Adjustment of Planned Surveying and Geodetic Networks Using Second-Order Nonlinear Programming Methods

Due to the huge amount of redundant data, the problem arises of finding a single integral solution that will satisfy numerous possible accuracy options. Mathematical processing of such measurements by traditional geodetic methods can take significant time and at the same time does not provide the required accuracy. This article discusses the application of nonlinear programming methods in the computational process for geodetic data. Thanks to the development of computer technology, a modern surveyor can solve new emerging production problems using nonlinear programming methods—preliminary computational experiments that allow evaluating the effectiveness of a particular method for solving a specific problem. The efficiency and performance comparison of various nonlinear programming methods in the course of trilateration network equalization on a plane is shown. An algorithm of the modified second-order Newton’s method is proposed, based on the use of the matrix of second partial derivatives and the Powell and the Davis–Sven–Kempy (DSK) method in the computational process. The new method makes it possible to simplify the computational process, allows the user not to calculate the preliminary values of the determined parameters with high accuracy, since the use of this method makes it possible to expand the region of convergence of the problem solution.

Kalman Filter Adaptation to Disturbances of the Observer’s Parameters

Currently, one of the most effective algorithms for state estimation of stochastic systems is a Kalman filter. This filter provides an optimal root-mean-square error in state vector estimation only when the parameters of the dynamic system and its observer are precisely known. In real conditions, the observer’s parameters are often inaccurately known; moreover, they change randomly over time. This in turn leads to the divergence of the Kalman estimation process. The problem is currently being solved in a variety of ways. They include the use of interval observers, the use of an extended Kalman filter, the introduction of an additional evaluating observer by nonlinear programming methods, robust scaling of the observer’s transmission coefficient, etc. At the same time, it should be borne in mind that, firstly, all of the above ways are focused on application in specific technical systems and complexes, and secondly, they fundamentally do not allow estimating errors in determining the parameters of the observer themselves in order to compensate them for further improving the accuracy and stability of the filtration process of the state vector. To solve this problem, this paper proposes the use of accurate observations that are irregularly received in a complex measuring system (for example, navigation) for adaptive evaluation of the observer’s true parameters of the stochastic system state vector. The development of the proposed algorithm is based on the analytical dependence of the Kalman estimate variation on the observer’s parameters disturbances obtained using the mathematical apparatus for the study of perturbed multidimensional dynamical systems. The developed algorithm for observer’s parameters adaptive estimation makes it possible to significantly increase the accuracy and stability of the stochastic estimation process as a whole in the time intervals between accurate observations, which is illustrated by the corresponding numerical example.

Dynamic Quantization of Digital Filter Coefficients

The possibility of quantizing the coefficients of a digital filter in the concept of dynamic mathematical programming, as a dynamic process of step-by-step quantization of coefficients with their discrete optimization at each step according to the objective function, common to the entire quantization process, is considered. Dynamic quantization can significantly reduce the functional error when implementing the required characteristics of a lowbit digital filter in comparison with classical quantization. An algorithm is presented for step-by-step dynamic quantization using integer nonlinear programming methods, taking into account the specified signal scaling and the radius of the poles of the filter transfer function. The effectiveness of this approach is illustrated by dynamically quantizing the coefficients of a cascaded high-order IIR bandpass filter with a minimum bit depth to represent integer coefficients. A comparative analysis of functional quantization errors is carried out, as well as a test of the quantized filter performance on test and real signals.

Optimization of the combined explosion hardening processes

The proposed method for calculating the loading parameters makes it possible to determine the wear parameters after explosion hardening. The calculation method is simple and less time consuming compared with calculation methods that involve the use of nonlinear programming methods. The main methods of increasing the wear resistance of mining equipment parts using explosion methods are generalized. The reserve for increasing the wear resistance consists in the optimization of deformation parameters during the power and thermal intensification of processes and the development of new methods and technologies of hardening. The factors (parameters) of the studied processes: explosive cladding, alloying, hardening, are formulated. Optimization of the processes under consideration is possible by decomposing the process into simpler ones with subsequent optimization of the parameters of these processes and the synthesis of the obtained solutions. For the first time, a solution to the multicriteria problem of two-stage explosion hardening is presented. It is proposed to split the process into simpler ones. Optimization criteria are proposed for each of the simplified processes. The problem is reduced to a conditional extremum problem, which is solved by composing the Lagrange function. By transforming the wear equation, the optimal ratio of strength and ductility for parts operating under abrasive wear conditions is determined.

Application of Algorithms for Placement of Orthogonal Polyhedrons for Solving the Problems of Packing Objects of Complex Geometric Shape

The article is devoted to the development and research of algorithms for placing objects of complex geometric shapes. To solve the placement problem is proposed an approach which consists in transforming the shape of all objects and further application of the developed algorithm for placing orthogonal polyhedrons of arbitrary dimension to the resulting transformed objects. In the process of transforming the shape of the objects being placed, they are initially voxelized, after which the developed decomposition algorithm is applied to the resulting voxelized objects, which provides the formation of orthogonal polyhedrons consisting of the largest possible orthogonal objects. The proposed model of potential containers is used to describe the free space of containers as a set of orthogonal areas. The developed algorithm for the placement of orthogonal polyhedrons provides a fast solution to NP-hard problems of placing objects of complex geometric shapes without resorting to the use of time-consuming nonlinear programming methods. Examples of the practical application of the developed algorithms for modeling the dense layout of parts of complex geometric shapes on the platform of a 3D printer are given.

A QFD-Based Quality and Capability Design Method for Transboundary Services

The “transboundary”, an emerging phenomenon in the Internet service ecosystem, is leading to the flourishing of innovative services. A transboundary service incorporates services, resources, and technologies from multiple domains into its business to create a particular competitive advantage and unique user experiences. It is difficult to comprehensively consider all the constraints from multiple domains to precisely design the nonfunctional characteristics of transboundary services, such as quality attributes and capability attributes. We propose a two-phase quality design method for transboundary services called value quality deployment-quality capability deployment (VQD-QCD) based on quality function deployment (QFD). Given the restrictions of transboundary services, VQD-QCD translates the value expectations of multiple stakeholders into an optimal configuration for global quality parameters (GQPs), local quality parameters, and capability parameters. Details of VQD are illustrated. Considering the inherent vagueness and uncertainty of relationships between value expectations and GQPs, and among GQPs, fuzzy least absolute regression and fuzzy nonlinear programming methods are incorporated into QFD to identify the quantitative relations between value indicators and GQPs, and among GQPs, and obtain an optimal configuration scheme for GQPs. Usability of the proposed method is validated through a case study on the “DiDi mobile transportation service”, which is a representative transboundary service in China. Compared with the current method, which is inaccurate and inefficient because its translation between value expectations and relevant quality and capability parameters is artificial and subjective, the proposed method integrates fuzzy least absolute regression and fuzzy nonlinear programming methods into QFD, which facilitate transboundary service designers to precisely and efficiently design the quality and capability characteristics of innovative services in the manner of semiautomatisation, which promotes the innovative design of transboundary services.

Application of the Ansys Electronics Desktop Software Package for Analysis of Claw-Pole Synchronous Motor

The article presents the method of synthesis and analysis of the brushless motor with claw-poles. The motor is designed for the pilger mill drive for manufacturing seamless tubes. The peculiarity of the drive is that electric machines of this class for high power have not yet been used in world practice. In this regard, a very thorough analysis of the designed motor is required to remove technical risks in the manufacture of prototypes. For design of this motor the synthesis system and the analysis system were developed. The synthesis system is developed on the basis of nonlinear programming methods. For the analysis, it is proposed to use the program Ansys Electronics Desktop, which implements the finite element method. The peculiarity of using this program is the need to use large computer resources. Herewith, the calculation time of the main characteristics is often not acceptable for practical calculations and takes several hours. The authors propose a simplification of the computational model without significantly reducing the accuracy of the calculation. The brushless motor with claw-poles is replaced by a brushless motor with tangential magnets. The stator designs and the magnetic fluxes of the motors are the same. The effectiveness of such a replacement is shown in the real project. Calculation time with acceptable quality is reduced to a few minutes. This approach is recommended for the creation of design systems of other types of brushless machines. This scientific research was carried out for a real customer.