A Stochastic Model for the Random Impact Series Method in Modal Testing

2006 ◽  
Vol 129 (3) ◽  
pp. 265-275 ◽  
Author(s):  
W. D. Zhu ◽  
N. A. Zheng ◽  
C. N. Wong
Keyword(s):  
Stochastic Model ◽  
Numerical Solutions ◽  
Average Power ◽  
Modal Testing ◽  
Time Interval ◽  
Wide Sense ◽  
Random Series ◽  
Arrival Times ◽  
Stationary Part ◽  
Force Signal

A novel stochastic model is developed to describe a random series of impacts in modal testing that can be performed manually or by using a specially designed random impact device. The number of the force pulses, representing the impacts, is modeled as a Poisson process with stationary increments. The force pulses are assumed to have an arbitrary, deterministic shape function, and random amplitudes and arrival times. The force signal in a finite time interval is shown to consist of a wide-sense stationary part and two nonstationary parts. The expectation of the force spectrum is obtained from two approaches. The expectations of the average power densities associated with the entire force signal and the stationary part of it are determined and compared. The analytical expressions are validated by numerical solutions for two different types of shape functions. A numerical example is given to illustrate the advantages of the random impact series over a single impact and an impact series with deterministic arrival times of the pulses in estimating the frequency response function. The model developed can be used to describe a random series of pulses in other applications.

A Stochastic Model for the Random Impact Series Method in Modal Testing

2003 ◽  
Author(s):  
C. N. Wong ◽  
W. D. Zhu ◽  
N. A. Zheng
Keyword(s):  
Stochastic Model ◽  
Energy Input ◽  
Shape Function ◽  
Signal To Noise Ratio ◽  
Modal Testing ◽  
Time Interval ◽  
Series Method ◽  
Finite Time Interval ◽  
Random Series ◽  
Arrival Times

A novel stochastic model is developed to describe a random series of impacts in modal testing. The number of the force pulses in a finite time interval is modeled as a Poisson process. The force pulses in the series are assumed to have an arbitrary, deterministic shape function and random amplitudes and arrival times. A detailed stochastic analysis is undertaken and is validated by numerical simulation. The main advantages of the random impact series method are increased energy input to the test structure and improved signal-to-noise ratio. The method can also average out the slight nonlinearities that can exist in the structure and extract the linearized modal parameters. The model developed in this work can be used to describe a random series of pulses in other applications.

scholarly journals Coupling Disease-Progress-Curve and Time-of-Infection Functions for Predicting Yield Loss of Crops

2000 ◽  
Vol 90 (8) ◽  
pp. 788-800 ◽  
Author(s):  
L. V. Madden ◽  
G. Hughes ◽  
M. E. Irwin
Keyword(s):  
Yield Loss ◽  
Numerical Solutions ◽  
Disease Incidence ◽  
Time Interval ◽  
Short Time Interval ◽  
Time Duration ◽  
Plant Yield ◽  
Disease Progress ◽  
Time Of Infection ◽  
Over Time

A general approach was developed to predict the yield loss of crops in relation to infection by systemic diseases. The approach was based on two premises: (i) disease incidence in a population of plants over time can be described by a nonlinear disease progress model, such as the logistic or monomolecular; and (ii) yield of a plant is a function of time of infection (t) that can be represented by the (negative) exponential or similar model (ζ(t)). Yield loss of a population of plants on a proportional scale (L) can be written as the product of the proportion of the plant population newly infected during a very short time interval (X′(t)dt) and ζ(t), integrated over the time duration of the epidemic. L in the model can be expressed in relation to directly interpretable parameters: maximum per-plant yield loss (α, typically occurring at t = 0); the decline in per-plant loss as time of infection is delayed (γ; units of time-1); and the parameters that characterize disease progress over time, namely, initial disease incidence (X0), rate of disease increase (r; units of time-1), and maximum (or asymptotic) value of disease incidence (K). Based on the model formulation, L ranges from αX0 to αK and increases with increasing X0, r, K, α, and γ-1. The exact effects of these parameters on L were determined with numerical solutions of the model. The model was expanded to predict L when there was spatial heterogeneity in disease incidence among sites within a field and when maximum per-plant yield loss occurred at a time other than the beginning of the epidemic (t > 0). However, the latter two situations had a major impact on L only at high values of r. The modeling approach was demonstrated by analyzing data on soybean yield loss in relation to infection by Soybean mosaic virus, a member of the genus Potyvirus. Based on model solutions, strategies to reduce or minimize yield losses from a given disease can be evaluated.

On the Scaling of Impulsively Started Incompressible Turbulent Round Jets

1982 ◽  
Vol 104 (2) ◽  
pp. 191-197 ◽  
Author(s):  
T.-W. Kuo ◽  
F. V. Bracco
Keyword(s):  
Steady State ◽  
Kinetic Energy ◽  
Time Scales ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Scaling Law ◽  
Navier Stokes ◽  
Centerline Velocity ◽  
Arrival Times ◽  
Round Jets

A scaling law for transient, turbulent, incompressible, round jets is reported. Numerical solutions of the Navier-Stokes equations were obtained using a k-ε model for turbulence. The constants of the k-ε model were optimized by comparing computed centerline velocity, mean radial velocity distribution, longitudinal kinetic energy distributions with those measured by other authors in steady round jets. The resulting constants are those also used in computations of steady planar jets except for the one that multiplies the source term in the ε-equation. After optimization, the agreement is satisfactory for all mean quantities but is still rather poor for the kinetic energy distribution. Parameteric studies of the transient were performed for 9•103 ≤ ReD ≤ 105. Then the definition was adopted that a jet reaches steady state between the nozzle and an axial location when, at that location, the centerline velocity achieves 70 percent of its steady state value, and characteristic steadying length and time scales (D•ReD0.053 and D•ReD0.053/u cL,0 respectively) were determined as well as a unique function that relates dimensionless steadying time to dimensionless steadying length. This function changes in a predictable way if a percent other than 70 is selected but the characteristic length and time scales do not. It is found that the 70 percent threshold is reached within the head vortex of the transient jet. Thus a transient jet, practically, is a steady jet except within its head vortex. This, in part, justifies our use of steady state k-ε constants in our transient computations. The computed jet tip arrival times are shown to compare favorably with measured ones.

scholarly journals On the use of earthquake multiplets to study fractures and the temporal evolution of an active volcano

1996 ◽  
Vol 39 (2) ◽  
Author(s):  
G. Poupinet ◽  
A. Ratdomopurbo ◽  
O. Coutant
Keyword(s):  
Seismic Velocity ◽  
Active Volcano ◽  
Temporal Changes ◽  
Time Interval ◽  
Velocity Change ◽  
P Waves ◽  
Merapi Volcano ◽  
Arrival Times ◽  
Cross Spectrum ◽  
Window Technique

Multiplets, i.e. events with similar waveforms, are common features on active volcanoes. The seismograms of multiplets are analyzed by cross-spectrum techniques: this procedure improves by a factor of about 10 the precision of differential P-arrival times and therefore the accuracy of the relative location of earthquakes. Long period events which cannot be located because of the impossibility to pick up P-waves on individual seismograms can be located with a precision of about 10 m. Such a precision permits fault planes to be mapped inside a volcanic edifice and the azimuth and strike of fractures to be defined. Seismograms of the two events (of a doublet) that occur on different dates are analyzed by the Cross Spectrum Moving Window technique (CSMW) for measuring the time delay between waves in the coda. The pattern of the delays in the coda is a function of the temporal changes of seismic velocity that occurred inside the volcano during the time interval that separates the two events of a doublet. We illustrate the potential of the doublet technique for detecting temporal changes inside a volcano by performing computations of synthetic seismograms. The case of a dyke injected inside the volcano is considered as well as that of the replenishment of a superficial magma chamber and of a general increase in velocity in the summit of the volcano. Data from Merapi volcano (Indonesia)illustrate a possible temporal velocity change inside the volcano several months before the 1992 eruption.

A fall in P-wave velocity before the Gisborne, New Zealand, earthquake of 1966

1974 ◽  
Vol 64 (5) ◽  
pp. 1501-1507 ◽  
Author(s):  
D. J. Sutton
Keyword(s):  
New Zealand ◽  
Wave Velocity ◽  
Significant Variation ◽  
Arrival Time ◽  
P Wave ◽  
Time Interval ◽  
P Waves ◽  
Arrival Times ◽  
P Wave Velocity ◽  
Seismograph Station

Abstract A fall in P-wave velocity before the Gisborne earthquake of March 4, 1966 is indicated by arrival-time residuals of P waves from distant earthquakes recorded at the Gisborne seismograph station. Residuals were averaged over 6-month intervals from 1964 to 1968 and showed an increase of about 0.5 sec, implying later arrival times. The change began about 480 days before the earthquake. This precursory time interval is about that expected for an earthquake of this magnitude (ML = 6.2), but unlike most other reported instances, there was no obvious delay between the return of the velocity to normal and the occurrence of the earthquake. Similar analyses were carried out over the same period for two other New Zealand seismograph stations; at Karapiro there was no significant variation in mean residuals, and at Wellington the scatter was too large for the results to be meaningful. The Gisborne earthquake had a focus in the lower crust, about 25 km deep and was deeper than other events for which such precursory drops in P-wave velocity have been reported.

On the mean field approximation of a stochastic model of tumour-induced angiogenesis

2018 ◽  
Vol 30 (04) ◽  
pp. 619-658 ◽  
Author(s):  
V. CAPASSO ◽  
F. FLANDOLI
Keyword(s):  
Stochastic Model ◽  
Mean Field ◽  
Field Approximation ◽  
Angiogenic Factor ◽  
Mean Field Approximation ◽  
Time Interval ◽  
Biomedical Problem ◽  
The Family ◽  
The Mean ◽  
Points Of View

In the field of Life Sciences, it is very common to deal with extremely complex systems, from both analytical and computational points of view, due to the unavoidable coupling of different interacting structures. As an example, angiogenesis has revealed to be an highly complex, and extremely interesting biomedical problem, due to the strong coupling between the kinetic parameters of the relevant branching – growth – anastomosis stochastic processes of the capillary network, at the microscale, and the family of interacting underlying biochemical fields, at the macroscale. In this paper, an original revisited conceptual stochastic model of tumour-driven angiogenesis has been proposed, for which it has been shown that it is possible to reduce complexity by taking advantage of the intrinsic multiscale structure of the system; one may keep the stochasticity of the dynamics of the vessel tips at their natural microscale, whereas the dynamics of the underlying fields is given by a deterministic mean field approximation obtained by an averaging at a suitable mesoscale. While in previous papers, only an heuristic justification of this approach had been offered; in this paper, a rigorous proof is given of the so called ‘propagation of chaos’, which leads to a mean field approximation of the stochastic relevant measures associated with the vessel dynamics, and consequently of the underlying tumour angiogenic factor (TAF) field. As a side, though important result, the non-extinction of the random process of tips has been proven during any finite time interval.

A stochastic model for time lag in reporting of claims

1974 ◽  
Vol 11 (02) ◽  
pp. 382-387 ◽  
Author(s):  
Jan-Erik Karlsson
Keyword(s):  
Integral Equation ◽  
Stochastic Model ◽  
Renewal Process ◽  
Value Function ◽  
Time Lag ◽  
Mean Value ◽  
Time Interval ◽  
Asymptotic Expressions ◽  
The Laplace Transform ◽  
The Mean

We assume that the number of claims occur according to a renewal process and treat the number of claims that occur and are reported in a certain time interval as a renewal process with random displacements. We obtain a renewal equation for the mean value function and an integral equation for the Laplace transform of the distribution of the claims that are reported. We also give asymptotic expressions for the mean value function and calculate the generating function in the case where the renewal process is a Poisson process. This matter is a part of the IBNR-problem in insurance mathematics.

Explicit Solution for Time-Fractional Batch Reactor System

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Najeeb Alam Khan ◽  
Muhammad Jamil ◽  
Asmat Ara ◽  
Subir Das
Keyword(s):  
Homotopy Perturbation Method ◽  
Analytical Procedure ◽  
Numerical Solutions ◽  
Approximate Analytical Solution ◽  
Batch Reactor ◽  
Reactor System ◽  
Time Interval ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Good Agreement

In this paper, the new homotopy perturbation method (NHPM) has been successively applied for finding approximate analytical solutions of the fractional order batch reactor system. An approximate analytical solution for the concentration of reactants and products that is valid for a time interval. The approximate analytical procedure is depends only on two components. The behavior of the solution and effects of different parameters and fractional index are shown graphically. Numerical solutions of ordinary batch reactor system verify our approximate solution with good agreement.

Seismic detection of a hydraulic fracture from shear‐wave VSP data at Lost Hills Field, California

Geophysics ◽  
1994 ◽  
Vol 59 (1) ◽  
pp. 11-26 ◽  
Author(s):  
Mark A. Meadows ◽  
Don F. Winterstein
Keyword(s):  
Shear Wave ◽  
Numerical Solutions ◽  
Scattered Wave ◽  
Hydraulic Fractures ◽  
Fast Wave ◽  
S Wave ◽  
Wave Source ◽  
Arrival Times ◽  
Fractured Medium ◽  
Fracture Closure

A shear‐wave (S‐wave) VSP experiment was performed at Lost Hills Field, California, in an attempt to detect hydraulic fractures induced in a nearby well. The hydrofrac well was located between an impulsive, S‐wave source on the surface and a receiver well containing a clamped, three‐component geophone. Both direct and scattered waves were detected immediately after shut‐in, when the hydraulic pumps were shut off and recording started. The scattered energy disappeared within about an hour, which is consistent with other measurements that indicate some degree of fracture closure and leak‐off within that period. Although S‐wave splitting was evident, no change was detected in the fast wave (polarized parallel to the fracture). However, the slow wave (polarized perpendicular to the fracture) did change over a period of about an hour, after which the prehydrofrac wavelet shape was recovered. The fact that only the wave polarized perpendicular to the fracture was affected is a dramatic confirmation of both theoretical predictions and laboratory observations of S‐wave behavior in a fractured medium. Subtracting the prehydrofrac wavelet from the wavelets recorded within the first hour after shut‐in revealed scattered wavelets that were diminished and phase‐rotated versions of the incident (prehydrofrac) wavelet. Arrival times of the direct and scattered waves were matched by ray tracing. We accounted for the scattered‐wave amplitudes by using numerical solutions of S‐wave diffractions off of ribbon‐shaped fractures. Amplitudes derived from full‐wavefield Born scattering, however, did not match recorded amplitudes. The phase of the scattered wavelets was matched very well by Born scattering when the incident wavelet was input, but only for fracture lengths no larger than half those predicted from fracture‐simulator models. These results show that a carefully controlled experiment, combined with accurate modeling, can provide important information about the geometry of induced fractures.

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