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Recently, star variables and the post-crisis nature of cyclical fluctuations have attracted a great deal of interest. In this chapter, the authors investigate different methods of assessing business cycles (BCs) for the European Union in general and the euro area in particular. First, the authors conduct a Monte Carlo (MC) experiment using a broad spectrum of univariate trend-cycle decomposition methods. The simulation aims to examine the ability of the analysed methods to find the observed simulated cycle with structural properties similar to actual macroeconomic data. For the simulation, the authors used the structural model’s parameters calibrated to the euro area’s real gross domestic product (GDP) and unemployment rate. The simulation outcomes indicate the sufficient composition of the suite of models (SoM) consisting of popular Hodrick–Prescott, Christiano–Fitzgerald and structural trend-cycle-seasonal filters, then used for the real application. The authors find that: (i) there is a high level of model uncertainty in comparing the estimates; (ii) growth rate (acceleration) cycles have often the worst performances, but they could be useful as early-warning predictors of turning points in growth and BCs; and (iii) the best-performing MC approaches provide a reasonable combination as the SoM. When swings last less time and/or are smaller, it is easier to pick a good alternative method to the suite to capture the BC for real GDP. Second, the authors estimate the BCs for real GDP and unemployment data varying from 1995Q1 to 2020Q4 (GDP) or 2020Q3 (unemployment), ending up with 28 cycles per country. This analysis also confirms that the BCs of euro area members are quite synchronized with the aggregate euro area. Some major differences can be found, however, especially in the case of periphery and new member states, with the latter improving in terms of coherency after the global financial crisis. The German cycles are among the cyclical movements least synchronized with the aggregate euro area.

The purpose of this paper is to utilize document expansion techniques for improving image representation and retrieval. This paper proposes a concise framework for tag-based image retrieval (TBIR).

The proposed approach includes three core components: a strategy of selecting expansion (similar) images from the whole corpus (e.g. cluster-based or nearest neighbor-based); a technique for assessing image similarity, which is adopted for selecting expansion images (text, image, or mixed); and a model for matching the expanded image representation with the search query (merging or separate).

The results show that applying the proposed method yields significant improvements in effectiveness, and the method obtains better performance on the top of the rank and makes a great improvement on some topics with zero score in baseline. Moreover, nearest neighbor-based expansion strategy outperforms the cluster-based expansion strategy, and using image features for selecting expansion images is better than using text features in most cases, and the separate method for calculating the augmented probability P(q|R_D) is able to erase the negative influences of error images in R_D.

Despite these methods only outperform on the top of the rank instead of the entire rank list, TBIR on mobile platforms still can benefit from this approach.

Unlike former studies addressing the sparsity, vocabulary mismatch, and tag relatedness in TBIR individually, the approach proposed by this paper addresses all these issues with a single document expansion framework. It is a comprehensive investigation of document expansion techniques in TBIR.

The purpose of this study is to build a high accuracy thrust model under various small turbojet engine shaft speeds by using robust, ordinary, linear and nonlinear least squares estimation methods for target drone applications.

The dynamic shaft speeds from the test experiment of a target drone engine is conducted. Then, thrust values are calculated. Based on these, the engine thrust is modeled by robust linear and nonlinear equations. The models are benefited from quadratic, power and various series expansion functions with several coefficients to optimize the model parameters.

The error terms and accuracy of the model are given using sum of squared errors, root mean square error (RMSE) and R-squared (R²) error definitions. Based on the multiple analyses, it is seen that the RMSE values are no more than 17.7539 and the best obtained result for robust least squares estimation is 15.0086 for linear at all cases. Furthermore, the R² value is found to be 0.9996 as the highest with the nonlinear Fourier series expansion model.

The motivation behind this paper is to propose robust nonlinear thrust models based on power, Fourier and various series expansion functions for dynamic shaft speeds from the test experiments.

This paper presents an efficient methodology to calculate fuzzy eigenvalues and eigenvectors of finite element structures defined by imprecise parameters. The material and geometric parameters are then described by fuzzy numbers. The proposed methodology, based on α‐cut discretization of fuzzy numbers and Taylor's expansion, determines the extreme eigensolutions for each α‐cut. The study of a finite element model and the comparison of results with a combinatorial approach, based on Zadeh's extension principle, show the efficiency of this methodology.

This paper aims to present a new method, named as augmented polynomial dimensional decomposition (PDD) method, for robust design optimization (RDO) and reliability-based design optimization (RBDO) subject to mixed design variables comprising both distributional and structural design variables.

The method involves a new augmented PDD of a high-dimensional stochastic response for statistical moments and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms.

New closed-form formulae are presented for the design sensitivities of moments that are simultaneously determined along with the moments. A finite-difference approximation integrated with the embedded Monte Carlo simulation of the augmented PDD is put forward for design sensitivities of the failure probability.

In conjunction with the multi-point, single-step design process, the new method provides an efficient means to solve a general stochastic design problem entailing mixed design variables with a large design space. Numerical results, including a three-hole bracket design, indicate that the proposed methods provide accurate and computationally efficient sensitivity estimates and optimal solutions for RDO and RBDO problems.

To present the models with many model parameters by polynomial chaos expansion (PCE), and improve the accuracy, this paper aims to present dimension-adaptive algorithm-based PCE technique and verify the feasibility of the proposed method through taking solid rocket motor ignition under low temperature as an example.

The main approaches of this work are as follows: presenting a two-step dimension-adaptive algorithm; through computing the PCE coefficients using dimension-adaptive algorithm, improving the accuracy of PCE surrogate model obtained; and applying the proposed method to uncertainty quantification (UQ) of solid rocket motor ignition under low temperature to verify the feasibility of the proposed method.

The result indicates that by means of comparing with some conventional non-invasive method, the proposed method is able to raise the computational accuracy significantly on condition of meeting the efficiency requirement.

This paper proposes an approach in which the optimal non-uniform grid that can avoid the issue of overfitting or underfitting is obtained.

This paper aims to propose a simple, derivative-free novel method named as Nelder–Mead optimization algorithm to estimate the unknown parameters of the photovoltaic (PV) module considering the environmental conditions.

At a particular temperature and irradiation, experimental current-voltage (I-V) and power-voltage (P-V) characteristics are drawn and considered as a reference model. The PV system model with unknown model parameters is considered as the adaptive model whose unknown model parameters are to be adapted so that the simulated characteristics closely matches with the experimental characteristics. A single diode (Rsh) model with five unknown model parameters is considered here for the parameter estimation.

The key advantages of this method are that parameters are estimated considering environmental conditions. Experimental characteristics are considered for parameter estimation which gives accurate results. Parameters are estimated considering both I-V and P-V curves as most of the applications demand extraction of the actual power from the PV module.

The proposed model is compared with other three well-known models available in the literature considering various statistical errors. The results show the superiority of the proposed model with a minimum error for both I-V and P-V characteristics.

Tolerance analysis is a very important tool for chip design in the microelectronics industry. The usual method for tolerance analysis is Monte Carlo simulation, which, however, is extremely CPU intensive, because in order to yield statistically significant results, it needs to generate a large sample of function values. Here we report on another method, recently introduced in several fields, called stochastic response surface method, which might be a viable alternative to Monte Carlo simulation for some classes of problems. The application considered here is on the tolerance analysis of the current of a submicrometer n⁺‐n‐n⁺ diode as a function of the channel length and the channel doping. The numerical simulator for calculating the current is based on the energy transport hydrodynamical model introduced by Stratton, which is one of the most widely used in this field.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion). The dynamic model of VSI-PMSMs is multivariable and exhibits complicated nonlinear dynamics. The inverters’ currents, which are generated through a pulsewidth modulation process, are used to control the stator currents of the PMSM, which in turn control the rotational speed of this electric machine. So far, several nonlinear control schemes for VSI-PMSMs have been developed, having as primary objectives the precise tracking of setpoints by the system’s state variables and robustness to parametric changes or external perturbations. However, little has been done for the solution of the associated nonlinear optimal control problem. The purpose of this study/paper is to provide a novel nonlinear optimal control method for VSI-fed three-phase PMSMs.

The present article proposes a nonlinear optimal control approach for VSI-PMSMs. The nonlinear dynamic model of VSI-PMSMs undergoes approximate linearization around a temporary operating point, which is recomputed at each iteration of the control method. This temporary operating point is defined by the present value of the voltage source inverter-fed PMSM state vector and by the last sampled value of the motor’s control input vector. The linearization relies on Taylor series expansion and the calculation of the system’s Jacobian matrices. For the approximately linearized model of the voltage source inverter-fed PMSM, an H-infinity feedback controller is designed. For the computation of the controller’s feedback gains, an algebraic Riccati equation is iteratively solved at each time-step of the control method. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control for this system, the H-infinity Kalman filter is proposed as a state observer. The proposed control method achieves fast and accurate tracking of the reference setpoints of the VSI-fed PMSM under moderate variations of the control inputs.

The proposed H-infinity controller provides the solution to the optimal control problem for the VSI-PMSM system under model uncertainty and external perturbations. Actually, this controller represents a min–max differential game taking place between the control inputs, which try to minimize a cost function that contains a quadratic term of the state vector’s tracking error, the model uncertainty, and exogenous disturbance terms, which try to maximize this cost function. To select the feedback gains of the stabilizing feedback controller, an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. To analyze the stability properties of the control scheme, the Lyapunov method is used. It is proven that the VSI-PMSM loop has the H-infinity tracking performance property, which signifies robustness against model uncertainty and disturbances. Moreover, under moderate conditions, the global asymptotic stability properties of this control scheme are proven. The proposed control method achieves fast tracking of reference setpoints by the VSI-PMSM state variables, while keeping also moderate the variations of the control inputs. The latter property indicates that energy consumption by the VSI-PMSM control loop can be minimized.

The proposed nonlinear optimal control method for the VSI-PMSM system exhibits several advantages: Comparing to global linearization-based control methods, such as Lie algebra-based control or differential flatness theory-based control, the nonlinear optimal control scheme avoids complicated state variable transformations (diffeomorphisms). Besides, its control inputs are applied directly to the initial nonlinear model of the VSI-PMSM system, and thus inverse transformations and the related singularity problems are also avoided. Compared with backstepping control, the nonlinear optimal control scheme does not require the state-space description of the controlled system to be found in the triangular (backstepping integral) form. Compared with sliding-mode control, there is no need to define in an often intuitive manner the sliding surfaces of the controlled system. Finally, compared with local model-based control, the article’s nonlinear optimal control method avoids linearization around multiple operating points and does not need the solution of multiple Riccati equations or LMIs. As a result of this, the nonlinear optimal control method requires less computational effort.

Voltage source inverter-fed permanent magnet synchronous motors (VSI-PMSMs) are widely used in industrial actuation and mechatronic systems in water pumping stations, as well as in the traction of transportation systems (such as electric vehicles and electric trains or ships with electric propulsion), The solution of the associated nonlinear control problem enables reliable and precise functioning of VSI-fd PMSMs. This in turn has a positive impact in all related industrial applications and in tasks of electric traction and propulsion where VSI-fed PMSMs are used. It is particularly important for electric transportation systems and for the wide use of electric vehicles as expected by green policies which aim at deploying electromotion and at achieving the Net Zero objective.

Unlike past approaches, in the new nonlinear optimal control method, linearization is performed around a temporary operating point, which is defined by the present value of the system’s state vector and by the last sampled value of the control input vector and not at points that belong to the desirable trajectory (setpoints). Besides, the Riccati equation, which is used for computing the feedback gains of the controller, is new, as is the global stability proof for this control method. Comparing with nonlinear model predictive control, which is a popular approach for treating the optimal control problem in industry, the new nonlinear optimal (H-infinity) control scheme is of proven global stability, and the convergence of its iterative search for the optimum does not depend on initial conditions and trials with multiple sets of controller parameters. It is also noteworthy that the nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations (SDRE). The SDRE approaches can be applied only to dynamical systems that can be transformed to the linear parameter varying form. Besides, the nonlinear optimal control method performs better than nonlinear optimal control schemes which use approximation of the solution of the Hamilton–Jacobi–Bellman equation by Galerkin series expansions.

Given the regional heterogeneity of economic development, electricity consumption in various regions exhibits a discrepant growth pattern. The purpose of this study is to construct a grey system forecasting model with intelligent parameters for predicting provincial electricity consumption in China.

First, parameter optimization and structural expansion are simultaneously integrated into a unified grey system prediction framework, enhancing its adaptive capabilities. Second, by setting the minimum simulation percentage error as the optimization goal, the authors apply the particle swarm optimization (PSO) algorithm to search for the optimal grey generation order and background value coefficient. Third, to assess the performance across diverse power consumption systems, the authors use two electricity consumption cases and select eight other benchmark models to analyze the simulation and prediction errors. Further, the authors conduct simulations and trend predictions using data from all 31 provinces in China, analyzing and predicting the development trends in electricity consumption for each province from 2021 to 2026.

The study identifies significant heterogeneity in the development trends of electricity consumption systems among diverse provinces in China. The grey prediction model, optimized with multiple intelligent parameters, demonstrates superior adaptability and dynamic adjustment capabilities compared to traditional fixed-parameter models. Outperforming benchmark models across various evaluation indicators such as root mean square error (RMSE), average percentage error and Theil’s index, the new model establishes its robustness in predicting electricity system behavior.

Acknowledging the limitations of traditional grey prediction models in capturing diverse growth patterns under fixed-generation orders, single structures and unadjustable background values, this study proposes a fractional grey intelligent prediction model with multiple parameter optimization. By incorporating multiple parameter optimizations and structure expansion, it substantiates the model’s superiority in forecasting provincial electricity consumption.