Genetic optimization for engine combustion system calibration: A case study of optimization performance sensitivity to algorithm search parameters

The use of genetic optimization algorithms (GOA) has been shown to significantly reduce the resource intensity of engine calibration, motivating investigation into the development of these methods. The objective of this work was to quantify the sensitivity of GOA performance to the algorithm search parameter values, in a case study of engine calibration. A GOA was used to calibrate four combustion system control parameters for a direct-injection gasoline engine at a single operating condition, with an optimization goal to minimize brake specific fuel consumption (BSFC) for a specified engine-out NOx concentration limit. The calibration process was repeated for two NOx limit values and a wide range of values for five GOA search parameters, including the number of genes, mutation rate, and convergence criteria. Results indicated GOA performance is very sensitive to algorithm search parameter values, with converged calibrations yielding BSFC values from 1 to 14% higher than the global minimum value, and the number of iterations required to converge ranging from 10 to 3,000. Broadly, GOA performance sensitivity was found to increase as the NOx limit was decreased from 4,500 to 1,000 ppm. GOA performance was the most sensitive to the number of genes and the gene mutation rate, whereas sensitivity to convergence criteria values was minimal. Identification of one set of algorithm search parameter values which universally maximized GOA performance was not possible as ideal values depended strongly on engine behavior, NOx limit, and the maximum level of error acceptable to the user.

Convergence Criteria of Three Step Schemes for Solving Equations

We develop a unified convergence analysis of three-step iterative schemes for solving nonlinear Banach space valued equations. The local convergence order has been shown before to be five on the finite dimensional Euclidean space assuming Taylor expansions and the existence of the sixth derivative not on these schemes. So, the usage of them is restricted six or higher differentiable mappings. But in our paper only the first Frèchet derivative is utilized to show convergence. Consequently, the scheme is expanded. Numerical applications are also given to test convergence.

Assessing the optimality of euro adoption in Romania through shock correlations

The present paper is concerned with the prospect of euro adoption in Romania. The study starts from the relevant literature of the Optimum Currency Areas and identifies the most widely acknowledged meta property and methodological model for this purpose: the SVAR Blanchard and Quah decomposition for identifying the supply and demand shocks. Employing the indicated model and the most recent data, we are able extract and analyse the underlying shocks that hit 34 European economic entities in the period 1995-2019, while also taking into account two crucial structural changes for the Romanian economy – central bank independence and EU accession. After performing the pairwise correlations between Romania and the rest of the economic entities for both the supply and demand disturbances, we map them on a bidimensional graph. We discover that while there is relevant integration and connectedness that ensures relatively high correlations between supply shocks, the politically-motivated monetary and fiscal policy disturbances that created ample and hectic demand side movements, are a factor of great concern for the prospect of single currency adoption in this Eastern European country. The findings support the view that there is room for the conduct of macro policies to become more supportive to the process of euro adoption and that the respect of convergence criteria would help in this respect. To our knowledge, this is the first study performing pairwise shock correlations between Romania and many other European economic entities, while also isolating the effect of post 2005 structural changes.

Thermal Instabilities and Shattering in the High-redshift WHIM: Convergence Criteria and Implications for Low-metallicity Strong H i Absorbers

Using a novel suite of cosmological simulations zooming in on a megaparsec-scale intergalactic sheet (pancake) at z ∼ (3–5), we conduct an in-depth study of the thermal properties and H i content of the warm-hot intergalactic medium (WHIM) at those redshifts. The simulations span nearly three orders of magnitude in gas cell mass, ∼(7.7 × 106–1.5 × 104)M ⊙, one of the highest-resolution simulations of such a large patch of the intergalactic medium (IGM) to date. At z ∼ 5, a strong accretion shock develops around the pancake. Gas in the postshock region proceeds to cool rapidly, triggering thermal instabilities and generating a multiphase medium. We find the mass, morphology, and distribution of H i in the WHIM to all be unconverged, even at our highest resolution. Interestingly, the lack of convergence is more severe for the less-dense, metal-poor intrapancake medium (IPM) in between filaments and far outside galaxies. With increased resolution, the IPM develops a shattered structure with most of the H i in kiloparsec-scale clouds. From our lowest-to-highest resolution, the covering fraction of metal-poor (Z < 10−3 Z ⊙) Lyman-limit systems (N H I > 1017.2cm−2) in the z ∼ 4 IPM increases from ∼(3–15)%, while that of metal-poor damped Lyα absorbers (N H I > 1020cm−2) increases from ∼(0.2–0.6)%, with no sign of convergence. We find that a necessary condition for the formation of a multiphase shattered structure is resolving the cooling length, l cool = c s t cool, at T ∼ 105 K. If this is unresolved, gas “piles up” at T ≲ 105 K and further cooling becomes very inefficient. We conclude that state-of-the-art cosmological simulations are still unable to resolve the multiphase structure of the WHIM, with potentially far-reaching implications.

Generalized Hypergeometric Function 3F2 Ratios and Branched Continued Fraction Expansions

The paper is related to the classical problem of the rational approximation of analytic functions of one or several variables, particulary the issues that arise in the construction and studying of continued fraction expansions and their multidimensional generalizations—branched continued fraction expansions. We used combinations of three- and four-term recurrence relations of the generalized hypergeometric function 3F2 to construct the branched continued fraction expansions of the ratios of this function. We also used the concept of correspondence and the research method to extend convergence, already known for a small region, to a larger region. As a result, we have established some convergence criteria for the expansions mentioned above. It is proved that the branched continued fraction expansions converges to the functions that are an analytic continuation of the ratios mentioned above in some region. The constructed expansions can approximate the solutions of certain differential equations and analytic functions, which are represented by generalized hypergeometric function 3F2. To illustrate this, we have given a few numerical experiments at the end.

Impact of domain discretization on the accuracy of a 2D model of PCM module for ventilation application

Optimal selection of domain discretization for numerical Phase Change Material (PCM) models is useful to establish confidence in model predictions and minimize the time consumption for conducting design analysis. Very detailed and geometrically complex models are usually applied utilizing several million cells. A 2D numerical PCM model of a climate module for thermal comfort ventilation is investigated. The mesh independence was conducted on 22 different mesh sizes ranging from 70 to 10.870 nodes. Convergence criteria was evaluated based on average air supply temperature and total heat transfer between the PCM and the air within the simulation time interval. Less than 0.1 % change in the air supply temperature and the heat transfer between the PCM and the air was achieved with 5250 and 9870 nodes, respectively. Thereby highlighting that a relatively small amount of nodes can be considered to achieve sufficient accuracy to conduct analysis of PCM applications.

Projection methods for high numerical aperture phase retrieval

We develop for the first time a mathematical framework in which the class of projection algorithms can be applied to high numerical aperture (NA) phase retrieval. Within this framework, we first analyze the basic steps of solving the high-NA phase retrieval problem by projection algorithms and establish the closed forms of all the relevant projection operators. We then study the geometry of the high-NA phase retrieval problem and the obtained results are subsequently used to establish convergence criteria of projection algorithms in the presence of noise. Making use of the vectorial point-spread-function (PSF) is, on the one hand, the key difference between this paper and the literature of phase retrieval mathematics which deals with the scalar PSF. The results of this paper, on the other hand, can be viewed as extensions of those concerning projection methods for low-NA phase retrieval. Importantly, the improved performance of projection methods over the other classes of phase retrieval algorithms in the low-NA setting now also becomes applicable to the high-NA case. This is demonstrated by the accompanying numerical results which show that available solution approaches for high-NA phase retrieval are outperformed by projection methods.

A computationally efficient technique for the solution of pulp washing models

An efficient numerical technique for the solution of the pulp washing model is proposed in this study. Two linear and one nonlinear model are explained with quintic Hermite collocation method. In this technique, quintic Hermite polynomials (C2 continuous) are used as a basis function and orthogonal collocation method is applied within each element of the partitioned domain. For accuracy and applicability of the method, a comparison of the numerical results with analytic ones is made. The method is found to be stable using stability analysis and convergence criteria. The effect of Peclet number on exit solute concentration and other parameters is presented in the form of breakthrough curves. The results are derived for a broad range of parameters and the present method is found to be more useful and refined for solving the two-point boundary value problems.

Extended Kung–Traub Methods for Solving Equations with Applications

Kung and Traub (1974) proposed an iterative method for solving equations defined on the real line. The convergence order four was shown using Taylor expansions, requiring the existence of the fifth derivative not in this method. However, these hypotheses limit the utilization of it to functions that are at least five times differentiable, although the methods may converge. As far as we know, no semi-local convergence has been given in this setting. Our goal is to extend the applicability of this method in both the local and semi-local convergence case and in the more general setting of Banach space valued operators. Moreover, we use our idea of recurrent functions and conditions only on the first derivative and divided difference, which appear in the method. This idea can be used to extend other high convergence multipoint and multistep methods. Numerical experiments testing the convergence criteria complement this study.

Generalized Higher Order Preinvex Functions and Equilibrium-like Problems

Equilibrium problems and variational inequalities are connected to the symmetry concepts, which play important roles in many fields of sciences. Some new preinvex functions, which are called generalized preinvex functions, with the bifunction ζ(.,.) and an arbitrary function k, are introduced and studied. Under the normed spaces, new parallelograms laws are taken as an application of the generalized preinvex functions. The equilibrium-like problems are represented as the minimum values of generalized preinvex functions under the kζ-invex sets. Some new inertial methods are proposed and researched to solve the higher order directional equilibrium-like problem, Convergence criteria of the our methods is discussed, along with some unresolved issues.