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At least 235 records · Page 13

A structure-preserving machine learning framework for accurate prediction of structural dynamics for systems with isolated nonlinearities

The nonlinearities present in structural systems are often found in isolated regions within the structure, such as those containing joints or interfaces. However, despite the localized nature of these nonlinearities their presence serves to couple together the modes of the underlying linear system and significantly complicate the development of appropriate reduced-order models; the localized nonlinearities have a global effect on the dynamics of the system. Further, in the presence of evolving structural health the nonlinearities can arise from accumulating damage, with dynamics distinct from those observed in the healthy state. The present work develops a data-driven formulation to identify and include the contributions of the isolated nonlinearities on the dynamics of the underlying linear structure. A novel coordinate separation is developed that decomposes those nonlinearities restricted to the isolated subdomain from the known linear system defined over the entire domain, and the influence of the isolated nonlinearities is reintroduced as an appropriately identified traction at the boundary of the isolated subdomain, referred to as the deviatoric force. In the region exterior to the nonlinear subdomain the response of the ideal linear system recovers that of the original nonlinear system. In this work, the deviatoric force component is predicted using a structure-preserving multilayer perceptron, based only on measured responses at the boundary of the isolated subdomain. Therefore introduction of the perceptron is able to bypass the direct numerical simulation of the nonlinearities within the isolated subdomain. This approach is illustrated through a simple structural system in which an interior region contains cubic nonlinearities and hysteretic damping. Once trained, the machine learning system is able to accurately predict the deviatoric force so that the ideal system recovers the response of the original system in the region outside the isolated nonlinear subdomain. Moreover, the data-driven approach is able to accurately predict the response when the system is subject to differing initial conditions and external excitation without the need for retraining, so that the proposed approach provides a robust description of the structural dynamics of the overall system.

Machine learning↗

ROM-Based Surrogate Systems Modeling of EBR-II

We report the System Analysis Module (SAM), developed and maintained by Argonne National Laboratory, is designed to provide whole-plant transient safety analysis capabilities for a number of advanced non-light water reactors, including sodium-cooled fast reactor (SFR), lead-cooled fast reactor (LFR), and molten salt reactor (MSR)/fluoride-salt-cooled high-temperature reactor (FHR) designs. SAM is primarily constructed as a systems-level analysis tool, with the potential to incorporate reduced order models from three-dimensional computational fluid dynamics (CFD) simulations to improve characterization of complex, multidimensional physics. It is recognized that the computational expense associated with CFD can be intractable for various engineering analyses, such as uncertainty quantification, inference, and design optimization. This paper explores the reducibility of a SAM model using recent advances in randomized linear algebra techniques, which attempt to find recurring patterns in the various realizations generated by a model after randomly perturbing all its input parameters. The reduction is described in terms of fewer degrees of freedom (DOFs), referred to as the active DOFs, for the model variables such as input model parameters and model responses. The results indicate that there is significant room for additional reduction that may be leveraged for additional computational gains when employing SAM for engineering-intensive analyses that require repeated model executions. Different from physics-based reduction approaches, the proposed approach allows one to estimate upper bounds on the reduction errors, which are rigorously developed in this work. Finally, different methods for surrogate model construction, such as regression and neural network-based training, are employed to correlate the input and output active DOFs, which are related back to the original variables using matrix-based linear transformations.

42 ENGINEERING↗

Analysis of the Effects of Surface Pitting and Wear on the Vibrations of a Gear Transmission System

A comprehensive procedure to simulate and analyze the vibrations in a gear transmission system with surface pitting, 'wear' and partial tooth fracture of the gear teeth is presented. An analytical model was developed where the effects of surface pitting and wear of the gear tooth were simulated by phase and magnitude changes in the gear mesh stiffness. Changes in the gear mesh stiffness were incorporated into each gear-shaft model during the global dynamic simulation of the system. The overall dynamics of the system were evaluated by solving for the transient dynamics of each shaft system simultaneously with the vibration of the gearbox structure. In order to reduce the number of degrees-of-freedom in the system, a modal synthesis procedure was used in the global transient dynamic analysis of the overall transmission system. An FFT procedure was used to transform the averaged time signal into the frequency domain for signature analysis. In addition, the Wigner-Ville distribution was also introduced to examine the gear vibration in the joint time frequency domain for vibration pattern recognition. Experimental results obtained from a gear fatigue test rig at NASA Lewis Research Center were used to evaluate the analytical model.

Choy, F. K.↗

Reduced order component models for flexible multibody dynamics simulations

Many flexible multibody dynamics simulation codes require some form of component description that properly characterizes the dynamic behavior of the system. A model reduction procedure for producing low order component models for flexible multibody simulation is described. Referred to as projection and assembly, the method is a Rayleigh-Ritz approach that uses partitions of the system modal matrix as component Ritz transformation matrices. It is shown that the projection and assembly method yields a reduced system model that preserves a specified set of the full order system modes. Unlike classical component mode synthesis methods, the exactness of the method described is obtained at the expense of having to compute the full order system modes. The paper provides a comprehensive description of the method, a proof of exactness, and numerical results demonstrating the method's effectiveness.

Tsuha, Walter S.↗

On model reduction

Three model reduction methods are described. These are the discrete balanced realizations of Mullis and Roberts (1976) where a characterization of the reduction error is given and a previously unknown L(infinity) norm bound on the reduction error, is obtained. Another method is a new model reduction technique for discrete time systems which has the advantage that the reduced order model is balanced and has an L(infinity) norm bound on the reduction error. The last method derived is a frequency weighting technique for continuous and discrete systems where it is possible to specify the approximation accuracy with frequency and also, for this method, an L(infinity) norm on the weighted reduction error is obtained.

Al-Saggaf, Ubaid M.↗

Results of the space shuttle vehicle ascent air data system probe calibration test using a 0.07-scale external tank forebody model (68T) in the AEDC 16-foot transonic wind tunnel (IA-310), volume 1

A recalibration of the Space Shuttle Vehicle Ascent Air Data System probe was conducted in the Arnold Engineering Development Center (AEDC) transonic wind tunnel. The purpose was to improve on the accuracy of the previous calibration in order to reduce the existing uncertainties in the system. A probe tip attached to a 0.07-scale External Tank Forebody model was tested at angles of attack of -8 to +4 degrees and sideslip angles of -4 to +4 degrees. High precision instrumentation was used to acquire pressure data at discrete Mach numbers ranging from 0.6 to 1.55. Pressure coefficient uncertainties were estimated at less than 0.0020. Data is given in graphical and tabular form.

Collette, J. G. R.↗

gLaSDI: Parametric physics-informed greedy latent space dynamics identification

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. Here, an interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a -nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658× speed-up with 1 to 5% relative errors.

97 MATHEMATICS AND COMPUTING↗

Modeling District Heating and Cooling Systems with URBANopt, GeoJSON to Modelica Translator, and the Modelica Buildings Library

The URBANopt project has successfully leveraged OpenStudio/EnergyPlus to model buildings and electrical systems at an urban scale; however, URBANopt has lacked the ability to model district thermal energy systems until recently. This paper will present the modeling infrastructure that was developed specifically for the analysis of district heating and cooling systems, and how it is integrated into the existing URBANopt framework. The paper also discusses the development of new models added to the Modelica Buildings Library to model various district energy system components including loads, energy transfer stations (ETS), distribution networks, and central plants. The paper describes how different building loads can be modeled including time series, TEASER reduced-order models, or Spawn of EnergyPlus models. URBANopt District Energy Systems allows the user to switch between the various configurations.

district heating and cooling↗

Lower Level Repair Can Easily Fail Due to High Complexity

The International Space Station (ISS) uses Orbital Replacement Units (ORU’s) to repair failures on orbit. Using ORU’s reduces the crew time required to repair failures, but several copies of each ORU must be stored on ISS to ensure system availability. A typical ORU contains many components and has significant mass, but each ORU can repair only a single component failure. A full set of the ORU internal components could repair many different failures. Lower level assembly or component repair should reduce total spares mass. Successful electronics repair experiments were conducted on ISS. However, implementing component level repair would require a significant effort. The systems must be designed so they can be repaired during a mission, considering component layout and accessibility. The repair procedures must be developed and repair facilities, tools, and diagnostic and test instruments provided. Tracing a fault to a component is much more difficult than isolating it to an ORU. Replacing a component is much more difficult than replacing an ORU. Some problems with lower level repair are discussed. The mass savings of lower level repair will not save as much launch cost as before since launch cost has recently been reduced by an order of magnitude. Most system failures are not component failures that can be fixed by replacing a component but are due to system level problems. Repair and maintenance should be planned as part of an overall maintainability design. The risk that a lower level repair will fail is considerably greater than when using ORUs. With modern high reliability packaged systems, failure diagnosis and repair has become a lost art. However, diagnosis and repair data from the 1960’s show that increasing complexity often causes much longer diagnosis and repair times and may prevent successful repair. Increasing complexity by using lower level repair directly increases system cost, failure rate, crew time for repair, and the risk of an unrepairable system failure.

Harry W Jones↗

Results of the space shuttle vehicle ascent air data system probe calibration test using a 0.07-scale external tank forebody model (68T) in the AEDC 16-foot transonic wind tunnel (IA-310), volume 2

A recalibration of the Space Shuttle Vehicle Ascent Air Data System probe was conducted in the Arnold Engineering and Development Center (AEDC) transonic wind tunnel. The purpose was to improve on the accuracy of the previous calibration in order to reduce the existing uncertainties in the system. A probe tip attached to a 0.07-scale External Tank Forebody model was tested at angles of attack of -8 to +4 degrees and sideslip angles of -4 to +4 degrees. High precision instrumentation was used to acquire pressure data at discrete Mach numbers ranging from 0.6 to 1.55. Pressure coefficient uncertainties were estimated at less than 0.0020. Additional information is given in tabular form.

Collette, J. G. R.↗

On eigensystem assignment with dissipativity constraints

Stability of the closed-loop system is of vital importance when controller synthesis is being performed using a reduced order model of the open-loop plant. For passive systems such as flexible space structures, closed-loop stability is often ensured by low-authority dissipative controllers using collocated and compatible sensors and actuators. This paper considers the problem of eigensystem assignment for flexible structures using constant-gain output feedback, under the dissipativity constraints requiring that the gain matrices be nonnegative definite. A novel method is developed in which a sequential procedure is used to assign one complex-conjugate pair of closed-loop eigenvalues in each step. At each step, an iterative technique is employed for generating a nonnegative definite gain matrix that assigns a new pair while keeping the previously assigned pairs unchanged. This method can assign up to m closed-loop system eigenvalues, where m is the number of control inputs. A numerical example of damping enhancement for a large flexible structure is presented to demonstrate the approach.

Maghami, Peiman G.↗

Developing Reaction Chemistry Models from Reactive Molecular Dynamics: TATB

Reactive Molecular Dynamic (RMD) are used to simulate the cook-off chemistry of TATB at a variety of fixed density and fixed temperature conditions. The chemical transformations are monitored using a Coordination Geometry Analysis (CGA) approach which tracks which atom types are bonded to each specific atom. This particularly identifies oxidation state changes that occur during the transformations. Correlations between these different chemical changes are identified using a Non-negative Matrix Factorization (NMF) approach. These identify reduced order chemistry models for the TATB system which contains six components whose concentration profiles are a function of both the temperature and density/pressure. The time histories of these transformations appear to show exponential growth/decay properties that could be fit with Arrhenius rates. These components should form the basis of deflagration rate models for these materials which could then be used in mesoscale simulations to analyze accidental initiation, shock-to-detonation and detonation propagation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transient Thermal Analyses of Passive Systems on SCEPTOR X-57

As efficiency, emissions, and noise become increasingly prominent considerations in aircraft design, turning to an electric propulsion system is a desirable solution. Achieving the intended benefits of distributed electric propulsion (DEP) requires thermally demanding high power systems, presenting a different set of challenges compared to traditional aircraft propulsion. The embedded nature of these heat sources often preclude the use of traditional thermal management systems in order to maximize performance, with less opportunity to exhaust waste heat to the surrounding environment. This paper summarizes the thermal analyses of X-57 vehicle subsystems that don't employ externally air-cooled heat sinks. The high-power battery, wires, high-lift motors, and aircraft outer surface are subjected to heat loads with stringent thermal constraints. The temperature of these components are tracked transiently, since they never reach a steady-state equilibrium. Through analysis and testing, this report demonstrates that properly characterizing the material properties is key to accurately modeling peak temperature of these systems, with less concern for spatial thermal gradients. Experimentally validated results show the thermal profile of these systems can be sufficiently estimated using reduced order approximations.

Thermal Analyses↗

Two time scale design of output feedback systems

Singular perturbation techniques are used in this paper to develop a two time scale procedure for designing static gain output feedback controllers. It is shown that, if certain control spillover conditions are satisfied, control designs based on reduced-order models will stabilize the corrgsponding full system. Optimal output feedback control theory is used to derive the necessary conditions for the stabilizing gain matrix. The problem of stabilizing a model for a large space structure is used to illustrate the practicality of the approach.

Calise, A. J.↗

Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced order methods are demanded. Combining these techniques with nonlinearity, we will consider in this paper a dual-continuum model which is generalized as a multi-continuum model for a coupled system of nonlinear Richards equations as unsaturated flows, in complex heterogeneous fractured porous media; and we will solve it by a novel multiscale approach utilizing the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). In particular, such a nonlinear system will be discretized in time and then linearized by Picard iteration (whose global convergence is proved theoretically). Subsequently, we tackle the resulting linearized equations by the CEM-GMsFEM and obtain proper offline multiscale basis functions to span the multiscale space (which contains the pressure solution). More specifically, we first introduce two new sources of samples, and the GMsFEM is used over each coarse block to build local auxiliary multiscale basis functions via solving local spectral problems, that are crucial for detecting high-contrast channels. Second, per oversampled coarse region, local multiscale basis functions are created through the CEM as constrainedly minimizing an energy functional. Various numerical tests for our approach reveal that the error converges with the coarse-grid size and that only few oversampling layers as well as basis functions are needed.

97 MATHEMATICS AND COMPUTING↗

Global System Reduction Order Modeling for Localized Feature Inclusion

The development of reduced-order models remains an active research area, despite advances in computational resources. Here we develop a novel order-reduction approach that is designed to incorporate isolated regions that contain, for example, nonlinearitites or accumulating damage. The approach is designed to use global modes of the overall system response, which are then naturally coupled to the response in the isolated region of interest. Two examples are provided to demonstrate both the accuracy and the computational efficiency of the proposed approach. The performance of this approach is compared to the exact response corresponding to a finite element simulation for the chosen problems. In addition, the accuracy and computational efficiency are shown relative to a standard Galerkin reduction based on the linear normal modes. It is found that the proposed reduction offer computational efficiency comparable to a Galerkin reduction, but more accurately represents the response of the system when both are compared to the finite element simulation.

42 ENGINEERING↗

Solution and sensitivity analysis of nonlinear equations using a hypercomplex-variable Newton-Raphson method

Here, the classical Newton-Raphson (NR) method for solving nonlinear equations is enhanced in two ways through the use of hypercomplex variables and algebra. In particular, i) the Jacobian is computed in a highly accurate and automated way, and ii) the derivative of the solution to the nonlinear equations is computed with respect to any parameter contained within the system of equations. These advances provide two significant enhancements in that it is straightforward to provide an accurate Jacobian and to construct a reduced order model (ROM) of arbitrary order with respect to any parameter of the system. The ROM can then be used to approximate the solution for other parameter values without requiring additional solutions of the nonlinear equations. Several case studies are presented including 1D and 2D academic examples with fully functioning Python code provided. Additionally, a case of study of the catenary of an elastic cable subject to its own weight and a vertical point load. Derivatives up to 10th order were computed with respect to material, loading, and geometrical parameters. The derivatives were used to generate reduced order models of the cable deformation and reaction forces at its ends with respect to multiple input parameters. Results show that from a single hypercomplex evaluation of the cable under a single vertical point load, it is possible to generate an accurate reduced order model capable of predicting the cable deformation with 1.5 times the load in the opposite direction and with 3.5 times the load in the same direction without resolving the system of equations.

97 MATHEMATICS AND COMPUTING↗