基于一组Kalman滤波器信息融合的故障诊断

为了能及时准确地诊断发动机的传感器和执行机构故障,本文提出了基于一组Kalman滤波器信息融合的方法进行故障诊断。首先根据传感器特性设计了一组滤波器用于传感器故障诊断、隔离,每个滤波器针对一个传感器进行设计;其次根据执行机构故障特性设计了一组Kalman滤波器进行执行机构偏差估计,从而对执行机构进行故障诊断、隔离;接着给出了传感器、执行机构信息融合的诊断方案;最后分别给传感器、执行机构添加故障进行方案验证,仿真结果得出在传感器或者执行机构任意部件出故障的情况下,该融合方法可以有效地诊断并隔离出有故障的传感器或者执行机构。     

Sound radiation from rectangular baffled and unbaffled plates

The radiation efficiency of a flat rectangular plate is often used as a basis on which to represent the sound radiation from more complex plate-like structures. The solution for a plate set in a rigid baffle is well known, including the radiation efficiency for multi-modal response of the plate. In this case the assumption is usually made that each mode within a given frequency band has equal modal vibration energy. This paper explores a number of limitations of this simple result. First, the extent to which the radiation efficiency for a particular forcing point deviates from the modal-average result is investigated. Second, the difference is shown between the results for a baffled plate and an unbaffled plate. For a multi-modal response, an empirical formula is also presented which allows the radiation efficiency to be estimated for the unbaffled case. Finally, the effect of different boundary conditions on both baffled and unbaffled results is demonstrated by comparing the results for guided boundaries with those for simply supported boundaries.     

Effect of Finite Spectral Width on the Modulational Instability of Langmuir Waves described by a Nonlinear Schrödinger Equation

By using the two-point space correlation function an equation for the power spectral density for a random Langmuir field has been derived. The dispersion relation for a monochromatic wave is regained for a delta spectrum. For a Gaussian spectrum, the maximum growth rate is less than that for a monochromatic wave. For a “meander spectrum”, the growth rate is increased with the width of the spectrum in the first stage then decreased for further increase of the width.     

Peculiarities of Acoustic Wave Reflection from a Boundary or Layer of a Two-Phase Medium

A mathematical model is presented for determining the oblique incidence of an acoustic wave at both a boundary and layer of a gas–drop mixture or a bubbly liquid of finite thickness. The basic wave reflection and transmission patterns are established for the incidence of a low-frequency acoustic wave at an interface between a pure gas and a gas–drop mixture, as well as between a pure and bubbly liquid. A range of varying volume fractions for a drop is determined, for which the zero value of the reflection coefficient is possible for low frequencies at oblique incidence. It is shown that the reflection coefficient will never be zero at angles of incidence above 24.5° from a gas–drop mixture at a pure gas boundary; however, when a wave is incident from a pure gas at a gas–drop mixture boundary, a zero reflection coefficient is possible for nonzero angles of incidence and the volume fraction of inclusions. The results of calculating reflection of an acoustic wave from a two-phase layer of a medium with a finite thickness are presented. It is established that the minimum reflection coefficient is possible depending on the perturbation frequency for a certain range of angles of incidence for the boundary or the layer of the gas–drop mixture, which is governed mainly by difference in densities between it and the pure gas.     

Rigorous solution to a quantum statistical mechanical laser model

A quantum mechanical laser model with relaxation and pumping mechanisms is solved rigorously. A basic equation for the density matrix is derived by the damping theory and is transformed into a corresponding c-number equation for a (quasi-) probability density. This is done with the aid of the quantum phase space method. The probability density is expanded in terms of orthogonal polynomials. The expansion coefficients are solved to give a continued fraction. A complete solution is obtained, namely, time evolution of the probability density is determined as well as that for certain physical quantities. The solution is valid even for strong coupling between photons and atoms: it is free from restriction on system parameters. Detailed studies on dynamics are performed for typical values of the system parameters. This is a prototype of interacting quantum nonequilibrium systems. Relevance to systems other than a laser is briefly mentioned.     

On statistical mechanics of systems with highly singular two-body potentials

A finite volume statistical mechanics for highly singular two-body potentials is studied. The case of “point” hard-core particles (Lennard-Jones type two-body potentials) is discussed and the mathematical background for this physical idealization is given. Firstly the definition of a self-adjoint Hamiltonian for such a system is considered. Then a natural cutoff procedure for two-body highly singular potentials is proposed. The main result is the proof of a convergence theorem for partition sums (or free energies) when the cutoff parameter is removed to infinity. The question of stability of the cutoff interactions is also discussed. These results are illustrated by a consideration of the Lennard-Jones potential (12-6). Our results are valid in all dimensions greater than two and for potentials being not inevitably spherically symmetric.     

A path integral approach to inclusive processes

The single-particle inclusive differential cross-section for a reaction is written as the imaginary part of a correlation function in a forward scattering amplitude for in a modified effective theory. In this modified theory the interaction Hamiltonian equals in the original theory up to a certain time. Then there is a sign change and becomes nonlocal. This is worked out in detail for scalar field models and for QED plus the abelian gluon model. A suitable path integral for direct calculations of inclusive cross sections is presented. Received: 8 March 2000 / Published online: 6 July 2000     

The Casimir pressure regularization in two-dimensional field models

A method for Casimir pressure calculation with the help of the regular part of the Green surface function is considered in the two-dimensional case. Also, a method for the approximate calculation of the regular part of the Green surface function using a Born-type series is suggested. It is tested for a problem for which the exact solution is known.     

Cross sections for the photodisintegration of a deuteron and neutron capture by a proton calculated for the case of nonlocal potential

The processes of deuteron photodisintegration by a gamma-quantum and the radiative capture of a neutron by a proton with the emission of a gamma-quantum are considered. Interaction between nucleons is described by a nonlocal potential of the Yamaguchi type but allowing for repulsion due to the nucleon cores. In contrast to other potentials, the Schroedinger equation is solved exactly for the proposed potential. The potential is more exactly defined in comparison with the previously obtained values for the parameters; information on this potential is important in solving certain fundamental problems in nuclear theory. The effective cross sections for photodisintegration of a deuteron and for radiative capture are computed. Calculations show that the proposed potential makes it possible to describe the photodisintegration processes quite accurately for intermediate (up to 20 MeV) energies. The cross section computed for radiative capture is in somewhat better agreement with experiment than is the same cross section determined for other potentials.     

On the Gribov ambiguity in the Faddeev-Popov procedure

The standard Faddeev-Popov procedure for quantization of a gauge theory is modified so as to be valid even when the Gribov problem is present. The hamiltonian is employed and a definite expression for the path integral is obtained for a wide class of gauges.     

On detonation initiation by a temperature gradient for a detailed chemical reaction models

The evolution from a temperature gradient to a detonation is investigated for combustion mixture whose chemistry is governed by a detailed chemical kinetics. We show that a detailed chemical reaction model has a profound effect on the spontaneous wave concept for detonation initiation by a gradient of reactivity. The evolution to detonation due to a temperature gradient is considered for hydrogen-oxygen and hydrogen-air mixtures at different initial pressures. It is shown that the minimal length of the temperature gradient for which a detonation can be ignited is much larger than that predicted from a one-step chemical model.     

Revisiting the moving force problem

The problem of the vibration of a beam subject to a travelling force is considered. The purpose of the study is to develop simple tools for finding the maximum deflection of a beam for any given velocity of the travelling force. It is shown that, for given boundary conditions, there exists a unique response-velocity dependence function. A technique to determine this function is suggested, which is based on the assumption that the maximum beam response can be adequately approximated by means of the first beam mode. To illustrate this, the maximum response function is calculated analytically for a simply supported (SS) beam and constructed numerically for a clamped-clamped beam. The effect of the higher modes on the maximum response is investigated, and the relative error of the one-mode approximation for a SS beam is constructed. The estimates obtained substantiate the assumption about adequacy of the one-mode approximation in a wide range of velocities; in particular, the relative error in the neighborhood of the velocity that results in the largest response is less than one percent.     

On the theory of the condensed states of heteropolymers

The collapse (globulization) of an ideal heteropolymer chain under the action of an external attractive field is considered. The problem of the collapse of different types of primary structures, including mobile, periodic, large-block, and statistical structures, is formulated. It is shown that for a random heteropolymer, the mathematical image of the globular state is the chain-length independence of the probability distribution of a random thermal distribution function of the end monomer coordinates. The free energy per monomer of a chain in a globular state and local densities of monomers of all types are shown to be a self-averaging quantities. An exactly solvable model is proposed for a globule formed by a statistical heteropolymer chain. In this model, different types of monomers are attracted to different centers by linear elastic forces with identical elastic constants. The modulus of elasticity is obtained for a heteropolymer globule with respect to the attraction of different types of monomers in different directions. It is shown that this modulus is higher for a short-periodic polymer than for a statistical one.     

Time adaptive variational integrators: A space-time geodesic approach

The goal of this paper is to show that the space-time geodesic approach of classical mechanics can be used to generate a time adaptive variational integration scheme. The only assumption we make is that the Lagrangian for the system is in a separable form. The geometric structure which is preserved in the integration scheme is made explicit and the algorithm is illustrated with simulation for a compact case, a non-compact case, a chaotic system which arises as a perturbation of an integrable system and the figure eight solution for a three body problem.     

Sound radiation from perforated plates

A practical engineering noise control measure that can often be used for plate-like structures is to construct them from perforates. This can dramatically reduce the sound radiation from such structures. Here, a prediction model is developed to quantify this effect. It is an extension of Laulagnet's model for the radiation from an unbaffled plate, which expresses the surface pressure difference as well as the plate velocity as a sum over plate modes. The perforation is included in terms of a continuously distributed surface impedance, which for moderately sized holes is predominantly inertial. Results show that the radiation efficiency reduces, not only as the perforation ratio increases but also as the hole size reduces for a given perforation ratio. Experimental validation is given which shows a good agreement with the predictions. An approximate formula is also proposed for the effect of perforation which corresponds well with the analytical calculations up to half the critical frequency and could be used for an engineering application to predict the noise reduction due to perforation. A model for the case of a perforated plate embedded in an equally perforated baffle is also discussed for comparison.     

Beyond Einstein's radiation theory

Einstein's radiation mechanism is generalized to account for the possibility of population inversion by placing a nonlinear bound on the growth of an unstable perturbation. The nonstationary linear mechanism of relaxation to blackbody radiation below threshold is studied. The nonstationary photon distribution is the negative binomial distribution, and casting it as a law of error, for which the most probable value is the mean value, gives the expression for the statistical entropy. The second law yields a nonequilibrium generalization of Planck's radiation law. The nonlinear mechanism leading to the transformation from the negative binomial probability distribution, for chaotic light, to a Poisson probability distribution, for coherent light, is then analyzed. A criterion for lasing is given in terms of the chemical potential of radiation which is compared to the inequality for the transition from quantum to classical statistics.     

Numerical reconstruction stability of fiber Bragg gratings

Traditional algorithms for solving the inverse scattering problem for a fiber Bragg grating are described, and a new numerical method for this problem is developed. The method is based on the fast inversion of a matrix using its Toeplitz symmetry and on a special “inner-bordering” procedure. It is shown that the method is equally efficient as the well-known discrete layer peeling method but exceeds the latter in accuracy, especially for high-reflectance gratings. The stability of the proposed method with respect to initial data errors is demonstrated.     

A high‐accuracy complex‐phase method of simulating X‐ray propagation through a multi‐lens system

The propagation of X‐ray waves through an optical system consisting of many X‐ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite‐difference method is applied. The error of simulation is analytically estimated and investigated. It was found that a very detailed difference grid is required for reliable and accurate calculations of the propagation of X‐ray waves through a multi‐lens system. The reasons for using a very detailed difference grid are investigated. It was shown that the wave phase becomes a function, very quickly increasing with increasing distance from the optical axis, after the wave has passed through the multi‐lens system. If the phase is a quickly increasing function of the coordinates perpendicular to the optical axis, then the electric field of the wave is a quickly oscillating function of these coordinates, and thus a very detailed difference grid becomes necessary to describe such a wavefield. To avoid this difficulty, an equation for the phase function is proposed as an alternative to the equation of the electric field. This allows reliable and accurate simulations to be carried out when using the multi‐lens system. An equation for the phase function is derived and used for accurate simulations. The numerical error of the suggested method is estimated. It is shown that the equation for the phase function allows efficient simulations to be fulfilled for the multi‐lens system.     

Generalized Noether theorems in canonical formalism for field theories and their applications

A generalization of Noether's first theorem in phase space for an invariant system with a singular Lagrangian in field theories is derived and a generalization of Noether's second theorem in phase space for a noninvariant system in field theories is deduced. A counterexample is given to show that Dirac's conjecture fails. Some preliminary applications of the generalized Noether second theorem to the gauge field theories are discussed. It is pointed out that for certain systems with a noninvariant Lagrangian in canonical variables for field theories there is also a Dirac constraint. Along the trajectory of motion for a gauge-invariant system some supplementary relations of canonical variables and Lagrange multipliers connected with secondary first-class constraints are obtained.     

Time dependent Schrödinger equation on arbitrary structured grids: Application to photoionization

A systematic technique for conservatively discretizing the time dependent Schrödinger equation on an arbitrary structured grid is given. Spatial differencing is carried out by finite volumes, and temporal differencing is carried out semi-implicitly. It is shown that the resulting algorithm conserves probability to within a round-off error regardless of the grid geometry. The algorithm is efficient for both serial and parallel computation. The conservative nature of the algorithm, and its phase accuracy, are demonstrated for a bound state, and for a free state in an electromagnetic field. The ionization rate for a hydrogen atom in a strong electromagnetic field is computed, and compared with the rate from tunneling theory. The regime of validity of tunneling theory is clarified.