Modeling the Influence of Engine Dynamics on Its Indicator Diagram

This article presents a proposal to describe the pressure changes in the combustion chamber of an engine as a function of the angle of rotation of the crankshaft, taking into account changes in rotational speed resulting from acceleration. The aim of the proposed model is to determine variable piston forces in simulation studies of torsional vibrations of a crankshaft with a vibration damper during the acceleration process. Its essence is the use of a Fourier series as a continuous function to describe pressure changes in one cycle of work. Such a solution is required due to the variable integration step during the simulation. It was proposed to determine the series coefficients on the basis of a Fourier transform of the averaged waveform of a discreet open indicator diagram, calculated for the registration of successive cycles. Recording of the indicative pressure waveforms and shaft angle sensor signals was carried out during tests on the chassis dynamometer. An analysis of the influence of the adopted number of series coefficients on the representation of signal energy was carried out. The model can also take into account the phenomenon of work cycle uniqueness by introducing random changes in the coefficients with magnitudes set on the basis of determined standard deviations for each coefficient of the series. An indispensable supplement to the model is a description of changes in the engine rotational speed, used as a control signal for the PID controller in the simulation of the load performed by the dynamometer. The accuracy of determining the instantaneous rotational speed was analyzed on the basis of signals from the crankshaft position angle sensor and the piston top dead center (TDC) sensor. Limitations resulting from the parameters of digital signal recording were defined.

On zeros of an entire function coinciding with exponential typequasi-polynomials, associated with a regular third-order differential operator on an interval

In this paper, we consider the question on study of zeros of an entire function of one class, which coincides with quasi-polynomials of exponential type. Eigenvalue problems for some classes of differential operators on a segment are reduced to a similar problem. In particular, the studied problem is led by the eigenvalue problem for a linear differential equation of the third order with regular boundary value conditions in the space W^3_2(0, 1). The studied entire function is adequately characteristic determinant of the spectral problem for a third-order linear differential operator with periodic boundary value conditions. An algorithm to construct a conjugate indicator diagram of an entire function of one class is indicated, which coincides with exponential type quasi-polynomials with comparable exponents according to the monograph by A.F. Leontyev. Existence of a countable number of zeros of the studied entire function in each series is proved, which are simultaneously eigenvalues of the above-mentioned third-order differential operator with regular boundary value conditions. We determine distance between adjacent zeros of each series, which lies on the rays perpendicular to sides of the conjugate indicator diagram, that is a regular hexagon on the complex plane. In this case, zero is not an eigenvalue of the considered operator, that is, zero is a regular point of the operator. Fundamental difference of this work is finding the corresponding eigenfunctions of the operator. System of eigenfunctions of the operator corresponding in each series is found. Adjoint operator is constructed.

Working-condition diagnosis of a beam pumping unit based on a deep-learning convolutional neural network

At present, beam pumping units are the most extensively-applied component in rod pumping systems, and the analysis of the indicator diagram of a rod pump is an important means of judging its downhole working condition. However, the synthetic study and judgment of the indicator diagram by manual means has a low efficiency, large error, and poor immediacy, and it is difficult to apply the conclusions in time and accurately to adjust the operating parameters of the pumping units. Moreover, expert systems rely on expert experience and conventional machine learning requires manual pre-selection of geometric features such as moments and vector curves, which will reduce the accuracy of recognition when similar indicator diagrams appear. To solve the above technical defects, in this paper, a deep-learning convolutional neural network (CNN) is proposed using the CNN model based on AlexNet. The automatic recognition of the indicator diagram is thus realized, and, on the basis of previous studies, this model simplifies the structure of the model and takes into account 15 common downhole working conditions of the pumping unit. In this model, the batch normalization (BN) layer is used to replace the local response normalization (LRN) and dropout layers and all kinds of indicator diagrams are put into the same model frame for automatic identification. The experimental application of the measured data shows that the model not only has a short training time, but also has a working-condition diagnosis accuracy of 96.05%, which can solve the deficiencies and defects of artificial identification, expert systems, and conventional machine learning to a certain extent. A deep-learning CNN can provide a new reference for fast working-condition diagnosis of indicator diagram, making indicator-diagram judgment timely and accurate, and thus it is possible to provide a direct basis for parameter adjustment of pumping units.

Asymptotics of the Spectrum of a Periodic Boundary ValueProblem for an Odd-Order Differential Operator

The spectrum of a differential operator of high odd order with periodic boundary conditions is studied. The asymptotics of the fundamental system of solutions of the differential equation defining the operator are obtained by the method of successive Picard approximations. With the help of this fundamental system of solutions the periodic boundary conditions are studied. As a result, the equation for the eigenvalues of the differential operator under study is obtained, which is a quasi-polynomial. The indicator diagram of this equation, which is a regular polygon, is investigated. In each of the sectors of the complex plane, defined by the indicator diagram, the asymptotics of the eigenvalues of the operator under study is found. An equation for the eigenvalues of the differential operator under study is derived. The indicator diagram of this equation has been studied. The asymptotics of the eigenvalues of the studied operator in different sectors of the indicator diagram is found.