Examples on Simulation Model

Abstract

A new methodology was developed Further real-time determination gate control operations of a river-reservoir system to minimize ?ooding conditions. The methodology is based upon an optimization-simulation model approach interfacing the genetic algorithm within simulation software for short-term rainfall forecasting, rainfall–runoff modeling (HEC-HMS), and a one-dimensional (1D), two-dimensional (2D), and combined 1D and 2D combined unsteady ?ow models (HEC-RAS). Both real-time rainfall data from next-generation radar (NEXRAD) and gaging stations, and forecasted rainfall are needed to make gate control decisions (reservoir releases) in real-time so that at timet, rainfall is known and rainfall over the future time-period(?t)totimet+ ?t can be forecasted. This new model can be used to manage reservoir release schedules (optimal gate operations) before, during, and after a rainfall event. Through real-time observations and optimal gate controls, downstream water surface elevations are controlled to avoid exceedance of threshold ?ood levels at target locations throughout a river-reservoir system to minimize the damage. In an example application, an actual river reach with a hypothetical upstream ?ood control reservoir is modeled in real-time to test the optimization-simulation portion of the overall model.

Introduction

I. INTRODUCTION

Simulation model is a computer model that imitates a real-life situation. It is like other mathematical models, but it explicitly incorporates uncertainty in one or more inputs variable. When you run a simulation, you allow these random input variables top take on various values, and you keep track of any resulting outputs variables of interest. In this way, you are able to see how the outputs vary as a function of the varying inputs.

A. Definition of Simulation

1. Simulation is the imitation of an operation of a real-word processor system over time.
2. Simulation is a method of understanding, representing and solving complex interdependent system.
3. It is the process of designing a model of a real system and conducting experiments with this model for the purpose either of understanding the behavior of the system or of evaluating various strategies for the operation of the system.

B. Random Number

A random selection of a number from a set or range of numbers is one in which each number in the range is equally likely to be selected.

II. STEPS IN SIMULTION

1. Identify the measure of effectiveness.
2. Decide the variable which influence the measure of effectiveness-choose those variable which affects the measure of effectiveness signification.
3. Identify the measure of effectiveness.
4. Decide the variable which influence the measure of effectiveness-choose those variable which affects the measure of effectiveness signification.
5. Determine the probability distribution for each variable in step (2) and construct the cumulative probability distribution.
6. Choose an appropriate set of random number. Consider each random number as decimal value of the cumulative probability distribution.
7. Use the simulated value so generated into the formula derivate from the measure of effectiveness.
8. Repeat(5)&(6) until the sample is large enough to arrive at a satisfactory and reliable decision

III. WORKED EXAMPLES

A bakery keeps stock of popular brands of cake previous experience show that the daily demand pattened for the item with associated probability is given below:

Total Demand = 240

Average Demand =240/10 =24 Cakes/day

The automobile company manufactures around 150 scooters. The daily production variance from 146 to 154.

The finished scooters are transported in a lorry 150 scooters, using the following random variables simulate the following

• Along no of scooters waiting in the factors
• Along no of empty space in the lorry

ii) lorry = 9/15

3.  a bakery maintains stock of a particular brand of sweet. Previous experience shows the daily demand pattern for the item with associated probability as given below

Use the following sequence of random no’s to simulate the demand for next 10 days. Random number are 25, 39, 65, 76, 12, 5, 73, 89, 19, 49. Also estimate the daily average demand for the sweet on the basis of simulated data.

IV. APPLICATION

A. A hypothetical example application, referred to as the Muncie Project (for Muncie, Indiana), is based upon information from Burner.  

B. Muncie is located on the West and East Forks of the White River, which ?ows through Central and Southern Indiana.

C. The application is designed speci?cally for testing the optimization-simulation model to determine the optimal operation of the ?oodgates in a hypothetical reservoir with possible downstream ?ooding in the river and ?oodplain of the urban area of Muncie, Indiana.

D. The river reaching down stream of Muncie is real, but there server is hypothetical with one large ?oodgate as shown in Figure 3.

E. The application assumes a major in?ow hydrograph to the hypothetical reservoir so that the HEC-HMS, the rainfall input, and the rainfall forecasting portion of the overall model are not employed in this application. The unsteady ?ow modeling is performed using the combined 1D unsteady and 2D unsteady (diffusion-wave model) approaches.

F. The combined 1D/2D unsteady ?ow modeling is used with the river reach modeled using the 1D approach (see Figure 4) and the ?oodplain is modeled using the 2D approach as illustrated in Figure 5.

G. The hypothetical reservoir is connected to the river reach at the very ?rst upstream cross-section (see Figure 5) through a gated spillway in the inline structure.

H. The radial gate is large enough to allow a range of signi?cant discharges for the ?ooding event.

I. The total gate width is 30 feet with a maximum opening of 21 feet and a discharge coef?cient of 0.98.

J. The river channel is assumed to have an initial steady ?ow of 1000 cfs.

V. ACKNOWLEDGE

Thank you by T. Ramesh, Assistant professor in Department of Mathematics at Dr SNS Rajalakshmi College of Arts and Science which has supported this research.

Conclusion

In this paper, the process of designing a model of a real system and conduction experiments with this model for the purpose either of understanding the behavior of the system or of evaluating various strategies for the operation of the system is discussed. Also, some problem are solved using the simulation model. Moreover the real time flood operation of river reservoir system is applied using simulation model.

References

[1] Mays, L.W. Flood Simulation for a Large Reservoir System in the Lower Colorado River Basin, Texas. In U.S. Geological Survey Water-Supply; National Water Summary 1988–89—Floods and Droughts, Institutional and Management Aspects; USGS: Reston, VA, USA, 1991; Volume 2375, pp. 143–146. [2] Che,D.;Mays,L.W.ApplicationofanOptimization/SimulationModelforReal-TimeFlood-ControlOperationofRiver-Reservoirs Systems. Water Resour. Manag. 2017, 31, 2285–2297. [CrossRef] [3] Che, D.; Mays, L.W. Development of an Optimization/Simulation Model for Real-Time Flood-Control Operation of River Reservoirs Systems. Water Resour. Manag. 2015, 29, 3987–4005. [CrossRef] [4] Unver, O.I.; Mays, L.W.; Lansey, K.E. Real-time ?ood management model for the Highland Lakes. J. Water Resour. Plan. Manag. 1987, 113, 620–638. [CrossRef] [5] Unver, O.I.; Mays, L.W. Model for Real-Time Optimal Flood Control Operation of a Reservoir System. WaterResour. Manag. 1990, 4, 21–46. [CrossRef] [6] Ahmed, E.S.M.S.;Mays,L.W.ModelforDeterminingReal-TimeOptimalDamReleasesduringFloodingConditions. Nat. Hazards 2013, 65, 1849–1861. [CrossRef]

Copyright

Copyright © 2022 Pooja B, T. Ramesh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.