This application claims priority to India Patent Application No. 1204/CHE/2013, filed Mar. 20, 2013, the disclosure of which is hereby incorporated by reference in its entirety.
The present invention relates generally to a method and system for determining a life span of a mechanical asset. More specifically, the present invention relates to a method and system for determining a time-to-failure of pipeline assets.
A probability of failure of an asset such as a pipeline is usually dependent on a set of defect growth models of defects, resulting from wear and tear of the asset. To estimate parameters of the defect growth models of the pipeline such as a growth speed, a set of high quality inspection data is required to be collected from Pipeline Inspection Gauges at regular intervals of time. Acquiring such high quality inspection data at regular intervals of time tends to be a very expensive process. Existing methods for estimating the time-to-failure of the asset provide a probability of failure of the pipeline asset. The probability of failure needs to be estimated for several years, and extrapolated into the future for getting an estimate of the remaining life span of the asset. Further, the existing methods suffer from inaccuracy in estimating the time-to-failure from such probability of failure functions. Hence an alternative method is required for providing the estimate of the remaining life time of the asset directly and accurately.
Hence there is a need for an alternative method and a system that can provide the remaining life time or the time-to-failure of the asset directly in a cost effective manner. The alternate method must utilize the partial inspection data for estimating the remaining life time of the asset directly. Thus a method for estimating a time-to-failure or the remaining life time of an asset directly is proposed.
The present invention provides a method and system for determining a time-to-failure of an asset. In accordance with a disclosed embodiment, the method may include capturing a set of inspection data of a defect of the asset, simulating a probabilistic non-linear model, whereby the probabilistic non-linear model evaluates evolution of a limit state of the asset and evaluating a numerical scheme for computation of a conditional probability distribution of a size of the defect, where the conditional probability of the size of the defect is based on a value of the limit state. Further probability distribution of the limit state can be approximated by a predetermined set of particles where each particle is associated with a weight factor. An initial value to the weight factor of the each particle is assigned, and a set of future values of the weight factor of the each particle is predicted based on the initial value. The predicted future value of the weight factor of the each particle is updated when a new set of inspection data is captured, and a probability of the time-to-failure is estimated by summing the weights factor of a set of particles, the set of particles comprising particles at which the limit state is less than a zero limit threshold.
In an additional embodiment, a system for determining a time-to-failure of an asset is disclosed. The system comprises an input module configured to capture a set of inspection data of a defect of the asset, a simulating module configured to simulate a probabilistic non-linear model, whereby the probabilistic non-linear model evaluates evolution of a limit state of the asset. The simulating module is further configured to evaluate a numerical scheme for computation of a conditional probability distribution of a size of the defect, whereby the conditional probability of the size of the defect is based on a value of the limit state. The sampling module is configured to approximate a probability distribution of the limit state by a predetermined set of particles whereby each particle is associated with a weight factor. An initializing module is configured to assign an initial value to the weight factor of the each particle. A predicting module is configured to predict a set of future values of the weight factor of the each particle, based on the initial value, and an updating module is configured to update a predicted future value of the weight factor of the each particle when a new set of inspection data is captured. Finally an estimating module configured to estimate a probability of the time-to-failure by summing the weights factors of a set of particles, the set of particles comprising particles at which the limit state is less than a zero limit threshold.
These and other features, aspects, and advantages of the present invention will be better understood with reference to the following description and claims.
While systems and methods are described herein by way of example and embodiments, those skilled in the art recognize that systems and methods for electronic financial transfers are not limited to the embodiments or drawings described. It should be understood that the drawings and description are not intended to be limiting to the particular form disclosed. Rather, the intention is to cover all modifications, equivalents and alternatives falling within the spirit and scope of the appended claims. Any headings used herein are for organizational purposes only and are not meant to limit the scope of the description or the claims. As used herein, the word “may” is used in a permissive sense (i.e., meaning having the potential to) rather than the mandatory sense (i.e., meaning must). Similarly, the words “include”, “including”, and “includes” mean including, but not limited to.
Disclosed embodiments provide computer-implemented methods, systems, and computer-program products for determining a time-to-failure of an asset. More specifically the methods, and systems disclosed provide a framework for estimating the time-to-failure of pipelines, from high quality inspection data captured from Pipeline Inspection Gauges (PIG). The time-to-failure or life time of an asset is a more useful parameter while planning and optimizing maintenance schedules of the pipelines. The methods disclosed herein, incorporate a Sequential Monte Carlo method, alternatively known as a Particle Filtering Method, for simulating a limit state equation of the asset and thereby computing a time to failure of the asset. Current inspection data of the asset is utilized for correcting a prediction made in an earlier step of the particle filtering method.
MAOP=Maximum Allowable Operable Pressure of the asset. In the above equation, l (t), and d (t) are time-dependent variables, and represent length and depth of the defect respectively. The time-dependent variables, l (t) and d (t) are usually characterized by defect growth models that are random in nature. Further, a set of parameters D, T and S, represent a diameter, a thickness, and an elastic strength of the pipeline. C1, C2, C3 are certain constants, while ε1 represents a noise factor. The set of parameters appearing in the limit state equation g(t), are random functions of time, as a result a value of g(t) is also a random function of time. In a reliability theory framework, failure of a system usually occurs when the limit state equation g(t) becomes less than zero. Alternatively Probability of Failure (PoF) at any given time t, is defined as P(g(t)<0), and Time to Failure (TtF) is defined as TtF=min(t|g(t)<0). As g(t) is a random function of time, TtF shall also have a random distribution.
Further at step 106, a numerical scheme for computation of a conditional probability distribution of a size of the defect can be evaluated, where the conditional probability of the size of the defect is based on a value of the limit state. For instance, let the defect size be represented by x(t), a value of x(t) at time t, can be predicted by a value from a previous time step x(t−1), by a Markov process equation:
p(x(t)|y(1:t−1))=∫p(x(t)|x(t−1)p(x(t−1)|y(1:t−1)),
where x(t) represent the defect size, y(t) represents the limit state equation g(t), and p (x(t−1)|y(1: t−1)) is a conditional probability of the defect size at a time t−1 given a value of the limit state equation y(1: t−1), at time t−1.
Next, at step 108, the limit state equation y(t), shall be approximated by a predetermined set of particles. The approximation shall be represented as
where wi(t) is the weight factor of the ith particle.
At step 110 an initial value to a weight factor of the each particle is assigned. The weight factor shall be a time dependent factor for each particle. At step 112, a set of future values of the weight factor of the each particle shall be predicted, based on the initial value. Further at step 114, the predicted future value of the weight factor of the each particle shall be updated, when a new set of inspection data is captured. The predicted future value of the weight factor shall be updated by the following equation:
where w(t) is the predicted future value of the weight factor at time t, and w(t−1) is the initial value of the weight factor. Finally at step 114, a probability of the time-to-failure can be estimated by summing the weights factor of a set of particles, by the following equation:
where i=1 to N, represent the set of particles, for which the limit state equation falls below a zero limit threshold.
MAOP=Maximum Allowable Operable Pressure of the asset. In the above equation, parameters l (t), and d (t) are time-dependent variables, and represent length and depth of the defect respectively. The parameters l (t) and d (t) are usually characterized by defect growth models that are random in nature. Further, parameters D, T and S, represent a diameter, a thickness, and an elastic strength of the pipeline. C1, C2, C3 are certain constants, while ε1 represents a noise factor. Due to random nature of the parameters appearing in the limit state equation g(t), a value of g(t) also takes a random nature. In a reliability theory framework, failure of a system usually occurs when the limit state equation g(t) becomes less than zero. Alternatively Probability of Failure (PoF) at any given time t, is defined as P(g(t)<0), and Time to Failure (TtF) is defined as TtF=min(t|g(t)<0). As g(t) is a random function of time, TtF shall also have a random distribution.
Further at step 206, a numerical scheme for computation of a conditional probability distribution of a size of the defect can be evaluated, where the conditional probability of the size of the defect is based on a value of the limit state. For instance, let the defect size be represented by x(t), a value of x(t) at time t, can be predicted by a value from a previous time step x(t−1), by a Markov process equation:
p(x(t)|y(1:t−1))=∫p(x(t)|x(t−1))p(x(t−1)|y(1:t−1)),
where x(t) represent the defect size, y(t) represents the limit state equation g(t), and p(x(t−1)|y(1: t−1)) is a conditional probability of the defect size at a time t−1 given a value of the limit state equation y(1: t−1), at time t−1.
Next, at step 208, the limit state equation y(t), shall be approximated by a predetermined set of particles. The approximation shall be represented as
where wi(t) is the weight factor of the ith particle.
At step 210 an initial value to a weight factor of the each particle is assigned. The weight factor shall be a time dependent factor for each particle. At step 212, a set of future values of the weight factor of the each particle shall be predicted, based on the initial value. Further at step 214, a new set of inspection data can be captured. At step 216, the new set of inspection data is provided as an input to the numerical scheme to obtain a correction factor to be applied for the predicted set of future values. At step 218, the correction factor can be applied to the predicted set of future values for updating the predicted values. The correction factor so applied to the future value of the weight factor shall be applied by the following equation:
where w(t) is the predicted future value of the weight factor at time t, and w(t−1) is the initial value of the weight factor. Finally at step 220, a probability of the time-to-failure can be estimated by summing the weights factor of a set of particles, by the following equation:
where i=1 to N, represent the set of particles, for which the limit state equation falls below a zero limit threshold.
One or more of the above-described techniques can be implemented in or involve one or more computer systems.
With reference to
A computing environment may have additional features. For example, the computing environment 400 includes storage 440, one or more input devices 440, one or more output devices 460, and one or more communication connections 470. An interconnection mechanism (not shown) such as a bus, controller, or network interconnects the components of the computing environment 400. Typically, operating system software (not shown) provides an operating environment for other software executing in the computing environment 400, and coordinates activities of the components of the computing environment 400.
The storage 440 may be removable or non-removable, and includes magnetic disks, magnetic tapes or cassettes, CD-ROMs, CD-RWs, DVDs, or any other medium which can be used to store information and which can be accessed within the computing environment 400. In some embodiments, the storage 440 stores instructions for the software 480.
The input device(s) 450 may be a touch input device such as a keyboard, mouse, pen, trackball, touch screen, or game controller, a voice input device, a scanning device, a digital camera, or another device that provides input to the computing environment 400. The output device(s) 460 may be a display, printer, speaker, or another device that provides output from the computing environment 400.
The communication connection(s) 470 enable communication over a communication medium to another computing entity. The communication medium conveys information such as computer-executable instructions, audio or video information, or other data in a modulated data signal. A modulated data signal is a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media include wired or wireless techniques implemented with an electrical, optical, RF, infrared, acoustic, or other carrier
Implementations can be described in the general context of computer-readable media. Computer-readable media are any available media that can be accessed within a computing environment. By way of example, and not limitation, within the computing environment 400, computer-readable media include memory 420, storage 440, communication media, and combinations of any of the above.
Having described and illustrated the principles of our invention with reference to described embodiments, it will be recognized that the described embodiments can be modified in arrangement and detail without departing from such principles. It should be understood that the programs, processes, or methods described herein are not related or limited to any particular type of computing environment, unless indicated otherwise. Various types of general purpose or specialized computing environments may be used with or perform operations in accordance with the teachings described herein. Elements of the described embodiments shown in software may be implemented in hardware and vice versa.
As will be appreciated by those ordinary skilled in the art, the foregoing example, demonstrations, and method steps may be implemented by suitable code on a processor base system, such as general purpose or special purpose computer. It should also be noted that different implementations of the present technique may perform some or all the steps described herein in different orders or substantially concurrently, that is, in parallel. Furthermore, the functions may be implemented in a variety of programming languages. Such code, as will be appreciated by those of ordinary skilled in the art, may be stored or adapted for storage in one or more tangible machine readable media, such as on memory chips, local or remote hard disks, optical disks or other media, which may be accessed by a processor based system to execute the stored code. Note that the tangible media may comprise paper or another suitable medium upon which the instructions are printed. For instance, the instructions may be electronically captured via optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.
The following description is presented to enable a person of ordinary skill in the art to make and use the invention and is provided in the context of the requirement for a obtaining a patent. The present description is the best presently-contemplated method for carrying out the present invention. Various modifications to the preferred embodiment will be readily apparent to those skilled in the art and the generic principles of the present invention may be applied to other embodiments, and some features of the present invention may be used without the corresponding use of other features. Accordingly, the present invention is not intended to be limited to the embodiment shown but is to be accorded the widest scope consistent with the principles and features described herein.
While the foregoing has described certain embodiments and the best mode of practicing the invention, it is understood that various implementations, modifications and examples of the subject matter disclosed herein may be made. It is intended by the following claims to cover the various implementations, modifications, and variations that may fall within the scope of the subject matter described.
Number | Date | Country | Kind |
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1204/CHE/2013 | Mar 2013 | IN | national |