A Reduced Order Modeling Methodology for Steam Turbine Clearance Control Design

Power equipment deterioration occurs during operation, it causes loss in reliability and efficiency, unscheduled shutdowns, and accidents. Now predictive analytics is one of the promising directions in the field of power engineering which allows to control and analyze the technical condition of power equipment. The problems of localization of deviation of technological parameters and detection of anomaly in the operation of power equipment are consistently solved in the framework of predictive analytics. The problems of deviations localization and anomalies detection are solved by the methods of statistical modeling and the classification algorithms respectively. However, for steam turbines the localization of deviation and the detection of anomalies having slow-flowing character are a difficult problem. Therefore, the issue of development of a method for continuous monitoring of technical condition and maintenance diagnostics based on a mathematical model of the steam turbine section flow characteristics is worth noticing. The method allows us to consider the effect of changes in the open flow area of the individual sections of a steam turbine on the pressure distribution over the steam flow path. The model of a steam turbine has been developed within the matrix formalization methodology. The solution of the system of linear and nonlinear equations is carried out by methods of computational mathematics. The solution of the optimization problems of the steam flow path diagnostics is carried out by methods of mathematical programming. A mathematical model of the cogeneration steam turbine Т-250/305-23.5-DB and a method for continuous condition monitoring and maintenance diagnostics of steam turbine have been developed. It allows us to localize deviation and detect anomaly by recovery of the open flow area of the individual sections of a steam turbine based on the pressure distribution over the steam flow path. The results of the statistical analysis prove that a mathematical model of the cogeneration steam turbine Т-250/305-23.5-DB has been recognized adequate. The method for continuous condition monitoring and maintenance diagnostics of steam turbine has demonstrated consistency of the obtained results and ability to solve diagnostic problems in practice. The developed model and method can be used as a module in the development of a software package for predictive analytics of power equipment.

Uncertainty propagation in FE modelling of a fire resistance test using fractional factorial design based model reduction and deterministic sampling

<div class="section abstract"><div class="htmlview paragraph">Increasing demand for simulation accuracy often leads to increased finite element model complexity, which in turn, results in higher computational costs. As a provision, component mode synthesis approaches are employed to approximate the system response by using dynamic substructuring and model reduction techniques in linear systems. However, the use of available model reduction techniques in nonlinear problems containing the contact type of nonlinearities remains an interesting topic. In this paper, the application of a component mode synthesis method in squeak and rattle nonlinear simulation has been investigated. Critical regions for squeak and rattle of the side door model of a passenger car were modelled by nonlinear contact definition in finite element simulation. Craig-Bampton model reduction method was employed to substructure the finite element model while keeping the nonlinear contacts in the model. The model response was evaluated using the modal assurance criterion, frequency response analysis and contact force magnitude in comparison with the baseline model. Results showed that a great reduction in computational time (about 98%) can be achieved while the accuracy of the system response was maintained at an acceptable range for the intended application for squeak and rattle simulation. Although the prediction of impact events in time was done accurately, the contact force magnitude was estimated with average error of 2.5% to 22%, compared with the baseline results. The outcomes of the study show that to empower squeak and rattle prediction by including contact interfaces in finite element simulations, implementation of the model reduction approach can compensate the simulation cost.</div></div>

There has been a growing demand for nonlinear model updating procedures in the structural dynamics community as advanced vehicles have started to incorporate nonlinearity into their designs. Finite element (FE) model updating is difficult for a nonlinear structure for several reasons: there may be many unknown parameters in the FE model so that multiple solutions may exist, and it is very expensive to compute the structure’s nonlinear normal modes from a full FE model that are an excellent metric to use for nonlinear updating. A recent work showed that some of these challenges can be overcome by updating a nonlinear reduced order model (ROM) rather than the full FE model. The updated ROM can be used to compute response statistics, stresses and ultimately life of the structure. However, one drawback of this approach is that one does not gain physical insight into which parameters in the FE model were in error, and so it is difficult to transfer the lessons learned to future FE models. This work explores the feasibility of updating a FE model to correlate with a ROM with a set of known parameters. The target ROM parameters consist of the linear stiffness and the nonlinear stiffness coefficients which have been identified previously by updating the ROM to correlate with experimental measurements. In this process an optimization routine is setup in which the free parameters are those of the FE model, such as boundary stiffness springs, imperfections, pre-stress, etc. The optimization procedure is wrapped around a ROM creation algorithm that iteratively tunes the FE parameters, creates a ROM, and evaluates the ROM parameters with respect to the target ROM in order to minimize the objective function. This work will demonstrate the procedure on a numerical example of a curved beam in order to verify its effectiveness on the nonlinear model updating.

One important issue for the simulation of flexible multibody systems is the reduction of the flexible body's degrees of freedom. For the reduction process finite element data and user inputs are necessary. The model reduction program for elastic multibody systems MOREMBS, which is developed at the ITM, has an easy‐to‐use interface and the data can be gained from the programs ABAQUS or ANSYS. In this work, the simulation of a fuel injection process is investigated with MOREMBS. We focus on the interaction between valve and armature. These two bodies impact in every injection circle. The impacting bodies are modeled as flexible and the contact force is calculated by a penalty approach. One essential part of this work is the investigation of the influence of different model reduction techniques on the impact force calculation of the flexible multibody system. The main reduction techniques modal reduction, Krylov‐subspace based and Gramian matrix based techniques are compared. The results achieved with modal reduction, the state of the art reduction method, are not acceptable here. Krylov‐subspace based techniques are especially well‐suited for large sparse systems but are not error controlled. However, by choosing appropriate moment‐matching properties the impact force calculation is nearly as good as with a full finite element model. The Gramian matrix based reduction techniques can be fully automated and are error controlled but require high computational effort. Hence, appropriate approximation schemes have to be used for them. With Gramian matrix based methods we can even further reduce the size of the subsystems compared to Krylov‐subspace based methods and still have an impact force calculation nearly as good as with finite element results, but we gain a simulation speedup by the factor 4000. In addition, a parameter study of the parameters involved in the model reduction process is presented. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The very general problem of model reduction of nonlinear systems was made tractable by focusing on the very large subclass consisting of linear subsystems connected by nonlinear interfaces. Such problems constitute a large part of the nonlinear structural problems encountered in addressing the Sandia missions. A synthesis approach to this class of problems was developed consisting of: detailed modeling of the interface mechanics; collapsing the interface simulation results into simple nonlinear interface models; constructing system models by assembling model approximations of the linear subsystems and the nonlinear interface models. These system models, though nonlinear, would have very few degrees of freedom. A paradigm problem, that of machine tool vibration, was selected for application of the reduction approach outlined above. Research results achieved along the way as well as the overall modeling of a specific machine tool have been very encouraging. In order to confirm the interface models resulting from simulation, it was necessary to develop techniques to deduce interface mechanics from experimental data collected from the overall nonlinear structure. A program to develop such techniques was also pursued with good success.

Non-intrusive data-driven model reduction for differential–algebraic equations derived from lifting transformations

This paper provides three model reduction methods for linear time-invariant systems in the view of the Riemannian Newton method and the Jacobi-Davidson method. First, the computation of Hankel singular values is converted into the linear eigenproblem by the similarity transformation. The Riemannian Newton method is used to establish the model reduction method. Besides, we introduce the Jacobi-Davidson method with the block version for the linear eigenproblem and present the corresponding model reduction method, which can be seen as an acceleration of the former method. Both the resulting reduced systems can be equivalent to the reduced system originating from a balancing transformation. Then, the computation of Hankel singular values is transformed into the generalized eigenproblem. The Jacobi-Davidson method is employed to establish the model reduction method, which can also lead to the reduced system equivalent to that resulting from a balancing transformation. This method can also be regarded as an acceleration of a Riemannian Newton method. Moreover, the application for model reduction of nonlinear systems with inhomogeneous conditions is also investigated.

This paper extends some methods in model order reduction (MOR) of nonlinear models by trajectory piecewise-linear models based on output weighting (TPWLOW). The devised methods generalize the balanced-truncation method as the core for the proposed algorithms. These algorithms preserve the stability in some mentioned conditions. An error bound of reduction is calculated for these algorithms. In addition, a Krylov–TBR combinational MOR is also casted which benefits from the advantages of both balanced-truncation and Krylov subspace methods. The results show that in balanced-truncation-based algorithms, the efficiency of the first proposed algorithm fairly exceeds the second one. In addition, it is shown that the Krylov–TBR algorithm can reach the same efficiency despite remarkable lower order, provided that the designer can find a stable subspace. The robustness of TPWLOW-reduced models to linearization point movement is also evaluated, which shows the less sensitivity of the proposed methods in comparison with formerly introduced trajectory piecewise-linear models.

Vibration-based damage detection for structural connections using incomplete modal data by Bayesian approach and model reduction technique

Smart structures can sense and actuate in a controlled manner in response to variable ambient stimuli combined with load carrying functions. If we are using finite element analysis up-front to design parts of our smart structures it is beset with problems like uncertainties from the manufacturing and in material properties. Attempts to improve the model with more detailed, sophisticated, refined discretised models are limited in either way. Hence, uncertainties not can be eliminated by shear mesh refinement or more detailed modelling in general. Moreover, model reduction techniques might be necessary to make a dynamical simulation feasible. Model updating aims to correct or at least alleviate invalid assumptions, omissions, and uncertainties as well as model reduction errors by processing vibration test results so that the theoretical model is closer to reality. Yet, model updating is limited in its applicability as well by the choice of the right parameters and weighting matrices. It also requires substantial computational effort because of the inverse character of the mathematical problem it involves; successful application requires a number of preparatory steps. Several methods for validation and error localisation should be applied to the FE model and a good selection of correction parameters (either sensitive or representative - a big problem). Today a wide variety of different model updating methods exist. We will confine ourselves to iterative updating methods. The updating of FE model parameters is based on a minimisation of a cost or penalty function at each iteration. These parameter estimation methods depend on the proper choice of the weighting matrices used ensure a good initial in the numerical process, and in the results.KeywordsWeighting MatriceSmart StructureSensitivity MatrixParameter Estimation MethodSuitable AlgorithmThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Probabilistic finite element predictions of the human lower limb model in total knee replacement

This work concerns the implementation of nonlinear modal reduction to flexible multi-body dynamics. Linear elastic theory will lead to instability issues with rotating beamlike structures, due to the neglecting of the membrane-bending coupling on the beam cross-section. During the past decade, considerable efforts have been focused on the derivation of geometric nonlinear formulation based on nodal coordinates. In this work, in order to improve the convergence characteristic and also to reduce the computation time in flexible multi-body dynamics, which is extremely important for complicated large systems, a standard modal reduction procedure based on matrix operation is developed with essential geometric stiffening nonlinearities retained in the equation of motion. The example used in this work is a rotating Euler-Bernoulli beam, two nonlinear reduced models were established based on modal coordinates, the first reduced model created from theoretical bending and axial mode shapes by Galerkin method; the second reduced model is derived by the standard matrix operator from a full finite element model. Transient simulation results of lower degrees of freedom from above two reduced models are compared with those obtained from full nonlinear finite element model.

This work proposes a model-reduction methodology that both preserves Lagrangian structure and leads to computationally inexpensive models, even in the presence of high-order nonlinearities. We focus on parameterized simple mechanical systems under Rayleigh damping and external forces, as structural-dynamics models often t this description. The proposed model-reduction methodology directly approximates the quantities that dene the problem’s Lagrangian structure: the Riemannian metric, the potential-energy function, the dissipation function, and the external force. These approximations preserve salient properties (e.g., positive deniteness), behave similarly to the functions they approximate, and ensure computational eciency. Results applied to a simple parameterized trussstructure problem demonstrate the importance of preserving Lagrangian structure and illustrate the method’s ability to generate speedups while maintaining observed stability, in contrast with other model-reduction techniques that do not preserve structure.

Weighted model reduction for nonlinear systems and computation method