Patent Application
20090326754
This invention generally relates to diagnostic methods and systems, and more specifically relates to methods and systems for performing engine diagnosis.
Modern engines can be exceedingly complex. The complexities of modern engines, such as gas turbine engines used in aircraft systems and/or other vehicle systems, have led to increasing needs for automated diagnosis of such engines. Typical engine diagnostic systems and methods are designed to monitor the engines in an effort to predict the future performance of the engines and detect potential faults. These engine diagnostic systems and methods are typically designed to detect these potential faults such that the potential faults can be addressed before the potential faults lead to failure in the engine.
One type of engine for which diagnostics are of particular importance in aircraft systems is for gas turbine engines in aircraft systems. In aircraft systems, diagnosis of engines can detect potential faults such that they can be addressed before they result in serious engine or system failure and possible in-flight shutdowns, take-off aborts, delays or cancellations.
Some current engine diagnostic techniques have relied upon one or more assumptions regarding available data that is used by such current engine diagnostic techniques. For example, certain engine diagnostic techniques rely on an assumption that the available data conforms to a particular known distribution or format, such as a normal distribution. In addition, certain engine diagnostic techniques rely on an assumption that a certain amount of fault data exists for the particular type of engine. However, in certain circumstances, the available data may not fit a particular known distribution. In addition, in certain situations, fault data for the particular type of engine may be limited.
Also, typical engine diagnostic techniques and systems have failed to account for effects of correlation of the data over time and across variables. Typical engine diagnostic techniques and systems also often do not provide a parsimonious representation of large data sets with a minimal set of wavelet coefficients. Also, typical engine diagnostic techniques and systems often do not provide optimal results in situations in which there is an unavailability of a sufficient number of fault cases represented in a given data set.
Accordingly, it is desirable to provide an improved engine diagnostic method, for example that provides for potentially more accurate diagnosis of the engine, and/or that provides for accurate diagnosis of the engine when the available data pertaining to the engine may not conform to a particular known distribution and/or when fault data for the particular type of engine may be limited. It is also desirable to provide an improved engine diagnostic program product and/or engine diagnostic system, for example that provides for potentially more accurate diagnosis of the engine such as when the engine may not conform to a particular known distribution and/or when fault data for the particular type of engine may be limited. It is further desirable to provide improved engine diagnostic methods, program products, and engine diagnostic systems that address time correlation of data and correlation across variables. It is also desirable to provide improved engine diagnostic methods, program products, and engine diagnostic systems that provide a parsimonious representation of large data sets with a minimal set of wavelet coefficients. In addition, it is desirable to provide improved engine diagnostic methods, program products, and engine diagnostic systems that provide improved results in situations in which there is an unavailability of a sufficient number of fault cases represented in a given data set. Furthermore, other desirable features and characteristics of the present invention will become apparent from the subsequent detailed description of the invention and the appended claims, taken in conjunction with the accompanying drawings and this background of the invention.
In accordance with an exemplary embodiment of the present invention, a method for performing diagnosis on an engine of a vehicle is provided. The method comprises the steps of obtaining data for a plurality of variables pertaining to the engine, transforming the data with respect to each of the plurality of variables using a wavelet transformation, to thereby generate initial coefficients for each of the plurality of variables, and aggregating the initial coefficients for each of the plurality of variables, to thereby generate an aggregate set of coefficients for the plurality of variables.
In accordance with another exemplary embodiment of the present invention, a program product for performing diagnosis on an engine is provided. The program product comprises an engine diagnostic n program and a computer-readable signal bearing media. The engine diagnostic program is configured to at least facilitate obtaining data for a plurality of variables pertaining to the engine, transforming the data with respect to each of the plurality of variables using a wavelet transformation, to thereby generate initial coefficients for each of the plurality of variables, and aggregating the initial coefficients for each of the plurality of variables, to thereby generate an aggregate set of coefficients for the plurality of variables. The computer-readable signal bearing media bears the engine diagnostic program.
In accordance with yet another exemplary embodiment of the present invention, an engine diagnostic system for performing diagnostics on an engine is provided. The engine diagnostic system includes a memory and a processor. The memory is configured to at least facilitate storing data for a plurality of variables pertaining to the engine. The processor is coupled to the memory, and is configured to at least facilitate transforming the data with respect to each of the plurality of variables using a wavelet transformation, to thereby generate initial coefficients for each of the plurality of variables, and aggregating the initial coefficients for each of the plurality of variables, to thereby generate an aggregate set of coefficients for the plurality of variables.
The preferred exemplary embodiment of the present invention will hereinafter be described in conjunction with the appended drawings, where like designations denote like elements, and:
The following detailed description is merely exemplary in nature and is not intended to limit the invention or the application and uses of the invention. Furthermore, there is no intention to be bound by any theory presented in the preceding background or the following detailed description.
The present invention provides a method, program product, and system for performing diagnostics on an engine using wavelet transformations. In one preferred embodiment, the method, program product, and system are intended for use on gas turbine engines of a fleet of aircraft. However, it will be appreciated that in other embodiments, the method, program product, and system provided can be used for performing diagnostics on or with respect to gas turbine engines for any number of other different types of vehicles, devices, and/or systems, and/or on or with respect to any number of other different types of engines.
As shown in
The data is then transformed with respect to a first variable of which the data represents using a wavelet transformation (step 104). The transformation results in an initial coefficient for the first variable that is generated using the wavelet transformation. In a preferred embodiment, the first variable includes one of the following above-referenced variables: an exhaust gas temperature for the engine, power rear angles for the engine, an inlet temperature for the engine, and a veer flow for the engine. However, this may vary in other embodiments. Also in a preferred embodiment, the transformation and generation of the initial coefficients for the first variable is performed by a processor of a computer system, such as the processor 206 of the computer system 200 of
Next data is then transformed with respect to a subsequent, or next, variable of which the data represents using a wavelet transformation (step 106). The transformation results in an initial coefficient for the next variable that is generated using the wavelet transformation. In a preferred embodiment, the next variable transformed in step 106 also includes one of the following above-referenced variables: an exhaust gas temperature for the engine, power rear angles for the engine, an inlet temperature for the engine, and a veer flow for the engine. However, this may vary in other embodiments. Also in a preferred embodiment, the transformation and generation of the initial coefficients for the next variable is performed by a processor of a computer system, such as the processor 206 of the computer system 200 of
A determination is then made as to whether there are any additional variables to be transformed using the wavelet transformation (step 108). In a preferred embodiment, this determination is made by a processor of a computer system, such as the processor 206 of the computer system 200 of
If a determination is made in step 106 that there are one or more additional variables to be transformed using the wavelet transformation, then step 106 repeats for another subsequent, or next, variable of which the data represents using a wavelet transformation. In a preferred embodiment, this next variable transformed also includes one of the following above-referenced variables: an exhaust gas temperature for the engine, power rear angles for the engine, an inlet temperature for the engine, and a veer flow for the engine. However, this may vary in other embodiments. Steps 106 and 108 repeat in this manner until a determination is made in an iteration of step 108 that there are no additional variables to be transformed using the wavelet transformation, at which point the process proceeds to step 110, as described below.
In step 110, the initial coefficients are aggregated together (step 110). As a result, an aggregate set of coefficients for the plurality of variables is generated in step 110. In a preferred embodiment, the aggregate set of coefficients for the plurality of variables is generated in step 110 by taking a union of various values represented by the initial coefficients generated in steps 104-108 above, for example as described in greater detail further below. Also in a preferred embodiment, the aggregation of the initial coefficients into the aggregate set of coefficients in step 110 is performed by a processor of a computer system, such as the processor 206 of the computer system 200 of
Through steps 104-110, data can be represented in different resolutions or scales using wavelets. Such a representation can be referred to as a multi-resolution representation. This representation can be used to approximate a given data set by using information from few important scales. In a preferred embodiment, the initial coefficients for the variables as generated in steps 104-110 can serve as an approximation to the data using all of the initial variable coefficients in a coarsest-scale. Increasingly finer levels of resolution can then be introduced in step 112 described below. The approximation error reduces with the inclusion of additional levels through additional refinements in certain embodiments. The discontinuities in the data are manifested even at very finer scales. If these discontinuities are important features of the data, then they are preferably accounted in the approximation, although this increases the number of coefficients required for representing the data. Therefore, the additional refinement in step 112 as described below preserves the important features of the data with as much fewer wavelet coefficients as possible, in accordance with an exemplary embodiment of the present invention.
Specifically, in step 112, a revised set of coefficients for the plurality of variables is generated (step 112). In a preferred embodiment, the revised set of coefficients is generated based on the aggregate set of coefficients from step 110 along with one or more optimization criteria. Also in a preferred embodiment, the revised set of coefficients is generated based on the aggregate set of coefficients and a mean squared error for the data. Preferably, the revised set of coefficients is generated based on the aggregated set of coefficients and a weighted average of a normalized mean squared error for the data. In a most preferred embodiment, the revised set of coefficients for the plurality of variables is generated in step 112 based on the aggregate set of coefficients, the weighted average of the normalized mean squared error for the data, and a measure representing at least in part a number of values in the data. However, this may vary in other embodiments. In addition, in a preferred embodiment, the revised set of coefficients is generated by a processor of a computer system, such as the processor 206 of the computer system 200 of
Preferably, step 112 thus provides for greater refinement of the coefficients, as referenced above. Generally, coarser scales adequately represent low frequency components of the data. The sharp jumps in the data are manifested in coarser to finer scales. Owing to the localized nature of wavelet bases, coefficients within the neighborhood of this discontinuity will be significant and the rest will be insignificant. By retaining these coefficients with significant magnitude and assuming rest of the coefficients to be zero and then applying inverse wavelet transform in accordance with a preferred embodiment of the present invention, this results in potentially better reconstruction compared, for example, to a traditional multi-resolution method. For example, using this technique requires potentially fewer significant wavelet coefficients to represent entire multivariate time-series data, as compared to traditional methods.
In a preferred embodiment, in order to select an optimum number of wavelet coefficients, the following cost following cost function is used, which is referred herein as relative reconstruction error, or RRE. The relative reconstruction error, or RRE, is a weighted average of a normalized mean square error of the data and a fraction of coefficients (preferably the aggregate coefficients of step 110 in a preferred embodiment). In a preferred embodiment, the relative reconstruction error, or RRE, is calculated in accordance with the following equation:
RRE(C)=w x×nMSE+(1−w)×C/N(1) (Equation 1),
where nMSE is a normalized mean squared error between original and reconstructed data, w is a weight (0<=w<=1), N is the total number of coefficients and C is the selected number of coefficients. RRE is computed for each C and an optimal value (C*) of the one for which RRE is minimum is determined. Note that, this cost function balances between error in reconstruction and number of coefficients. The following procedure is used in selecting the wavelet bases and is repeated for each variable in the multivariate time-series data.
In a preferred embodiment, in step 112, an L-level wavelet decomposition is applied to each variable time series in the data. Also in a preferred embodiment, for each batch in the data, a number C is selected as representing a number of absolute significant coefficients, and is then used in computing the RRE, as referenced in Equation 1 above. Also in a preferred embodiment, this is repeated for different values of C, and ultimately a value of C is selected that minimizes the values of the RRE. Also in a preferred embodiment, the minimum of all the selected optimum C's is obtained for all the data is the optimum C, referred to herein as C*, for any particular variable.
In addition, in a preferred embodiment, for each batch, various C* absolute significant coefficients are selected, and their corresponding bases are noted, as part of steps 104-108 above. Also in a preferred embodiment, a union of all the selected bases is then selected in step 110 above and considered to be the optimum bases set for the time-series data. Preferably the optimum bases set are constructed for each variable in the dataset, for example corresponding to the initial coefficients for each of the variables in steps 104-108 described above. The above procedure is conservative in the sense that it selects more number of coefficients than required, but ensures that all the variations in the normal operation is captured and hence all the important features of the data are captured, in accordance with a preferred embodiment of the present invention.
Next, in step 114, a determination is made as to whether there are one or more faults in the engine represented by the data. This fault determination of step 114 is made using the revised coefficients of the plurality of variables from step 112. In one preferred embodiment, the determination of whether there is a fault in the engine is made at least in part by comparing the revised set of coefficients with a fault vector space and a no-fault vector space to determine whether there is a fault in the engine. Also in one preferred embodiment, boundaries of the fault vector space and the no-fault vector space using a set of actual fault data and using a bootstrap technique.
However, this may vary in other embodiments. Also in one preferred embodiment, the determination of whether there is a fault in the engine is based at least in part on the revised set of coefficients and using a bootstrap technique. However, this may also vary in other embodiments. In addition, in a preferred embodiment, the determination of whether there is a fault in the engine is made by a processor of a computer system, such as the processor 206 of the computer system 200 of
In addition, in a preferred embodiment, the various steps of the process 100 of
Then, database models such as principal components analysis (PCA) are preferably applied for finding an associated fault subspace (step 304). For this matrix X, mean scaling is preferably performed (step 306), after which the matrix X is preferably subjected to single value decomposition (SVD) techniques (step 308), preferably given by the following equation:
X=UΣVT (Equation 2),
where U and V are left and right singular vectors respectively and Σ is a diagonal matrix of singular values. The left singular vectors corresponding to significant singular values constitutes the subspace of interest in accordance with a preferred embodiment of the present invention. Also in a preferred embodiment, columns of the matrix signified as P contain the dominant left singular vectors and Σa is the diagonal matrix of corresponding singular values.
To test any given time-series data, its wavelet features are preferably extracted and projected onto the columns of P (step 310) and compared to various fault and no-fault vector spaces (step 312) representing known instances with representative data in which the engine was known to have certain faults (fault vector spaces) or in which the engine was known to be free of certain faults (no-fault vector spaces). In a preferred embodiment, s is used to represent the projection and test statistics such as T2 and Q, which can be used to check whether a given data is in the subspace or not. T2 and Q are preferably represented by the following equations given by:
In this exemplary embodiment, the T2 statistics is sensitive to inaccuracies in the PCA subspace corresponding to the smaller singular values because it directly measures the variation along each of the principal singular vectors. However, the Q statistic is robust to smaller singular values since it does not directly measure the variations along each singular vector but measures the total sum of variations in the residual space. It is not sensitive to the inaccuracies in the smaller singular values. The T2 and Q statistics along with their appropriate thresholds can detect different type of faults, and the advantages of both statistics can be utilized by using the two statistics together, in accordance with one exemplary embodiment of the present invention.
It will be appreciated that various steps/sub-steps of the embodiment of
Turning now to
In certain such preferred embodiments, the fault identification can also be posed as the following hypothesis testing problem:
Ho:T(s)<t (Equation 6), and
Hi:T(s)>t (Equation 7),
where Ho is a null hypothesis that the fault is not related to the fault under consideration. In classical hypothesis testing which is based on Neyman-Pearson theorem, the threshold t is obtained by specifying the false alarm rate α, which is generally 5% or 1%. If the data is normally distributed, the test statistics T2 and Q follow a chi-square distribution (of appropriate degrees of freedom) in accordance with one preferred embodiment, and the threshold t can be evaluated for a specified alpha (α).
For example, in one such exemplary preferred embodiment using hypothesis testing, a wavelet based re-sampling or bootstrapping method to obtain the distribution of T(s) under H0, such as is described directly below. For example, in one such exemplary embodiment of the present invention using a bootstrapping technique, we let x(t,ζ) represent a stochastic process from a probability space. In this embodiment, we also let Ω represent the set of all outcomes of the space, and we let ζ be an element of Ω. In most practical situations, only a finite number of observations or sample paths (or elements ζ ε Ω) from this probability space. Bootstrapping or re-sampling procedures are methods wherein sample paths or observations from the probability space are generated artificially from a given observation x(t, ζ). These observations are in turn preferably used to generate sampling distributions of any statistics (computed from the observations) of interest.
In one preferred embodiment, these methods are based on the assumption of mathematical exchangeability of the elements of the observation x(t). A set of n elements of x(t) is said to be exchangeable if the joint distribution p(x(1), x(2), . . . x(n) is invariant under any permutation of these elements. Therefore, several samples paths from a given probability space can be generated by simply permuting the elements of a given observation. However, in many applications the observed time-series has an inherent correlation structure and therefore is not exchangeable. Permuting the elements of the observed time-series destroy its correlation structure.
In order to alleviate this problem, in a preferred embodiment, the following procedure is used to generate the sampling distribution of T(s) under the null hypothesis and an appropriate threshold for a given false positive rate α is computed from this sampling distribution. Specifically, in such a preferred embodiment, for each time-series data under Ho, the following steps are repeated.
First, a hypothesis is generated for testing (step 402). In a preferred embodiment, the hypothesis corresponds to H0 as described above, and corresponds to one or more potential faults and/or the absence of one or more such potential faults in the engine, corresponding to a hypothesis H0 to be tested using the additional steps below in accordance with this embodiment.
Next, a J-level discrete wavelet transform (DWT) is preferably applied to the time series data (step 404). The wavelet coefficients are then preferably permuted at different scales using cyclic permutation (step 406). An inverse wavelet transform is then preferably applied to obtain a re-sampled or bootstrapped time-series (step 408).
In addition, the feature vector is then computed for this re-sampled data (step 410). In so doing, we also preferably let S represent the projection onto the range space of P. A test statistic T(s) is then computed for this projection (step 412). In a preferred embodiment, this is then preferably repeated in various iterations for re-sampled data and different corresponding projections, to thereby calculate various test statistics T(s) for various corresponding projections (step 412).
Next, preferably all of the T(S) values of re-sampled data under H0 are pooled together (step 414). We preferably let Tv represent the vector of T(s) values sorted in ascending order. We also preferably let the total number of elements in Tv be represented by the designation B. Then the value corresponding to Tv(b((1-α)B)c) provides the required threshold t for the given false positive rate α, in accordance with one preferred embodiment of the present invention.
Also in a preferred embodiment, the threshold value t is then calculated according to the above formula (step 416). The threshold value is then preferably used to test the required hypothesis H0 (step 418).
It will be appreciated that various steps/sub-steps of the embodiment of
In the depicted embodiment, the computer system 200 includes a processor 206, a memory 208, a computer bus 210, an interface 213 (also as mentioned above), and a storage device 214. The processor 206 performs the computation and control functions of the computer system 200, and may comprise any type of processor or multiple processors, single integrated circuits such as a microprocessor, or any suitable number of integrated circuit devices and/or circuit boards working in cooperation to accomplish the functions of a processing unit. During operation, the processor 206 executes one or more programs 212 preferably stored within the memory 208 and, as such, controls the general operation of the computer system 200.
In a preferred embodiment, the processor 206 executes the steps of the process 100 of
The memory 208 stores a program or programs 212 that executes one or more embodiments of processes such as the process 100 of
The computer bus 210 serves to transmit programs, data, status and other information or signals between the various components of the computer system 200. The computer bus 210 can be any suitable physical or logical means of connecting computer systems and components. This includes, but is not limited to, direct hard-wired connections, fiber optics, infrared and wireless bus technologies.
The interface 213 allows communication to the computer system 200, for example from a system operator and/or another computer system, and can be implemented using any suitable method and apparatus. It can include one or more network interfaces to communicate with the requester, or with one or more terminal interfaces to communicate with technicians, and/or one or more storage interfaces to connect to storage apparatuses such as the storage device 214, and/or one or more other components of the computer system 200 and/or other systems and/or devices.
The storage device 214 can be any suitable type of storage apparatus, including direct access storage devices such as hard disk drives, flash systems, floppy disk drives and optical disk drives. In one exemplary embodiment, the storage device 214 is a program product from which memory 208 can receive a program 212 that executes one or more embodiments of the process and/or steps thereof as described in greater detail further below. In one preferred embodiment, such a program product can be implemented as part of, inserted into, or otherwise coupled to the computer system 200 and/or one or more components thereof. As shown in
It will be appreciated that while this exemplary embodiment is described in the context of a fully functioning computer system, those skilled in the art will recognize that the mechanisms of the present invention are capable of being distributed as a program product in a variety of forms, and that the present invention applies equally regardless of the particular type of computer-readable signal bearing media used to carry out the distribution. Examples of signal bearing media include: recordable media such as floppy disks, hard drives, memory cards and optical disks (e.g., disk 215), and transmission media such as digital and analog communication links. It will similarly be appreciated that the computer system 200 may also otherwise differ from the embodiment depicted in
Also as shown in
Also as shown in
Turning now to
Accordingly, improved engine diagnostic methods, program products, and engine diagnostic systems are provided. In various exemplary embodiment, the improved engine diagnostic methods, program products, and engine diagnostic systems provide for more accurate diagnosis of the engine, for example when the data pertaining to the engine may not conform to a particular known distribution and/or when fault data for the particular type of engine may be limited. In addition, in various other embodiments, the improved engine diagnostic methods, program products, and systems address time correlation of data and correlation across variables, and provide a parsimonious representation of large data sets with a minimal set of wavelet coefficients, provide improved results in situations in which there is an unavailability of a sufficient number of fault cases represented in a given data set.
The embodiments and examples set forth herein were presented in order to best explain the present invention and its particular application and to thereby enable those skilled in the art to make and use the invention. However, those skilled in the art will recognize that the foregoing description and examples have been presented for the purposes of illustration and example only. The description as set forth is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching without departing from the spirit of the forthcoming claims.
While at least one exemplary embodiment has been presented in the foregoing detailed description of the invention, it should be appreciated that a vast number of variations exist. It should also be appreciated that the exemplary embodiment or exemplary embodiments are only examples, and are not intended to limit the scope, applicability, or configuration of the invention in any way. Rather, the foregoing detailed description will provide those skilled in the art with a convenient road map for implementing an exemplary embodiment of the invention. It being understood that various changes may be made in the function and arrangement of elements described in an exemplary embodiment without departing from the scope of the invention as set forth in the appended claims.
