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NESC0778 PROSA1.

PROSA-1 PROSA-2, Accidents Probability Analysis Using Response Surface Method

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1. NAME OR DESIGNATION OF PROGRAM:  PROSA1.
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2. COMPUTERS
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Program name Package id Status Status date
PROSA-2 NESC0778/02 Tested 21-FEB-1984

Machines used:

Package ID Orig. computer Test computer
NESC0778/02 IBM 3081 IBM 3081
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3. DESCRIPTION OF PROBLEM OR FUNCTION

PROSA2 is an implementation of  the probalistic response surface technique developed for use with accident analysis programs to conduct probability studies of hypothetical accidents. PROSA2 determines the distribution of a random variable that is a function of many other random variables when this functionality is not known analytically and can be obtained only through parametric studies with a deterministic computer code. The program first systematically provides input parameter combinations for evaluation by a deterministic code.
Then, with the output from the deterministic code for each of these  parameter combinations, multivariate quadratic response surfaces are generated approximating the functionality between the input and output of the deterministic code. Using these response surfaces PROSA2 calculates probability histograms and joint histograms for the output variables. Special features of the code generate or treat sensitivities, statistical moments of the input and output variables regionwise response surfaces, correlated input parameters, and conditional distribution.
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4. METHOD OF SOLUTION

As input data the program needs the probability distributions of the variable parameters (e.g., reactivity and heat  transfer coefficients considered as sources of uncertainties in an accident analysis). Uniform, normal, truncated normal, exponential,  beta, and log-normal probability distributions are available.
The first part of the program determines knot-point coordinates of the parameters, using a user-specified probability range, or confidence interval. These serve as input to deterministic codes, such as accident analysis codes, SACO or SAS, which calculate consequence values in the specified knot points.
The consequence values are used by the second part of PROSA1 to solve 1) the approximating functions or response surfaces; 2) the sensitivity/importance of each parameter with respect to the consequence variables; 3) the statistical moments of the input parameters; 4) the mean values and standard deviations of the consequences; and 5) the correlation coefficients for all pairs of the consequences. In the simplest case a single multivariate second- degree surface is matched to knot-point consequences.
It is possible to use regionwise response surfaces, distinct second-degree surfaces for every "quadrant" of the multivariate parameter space.
By use of the random-number sampling of the parameters distributions and simulation with the as-calculated response surface the program also calculates 6) the probability distributions and the first four moments of the consequences; 7) the joint distribution; and 8) the statistical-error estimates for the distributions.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The maximum number of variable input parameters and consequence variables that can be analyzed simultaneously are 12 and 6, respectively. Eight different  probability distributions are available for the input parameters.
The correlations, if any, between the input parameters are limited to linear correlations. Up to four simultaneous criteria or conditions can be specified for the consequences.
The individual and joint distributions are obtained in forms of histograms with 12 and 144 categories, respectively. The width of the categories is a user-specified fraction of the standard deviations of the consequences.
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6. TYPICAL RUNNING TIME

Typical running time in the case of four input parameters and six consequence variables in 95 seconds for 50000 simulations on an IBM370/195.
NESC0778/02
NEA-DB executed the test case included in the package on IBM 3081 in 21 seconds of CPU time.
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7. UNUSUAL FEATURES OF THE PROGRAM

By defining one or more input parameters to be consequences as well, it is possible to use the code for calculating optimal importance distributrions for the input parameters.
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8. RELATED AND AUXILIARY PROGRAMS

The PROSA1 code is designed for use in conjunction with a deterministic/mechanistic accident analysis code, such as SACO, SAS, or RELAP. The first part of PROSA1 provides input for the accident analysis code, which in turn provides to the  second part of PROSA1.
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9. STATUS
Package ID Status date Status
NESC0778/02 21-FEB-1984 Tested at NEADB
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10. REFERENCES

- J.K. Vaurio anc C. Mueller,
  Probabilistic Analysis of Liquid-Metal Fast Breeder Reactor
  Accident Consequences with Response Surface Techniques,
  Nuclear Science and Engineering, vol. 65, pp.401-413, 1978.
- J.K. Vaurio and C. Mueller,
  PROSA1: A Probabilistic Response-Surface Analysis Code,
  ANL-78-56, June 1978.
  PROSA1, NESC No. 778.370B, PROSA1 Sample Problem Output,
  National Energy Software Center Note 80-49, April 30, 1980.
NESC0778/02, included references:
- J.K. Vaurio:
  PROSA-2: A Probabilistic Response-Surface Analysis and Simulation
  Code.  ANL-81-33  (May 1981)
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11. MACHINE REQUIREMENTS

250K bytes of storage, system input, output,  and punch units are required.
NESC0778/02
The test case was run on IBM 3081 in 400K bytes of main storage.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NESC0778/02 FORTRAN+ASSEMBLER
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  OS/370.
MVS (IBM 3081).
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

The
program contains a few FORMAT statements using T format, an IBM extension to ANSI FORTRAN.
PROSA1 obtains random numbers U, uniformly distributed between 0 and 1, using th FLTRNF function subprogram supplied as an Assembly language routine. Other random variates are calculated from U.
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15. NAME AND ESTABLISHMENT OF AUTHOR

             J.K. Vaurio* and C. Mueller
             Reactor Analysis and Safety Division
             Argonne National Laboratory
             9700 South Cass Avenue
             Argonne, Illinois 60439
* Contact
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16. MATERIAL AVAILABLE
NESC0778/02
File name File description Records
NESC0778_02.003 INFORMATION FILE 63
NESC0778_02.004 PROSA-2 SOURCE PROGRAM (FORTRAN-4) 5768
NESC0778_02.005 PROSA-2 SOURCE PROGRAM (ASSEMBLER) 365
NESC0778_02.006 PROSA-2 JCL 168
NESC0778_02.007 PROSA-2 TEST CASE INPUT DATA 90
NESC0778_02.008 PROSA-2 TEST CASE PRINTED OUTPUT 1133
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17. CATEGORIES
  • G. Radiological Safety, Hazard and Accident Analysis

Keywords: HCDA, LMFBR reactors, Monte Carlo method, accidents, fast reactors, probability, reactor safety, response functions, sensitivity.