"Вестник МГСУ"

Mesh cover design, a multi-element design, which ensures the correct geometrical arrangement of the elements, is a very important task. The purpose of the given article is the development of a mathematical model for selecting the geometric parameters of wooden arches with mesh orthogonal grid with different input data. In this article three variants of design were observed. The main differences between them are in the relative position of longitudinal and transverse components. When performing static calculations of such designs in order to achieve their subsequent correct assembly, the following location conditions were observed: all the items must strictly match with each other without a gap and without overlap. However, these conditions must be met for any ratio of height to the arch span, the number of longitudinal members and the thickness of longitudinal members. Inverse problems also take place. In this case, the geometric calculation is not possible to vary the cross-section elements, and the stress-strain state of the cover is provided by varying the pitch of the transverse arches of the elements, on which the geometric calculation has no influence. All this determines the need for universal mathematical models describing any geometrical parameter of the designs needed for their geometrical calculation. The basic approach for the development of such models is the use of the known trigonometric formulas, giving a complete description of the desired geometry of the arch. Finally three transcendental equations were obtained, the solution algorithm of which using Newton’s method is presented in the MathCAD. The complexity of solving such equations using the proposed algorithm in the MathCAD is reduced to a minimum.

In modern integrated monitoring systems and systems of automated control of technological processes there are several essential algorithms and procedures for obtaining primary information about an object and its behavior. The primary information is characteristics of static and moving objects: distance, speed, position in space etc. In order to obtain such information in the present work we proposed to use photos and video detectors that could provide the system with high-quality images of the object with high resolution. In the modern systems of video monitoring and automated control there are several ways of obtaining primary data on the behaviour and state of the studied objects: a multisensor approach (stereovision), building an image perspective, the use of fixed cameras and additional lighting of the object, and a special calibration of photo or video detector.In the present paper the authors develop a method of determining the distances to objects by analyzing a series of images using depth evaluation using defocusing. This method is based on the physical effect of the dependence of the determined distance to the object on the image from the focal length or aperture of the lens. When focusing the photodetector on the object at a certain distance, the other objects both closer and farther than a focal point, form a spot of blur depending on the distance to them in terms of images. Image blur of an object can be of different nature, it may be caused by the motion of the object or the detector, by the nature of the image boundaries of the object, by the object’s aggregate state, as well as by different settings of the photo-detector (focal length, shutter speed and aperture).When calculating the diameter of the blur spot it is assumed that blur at the point occurs equally in all directions. For more precise estimates of the geometrical parameters determination of the behavior and state of the object under study a statistical approach is used to determine the individual parameters and estimate their accuracy. A statistical approach is used to evaluate the deviation of the dependence of distance from the blur from different types of standard functions (logarithmic, exponential, linear). In the statistical approach the evaluation method of least squares and the method of least modules are included, as well as the Bayesian estimation, for which it is necessary to minimize the risks under different loss functions (quadratic, rectangular, linear) with known probability density (we consider normal, lognormal, Laplace, uniform distribution). As a result of the research it was established that the error variance of a function, the parameters of which are estimated using the least squares method, will be less than the error variance of the method of least modules, that is, the evaluation method of least squares is more stable. Also the errors’ estimation when using the method of least squares is unbiased, whereas the mathematical expectation when using the method of least modules is not zero, which indicates the displacement of error estimations. Therefore it is advisable to use the least squares method in the determination of the parameters of the function.In order to smooth out the possible outliers we use the Kalman filter to process the results of the initial observations and evaluation analysis, the method of least squares and the method of least three standard modules for the functions after applying the filter with different coefficients.

The recent decade has been the time of the rapid development of communication infrastructure, but very often the structures erected in the middle of the last century are used as a basis for new transmission units and antennas, which are considerably worn out. In this regard the control problems of the infrastructure facilities such as towers and masts are often emerging. Such tasks may be associated with the test required when installing additional equipment and modules, as well as during the scheduled inspection and certification of individual objects in accordance with the legal documents. Timely detection of critical deformations will to a large extent prevent the occurrence of accidents and disasters. For accurate detection of deformations load cells on the basis of the piezoelectric effect and fiber-optic sensors based on Bragg gratings are most commonly used, but in such distributed information measurement systems there are significant drawbacks, which narrow the scope of their possible application. Among the main disadvantages there are: high cost of initial installation and configuration, and the subsequent operation of such systems. Traditional measuring sensors require power, separate line of measurement information signal, as well as lines for supplying control signals. A significant limitation is that any sensor detects deformation or other parameters of the design only for its whole base, thus, active sensors should be installed in structures, in which an altered state was detected by visual inspection or by other means. The emergence of video and photo-detectors with high resolution and other settings to get a high-quality image of the object made it possible to establish the systems for infrastructure objects’ monitoring with the characteristics acceptable for practice. At the heart of such systems there are not only detectors with high sensitivity, but also the algorithms for the objects’ recognition, determination of their geometrical parameters by analyzing a series of images. This is the issue and the subject of this work, which developed the computational algorithms to detect external defects. At the stage of preliminary image processing there is the delineation of characteristic points in the image and the calculation of the optical flow in the area of these points. When determining the defect position, the characteristic points of the image are determined using the detector of Harris-Laplace, which are located in the central part of the image. The characteristic points outside the frame are considered to be background. There is an identification of the changes in characteristic points in the frame in relation to the background by using a pyramidal iterative scheme. In the second stage servo frame focuses on a specific point with the greatest change in relation to the background in the current time. The algorithm for object detection and determination of its parameters includes three procedures: detection procedure start; the procedure of the next image processing; stop procedure for determining the parameters of the object. The method described here can be used to create information-measuring system of monitoring based on the use of photodetectors with high-definition and recognition of defects (color differences and differences in the form compared to the background). Since almost each examination of a building or structure begins with a visual examination and determination of the most probable places of occurrence and presence of the defects, the proposed method can be combined with this stage and it will simplify the process of diagnosing, screening for the development of projects on reconstruction and placement of additional equipment on the existing infrastructure.