correspondingly assigned to each input variable. With symmetric Kullback–Leibler (SKL) divergence, the similarity is evaluated between the stored samples and a query sample. According to the values of the SKL divergence, data relevant for modeling are selected. Subsequently, Gaussian process regression (GPR) is utilized to establish a model between the input and the corresponding output at the query sample. In addition, owing to the common existence of missing data in output data set, the parameters and missing data in the GPR are estimated simultaneously. A practical debutanizer industrial process is utilized to illustrate the effectiveness of the proposed method.     

Semirigid inclusions in elastic bodies: Mechanical interplay and optimal control

The paper concerns an analysis of an equilibrium problem for 2D elastic body with two semirigid inclusions. It is assumed that inclusions have a joint point, and we investigate a junction problem for these inclusions. The existence of solutions is proved, and different equivalent formulations of the problem are proposed. We investigate a convergence to infinity of a rigidity parameter of the semirigid inclusion. It is proved that in the limit, we obtain an equilibrium problem for the elastic body with a rigid inclusion and a semirigid one. A parameter identification problem is investigated. In particular, the existence of a solution to a suitable optimal control problem is proved.     

Single-Crystalline TiO2(B) Nanobelts with Unusual Large Exposed {100} Facets and Enhanced Li-Storage Capacity

The {100} facet of single-crystalline TiO₂(B) is an ideal platform for inserting Li ions, but it is hard to be obtained due to its high surface energy. Here, the single-crystalline TiO₂(B) nanobelts from H₂Ti₃O₇ with nearly 70% {100} facets exposed are synthesized, which significantly enhances Li-storage capacity. The first-principle calculations demonstrate an ab in-plane 2D diffusion through the exposed {100} facets. As a consequence, the nanobelts can significantly accommodate Li ions in LiTiO₂ formula with specific capacity up to 335 mAh g⁻¹, which is in good agreement with the electrochemical characterizations. Coating with conductive and protective poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate), the cut-off discharge voltage is as low as 0.5 V, leading to a capacity of 160.7 mAh g⁻¹ after 1500 cycles with a retention rate of 66% at 1C. This work provides a practical strategy to increase the Li-ion capacity and cycle stability by tailoring the crystal orientation and nanostructures.     

An iterative method for suboptimal control of linear time-delayed systems

This article presents a new approach for solving the Optimal Control Problem (OCP) of linear time-delay systems with a quadratic cost functional. The proposed method can also be used for designing optimal control time-delay systems with disturbance. In this study, the Variational Iteration Method (VIM) is employed to convert the original Time-Delay Optimal Control Problem (TDOCP) into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Finally, Illustrative examples are included to demonstrate the validity and applicability of the technique.     

Optimal Control of the Primary Drying Stage of Freeze Drying of Solutions in Vials Using Variational Calculus

The problem of operating freeze drying of pharmaceutical products in vials placed in trays of a freeze dryer to remove free water (in frozen state) at a minimum time was formulated as an optimal control problem. Two different types of freeze dryer designs were considered. In type I freeze dryer design, upper and lower plate temperatures were controlled together, while in type II freeze dryer design, upper and lower plate temperatures were controlled independently. The heat input to the material being dried and the drying chamber pressure were considered as control variables. Constraints were placed on the system state variables by the melting and scorch temperatures during primary drying stage. Necessary conditions of optimality for the primary drying stage of freeze drying process in vials are derived and presented. Furthermore, an approach for constructing the optimal control policies that would minimize the drying time for the primary drying stage was given. In order to analyze optimal control policy for the primary drying stage of the freeze-drying process in vials, a rigorous multi-dimensional unsteady state mathematical model was used. The theoretical approach presented in this work was applied in the freeze drying of skim milk. Significant reductions in the drying times of primary drying stage of freeze drying process in vials were obtained, as compared to the drying times obtained from conventional operational policies.     

On regional nonlinear H-filtering

The structure of the nonlinear H^∞-filter in the neighborhood of the estimated trajectory is investigated and a bound on the size of the neighborhood that allows this structure is determined, both for finite and infinite horizons. Riccati inequalities that depend on the estimated trajectory are derived for finding the filter gain matrix and an algorithm for calculating the bound on the size of the above neighborhood is presented. Explicit formulas are obtained in the infinite horizon case for the minimum achievable disturbance attenuation level, the size of the neighborhood, and the corresponding filter gain.     

Minimum spanning trees made easier via multi-objective optimization

Many real-world problems are multi-objective optimization problems and evolutionary algorithms are quite successful on such problems. Since the task is to compute or approximate the Pareto front, multi-objective optimization problems are considered as more difficult than single-objective problems. One should not forget that the fitness vector with respect to more than one objective contains more information that in principle can direct the search of evolutionary algorithms. Therefore, it is possible that a single-objective problem can be solved more efficiently via a generalized multi-objective model of the problem. That this is indeed the case is proved by investigating the computation of minimum spanning trees.This work was supported by the Deutsche Forschungsgemeinschaft (DFG) as part of the Collaborative Research Center Computational Intelligence (SFB 531) and by the German-Israeli Foundation (GIF) in the project Robustness Aspects of Algorithms.     

Hybrid Approach for Addressing Uncertainty in Risk Assessments

Parameter uncertainty is a major aspect of the model-based estimation of the risk of human exposure to pollutants. The Monte Carlo method, which applies probability theory to address model parameter uncertainty, relies on a statistical representation of available information. In recent years, other uncertainty theories have been proposed as alternative approaches to address model parameter uncertainty in situations where available information is insufficient to identify statistically representative probability distributions, due in particular to data scarcity. The simplest such theory is possibility theory, which uses so-called fuzzy numbers to represent model parameter uncertainty. In practice, it may occur that certain model parameters can be reasonably represented by probability distributions, because there are sufficient data available to substantiate such distributions by statistical analysis, while others are better represented by fuzzy numbers (due to data scarcity). The question then arises as to how these two modes of representation of model parameter uncertainty can be combined for the purpose of estimating the risk of exposure. This paper proposes an approach (termed a hybrid approach) which combines Monte Carlo random sampling of probability distribution functions with fuzzy calculus. The approach is applied to a real case of estimation of human exposure, via vegetable consumption, to cadmium present in the surficial soils of an industrial site located in the north of France. The application illustrates the potential of the proposed approach, which allows the uncertainty affecting model parameters to be represented in a way that is consistent with the information at hand. Also, because the hybrid approach takes advantage of the “rich” information provided by probability distributions, while retaining the conservative character of fuzzy calculus, it is believed to hold value in terms of a “reasonable” application of the precautionary principle.