An advanced algorithm for partitioning and parameter estimation in local model networks and its application to vehicle vertical dynamics

In this paper, advanced concepts for the identification of complex nonlinear systems are discussed. Three major problems are addressed: The nonlinearity of the system, noise in the data upon which the model has to be built, and the potential to incorporate qualitative and quantitative prior knowledge about the system. As an integrated solution approach, local model networks (LMNs) with appropriate parameter estimation schemes are proposed. LMNs generally offer a versatile structure for the identification of nonlinear dynamic systems. In order to account for a realistic situation when noise is present both in input and output data, an equality constrained generalised total least squares algorithm for the local model parameter estimation of the LMN is presented; the incorporation of equality constraints allows to mathematically enforce desired system properties. As an application and benchmark problem, the vertical dynamics of a vehicle is considered. After training the LMN on a rough road, excellent predictions of the behaviour of the vehicle at crossing a single obstacle are obtained, thus proving the effectiveness of the proposed algorithm. It is illustrated how both the application of a proper parameter estimation scheme and the integration of system constraints systematically improve the performance of the model.     

Indirect measurement of state variables for the diagnostics of electromechanical systems

A method of estimating the actual state of electromechanical systems based on the use of a model, connected in parallel with the diagnosed equipment, and an indirect measurement of the state variables is considered. A diagnostic system structure is proposed and also versions of models which take the operating features into account. __________ Translated from Izmeritel’naya Tekhnika, No. 7, pp. 43–46, July, 2007.     

Exposing the nonlinear viscoelastic behavior of asphalt-aggregate mixes

In this study asphalt-aggregate mixes are treated as both viscoelastic and viscoplastic. Following a damage mechanics approach, a nonlinear viscoelastic constitutive formulation is generated from a linear formulation by replacing ‘applied stresses’ with ‘effective viscoelastic stresses’. A non-dimensional scalar entity called ‘relative viscoelastic stiffness’ is introduced; it is defined as the ratio of applied to effective viscoelastic stress and encapsulates different types of nonlinearities. The paper proposes a computational scheme for exposing these nonlinearities by uncovering, through direct analysis of any test data, changes experienced by the ‘relative viscoelastic stiffness’. In general terms, the method is based on simultaneous application of creep and relaxation formulations while preserving the interrelationship between the corresponding time functions. The proposed scheme is demonstrated by analyzing a uniaxial tension test and a uniaxial compression test (separately). Results are presented and discussed, unveiling and contrasting the character of viscoelastic nonlinearities in both cases. A conceptual viewpoint is offered to explain the observations, illustrating the requirements from any candidate constitutive theory.     

一种热线式MAF传感器分段块联模型辨识

采用静态非线性函数与动态线性环节的块连接模型来描述热线式空气质量流量（MAF）传感器的动态特性,非线性环节用多项式表示,动态线性环节采用OE模型结构．基于静、动态标定实验数据,分别建立了热线式MAF传感器在正、负阶跃激励下各校准点的Hammerstein模型,并利用非建模数据对其进行了相互验证．通过合理选择分段区间,确定出热线式MAF传感器各工作区域的最佳局部动态数学模型．模型检验结果表明：基于Hammerstein模型的分段模型比由任意一组动态数据所建模型具有更高的预测精度．     

Determination of the limit of applicability of the parabolic equation of heat conduction

A criterion is proposed which enables breakdown of the parabolic model of heat conduction for isotropic materials, in which there are no phase transitions, to be revealed, and which defines the conventional boundary between the linear and nonlinear regimes of nonequilibrium thermodynamics in heat problems. __________ Translated from Izmeritel’naya Tekhnika, No. 6, pp. 38–42, June, 2008.     

A meshless local boundary integral equation method for two-dimensional steady elliptic problems

A novel meshless local boundary integral equation (LBIE) method is proposed for the numerical solution of two-dimensional steady elliptic problems, such as heat conduction, electrostatics or linear elasticity. The domain is discretized by a distribution of boundary and internal nodes. From this nodal points’ cloud a “background” mesh is created by a triangulation algorithm. A local form of the singular boundary integral equation of the conventional boundary elements method is adopted. Its local form is derived by considering a local domain of each node, comprising by the union of neighboring “background” triangles. Therefore, the boundary shape of this local domain is a polygonal closed line. A combination of interpolation schemes is taken into account. Interpolation of boundary unknown field variables is accomplished through boundary elements’ shape functions. On the other hand, the Radial Basis Point Interpolation Functions method is employed for interpolating the unknown interior fields. Essential boundary conditions are imposed directly due to the Kronecker delta-function property of the boundary elements’ interpolation functions. After the numerical evaluation of all boundary integrals, a banded stiffness matrix is constructed, as in the finite elements method. Several potential and elastostatic benchmark problems in two dimensions are solved numerically. The proposed meshless LBIE method is also compared with other numerical methods, in order to demonstrate its efficiency, accuracy and convergence.     

Progressive combustion in SI-Engines—Experimental investigation on influence of combustion related parameters

The fuel heat release rate which virtually controls the combustion process is dependent on the ‘Mass-Fraction-Burnt (MFB)’. In the present research work, a ‘logistic model with conditional variability in MFB’, has been developed for precise simulation of combustion in SI engines as the model has built in routines to take into account such factors as location of spark plug, single/dual spark plugs, intake generated swirl, combustion chamber geometry (associated with Bore/Stroke ratio), etc. A major contribution of this paper is that new and improved models for the ‘overall combustion duration’, and ‘ignition delay/flame development angle’, taking into account primarily the influence of compression ratio on the overall combustion process in SI engine have been developed. Taylor’s original equation for estimating the overall combustion duration has been modified by including a logistic equation for the error term and incorporating it in the original equation. Ignition delay as proposed by Keck et al has been modified by incorporating a polynomial of 3^rd order into the original equation. The empirical correlations that have been proposed in this paper may serve to be the starting point for simulation of ‘photodetonation concept’ to simulate HCCI combustion which is presently the hot research work in the area of pre-mixed combustion. A program in Turbo-C++ has been developed for the complete simulation of SI engine combustion, taking into account the conditional variability effect, variable specific heats of burnt gases, dissociation of gases at high temperatures, progressive combustion phenomena, heat transfer (based onWoschni’s equation), gas exchange process based on 1D-steady gas flow equation employing Taylor’s mach index of 0.6 for valve design.     

Robust correlation tracker

Correlation tracking plays an important role in the automation of weapon systems. Area correlation is an effective technique for tracking targets that have neither prominent features nor high contrast with the background and the ‘target’ can even be an area or a scene of interest. Even though this technique is robust under varying conditions of target background and light conditions, it has some problems like target drift and false registration. When the tracker or target is moving, the registration point drifts due to the discrete pixel size and aspect angle change. In this research work, an attempt has been made to improve the performance of a correlation tracker for tracking ground targets with very poor contrast. In the present work only the CCD visible images with very poor target to background contrast are considered. Applying novel linear and nonlinear filters, the problems present in the correlation tracker are overcome. Confidence and redundancy measures have been proposed to improve the performance by detecting misregistration. The proposed algorithm is tested on different sequences of images and its performance is satisfactory.     

Non-intrusive and exact global/local techniques for structural problems with local plasticity

This paper introduces a computational strategy to solve structural problems featuring nonlinear phenomena that occur within a small area, while the rest of the structure retains a linear elastic behavior. Two finite element models are defined: a global linear model of the whole structure, and a local nonlinear “submodel” meant to replace the global model in the nonlinear area. An iterative coupling technique is then used to perform this replacement in an exact but non-intrusive way, which means the model data sets are never modified and the computations can be carried out with standard finite element software. Several ways of exchanging data between the models are discussed and their convergence properties are investigated on two examples. This work is supported by Snecma and is part of the MAIA-MM1 research program.     

Nonlinear zero-range potential model for the scattering of sound intensity by a Helmholtz resonator

The scattering of an intense sound wave by a Helmholtz resonator can be described by a nonlinear (to take into account the hydrodynamic effects in the resonator throat) zero-range potential model. The case in which the wave is linear everywhere except in the resonator throat is considered. A comparison with the results of other models is made. Pis’ma Zh. Tekh. Fiz. 25, 70–75 (June 26, 1999)     

Displacement tracking servo operation and real energy quality in power supplies

Performance is considered for linear analog displacement converters and digital angle ones as affected by changes in electrical energy quality. Analytical and statistical models are proposed for describing the accuracy characteristics of these in relation to energy quality. __________ Translated from Izmeritel’naya Tekhnika, No. 10, pp. 21–25, October, 2007.     

A local multiple proper generalized decomposition based on the partition of unity

It is well known that model order reduction techniques that project the solution of the problem at hand onto a low-dimensional subspace present difficulties when this solution lies on a nonlinear manifold. To overcome these difficulties (notably, an undesirable increase in the number of required modes in the solution), several solutions have been suggested. Among them, we can cite the use of nonlinear dimensionality reduction techniques or, alternatively, the employ of linear local reduced order approaches. These last approaches usually present the difficulty of ensuring continuity between these local models. Here, a new method is presented, which ensures this continuity by resorting to the paradigm of the partition of unity while employing proper generalized decompositions at each local patch.     

Viscoelastic properties of hybrid copolymers based on methacryloxypropyl-grafted nanosilica and methyl methacrylate

The linear viscoelastic behavior of “model” hybrid materials based on methyl methacrylate and methacryloxypropyl-grafted nanosilica was investigated. As unique features, the materials under study present an excellent dispersion of silica within the polymer matrix and are almost free of uncross-linked chains. In addition, very progressive changes in network architecture are available, resulting from changes in particle diameter, d, volume fraction of filler, Φ, number of methacryloyl units grafted per surface unit of silica particle, n, and nature of the grafting agent. The influence of these parameters on the characteristics of the mechanically active relaxations α and β was examined. Emphasis was put on the storage modulus, E′, on the loss modulus, E′′, and on their dependence on filler volume fraction. E′′ values were shown to simply account for the reduction of the mechanical energy lost within the material, in connection to the occurrence of polymer molecular motions. Analysis of E′ variations as a function of Φ was based on the theoretical models available in the literature to account for the contribution of the spherical filler particles. In the glassy state, Kerner’s and Christensen and Lo’s models yielded comparable results. In the rubbery state, Guth and Gold’s model was shown to prevail on Kerner’s model.     

Structural identification for electromagnetic system linear dynamic models and the relation to total power resolution

A structural identification method is proposed for linear dynamic models for single-phase alternating-current electromagnetic systems of source-load type. Matrix equations are derived that relate the Gram matrices of the Krylov bases to the power matrix, from which one can obtain the resolution of the total power. __________ Translated from Izmeritel’naya Tekhnika, No. 6, pp. 26–29, June, 2006.     

Information transmission using a synchronous chaotic response with filtering in the communication channel

A principle is proposed for obtaining a chaotic synchronous response in a driven nonlinear oscillatory system under conditions where the signal of the driving chaotic system is filtered by the coupling channel. Music and speech signals are used to demonstrate the efficiency of applying this principle to transmit information through a channel having a limited frequency band. Pis’ma Zh. Tekh. Fiz. 25, 71–77 (August 26, 1999)     

RBF neural network based <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> synchronization for unknown chaotic systems

In this paper, we propose a new H _∞ synchronization strategy, called a Radial Basis Function Neural NetworkH _∞ synchronization (RBFNNHS) strategy, for unknown chaotic systems in the presence of external disturbance. In the proposed framework, a radial basis function neural network (RBFNN) is constructed as an alternative to approximate the unknown nonlinear function of the chaotic system. Based on this neural network and linear matrix inequality (LMI) formulation, the RBFNNHS controller and the learning laws are presented to reduce the effect of disturbance to an H _∞ norm constraint. It is shown that finding the RBFNNHS controller and the learning laws can be transformed into the LMI problem and solved using the convex optimization method. A numerical example is presented to demonstrate the validity of the proposed RBFNNHS scheme.     

Integrated-optics detectors with recording of the reflection coefficient in a prism excitation system

Detectors whose operating principle is based on recording the energy reflection coefficient in a prism waveguide excitation system are proposed for measuring physical quantities. The possibilities of maximizing the sensitivity of these devices is determined. An experimental investigation was made of a detector for the ammonia concentration in the atmosphere. Pis’ma Zh. Tekh. Fiz. 23, 46–51 (July 12, 1997)     

Estimating parameterized scalable models from the best linear approximation of nonlinear systems for accurate high-level simulations

System designers of communication systems need to compare the simulated behavior of a system with the linear and nonlinear specifications. They need high-level models to perform these simulations fast. The existing high-level models for nonlinear components do not scale smoothly with external parameters like the input power. To overcome this problem, a modeling technique based on the best linear approximation is developed. The parameterized models describe trajectories of the poles and zeros as a function of the input power. The resulting models accurately describe both the linear and nonlinear behavior of the system components. They can easily be implemented in modern simulators.     

Novel interpretable mechanism of neural networks based on network decoupling method

The lack of interpretability of the neural network algorithm has become the bottleneck of its wide application. We propose a general mathematical framework, which couples the complex structure of the system with the nonlinear activation function to explore the decoupled dimension reduction method of high-dimensional system and reveal the calculation mechanism of the neural network. We apply our framework to some network models and a real system of the whole neuron map of Caenorhabditis elegans. Result shows that a simple linear mapping relationship exists between network structure and network behavior in the neural network with high-dimensional and nonlinear characteristics. Our simulation and theoretical results fully demonstrate this interesting phenomenon. Our new interpretation mechanism provides not only the potential mathematical calculation principle of neural network but also an effective way to accurately match and predict human brain or animal activities, which can further expand and enrich the interpretable mechanism of artificial neural network in the future.