Forcing Function Research Articles

Control law design for discrete linear repetitive processes with non-local updating structures

Repetitive processes are a class of 2D systems where information propagation in one direction is of finite duration. These processes make a series of sweeps, termed passes, through a set of dynamics and on completion of each pass resetting to the starting position occurs ready for the start of the next pass. The control problem is that the previous pass output, termed the pass profile, acts as a forcing function on the current pass and can result in oscillations that increase in amplitude from pass-to-pass. In the case of discrete dynamics, these processes have structural links with 2D systems described by the well known Roesser and Fornasini–Marchesini state-space models but some applications require updating structures that cannot be represented by these models. This requirement arises either in adequately modeling the dynamics or as a result of the control law structure and requires the development of a systems theory for eventual use in applications. In this paper such a theory is advanced through the development of new control law design algorithms.

Patient safety improvements in radiation treatment through 5 years of incident learning

PurposeTo quantify the impact of a comprehensive incident learning system in terms of safety improvements. Methods and MaterialsAn incident learning system tailored for radiation treatment and based on published principles has been used consistently in our large academic cancer center for more than 5 years. In the adopted system, every incident, whether or not there is a resulting direct impact on a patient treatment, is recorded and investigated to determine basic causes. The scope of the program thus includes potential, or near miss, events which have no impact on patients but which provide valuable insights into program weaknesses and hence facilitate proactive measures to minimize risk. ResultsAnalysis of 2506 incident reports generated over a 5-year period demonstrate a substantial decline in actual, nonminor incidents; ie, those with a dose variation from that prescribed of greater than 5%. Only 49 incidents (1.95%) had an impact on patients. The actual incident rate at the point of treatment delivery, the most vulnerable point in our process, has also decreased. The system has provided rapid feedback to monitor several initiatives including implementation of new technology and several new treatment techniques. Using the evidence provided by these incident reports, strategies were developed by a multidisciplinary team to address system weaknesses. Interventions introduced include several human error reduction strategies including forcing functions and constraints to improve system resilience. ConclusionsOur results demonstrate that effective use of an incident learning system will strongly encourage the reporting of incidents, whether or not they directly impact a patient, and serve as a proactive means of enhancing safety and quality. As a side benefit, addressing and overcoming the cultural barriers between the 3 professional groups involved in radiation treatment has resulted in an improvement in the safety culture in our center.

Comparison of Ares I-X Wind-Tunnel-Derived Buffet Environment with Flight Data

The Ares I-X Flight Test Vehicle (FTV), launched in October 2009, carried with it over 243 buffet verification pressure sensors and was one of the most heavily instrumented launch vehicle flight tests. This flight test represented a unique opportunity for NASA and its partners to compare the wind-tunnel derived buffet environment with that measured during the flight of Ares I-X. It is necessary to define the launch vehicle buffet loads to ensure that structural components and vehicle subsystems possess adequate strength, stress, and fatigue margins when the vehicle structural dynamic response to buffet forcing functions are considered. Ares I-X buffet forcing functions were obtained via wind-tunnel testing of a rigid buffet model (RBM) instrumented with hundreds of unsteady pressure transducers designed to measure the buffet environment across the desired frequency range. This paper discusses the comparison of RBM and FTV buffet environments, including fluctuating pressure coefficient and normalized sectional buffet forcing function root-mean-square magnitudes, frequency content of power-spectral density functions, and force magnitudes of an alternating flow phenomena. Comparison of wind-tunnel model and flight test vehicle buffet environments show very good agreement with root-mean-square magnitudes of buffet forcing functions at the majority of vehicle stations. Spectra proved a challenge to compare because of different wind-tunnel and flight test conditions and data acquisition rates. However, meaningful and promising comparisons of buffet spectra are presented. Lastly, the buffet loads resulting from the transition of subsonic separated flow to supersonic attached flow were significantly over-predicted by wind-tunnel results.

Structural acoustic optimization of ribbed panels excited by complex forcing functions

Structural acoustic optimization is performed on a ribbed panel exited by diffuse acoustic field and turbulent boundary layer (TBL) flow. In order to vary the rib location during the optimization, component mode synthesis (CMS) was used with the rib and plate treated as separate substructures. The CMS approach couples the individual modes of the rib and plate using impedances at the connection points thus only requiring full eigenanalysis and radiation resistance calculations once and allowing for more rapid function evaluation during the optimization. The optimization was then performed using an evolutionary strategy with covariance matrix adaption. The rib location and properties were varied by the optimizer to find the best low-noise panel. An exhaustive search was performed to verify the optimum solution and compare results for several objective functions. Alternative design variables and constraints will also be discussed.

On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions

This work is a continuation of the authors efforts to develop high-order numerical methods for solving elliptic problems with complex boundaries using a fictitious domain approach. In a previous paper, a new method was proposed, based on the use of smooth forcing functions with identical shapes, mutually disjoint supports inside the fictitious domain and whose amplitudes play the role of Lagrange multipliers in relation to a discrete set of boundary constraints. For one-dimensional elliptic problems, this method shows spectral accuracy but its implementation in two dimensions seems to be limited to a fourth-order algebraic convergence rate. In this paper, a spectrally accurate formulation is presented for multi-dimensional applications. Instead of being specified locally, the forcing function is defined as a convolution of a mollifier (smooth bump function) and a Lagrange multiplier function (the amplitude of the bump). The multiplier function is then approximated by Fourier series. Using a Fourier Galerkin approximation, the spectral accuracy is demonstrated on a two-dimensional Laplacian problem and on a Stokes flow around a periodic array of cylinders. In the latter, the numerical solution achieves the same high-order accuracy as a Stokes eigenfunction expansion and is much more accurate than the solution obtained with a classical third order finite element approximation using the same number of degrees of freedom.

Investigations into the Vibrational Response of an Aero-Engine Turbine Blade under Thermosonic Excitation

Thermosonics is a rapid and potentially cost-saving non-destructive testing (NDT) screening technique that can be applied to the identification of cracks in high pressure compressor turbine blades in turbofan engines. The reliability of the thermosonic technique is not well established for inspecting these complex components; in particular the vibrational energy generated within a component during a thermosonic test is often highly non-uniform, leading to the possibility of missing critical defects. The aim of this study was to develop a methodology, using a combination of vibration measurements and finite element analysis (FEA), to model the vibrational energy within a turbine blade in a typical thermosonic inspection scenario. Using a laser vibrometer, the steady-state vibration response (i.e. frequency response) at several locations on a blade was measured and used to identify the prominent peaks in the frequency spectra. These were then used to generate an excitation function for the finite element modelling approach. Acceptable correlation between the measured and simulated vibration response at a number of specific locations on the blade allowed the forcing function to simulate the vibration response across the whole blade. Finally, the predicted displacement field was used to determine the vibrational energy at every point on the blade which was mapped onto a CAD representation of the blade, thereby highlighting areas on the blade that were below the defect detection threshold.

Structurally dynamic models of lakes

Abstract Lakes as all other ecosystems are adaptive, have self-organization, and change the species compositions in accordance with the variable forcing functions. We need therefore models that are able to capture this dynamic, which means that the properties (represented in models by the parameter) of the biological components of the model are continuously changed. This paper presents structurally dynamic models (SDMs), which are able to capture this dynamic of changing the ecosystem structure. An SDM uses a goal function to determine the changes of the parameters. As goal function is used eco-exergy which is the work capacity (work energy) of the ecosystem. The use of this goal function can be considered a translation of Darwin’s theory to thermodynamics. SDM has been used in 23 case studies to describe the structural changes with an acceptable standard deviation. Twelve of these cases were lake models, and this paper attempts to summarize the experience gained by using SDMs on lakes. The three most characteristic case studies are presented in more detailand conclusions on the applicability of SDM on lakes are summarized.

An algorithm for the solution of second order fuzzy initial value problems

In this paper, we state a fuzzy initial value problem of the second order fuzzy differential equations. Here we investigate problems with fuzzy coefficients, fuzzy initial values and fuzzy forcing functions. We propose an algorithm based on alpha-cut of a fuzzy set. Finally we present some examples by using our proposed algorithm.

A new approach to non-homogeneous fuzzy initial value problem

In this paper, we consider a high-order linear differential equation with fuzzy forcing function and with fuzzy initial values. We assume the forcing function be in a special form, which we call triangular fuzzy function. We present solution as a fuzzy set of real functions such that each real function satisfies the initial value problem by some membership degree. We propose a method to find the fuzzy solution. We present an example to illustrate applicability of the proposed method.

Vibrations due to Walking in a Long-Cantilevered Office Building Structure

AbstractInnovative architectural designs create new challenges for structural designers such as annoying vibrations because of the everyday occupant activities such as walking. The designer needs to predict the excitation levels to evaluate the structural response and assess the resulting vibrations for acceptable human exposure. This paper uses a long-cantilevered office building structure to study the floor response subjected to various measured and Fourier series-based forcing functions representing human walks suggested in standards, design guides, and research studies. In addition, the vibration evaluation parameters proposed by several standards are computed and compared by using computer analyses and field measurements. For the majority of the cases studied in this paper, use of the Fourier series-based forcing functions resulted in an overestimation of the structural response. In addition, the in-place marching excitations to represent walking recommended in some design guides can grossly overesti...

Uncertainty Quantification of Sloshing Motion in Partially Filled Rectangular Tanks

Increasing computing power has made it not only possible but also highly practical to apply the Monte Carlo technique to a large variety of engineering problems. In this paper, the Monte-Carlo technique is used for calculating the statistical properties of inviscid incompressible fluid partially filled in a rectangular tank. First, uncertainty in the slosh and acoustic modes is estimated considering the gravitational forces and bulk modulus of the fluid as random variables. Second, uncertainty in the vibration frequencies in the rectangular tank with a baffle fixed inside it is studied. Later, linear slosh wave response analysis is carried out considering uncertainty in the external forcing function. Numerical results of the dynamic analyses show that the local minima and maxima of the slosh wave heights shift in time due to uncertainties in the frequency, whereas the local minima and maxima of the slosh wave heights change in magnitude only at a given time due to uncertainties in the amplitude. It is also found that the baffle, which is typically used to create desirable mode shifts, can also lead to increase in dispersion of the slosh and acoustic frequencies due to uncertainty.

Pharmacokinetics of doripenem in CSF of patients with non-inflamed meninges

To investigate intact blood-brain barrier (BBB) penetration by doripenem and characterize doripenem pharmacokinetics in CSF using a pharmacokinetic model. Thirty-eight neurological patients with no active neurological disease or CNS infection received a single 500 mg doripenem dose before pump implantation surgery, or lumbar puncture, for intrathecal baclofen administration. In most cases single CSF and blood samples were collected per patient and analysed for doripenem with HPLC. A two-stage pharmacokinetic analysis was performed to estimate: (i) empirical Bayesian estimates (EBEs) of individual doripenem plasma pharmacokinetic parameters, using plasma doripenem concentrations and literature population priors for a two-compartment model; and (ii) doripenem CSF pharmacokinetic parameters using simulated plasma concentrations from stage (i) as a forcing function. The mean values of the structural model parameters, k(CSF) (distribution rate constant) and PC (CSF/plasma partition coefficient), and the residual variability were estimated. The mean estimates of the parameters were k(CSF)= 0.105 h(-1) and PC= 0.053, corresponding to mean steady-state doripenem CSF concentrations of 0.20 mg/L and 0.40 mg/L for regimens of 3 × 500 mg daily and 3 × 1000 mg daily, respectively, and a mean equilibrium half-life of 6.6 h. The model was validated internally using a visual predictive check (VPC) and bootstrap. Simulating two dosing scenarios gave doripenem levels in the CSF above or close to the literature MIC values. The present NONMEM software analysis shows that doripenem crosses intact BBB significantly and suggests that the drug should be further evaluated as a candidate to treat certain CNS infections, since drug penetration through BBB is enhanced by meningeal inflammation.

A nonmonotone line search method and its convergence for unconstrained optimization

In this paper, by using a forcing function and the reverse modulus of continuity of gradient, we propose a generalization and development of the nonmonotone line search method for unconstrained optimization problems. The global convergence property of the new method is established under some reasonable conditions that are weaker than those of the existing nonmonotone line search methods. Furthermore, the proof of convergence is simpler than other methods.

Flexural Characteristics of Tapered Bar in Relation to Taper Angle Measurements

Flexural motion of a cantilever bar can be used to monitor the taper angle measurements of the bar without incorporating any geometric measurement. This provides non-destructive taper measurement with fast processing in manufacturing line. The laser ablation of a free end of the cantilever bar enables to generate a recoil pressure at the irradiated surface while resulting in external forcing function for the initiation of the flexural motion. Consequently, in the present study, laser induced ablation of free end tapered cantilever bar and resulting displacement and frequency of the flexural motion is examined. The study is extended to include influence of positive and negative bar taper angles on the flexural characteristics. In addition, deviation of displacement and frequency of the flexural motion due to tapered bar from the parallel bar is examined. It is found that the flexural characteristics of the tapered bar enable to determine taper angle of the bar with high accuracy.

Bayesian inverse problems in measure spaces with application to Burgers and Hamilton–Jacobi equations with white noise forcing

This paper formulates Bayesian inverse problems for inference in a topological measure space given noisy observations. Conditions for the validity of the Bayes’ formula and the well posedness of the posterior measure are studied. The abstract theory is then applied to Burgers and Hamilton–Jacobi equations on a semi-infinite time interval with forcing functions which are white noise in time. Inference is made on the white noise forcing, assuming the Wiener measure as the prior.

Simulation of memristors in presence of high-frequency forcing function

This reported work is concerned with the simulation of memristors when they are subject to high-frequency forcing functions. A novel asymptotic-numeric simulation method is applied. For systems involving high-frequency signals or forcing functions, the superiority of the proposed method in terms of accuracy and efficiency when compared to standard simulation techniques is illustrated. Relevant dynamical properties in relation to the method are also considered.

Efficient Transient Simulation of Non-linear Dynamic Networks with Discontinuous Forcing

AbstractNew technologies produce highly complex hybrid systems containing analogue components next to digital hardware and software. Simulating those mixed-signal systems exhibits discontinuities in signals due to the nature of the digital components. In this paper, an efficient and accurate method for the transient analysis of non-linear dynamic systems is presented that can handle discontinuous forcing functions which may occur as prescribed voltages or forces, for instance. It is based on a transformation of a model's equation system by substituting the time for a new independent variable. This approach facilitates suitable system-level models that altogether maintain the performance that is needed for an overall system-level simulation of complex application scenarios.

Using Ecopath with Ecosim to Explore Nekton Community Response to Freshwater Diversion into a Louisiana Estuary

AbstractCurrent methods to restore Louisiana's estuaries include the reintroduction of Mississippi River water through freshwater diversions to wetlands that are hydrologically isolated from the main channel. The reduced salinities associated with freshwater input are likely affecting estuarine nekton, but these effects are poorly described. Ecopath with Ecosim was used to simulate the effects of salinity changes caused by the Caernarvon freshwater diversion on species biomass distributions of estuarine nekton. A base model was first created in Ecopath from 5 years of monitoring data collected prior to the opening of the diversion (1986–1990). The effects of freshwater discharge on food web dynamics and community composition were simulated using a novel application of Ecosim that allows the input of salinity as a forcing function coupled with user‐specified salinity tolerance ranges for each biomass pool. The salinity function in Ecosim not only reveals the direct effects of salinity (i.e., increases in species biomass at their optimum salinity and decreases outside the optimal range) but also the indirect effects resulting from trophic interactions. Through multivariate analyses we determined that the simulated species biomass distributions in the estuary change significantly with distance from the diversion. However, the simulations do not show a significant difference estuarywide between the modeled distributions (with pooling of the data from different distances) before and after the opening of the diversion. This indicates a redistribution of species in the estuary rather than the replacement of species within the estuarine nekton community. The salinity function is a useful addition to the Ecopath with Ecosim software for estuarine ecologists and fisheries managers.Received January 31, 2011; Acceptdate November 30, 2011

Residual Minimizing Model Interpolation for Parameterized Nonlinear Dynamical Systems

We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the governing equations. The approximation properties of this residual minimizing scheme are comparable to existing reduced basis and POD-Galerkin model reduction methods, but its implementation requires only independent evaluations of the nonlinear forcing function. It is particularly appropriate when one wishes to approximate the states at a few points in time without time marching from the initial conditions. We prove some interesting characteristics of the scheme, including an interpolatory property, and we present heuristics for mitigating the effects of the ill-conditioning and reducing the overall cost of the method. We apply the method to representative numerical examples from kinetics---a three-state system with one parameter controlling the stiffness---and conductive heat transfer---a nonlinear parabolic PDE with a random field model for the thermal conductivity.

Higher-Order Corrections to the Pi Criterion Using Center Manifold Theory

The frequency-dependent pi criterion of Bittanti et al. [7] is a very important tool that has been used extensively in applications, to predict potential performance improvement under periodic forcing in a nonlinear system. The pi criterion is local in nature and provides an approximate formula for the performance index under small-amplitude periodic forcing. Motivated by basic results from Center Manifold theory, the present work develops higher-order approximations, suitable for periodic forcing functions of larger amplitude. The proposed method is based on solving the Center Manifold partial differential equation via power series. The end result of the proposed approach is the approximate calculation of the performance index in the form of a truncated series expansion, which provides accurate results under larger amplitudes. The proposed method is applied to a continuous stirred tank reactor, where the yield of the desired product must be maximized.