NAME OR DESIGNATION OF PROGRAM, COMPUTER, DESCRIPTION OF PROBLEM OR FUNCTION, METHOD OF SOLUTION, RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED, OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

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Program name | Package id | Status | Status date |
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PROSA-2 | NESC0778/02 | Tested | 21-FEB-1984 |

Machines used:

Package ID | Orig. computer | Test computer |
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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.

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.

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.

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.

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.[ top ]

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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.

- 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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NESC0778/02

The test case was run on IBM 3081 in 400K bytes of main storage.[ top ]

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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.

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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NESC0778/02

File name | File description | Records |
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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 |

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