Input Forcing Function Research Articles

Using Self-Organizing Map Algorithm to Reveal Stabilities of Parameter Sensitivity Rankings in Microbial Kinetic Models: A Case for Microalgae

Microalgae are multi-purpose microbial agents due to their capability to efficiently sequester carbon dioxide and produce valuable biomass such as protein and single-cell oils. Formulation and tuning of microalgae kinetics models can significantly contribute to the successful design and operation of microalgae reactors. This work aimed to demonstrate the capability of self-organizing map (SOM) algorithm to elucidate the patterns of parameter rankings in microalgae models subject to stochastic variations of input forcing functions–bioprocess influent component concentration levels. These stochastic variations were implemented on a modeled chemostat with a deterministic microalgae kinetic model consists of ten time-dependent variables and eighteen model parameters. The methodology consists of two major stages: (1) global sensitivity analysis (GSA) on the importance of model parameters with stochastic sampling of bioreactor influent component concentrations, and (2) training of self-organizing maps on the datasets of model parameter rankings derived from the GSA indices. Results reveal that functional principal components analysis can project at least 99% of the time-dependent dynamic patterns of the model variables on B-splines basis functions. The component planes for hexagonal lattice SOMs reveal that the sensitivity rankings some parameters in the algae model tested can be stable over a wide range of variations in the levels of influent component concentrations. Therefore, SOM can be used to reveal the trends in multi-dimensional data arrays arising from the implementation of GSA of kinetic models under stochastic perturbation of input forcing functions.

A wavelet-based dynamic mode decomposition for modeling mechanical systems from partial observations

Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems with external forcing, the identified model should not only be suitable for a specific forcing function but should generally approximate the input–output behavior of the underlying dynamics. A novel methodology for modeling those classes of dynamical systems is proposed in the present work, using wavelets in conjunction with the input–output dynamic mode decomposition (ioDMD). The wavelet-based dynamic mode decomposition (WDMD) builds on the ioDMD framework without the restrictive assumption of full state measurements. Our non-intrusive approach constructs numerical models directly from trajectories of the full model’s inputs and outputs, without requiring the full-model operators. These trajectories are generated by running a simulation of the full model or observing the original dynamical systems’ response to inputs in an experimental framework. Hence, the present methodology is applicable for dynamical systems whose internal state vector measurements are not available. Instead, data from only a few output locations are only accessible, as often the case in practice. The present methodology’s applicability is explained by modeling the input–output response of an Euler–Bernoulli finite element beam model. The WDMD provides a linear state-space representation of the dynamical system using the response measurements and the corresponding input forcing functions. The developed state-space model can then be used to simulate the beam’s response towards different types of forcing functions. The method is further validated on a real (experimental) data set using modal analysis on a simple free–free beam, demonstrating the efficacy of the proposed methodology as an appropriate candidate for modeling practical dynamical systems despite having no access to internal state measurements and treating the full model as a black-box.

Analytical stochastic framework for assessment of base- and mass-excited structures under equal input energy pertinent to multi-hazard engineering

ABSTRACT Analytical framework for probabilistic assessment of dynamical system under base- and mass- excitations with equal input energy is presented with reference to multi-hazard engineering. Closed-form solutions for equivalent undamped and damped dynamical systems under harmonic sinusoidal base- and mass- excitations are obtained. Uncertainties are considered in the excitation frequency and peak amplitude for sinusoidal base excitations, whereas for the mass excitations, the input forcing functions have variations in excitation frequency, mean speed, and fluctuating wind speeds. Dynamic response quantities (acceleration and displacement) are obtained under the suite of stochastic base and mass excitation forces. Structural failure under the independent excitations is determined as joint probability density functions and fragility surfaces. Under equal input energy from such separate dynamic excitations, dissimilar vulnerability is exhibited by the structure when exposed to two independent time-dependent excitations, base-induced earthquake and mass-induced wind forces. Moreover, the uncertainty in the input excitation parameters has significant influence on the probability of failure in the design life of structure under the non-simultaneous excitations.

Comparative Study, Design and Analysis of a G+12 Structure in Earthquake Zone in India

Seismic isolation is a technology that decouples a building structure from the damaging earthquake motion. It is a simple structural design approach to mitigate or reduce potential earthquake damage. In base-isolated structures, the seismic protection is obtained by shifting the natural period of the structure away from the range of the frequencies for which the maximum amplification effects of the ground motion are expected; thus, the seismic input energy is significantly reduced. At the same time, the reduction of the high deformations attained at the base of the structure is possible, thanks to the energy dissipation caused by the damping and the hysteretic properties of these devices, further improving the reduction of responses of the structures. Base isolation is also an attractive retrofitting strategy to improve the seismic performance of existing bridges and monumental historic building.  The method of base isolation was developed in an attempt to mitigate the effects of earthquakes on buildings during earthquakes and has been practically proven to be the one of the very effective methods in the past several decades.  Base isolation consists of the installation of support mechanism which decouples the structure from earthquake induced ground motions.  Base isolation allows to filter the input forcing functions and to avoid acceleration seismic forces on the structure.  If the structure is separated from the ground during an earthquake, the ground is moving but the structure experienced little movement. To minimize the transmission of potentially damaging earthquake ground motions into a structure is achieved by the introduction of flexibility at the base of the structure in the horizontal direction while at the same time introducing damping elements to restrict the amplitude or extent of the motion caused by the earthquake somewhat akin to shock absorbers. In recent years this relatively new technology has emerged as a practical and economic alternative to conventional seismic strengthening. This concept has received increasing academic and professional attention and is being applied to a wide range of civil engineering structures. To date there are several hundred buildings in Japan, New Zealand, United States, India which use seismic isolation principles and technology for their seismic design.

Time-domain stochastic finite element simulation of uncertain seismic wave propagation through uncertain heterogeneous solids

This paper presents an efficient numerical methodology in probabilistically solving the governing partial differential equation of solid mechanics with uncertainties in both the material parameter and forcing function in the time domain using the stochastic Galerkin approach. The methodology hypothesizes the input forcing function and the elastic modulus of the solid to be a nonstationary random process and a heterogeneous random field, respectively, and efficiently represents them in terms of multidimensional Hermite polynomial chaos – orthogonal and uncorrelated polynomials of zero-mean, unit variance Gaussian random variables – by taking advantage of the optimality of the Kosambi-Karhunen-Loève theorem. The methodology allows for any non-Gaussian marginal distributions and any arbitrary correlation structures for the input process and field. The solution random processes (displacement, velocity, and acceleration) are also represented in terms of multidimensional Hermite polynomial chaos expansions whose coefficients at each time step are estimated by applying a stochastic Galerkin projection with the time integration performed via the Newmark's method. The methodology is illustrated, keeping the geotechnical site response analysis in mind, with fully probabilistic, time-domain propagations of bedrock motions through an elastic soil deposit in one-dimension, and is verified using the Monte Carlo method. The effects of input uncertainty parameters of the soil modulus and bedrock motion on the simulated surface motion are also quantified through a parametric sensitivity study.

Discrete-Time $H_{\infty}$ Filtering for Mobile Robot Localization Using Wireless Sensor Network

This paper proposes a localization technique for mobile robots using a wireless sensor network (WSN), based on chirp spread spectrum ranging and an inertial measurement unit (IMU). A discrete-time <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter with input forcing function is newly derived for mobile robot localization. The position of the robot is estimated by the filter using an integration of position information collected by the WSN and absolute acceleration data obtained by the IMU. From the dynamics of the robot, the solution existence of the proposed filter is shown, and a low-complexity computational method to obtain a solution from the filter is proposed by a generalized eigenvector approach. Through simulation and experiments, we evaluate the performance of the proposed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter and compare it with the standard Kalman filter.

Estimation of the 18F-FDG input function in mice by use of dynamic small-animal PET and minimal blood sample data.

Derivation of the plasma time-activity curve in murine small-animal PET studies is a challenging task when tracers that are sequestered by the myocardium are used, because plasma time-activity curve estimation usually involves drawing a region of interest within the area of the reconstructed image that corresponds to the left ventricle (LV) of the heart. The small size of the LV relative to the resolution of the small-animal PET system, coupled with spillover effects from adjacent myocardial pixels, makes this method reliable only for the earliest frames of the scan. We sought to develop a method for plasma time-activity curve estimation based on a model of tracer kinetics in blood, muscle, and liver. Sixteen C57BL/6 mice were injected with (18)F-FDG, and approximately 15 serial blood samples were taken from the femoral artery via a surgically inserted catheter during 60-min small-animal PET scans. Image data were reconstructed by use of filtered backprojection with CT-based attenuation correction. We constructed a 5-compartment model designed to predict the plasma time-activity curve of (18)F-FDG by use of data from a minimum of 2 blood samples and the dynamic small-animal PET scan. The plasma time-activity curve (TACp) was assumed to have 4 exponential components (TAC(P)=A(1)e(lambda(1)t)+A(2)e(lambda(2)t)+A(3)e(lambda(3)t)-(A(1)+A(2)+A(3))e(lambda(4)t)) based on the serial blood samples. Using Bayesian constraints, we fitted 2-compartment submodels of muscle and liver to small-animal PET data for these organs and simultaneously fitted the input (forcing) function to early small-animal PET LV data and 2 blood samples (approximately 10 min and approximately 1 h). The area under the estimated plasma time-activity curve had an overall Spearman correlation of 0.99 when compared with the area under the gold standard plasma time-activity curve calculated from multiple blood samples. Calculated organ uptake rates (Patlak K(i)) based on the predicted plasma time-activity curve had a correlation of approximately 0.99 for liver, muscle, myocardium, and brain when compared with those based on the gold standard plasma time-activity curve. The model was also able to accurately predict the plasma time-activity curve under experimental conditions that resulted in different rates of clearance of the tracer from blood. We have developed a robust method for accurately estimating the plasma time-activity curve of (18)F-FDG by use of dynamic small-animal PET data and 2 blood samples.

Modal Scheduling and Switching Systems

This paper defines a modal scheduling method for obtaining reduced order systems. In contrast to most order reduction schemes for linear structural systems, the methodology in this paper introduces a switched system to achieve order reduction. The switched system model is based on modal participation factors calculated from an input forcing function and the initial conditions at each switching time. Stability of the reduced order model is discussed, and necessary conditions for stability of the proposed switched model are derived. A numerical example that considers a flexible beam provides a testbed for the study of mode switching. The transient response in the testbed example is constructed such that it oscillates between two distinct subspaces. Numerical experiments show that an error indicator based on modal participation factors provides an effective switching strategy.

Evaluation of the damping ratio for a base-excited system by the modulations of responses

The present article gives a method for evaluating or identifying the linear viscous damping ratio of single-degree-of-freedom systems, which are excited from its base. Unlike most of the existing methods that are based on transient responses and the assumption of small damping, the present method does not require the system to have a small damping. The novel method is derived using the input-forcing function as the reference signal, and the corresponding system responds as the modulator. However, in order to get the phase-lag signal without measuring the amplitudes of input and response, a second reference signal has been proposed in the present report. That is, the input-forcing function with 90 ∘ shift in its phase is taken as the second reference. The two modulated signals are then independently split into two parts. The part, which is time-invariant, is the one containing the system damping. It has been shown by the numerical simulations that the given method identifies the damping ratio with a good accuracy if the excitation frequency is tuned to the phase-sensitive region. Finally, the experimental study in the present report also further substantiates the applicability and validity of the method.

Shock and Vibration Testing of an AMB Supported Energy Storage Flywheel

Shock and vibration testing of an Active Magnetic Bearing (AMB) supported energy storage flywheel is presented. The flywheel is under development at the University of Texas - Center for Electromechanics (UTCEM) for application in a transit bus. The flywheel is gimbal mounted to reduce the gyroscopic forces transmitted to the magnetic bearings during pitching and rolling motions of the bus. The system was placed on a hydraulic terrain simulator and driven through pitch, roll and shock motions equivalent to 150% of maximum expected bus frame values. Although the AMB control approach was originally developed specifically to ensure rotordynamic stability, relative rotor/housing motion was typically less than half of the backup bearing clearance under all tested conditions. Test results are presented and compared to analytical predictions for the 35,000 rpm nominal operating speed. The impact of the AMB control algorithm is discussed relative to the input forcing function.

On the effects of higher vibration modes in the analysis of three point bend testing

Influence of higher modes of vibration in the dynamic analysis of impact three point bend specimen based on Euler-Bernoulli and Timoshenko beam theories are investigated in an attempt to predict the oscillatory behavior seen in the measured dynamic SIF history. Forced vibration of the cracked beam is analyzed by normal mode summation method. Contact force history computed using fundamental mode approximation is applied as input forcing function and the computed SIF histories are compared with finite element model and experimental data. Analytical and finite element results show that modes higher than the third have practically no influence on the notched beam response.

A modeling via Hamilton's law with application to a model following resembling technique

As a result of direct application of Hamilton's law of varying action on the treatment of mechanical systems, solving both dynamic and control problems is done using algebraic equations only; no differential equations are needed. In these techniques both the dynamic response and control forces are assumed to be a truncated power series. The target was only to solve the concerned problem. Using the coefficients of the above-mentioned polynomials in the vector form, an input-output model for the mechanical system to follow a specified path, while it is perturbed out of that path, is introduced herein. The modeling uses only algebraic equations. In this work, a model following resembling technique is demonstrated as a useful application of this modeling way. That is to get the required input forcing function to obligate the mechanical system to behave like a reference system when it is shifted away from the specified path.

Comparison of Experimental and Finite Element Structure-Borne Flexural Power Measurements for a Straight Beam

Experimental and finite element methods are used to measure flexural powers in a straight beam model. The experimental methods use wave decomposition theory to obtain expressions for the incident, reflected and near-field wave spectra for a beam vibrating in flexure in terms of the measured auto- and cross-spectra of an array of closely spaced accelerometers. With expressions for the wave spectra, it is possible to measure the structural power and termination impedances related to the bending waves in the beam. The finite element approach models beams numerically by discretizing structures into elements which model elastic wave motions. The structural response is predicted for given loading and boundary conditions, and the power variables are calculated from element forces and velocities. The input forcing functions and end impedances (boundary conditions) of two experimental cases were applied to a finite element model. In one case, the beam was attached to a lightly damped mount and in the other case a heavily damped mount was used. Measured and predicted flexural powers were compared and showed mixed agreement. The directionality of power was accurately predicted, as was the general character of the power spectra. However, differences in power magnitudes, particularly in the lightly damped mounting case, were discovered. The power magnitude errors were attributed to accuracy limitations in the applied termination impedances. The results suggest that the finite element method may be used to predict accurately the direction and spectral trends of beam flexural power, but that numerical power magnitudes are highly dependent on accurate boundary condition quantification.

Proposed formulae for the power spectral densities of fluctuating lift and torque on rectangular 3-D cylinders

New empirical formulae are presented for the spectra of lift and torque for square and rectangular section buildings with different side ratios and their validity and applicability are discussed comparing with experimental data in three different boundary layers. As a results, it is shown that the new empirical formulae may provide more accurate input forcing functions for preliminary design of isolated tall buildings with various geometrical conditions than existing formulae.

A fast time-domain algorithm for the simulation of switching power converters

An efficient algorithm for the simulation of switched-mode power converters is developed. A Chebyshev series expansion is used to effectively solve the differential equations describing the system in each topology. The power of the new simulation technique lies both in the simple, but accurate, polynomial approximation for the state transition matrices and in the ability to explicitly obtain the instants at which the switching of the circuit topology takes place. The simulation technique is illustrated with reference to a simple Buck converter operating at a constant frequency. The derivation of the new algorithm is presented and its performance is analyzed. The case of a rapidly varying input forcing function is analyzed. Examples illustrating the generality and the computational efficiency of the algorithm are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Large-Displacement Finite Element Analysis of Flexible Linkages

A finite element model is derived for flexible planar linkages, treating the total mechanism displacements as the primary unknowns in the dynamic equations of motion. These displacements consist of the combination of large rigid-body mechanism motion and small elastic deformations. Beam elements are used in the model formulation. The resulting nonlinear equations can be solved under conditions of either specified input motion of the mechanism or specified input forcing functions. In either case, the differential equations are integrated numerically. Illustrative examples are presented, and comparisons are made with results of previous investigators and with results from a commercial finite element code.

Robust adaptive Kalman filtering with unknown inputs

A method is proposed to adapt the Kalman filter to the changes in the input forcing functions and the noise statistics. The resulting procedure is stable in the sense that the duration of divergences caused by external disturbances are finite and short and, also, the procedure is robust with respect to impulsive noise (outlier). The input forcing functions are estimated by a running window curve-fitting algorithm, which concurrently provides estimates of the measurement noise covariance matrix and the time instant of any significant change in the input forcing functions. In addition, an independent technique for estimating the process noise covariance matrix is suggested which establishes a negative feedback in the overall adaptive Kalman filter. This procedure is based on the residual characteristics of the standard optimum Kalman filter and a stochastic approximation method. The performance of the proposed method is demonstrated by simulations and compared to the conventional sequential adaptive Kalman filter algorithm. >

Experimental Investigation of Pressure Oscillations in a Side Dump Ramjet Combustor

A two-inlet, side dump ramjet combustor configuration was tested in a connected-pipe setup using uncooled and uninsulated chamber walls. High amplitude combustion induced pressure oscillations were observed during most test conditions with a predominant frequency of around 300 Hz. Special efforts were made to relate the oscillations to longitudinal acoustic modes. A simplified no flow, uniform temperature acoustic cavity prediction method (NASTRAN) was utilized to model the longitudinal acoustic modes. This model was verified via room temperature laboratory tests using the actual test hardware and a loudspeaker as an input forcing function to excite the acoustic modes. During combustion tests, the measured oscillation modes were tentatively identified as second or third longitudinal modes or a bulk mode, depending on the test conditions.

Application of frequency domain analysis to transient response of nuclear containment structures

A combination of frequency domain and time domain analyses is proposed to obtain the dynamic responses of nuclear power plant containment structures. A soil-structure model of a boiling water reactor containment subjected to an assumed safety relief valve blowdown load is used as illustration. Linear time-invariant systems are analyzed using input forcing functions with varying frequency contents. Time domain analysis is performed using a synthesized input forcing function. The system characteristic function is generated in the frequency domain through Fourier transforms of the response time history and the synthesized input time history. The frequency response due to any other forcing function is obtained in frequency domain by using the system characteristic function, and the response time history is obtained by inverse Fourier transforms of the frequency response. The results obtained by the proposed method are in close agreement with the conventional time domain dynamic finite element analysis.

Estimation of Payload Loads Using Rigid-Body Interface Accelerations

In the design/analysis process of a payload structural system, the accelerations at the payload/launch vehicle interface obtained from a system analysis using a rigid payload are often used as the input forcing function to the elastic payload to obtain structural design loads. Such an analysis is at best an approximation since the elastic coupling effects are neglected. This paper develops a method wherein the launch vehicle/rigid payload interface accelerations are modified to account for the payload elasticity. The advantage of the proposed method, which is exact to the extent that the physical system can be described by a truncated set of generalized coordinates, is that the complete design/analysis process can be performed within the organization responsible for the payload design. The method requires the updating of the system normal modes to account for payload changes, but does not require a complete transient solution using the composite system model. An application to a real complex structure, the Viking Spacecraft System, is given.