Data processing: structural design – modeling – simulation – and em – Simulating nonelectrical device or system – Mechanical
Reexamination Certificate
1995-02-15
2001-02-27
Stamber, Eric B. (Department: 2765)
Data processing: structural design, modeling, simulation, and em
Simulating nonelectrical device or system
Mechanical
C703S002000, C702S034000, C073S598000, C706S920000
Reexamination Certificate
active
06195624
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to the assessment of corrosion, and more particularly, to a system and method for predicting the degree to which a tube array has degraded over a period of time due to corrosion in a particular operating environment.
Arrays of tubes can be found in a variety of industrial and process plants, where multiple sources, or mechanisms, of corrosion can attack the tubes, leading to deterioration and perforation. This problem is of particular concern in nuclear power plants, where nuclear steam generators, each containing upwards of a thousand tubes, can be subject to concurrent corrosion attacks on both primary (inner) and secondary (outer) tube surfaces. More so than in other industrial or process contexts, tube deterioration or failure in a nuclear steam generator, poses safety risks, in addition to performance (e.g., heat transfer) degradation. Moreover, excessive leakage resulting from failed tubes in the steam generator, can require the unscheduled shut-down of the power plant.
For these and other reasons, operators of power plants which employ nuclear steam generators, inspect and plug or repair tubes as necessary during cycle outages, to minimize total leakage during the next operating cycle. The prediction of which particular tubes in the array will be the next to fail, is virtually impossible. Because every tube cannot be inspected at every plant outage, yet the operator must be reasonably confident that the number of failures expected to occur during the next operating cycle will not result in the premature shut-down of the plant, efforts have been made to model, and therefore predict, the gross failure rates of tubes in the steam generator.
The failure rates of tubes in steam generators are typically computed using the so-called Weibull failure model, which takes the general form:
P
N
(
t
)=1−exp(−(
t/a
)
b
) [1]
where:
P
N
(t)=proportion failed at time (t) (failure mode N)
b=shape parameter of Weibull distribution
a=scale parameter of Weibull distribution
The total numbers of tubes requiring repair from N separate causes is obtained by Boolian summation involving risks associated with each failure mode. This process has proven adequate for cases in which the parameters b,a of each Weibull distribution are well known. The major deficiency in the existing methodology is the lack of a fully probabilistic method for dealing with large uncertainties in the values of the two Weibull parameters, and the subsequent inability to obtain quantifiable confidence estimates of the minimum and maximum tube repair requirements.
SUMMARY OF THE INVENTION
The present invention provides a system and method to permit a meaningful and quantifiable estimation of the uncertainties inherent in predictive modelling of corrosion failure in tube arrays.
In particular, the present invention utilizes a probabilistic model, preferably the so-called Monte Carlo simulation, combined with traditional failure models, such as the Weibull model, to generate a fully probabilistic index commensurate with the degree to which a tube array will degrade due to single or multiple corrosion sources.
In a system embodiment, the invention includes a computer platform having data processing means for performing arithmetic and logic operations on digitized data, data storage means, data input means, output means, for recording at least some of the results of the arithmetic and logic operations of the data processor means, and monitor means, for displaying data in response to the operation of the data processor means. The data storage means contains a stored computer program, which term is used in the broadest sense, to mean a series of statements or instructions usable directly by the processor means, for carrying out a sequence of logic and arithmetic operations. In this context, the stored computer program should be understood as including multiple individual programs or modules or routines of a single program that are linked together, i.e., modularized, even if the source code for such programs are in different languages. The computer platform and program together form a system which executes a corrosion failure prediction process. The functionality of this process can be described in terms of “functional modules” which each perform a particular function, but which can share hardware and program elements.
The computer program includes a first series of instructions for modelling the proportion of the tubes in the tube array, that fail at any time due to a particular source of corrosion. This first series of instructions includes at least one modelling parameter that has been treated as a constant conventionally, e.g., b and a when the failure model is of the Weibull type. A second series of instructions define a probabilistic model of uncertainties in the values of the failure model parameters, e.g., b and a of the Weibull model. Preferably, the second series of instructions is a Monte Carlo simulation. Additional series of instructions are provided in the computer program, for computing the distribution of the uncertainties in the number of tube failures at a given time, due to the probabilistic variation in the parameters.
The user of the system interacts therewith, through the data input means, for supplying instruction and operand data to the processor, and the monitor, on which the user sees information displayed in response to the operation of the data processor means. Preferably, the output means includes a printer or other media, e.g., “floppy” disc storage media, for recording at least some of the results of the arithmetic and logic operations of the data processor means.
The present invention thus provides two important advantages relative to the prior art. These include the ability to treat uncertainties in the failure model parameters, explicitly. Secondly, the invention provides the ability to display and record a distributional presentation of the results, with explicit confidence limits.
A method embodiment is also provided for generating an index commensurate with the degree to which a tube array degrades over a period of time due to corrosion in a particular operating environment. This comprises creating a data array defining the number of tubes in the tube array, a plurality of time points defining time intervals during which the degradation is to be assessed, and operating conditions that induce corrosion during each time interval. The expected degradation value of the array over each of a plurality of time points is computed using a deterministic failure model having at least one parameter that is assumed constant at each time point. For each time point and at least one parameter, a plurality of values of the parameter that deviate from the assumed constant value, are generated. For each time point, a plurality of degradation values are computed using the deterministic model with each of the said plurality of deviated values of the parameter, thereby defining a distribution of degradation values at the time point surrounding the expected degradation value at the time point. The final step is generating an index from the distribution of values, commensurate with the uncertainty at each time point, in the expected degradation value as computed by the deterministic model.
It should be understood that the term “degradation” or “failure” as used herein, does not necessarily denote loss of function or compromise in structural integrity or safety. Rather, these terms can be understood as denoting the presence of a non-through wall defect requiring attention or repair. In this context, the word “failure” is used primarily to preserve consistency with traditional usage in statistical and reliability technologies.
REFERENCES:
patent: 3903403 (1975-09-01), Ferguson et al.
patent: 4213183 (1980-07-01), Barron et al.
patent: 4671097 (1987-06-01), Kurki et al.
patent: 4763274 (1988-08-01), Junker et al.
patent: 4801421 (1989-01-01), Ackerson et al.
patent: 4953147 (1990-08-01), Cobb
patent:
Hall John F.
Woodman Brian Wilder
Alix Yale & Ristas, LLP
Combustion Engineering Inc.
Stamber Eric B.
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