WO2008157498A1

WO2008157498A1 - Methods and systems for predicting equipment operation

Info

Publication number: WO2008157498A1
Application number: PCT/US2008/067125
Authority: WO
Inventors: Manish Harish Bharati; James Po Kong; Weihua Li
Original assignee: Shell Oil Company; Shell Internationale Research Maatschappij B.V.
Priority date: 2007-06-15
Filing date: 2008-06-16
Publication date: 2008-12-24
Also published as: GB2464002A; GB2462394B; US20100257410A1; CA2689237C; CA2689252A1; US8688405B2; CA2689252C; WO2008157494A3; US20140240095A1; GB2462768B; WO2008157494A2; GB2462394A; WO2008157503A1; GB2462047B; GB2464002B; CA2690459A1; GB0921377D0; GB0920915D0; WO2008157505A1; CA2689238A1

Abstract

A system comprising a piece of equipment; a sensor adapted to measure an operating parameter of the equipment; a database adapted to store the operating parameter of the equipment; a model to approximate future operation of the equipment; and a modeling engine adapted to take an input of the current and past operating parameters of the equipment and predict future operations.

Description

METHODS AND SYSTEMS FOR PREDICTING EQUIPMENT OPERATION

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority, pursuant to 35 U.S.C. § 119(e), of U.S.

Provisional Application Serial No. 60/944,286 entitled "REMOTE MONITORING SYSTEMS AND METHODS," filed on June 15, 2007 in the name of James Kong and is hereby incorporated by reference.

BACKGROUND

[0002] U.S. Patent Application Publication 2008/0129507 discloses a method for employing radio frequency (RF) identifier (ID) transponder tags (RFID tags) to create a unique identifier, termed an RFID signature, for use within a data processing system with respect to a person or an object. An interrogation signal is transmitted toward a person or an object with which a set of one or more RFID tags are physically associated. A first set of RFID tag identifiers are obtained from an interrogation response signal or signals returned from the set of one or more RFID tags. A mathematical operation is performed on the first set of RFID tag identifiers to generate an RFID signature value, which is employed as an identifier for the person or the object within the data processing system with respect to a transaction that is performed by the data processing system on behalf of the person or the object. U.S. Patent Application Publication 2008/0129507 is herein incorporated by reference in its entirety. [0003] U.S. Patent Application Publication 2008/0016353 discloses a method and system for verifying the authenticity and integrity of files transmitted through a computer network. Authentication information is encoded in the filename of the file. Authentication information may be provided by computing a hash value of the file, computing a digital signature of the hash value using a private key, and encoding the digital signature in the filename of the file at a predetermined position or using delimiters, to create a signed filename. Upon reception of a file, the encoded digital signature is extracted from the signed filename. Then, the encoded hash value of the file is recovered using a public key and extracted digital signature, and compared with the hash value computed on the file. If the decoded and computed hash values are identical, the received file is processed as authentic. U.S. Patent Application Publication 2008/0016353 is herein incorporated by reference in its entirety.

SUMMARY [0004] In one embodiment, the invention provides a system comprising a piece of equipment; a sensor adapted to measure an operating parameter of the equipment; a database adapted to store the operating parameter of the equipment; a model to approximate future operation of the equipment; and a modeling engine adapted to take an input of the current and past operating parameters of the equipment and predict future operations.

[0005] In another embodiment, the invention provides a method comprising operating a piece of equipment; collecting operating data from the equipment; selecting a model to approximate the equipment; and calculating future key performance indicators for the equipment using the model. [0006] Other aspects of the invention will be apparent from the following description and the appended claims.

BRIEF DESCRIPTION OF DRAWINGS

[0007] Figure 1 shows a system in accordance with one or more embodiments of the invention. [0008] Figures 2 - 4 show flowcharts in accordance with one or more embodiments of the invention.

[0009] Figure 5 shows a computer system in accordance with one or more embodiments of the invention.

[0010] Figures 6-11 show graphs of sample data and predicted data in accordance with one or more embodiments of the invention.

DETAILED DESCRIPTION [0011] Specific embodiments of the invention will now be described in detail with reference to the accompanying figures. Like elements in the various figures are denoted by like reference numerals for consistency.

[0012] In the following detailed description of embodiments of the invention, numerous specific details are set forth in order to provide a more thorough understanding of the invention. In other instances, well-known features have not been described in detail to avoid obscuring the invention.

[0013] In general, embodiments of the invention relate to methods and systems for making predictions regarding equipment behavior to adjust planning and operation of the equipment. More specifically, embodiments of the invention provide methods and systems for using process data to select and train models or develop recursive methods to predict future values of key process indices (KPI values) and use the KPI values to adjust planning and operation of the equipment.

Figure 1: [0014] Figure 1 shows a system in accordance with one or more embodiments of the invention. In one or more embodiments of the invention, the system has an equipment set (102) including, for example, multiple pieces of equipment, (e.g., equipment A (102A), equipment N (102N)). Each piece of equipment (e.g., equipment A (102A), equipment N (102N)) is a type of processing equipment (e.g., a reciprocating compressor, centrifugal compressor, or centrifugal pump) used to produce, manufacture, and/or distribute produced, procured, or created products (e.g., used in refining and/or chemical operating facilities). Each piece of equipment (e.g., equipment A (102A), equipment N (102N)) produces process data (110). [0015] In one or more embodiments of the invention, the equipment (e.g., equipment A (102A), equipment N (102N)) may be connected to instrument sensors to collect process and/or equipment data (hereinafter collectively referred to as process data (HO)). Process data (110) are real-time data such as flows, pressures, temperatures, density, and viscosity, etc. The process data (110) may be transmitted continuously or in batch processes, such as every 30 seconds or every minute or few minutes to a storage and/or processing medium (e.g., a database).

[0016] In one or more embodiments of the invention, process data (110) may be transmitted to a database (106) for storage. The database (106) may also store other data, such as information derived from years of research and development investment and operating experience of various manufacturing processes that were operated in the past and/or is currently operating, and vendor data to be used in conjunction with the other data. The database may also include plant history data providing, for example, parameters such as: performance data, efficiency and deviations between actual and theoretical values of power, flows and temperatures. The data in the database (106) may provide an indication of when preventive maintenance should be performed on the equipment. For example, the data may be used to make changes to the equipment or to plan equipment maintenance. The process data collected in the database and all or select portions of the process data may be selectively sent to the modeling engine (100).

[0017] The modeling engine (100) processes various types of data, including but not limited to, data received from the database (106) and models (108). Models (108) may include vendor-provided models, first principle models, mathematical models, and/or any other type of model or combination thereof. First principle models are models used to calculate equipment performance (e.g., a KPI value).

For example, first principle models use process dynamic data and static data (obtained from vendors) to produce current KPI values for a piece of equipment. If first principle models cannot be directly applied to sample data (due to lack of information or incomplete information), then other models such as multivariate statistical (MVS) models may be applied to obtain current KPI values. MVS models may include, but are not limited to, principle component analysis, partial least squares, principal component regression and canonical variate analysis. The modeling engine (100) also includes models for calculating future KPI values, as described below in Figures 2 and 3. In one or more embodiments of the invention, the modeling engine (100) may interface with a user through a graphical user interface (GUI) (104). The user may control the modeling engine (100) to select process data (110) or other data from the database (106) and modeling data from models (108) to be used in the modeling engine (100).

[0018] In one or more embodiments of the invention, the modeling engine (100) may use process data (110) along with models (108) to generate KPI values (112), as described below in Figures 2 and 3. The KPI values (112) are performance and/or health data for a number of pieces of equipment (e.g., equipment A (102A), equipment N (102N)), and may include such indications as process trends and alert messages for abnormal situations (discussed below in Figure 3). In one or more embodiments of the invention, KPI values (112) may be returned to the modeling engine (100) and/or displayed to the user through the GUI (104). The user may make process decisions based on the information provided through the KPI values (112). For example, KPI values may be future KPI values, used for future planning on preventive maintenance, near term operation change to bring the equipment into a less distressed mode to make sure it will last until the next scheduled shutdown, and benchmarking of similar equipment. These uses of KPI values are for example only and not meant to limit the invention.

Figure 2:

[0019] Figure 2 shows a flowchart in accordance with one or more embodiments of the invention. In one or more embodiments of the invention, one or more of the steps shown in Figure 2 may be omitted, repeated, and/or performed in a different order. Accordingly, embodiments of the invention should not be considered limited to the specific arrangement of steps shown in Figure 2.

[0020] In one or more embodiments of the invention, Figure 2 shows a method for modeling future KPI values of equipment. In step 200, sample data are collected. In this step, sample data from the equipment are collected using the instrument sensors. For example, the sample data may be process data (110), including but not limited to, power, polytropic head, molecular weight, specific heat ratio, compressibility factor, temperatures, flow rates, pressures, and amperage and speed of equipment. The sample data may include, but are not limited to, actual, predicted and theoretical measurements of data. The sample data may also be obtained from inputs to first principle models, or from outputs from first principle models, as discussed below in Figure 3. [0021] In step 202, one or more subsets of sample data are selected from the sample data to use for model identification. The subsets of sample data may be selected from the sample data collected in step 200.

[0022] In step 204, in one or more embodiments of the invention, one or more models are selected based on relationships amongst data in the data subset. A model may be selected from models including, but not limited to statistical models and models for predicting future values. Additionally, a model may be a static model or a dynamic model. For example, a model may be a multivariate statistical model including, but not limited to, a principal component analysis (PCA), a partial least squares (PLS), a principal component regression (PCR), and/or a canonical variate analysis (CVA). A model may also be selected from models that predict future behavior, including but not limited to, time series analysis (TSA), autoregressive moving average model with exogenous inputs (ARMAX), multi-terms polynomials (MTP), Kalman filtering (KF), and non- linear least squares (NLLS). Those skilled in the art will appreciate that the models for use in step 204 are not limited to those described above. Those skilled in the art will also appreciate that more than one model may be selected for use. For example, TSA, MTP, and KF may be incorporated with NLLS to handle nonlinear process data. Selection of model(s) may be based on various criteria, for example relationships amongst data in the data subset.

[0023] Continuing with step 204, in one or more embodiments of the invention, a model may be selected based on relationships amongst data in the data subset. For example, PCA may be selected when there is no information on the grouping of data in the data subset, PCR may be selected when there are correlations amongst the inputs in the data subset, PLS may be selected when there are correlations amongst inputs and outputs in the data subset, CVA may be selected when the number of inputs and outputs in the data subset are close. Those skilled in the art will appreciate that the term "close" is a relative term and references various relative differences between numbers of inputs and outputs. As a further example, TSA may be selected where the sample data are highly correlated in time and when the sample data may be highly predictive of future behavior, MTP may be selected when the sample data is collected from a single input single output process, and KF may be selected when the sample data is collected from a multi-input multi-output process. Those skilled in the art will appreciate that a model may be selected for reasons other than those listed above.

[0024] In step 206, the selected model(s) are validated using the sample data. In one or more embodiments of the invention, the subset of data selected in step 202 may be used to validate the model(s). In an alternative embodiment, a separate subset of data or the entire set of sample data may be used. To validate the model, the sample data or subset of sample data may be filtered and/or training data may be denoted. The training data may be input to the selected model(s) to calculate variables within the model. These variables may identify polynomials, discussed below in Figure 3, to train the model to fit the sample data and determine an identified model. In the following steps, the identified model may replace, or be used in conjunction with, the selected model(s). The sample data or a subset of sample data may be input to the selected model(s) to calculate output. To validate the selected model(s), the output may be compared to the sample data. Methods of comparing the output with the sample data may include, but are not limited to, plotting output of the model on a graph, numerical comparison, or calculating delta values between the calculated and actual values. If the comparison shows sufficiently low variation between the calculated and actual values, then the selected model(s) may be considered to be validated. Those skilled in the art will appreciate that the term "sufficiently low" is a relative term and references various relative differences between the calculated and actual values. Those skilled in the art will also appreciate that depending on the calculated data, the level of accuracy to determine sufficiency may vary and, as such, the type of calculated values that are considered "sufficiently low" may vary.

[0025] In step 208, future KPI values are calculated using the selected model(s).

Future KPI values may be calculated using sample data or, alternatively, other process data, to input to the selected model(s). Using this input and the selected model(s), output is calculated for a future time (i.e., future KPI values). These future KPI values may be graphed, charted, or otherwise displayed and/or organized for observation. [0026] In step 210, in one or more embodiments of the invention, the trends in future KPI values are observed. Observation may be performed manually and/or using a computer to recognize trends.

[0027] In step 212, the planning and operation of equipment is adjusted using the trends observed in step 210. For example, future planning and operation may include, but is not limited to, preventive maintenance, near term operation change to bring the equipment into a less distressed mode to make sure it will last until the next schedule shutdown, and benchmarking of similar equipment. Various types of planning may be adjusted, including but not limited to, planned preventative maintenance, planned process adjustments, and/or planned equipment replacement.

Figure 3:

[0028] Figure 3 shows a flowchart in accordance with one or more embodiments of the invention. In one or more embodiments of the invention, one or more of the steps shown in Figure 3 may be omitted, repeated, and/or performed in a different order. Accordingly, embodiments of the invention should not be considered limited to the specific arrangement of steps shown in Figure 3.

[0029] In one or more embodiments of the invention, Figure 3 shows a method for modeling future values of equipment using an ARMAX model. [0030] In step 300, the equipment from which to collect sample data is selected. In step 302, sample data from the equipment are collected using the instrument sensors. For example, the sample data for a compressor may be process data (110), including but not limited to, power (actual, theoretical, etc.), polytropic head (actual, predicted, theoretical, etc.), molecular weight, specific heat ratio, compressibility factor, temperatures, flow rates, pressures, and amperage and speed of equipment. The sample data may be collected from inputs to first principle models, or from outputs from first principle models, as discussed below, and are denoted with the variable x. One instance of data may be referred to as a point of data. Sample data may be collected for k - I points, and as such are denoted as X^. [0031] In step 304, one or more subsets of sample data are identified to use as training data. The subsets of sample data are selected from the sample data collected in step 302. The training data may be a set of data within the sample data that precedes a separate set of data within the sample data. The training data are used to identify numerical values in a model, such that the model provides an accurate representation of equipment and/or process behavior. For example, with sample data taken at k = 2000 points, the training data may be the subset of data from points 1 through 1000. In this example, the remaining sample data, from k = 1001 through k = 2000, would be used to verify a model trained by the training data. One or more embodiment of the process to train and verify the model is described below, starting at step 310.

[0032] In step 306, in one or more embodiments of the invention, an exponentially weighted moving average (EWMA) filter is applied to de-noise the training data (if necessary). An EWMA filter is applied to de-noise the training data by identifying and removing outliers from the training data (outliers are defined as data points that have values higher than a cutoff value). It may be necessary to de-noise the training data to create a more robust model, as discussed below in steps 310-324. The filter applied to the training data is not limited to an EWMA filter, and may be any other type of filter including, but not limited to, a least mean squares filter or a recursive least squares filter.

[0033] In step 308, JC_# ^and yu are denoted in the training data. In one or more embodiments of the invention, x_k are selected from the sample data collected in step 302 (e.g., power, polytropic head, molecular weight, specific heat ratio, compressibility factor, temperatures, flow rates, pressures, and amperage and speed of equipment) and yt is one or more KPI (e.g., polytropic efficiency) to be calculated using a model. The variable k refers to the k'^h point of a date set, e.g., A: = 1000 is the 1000* point in a set.

[0034] In step 310, A(q^Λ), B(q^Λ), and C(q^Λ) are polynomials in an ARMAX model. In one or more embodiments of the invention, a multiple inputs single output (MISO) model, such as the ARMAX model, is selected to model the equipment. [0035] In one or more embodiments of the invention, the following equation

(Equation 1) corresponds to the ARMAX model:

4r^!k = Σ⁵Vk* +^r¹K (i)

[0036] In Equation 1, X_{1 k} is the i^th element of X_k, ε_k is an independently and identically distributed (i.i.d.) white noise to represent process disturbances including, for example, modeling errors and measurements, and q ^~! is the back- shifted operator (i.e., y_kq^ = y_k_ι )-

[0037] The following are polynomials in q^~λ :

A(q-¹ ) = l + a₁q-¹ + a₂q-² (2)

B{q-^l ) = b_hl (3)

C(^ ) = I + C₁^-¹ (4)

[0038] Additionally, B(q^"1) is a polynomial vector, defined as follows:

[0039] Thus, the ARMAX model may be rewritten as:

A(g-% = B(g-^l )x_k + c(g-% (6)

[0040] In one or more embodiments of the invention, the EWMA-filtered training data is applied to train the ARMAX model. Using the EWMA-filtered training data, the polynomials, A(q^Λ), B(q^Λ), and C(q^Λ), are identified. Together, these identified polynomials form the identified ARMAX model (e.g., Equation 6). [0041] In step 312, in one or more embodiments of the invention, values for y^ are calculated, yt represents a KPI value for a piece of equipment. For example, yt may represent, but is not limited to, equipment efficiency.

[0042] In step 314, values for y^ calculated in step 312 are validated using the sample data from step 302. To validate the calculated values for y^, the values for yu calculated in step 312 are compared to the actual values for y^ from the sample data. In one or more embodiments of the invention, actual values for y^ may be calculated from the sample data obtained from the instrument sensors using first principle models. Methods of comparing calculated yt and actual^, may include, but are not limited to, plotting on a graph, numerical comparison, or calculating delta values between the calculated and actual numbers. If the comparison shows sufficiently low variation between the calculated and actual numbers, then the calculated values for y^ may be considered to be validated. Those skilled in the art will appreciate that the term "sufficiently low" is a relative term and references various relative differences between the calculated and actual numbers. Those skilled in the art will also appreciate that depending on the calculated data, the level of accuracy to determine sufficiency may vary and, as such, the type of calculated numbers that are considered "sufficiently low" may vary.

[0043] In step 316, in one or more embodiment of the invention, the Diophantine equation is derived from A(q^Λ), B(q^Λ), and C(q^Λ). The Diophantine equation may be used to predict future output. To predict future output, a timeframe may be defined in terms of steps where a step corresponds to a length of time, e.g., a sampling interval. In one or more embodiments of the invention, steps are denoted by the variable d. Therefore, if d steps prediction of future output is expected, the d steps may be calculated from past and current inputs and outputs using the following Diophantine equation:

[0044] In the preceding equation F(q^Λ) is a polynomial, defined as:

F{q-^l ) = \ + f_λq-¹ + f₂q-² ₊ ...f_d__χq<^ (8)

[0045] In the preceding equation, F(q^Λ) has order d-1, q^~d is the d step back shifted operator, e.g., y_kq^~d = y_k__d , and G[q^~ )= g_o + g₁q^~\ In a generic case, if the order of Aψ ^ι J is n, then Gψ ^ι ) is an (« - l)^Λ order polynomial, i.e.,

G(q-^l ) = g₀ + g_lq-^l + - - -g_n__lq^<n-^l) (9)

[0046] In step 318, the prediction of j^ at time k + d, e.g., y_k+d/k is derived. For example, in one or more embodiments of the invention, a value for d may be selected. In one or more embodiments of the invention, d may be selected based on the amount of time in the future that predicted values are desired. Alternatively, d may be selected based on the values of k or using other criteria. Those skilled in the art will appreciate that there are many values of d that may be selected. Using the Diophantine equation, the improved prediction of the output at time instant k + d from data collected before and at time instant k is:

[0047] In step 320, x^is used to approximate X_k+d- In Equation 10, the future inputs

X_k+d are not available at time instant k. Therefore, to apply the improved prediction equation in practice, the current inputs X_k to approximate X_k+d, resulting in:

or equivalently,

4T¹JjW = G(q-% + B(q-^l )F(q-% (12)

[0048] In step 322, values are set for k and d. To calculate values for y_k+dlk mm%

Equation 12, it is necessary to determine time instant k + d from the sample data at time instant k. After setting values for k and d, it is possible to calculate y^ using Equation 12.

[0049] In step 324, values for y_k+dik are calculated. In this step, the sample data (i.e., X_k) are input to Equation 10 (or, equivalently, Equation 12) to calculate values for y_k+dlk . In one or more embodiments of the invention, the y_k+dlk may correspond to KPI values discussed in Figure 1 above.

[0050] In step 326, planning and operation of the equipment are adjusted using values of y_k+d/k . In one or more embodiments of the invention, y_k+d/k may be used to calculate future values of the output at continuous time t , i.e., y_t . In other words, the variable y_t is the future value of y at a particular continuous time t. In Equation 11, y_k+dik is calculated from the sample data. After calculating 9_k+d/f 9_t ^may be calculated for any continuous time t, where t e ((k + d)T - T, (k + d)T) . To obtain y_t , the slope is calculated as follows:

[0051] s_k+d/k = ^{J k+dlk J k+d}-^llk (13)In Equation 13, T is the sampling interval

of the data. [0052] From Equation 13, the following equation is obtained:

y, = y_k+ll-v_k + s_k+dlk * (t + τ - kτ - dτ)

(14)

[0053] The values of y_t may also be referred to as KPI values for a particular piece of equipment (e.g., equipment A (102A), equipment N (102N)). The values of y_t indicate process trends because they predict future values for the equipment at any continuous time t e ((k + d)T - T, (k + d)T) . Based on these process trends, the values of y_t may be used for future planning and operation of the equipment. For example, future planning and operation may include, but is not limited to, preventive maintenance, near term operation change to bring the equipment into a less distressed mode to make sure it will last until the next schedule shutdown, and benchmarking of similar equipment.

[0054] A person of ordinary skill in the art will appreciate that while an ARMAX model is used, other modeling systems may be used in place of an ARMAX model. The model selected for use with the training data may be any other type of model including, but not limited to, time series analysis, multi-terms polynomials regression, Kalman filtering, and non-linear least squares. Further, a model may be selected through trial and error. As an example, a trial may be performed by calculating model output(s) based on a set of training data and comparing the model output(s) to the remaining sample data in order to determine if they are a close match. If the output(s) closely correlate to the sample data, then the model may be used to model the equipment. If the output(s) do not correlate well with the sample data, then another model may be selected to repeat the trial until a suitable model is chosen. [0055] In one or more embodiments of the invention, the process data may be time- varying, i.e., the mean and variance values of the process data may suddenly change at a particular point in time. The change in value of the process data may be unpredictable. For example, the process data may suddenly change due to an adjustment to the process or maintenance performed on the equipment. When the process data is time-varying, it is expected to estimate future KPI values by using most recent data points and at the same time discounting older data points. In one or more embodiments of the invention, a forgetting factor (FF) may be used to achieve this objective in the case of time -varying process data. The FF may be used with the model(s) to track the time-variability in the process data. The use of a FF is described below in Figure 4.

Figure 4:

[0056] Figure 4 shows a flowchart in accordance with one or more embodiments of the invention. In one or more embodiments of the invention, one or more of the steps shown in Figure 4 may be omitted, repeated, and/or performed in a different order. Accordingly, embodiments of the invention should not be considered limited to the specific arrangement of steps shown in Figure 4.

[0057] In one or more embodiments of the invention, Figure 4 shows recursive calculation of mean and variance from finite sample points of time -varying data, allowing calculation of future values by use of a forgetting factor. These future values may be used to adjust the planning and operation of the equipment.

[0058] In step 400, the objective function is obtained with the forgetting factor. In one or more embodiments of the invention, any point in a data sequence (x) collected from a physical equipment or a process, e.g., a compressor, may be represented as the following random variable:

X₁ = m + S₁ (15)

[0059] In Equation 15, m is the mean and may be time -varying, and S₁ is an i.i.d.

Gaussian noise with zero mean and variance σ² . The variable i indicates any time between 1 to k. The variable k refers to the total length of a set of sample data, e.g., k = 1000 is a set of sample data with 1000 points. In Equation 15, in order to estimate m from the k - \ samples, the following objective function is minimized:

[0060] In one or more embodiments of the invention, Equation 16 is called a weighted least squares (WLS) criterion-based optimal objective function. In Equation 16, λ is a forgetting factor (FF), which is used to forget old data points. For example, λ^{k ~ι→ k l 1} represents the weight given to the data point at the time i for a set of sample data with k - 1 points. Use of an FF means that the method discussed here in Figure 4 is an adaptive method of calculating future mean and variance. This is in contrast to other recursive methods of calculating mean and variance that are non-adaptive (i.e., without use of an FF).

[0061] In step 402, the least squares (LS) solution is determined for m_k__x . In one or more embodiments of the invention, the LS solution to m_k__x from the k - \ samples is:

[0062] In Equation 17, m_k__x is the estimated mean value of X₁ from a data set with k — \ samples (i.e., i = 1, 2, ..., k-\). Equation 17 is the consistent estimate

where m is the expectation of m_k_₁ and, in one or more embodiments of the invention, is equal to the true mean value.

[0063] Likewise, the consistent estimate of the variance σ² from the k - \ samples is:

[0064] In step 410, in one or more embodiments of the invention, a determination is made about whether to select a sample -wise or batch-wise recursive equation. If the sample data are determined best treated with a sample-wise calculation (i.e., if the sample data should be treated on a point-by-point basis), then the process proceeds to step 412. If the data are provided in block-wise (i.e., with the sample data divided into a number of blocks, each including a number of data points within), then block- wise is chosen and the process proceeds to step 416. [0065] In step 412, m_k is calculated. In this step, m_k is calculated predicted for the sample-wise case. By extending Equations 17 and 19, it follows that the mean and variance of A: samples, respectfully, are:

=1 m mk — ^{~ 1=x}

± k (20) λ^k-'

X - λ¹

VL(I - X ^-¹)^Σ^' U - m. (21)

[0066] Further,

E{m_k } = m and ε{σ_k ² }= σ² (22)

[0067] If mean value and variance of a data set with k - \ samples have been calculated, it is possible to calculate Arri_k. Equation 20 shows that:

m_k = m_{k l} + Am_k (23)

and

Am_k = ^_r^ = ^(x_k - m_k_,) (24)

\ - λ^k

∑Λ^k- [0068] Equation 24 is the recursive formula for mean update (also referred to as an adaptive mean). Equation 24 may be used to adjust planning and operation of equipment. In addition, it can be derived that

which facilitates the recursive calculation of the variance.

[0069] In step 422, rh_k and

are used to adjust planning and operation of the equipment. For example, future planning and operation may include, but is not limited to, preventive maintenance, near term operation change to bring the equipment into a less distressed mode to make sure it will last until the next schedule shutdown, and benchmarking of similar equipment.

[0070] Returning to step 410, if batch- wise calculation is chosen, the process proceeds to step 416. Optionally, in step 416, if batch-wise analysis is selected, then m_k is predicted. To predict m_k at time instant k , define k blocks of data, jjc ,jc ,jc ,..., jc } that are available. Each block of data has n_t points, for i = 1,2, ...k. Therefore, xt represents a vector:

Equation 25 has data points, ^"Σ> N_k =

is the total length of k data blocks. N_k+l is the total length of k+1 data blocks. Each data block has multiple samples. For instance, the (k + l)'^h block has n_k+1 samples. Therefore, N^₊₁ = ^τ£jι_ι

[0071] Based on this, it is possible to define m_k and

as follows:

m mk — ^{~ 1=} N^l ₁ (26) 1 2^{2 Nk}

(27)

[0072] In Equations 26 and 27, x, is an element in x^. At time k + 1, when a new data block, x_n e 9ϊ^%+1 , is collected, it is possible to define xt₊i as:

[0073] In Equation 28, N₄₊₁ = N_k + n_k+l .

[0074] In step 418, m_k+l (future mean) is predicted. It is possible to define:

and

1 - λ^{1 NkΛ} m ^■ _kJ^ (30)

[0075] In step 420, Ant_k+i (future variance) is predicted. If m_k and

are available, it may be necessary to recursively calculate m_k+l and σ_k ² _+ι from x_n . It can be derived that:

™_k+i = m_k + λm_k+ι (31)

[0076] In Equation 31, Ani_k+i is defined as: -'

!=1

[0077] Equations 31 and 32 may be used to calculate m_k+l . [0078] In step 422, future mean and variance are used to adjust planning and operation of the equipment. Alternatively, either future mean or future variance may be used alone to adjust planning and operation of equipment. As an example, planning and operation of the equipment may include, but is not limited to, preventive maintenance, near term operation change to alter the equipment's operation to make sure it will last until the next schedule shutdown, and benchmarking of similar equipment.

EXAMPLE

[0079] The following is an example of the method described in Figure 3 to model the future efficiency of a compressor. The following example is not intended to limit the scope of the application.

[0080] In one or more embodiments of the invention, sample data for a compressor used in refining and/or chemical operating facilities are collected using instruments measuring process or equipment variables. Table 1, below, shows variables corresponding to the sample data collected from the compressor. In

Table 1, each sample data variable has a label, a name, specific units it is measured in, a description, and in the far right column, each sample data variable is denoted as X_k or y_%. The variables denoted as X_k are the sample data obtained directly from the instrument sensors or obtained indirectly using first principle models to calculate the data from the directly obtained data. The variable representing polytropic efficiency, DPEFFl, is specified as yt. The yt will be calculated using the sample data as described below.

Table 1 1] In one or more embodiments of the invention, the variables in Table 1 are modeled using the ARMAX model described above in Figure 3. Sample data are collected for points k = 1 through k = 4544. The first 2000 sample data points (i.e., k = 1 through k = 2000) are used as training data to identify the ARMAX model, including . A(q^Λ), B(q^Λ), and C(q^Λ), while the remaining 2544 samples are used as validation data to validate the model quality [0082] In the ARMAX model, B(q^A) is a polynomial vector, defined as:

M*-¹) B₂(q-^l) ^...B_K(q-¹)] (33)

In addition,

A(q-¹ ) = 1 + 0.0085?-¹ - 0.0909^² , and (34)

C(^¹ ) = 1 + 0.9434^¹ (35)

[0083] The identified Byq^'1 ) has twenty-six elements (not shown). Using the identified ARMAX model and inputs in the validation data, the output y^ in the validation data set are calculated.

Figure 6:

[0084] The values for y^ calculated using the model are validated using the sample data collected from the compressor. The following graph shown in Figure 6 shows the actual y^ for the training data and the yu calculated with the identified

ARMAX model. The yt values are plotted on the y-axis (labeled y) versus k on the x-axis (labeled k). In Figure 6, curve 600 appears to be one line but it is, in fact, two: the actual y^ values and the yu values calculated with the identified ARMAX model. It is significant that the values for actual y^ and the yt calculated with the identified ARMAX model appear to be one line (600) because they are

99.15% the same (i.e., 99.15% of variations are captured by the identified

ARMAX model). Therefore, Figure 6 shows that the identified ARMAX model explains the compressor effectively, with 99.15% of variations in the output being captured. Using the identified ARMAX model, future values can be predicted as described below.

[0085] In one or more embodiments of the invention, to determine future values of yu, the Diophantine equation is derived from the identified ARMAX model, as discussed in Figure 3. Using the Diophantine equation, the improved prediction of yu at time k + d is derived. In the present example, in one or more embodiments of the invention, d = 16 is selected. In one or more embodiments of the invention, d may be selected based on the amount of time in the future that predicted values are desired. Alternatively, d may be selected based on the values of A: or using other criteria. The selection of d = 16 is small enough to calculate enough outputs to view the process trends, and yet large enough that multiple unnecessary values are not calculated. Those skilled in the art will appreciate that there are many values of d that may be selected and d = 16 is only one example. For d = 16, future values of yt are calculated from sample points k = 2001 through k = 4544, as shown in Exhibit 3 below.

Figure 7:

[0086] Figure 7 is a graph using the sample data (i.e., X_k) and starting at k = 2001, to calculate y_k+dik from the current inputs and output according the Diophantine equation. In Figure 7, using the equations presented in Figure 3 discussed above, the predicted future values for y_% are calculated and graphed on the y-axis versus k on the x-axis. The actual y_k from the sample data are also graphed versus k. As depicted in Figure 7, curve 700 is the future y_% as well as the actual y_% from the sample data. It is significant that curve 700 appears to be one line because the future y_k and the actual y_k are close enough to each other that there is no visible difference when graphed. However, curve 702 is the error {i.e., difference) between the predicted future values of y_k and the actual values of y^ As shown by curve 702, there is a small difference between the two lines represented in curve

700. Figure 7 uses the sample data to show that the description above for calculating future output (y_k) is an effective method of predicting future values. As an example, if future values for y_k were calculated for a future time when no sample data were available, the future y_k would provide accurate predicted values for use in adjusting the planning and operation of the equipment.

[0087] Finally, in this example, y_t may be calculated for any continuous time t s (kT + dT — T,kT + dT), as described in the Figure 3 discussion above, and planning and operation of the equipment may be adjusted using y_k+d and/or y_t.

The following example is not intended to limit the scope of the application. [0088] In one or more embodiments of the invention, as an alternative to using an

ARMAX model, a PLS model may be used. In one or more embodiments of the invention, the variables in Table 1, and the sample data collected in the above example corresponding to Table 1, may be modeled using a PLS and an autoregressive with exogenous inputs (ARX) model.

[0089] To determine a PLS model for use with the variables shown in Table 1, output is denoted as Y, input is denoted as X, B is the model parameter, and E is error. This may be written as:

Y = XB + E (36) [0090] In one or more embodiments of the invention, using Equation 36 and the sample data, it is possible to train the PLS model to represent the sample data, thus obtaining an identified PLS model. In Equation 36, X G y{^Nxm and Y e yi^Nxl are two data matrices, and 5 e 91^mx'is a parameter matrix. In the presence of correlations among each variable of X (i.e., X' X is singular), PLS may estimate B in order to further calculate future values of Y. Rather than directly using Xto regress Y, PLS may calculate a number of scores, T e yϊ^NxΛ for X, and U e yϊ^NxΛ for Y. T may be used to regress U, as described below.

[0091] In one or more embodiment of the invention, to regress U, a pair of score vectors, {t, u}, and a pair of weight vectors, {w,v} , may be determined for X and Y. The vectors may be determined such that:

[0092] Equation 37 may be minimized with constraints: Ww = I and v'v = l , where I is the squared Frobenius norm of a matrix or vector.

[0093] Equation 37 may be rewritten as:

J_Pls

j=\ W^, J)-^U(MJ)Y +

[0094] Where λ and A₂ are Lagrangian multipliers. If — #τ- = 0, — τ^ = 0,

— T^r = O, and — pr = 0 , then t(i), u(i), w(i), and v(i) may be calculated. Once dw(i) dv(i) t is determined, it is possible to project the values of X and 7, as follows:

[0095] Similarly, the deflations of X and 7 are:

X

_t = Y - tq' (40)

JTV Y't

[0096] In Equation 40, p = e 91 ^m is the loading vector for X and o = — e SR' ft ft for 7 Using Equation 40, successive scores and weights may be calculated until

X and 7 have been sufficiently explained by theirs scores and then an identified PLS model may be obtained. Once X and 7 have been sufficiently explained by their scores (i.e., trained), then the sample data may be sufficiently explained by the PLS model and the PLS model becomes the identified PLS model. Those skilled in the art will appreciate that there are various identified PLS models and that the phrase "sufficiently explained" is a relative term and references various relative differences between calculated values of 7 and actual values of 7

Figures 8 & 9:

[0097] Continuing with the example, the sample data collected from the compressor (corresponding with Table 1) is used to calculate 7, using the identified PLS model described above. In one or more embodiments of the invention, there may be correlations among the twenty-six input variables shown in Table 1 and PLS may be chosen (due to the correlations among the input variables) and applied to find B. Figure 8 is a graph showing the actual 7 from the sample data and the 7 calculated from the identified PLS model. The 7 values are plotted on the y-axis (labeled Y) and the time is plotted on the x-axis (labeled time). As shown in Figure 8, the times for the calculated 7 values are the same as the times for the actual 7 values from the sample data. Due to this, it is possible to compare the actual 7 with the 7 calculated using the identified PLS model at specific points in time. Figure 8 shows that the identified PLS model works well to model the sample data, because the actual 7 (802) and the calculated Y (800) are very close to each other, based on the small prediction errors (804).

[0098] As another alternative embodiment of the invention, a non-linear iterative partial least squares (NIPALS) model may be used with PLS to calculate future values. In one or more embodiment of the invention, the NIPALS model may be chosen, for example, for its numerical reliability and efficiency. Particularly, the NIPALS algorithm can handle missing data points, which is a reality. The following example is not intended to limit the scope of the application.

[0099] To use the NIPALS model, X and 7 may be scaled as follows. To scale X and Y, a column may be set in 7, which has the highest variance, as the initial value, u_old and a weight vector, w e 9ϊ^m , may be calculated for X, whose j'^h element is:

[00100] In Equation 41, u_old(i) is the i'^h element of w_oW and w may be normalized to calculate the score vector t e 9i^N , whose i'^h element is:

[00101] Similarly, a weight vector, v e SR' , may be calculated for 7, whose j'^h element is:

[00102] In Equation 43, i = !,^{■ ■ ■}, N and j = !,^{■ ■ ■}, L For i = 1, • • •, N , each element of u may be calculated as:

∑v(k)y(i,k) u(i) = ^S (44)

∑v²(k) k=\ [00103] In Equation 44, in one or more embodiment of the invention, if ||w - w_oW| is less than or equal to a convergence criterion, then a loading vector may be calculated, otherwise is may be necessary to set u_old <= u , and return to calculating a weight vector, as described above in Equation 41 to recalculate

.

[00104] To calculate a loading vector, p is defined as p e 91 ^m for X, whose j'^h element is:

[00105] Likewise, q is defined as q e 91 ' , for 7, whose j'^h element is:

[00106] In one or more embodiments of the invention, using Equations 45 and 46, it is possible to perform deflations X <= X - tp^r and Y <= Y - tq^r . Further, if enough components in X and Y have been explained, then it is possible to use Equation 47 to calculate future values of y. If further definition of X and Y is needed, it is possible to return to Equation 50 to obtain other X and Y. [00107] Using the score vectors, , t₂ ,..., t_Λ \ and loading vectors,

[q₁, q₂,..., q_A ] c ^^lxA , the prediction at the i'^h time instant for 7 may be calculated, as follows:

y(i,:) = I₁ (IJq₁ '+... + t_Λ(i)q_Λ ' (47) [00108] Similarly, using loading vectors, \p₁ , p₂ ,..., p_A \ <= ^ςR^mxΛ , it is possible to calculate the prediction for X, as follows:

k(i,:) = t₁ (ϊ)p₁ '+... + t_A (ϊ)p_A ' (48)

[00109] In one or more embodiments of the invention, using Equations 47 and 48 to calculate future values for x and y (not shown), it is possible to adjust the planning and operation of equipment.

[00110] As an alternative to using the ARMAX, or NIPALS models described above, it may be necessary to consider the time -variance of the process data. As discussed in Figure 4, this may be done using a forgetting factor.

[00111] In the following example, the method of Figure 4 is used to model future mean and deviation for time-varying sample data with 1500 points. Each of the first 500 samples follows a Gaussian distribution with mean 3 and variance 0.2² , while in the second 1000 samples, the mean and variance of the data jump to 4 and variance 0.1² , respectively. The following example is not intended to limit the scope of the application. Figure 10:

[00112] As stated, in this example there are a sequence of random data with 1500 points. Each of the first 500 samples follows a Gaussian distribution with mean 3 and variance 0.2² , while in the second 1000 samples, the mean and variance of the data jump to 4 and variance 0.1² , respectively. If a sample-wise calculation is chosen, Equations 21 and 23 are used to calculate the adaptive mean sequence of the sample data. In Figure 10, the sample data {i.e., data samples) (1000) are graphed on the x-axis (labeled k) versus the mean values calculated from the adaptive mean calculation as described in the Figure 4 discussion and the mean values calculated from a typical non-adaptive mean calculation (mean values are plotted on the y-axis, labeled mean). In Figure 10, the curve (1002) is the adaptive mean sequence calculated in terms of Equations 21 and 23, while the curve (1004) is calculated from an existing recursive but non-adaptive method.

[00113] As shown in Figure 10, the adaptive mean sequence (1002) tracks the time- varying sample data (1000) (i.e., the mean jump in the sample data) effectively, however this is not true for the non-adaptive mean sequence (1004). Figure 10 shows that the calculations performed using Equations 21 and 23 model the data jump with greater accuracy than a recursive but non-adaptive method. This is significant because the adaptive mean sequence (1002) may be used to identify future values of time -varying data with greater accuracy close to the point of data jump than the non-adaptive mean sequence (1004). Said another way, while it was previously difficult to predict future values following a data jump in time- varying data, it is now possible (in one embodiment using Equations 21 and 23) to accurately predict future values following a data jump. [00114] Using the same data presented in Figure 10, a batch-wise calculation may be performed. In the batch-wise calculation described in the Figure 4 discussion, the 1500 sample data points are split into 300 blocks with 5 points in each. For a batch-wise calculation, Equations 30 and 31 are used to calculate the adaptive variance sequence of the sample data. In Figure 11, the sample data (i.e., data samples) (1104) are graphed on the x-axis versus the variance values calculated from the adaptive variance calculation (1102) as described in the Figure 4 discussion and the variance values calculated from a non-adaptive variance calculation (1100). In Figure 11, curve 1102 is the adaptive variance sequence calculated in terms of Equations 30 and 31, while curve 1100 is calculated from an existing recursive but non-adaptive method. The true variance is curve (1104).

Figure 11 :

[00115] Figure 11 shows that again, that while it was previously difficult to predict future values following a data jump in time-varying data, it is now possible (in one embodiment using Equations 30 and 31) to accurately predict future values following a data jump.

Figure 5: [00116] The invention may be implemented on virtually any type of computer regardless of the platform being used. For example, as shown in Figure 5, a computer system (500) includes a processor (502), associated memory (504), a storage device (506), and numerous other elements and functionalities typical of today's computers (not shown). The computer (500) may also include input means, such as a keyboard (508) and a mouse (510), and output means, such as a monitor (512). The computer system (500) is connected to a local area network

(LAN) or a wide area network (e.g., the Internet) (not shown) via a network interface connection (not shown). Those skilled in the art will appreciate that these input and output means may take other forms.

[00117] Further, those skilled in the art will appreciate that one or more elements of the aforementioned computer system (500) may be located at a remote location and connected to the other elements over a network. Further, the invention may be implemented on a distributed system having a plurality of nodes, where each portion of the invention may be located on a different node within the distributed system. In one embodiment of the invention, the node corresponds to a computer system. Alternatively, the node may correspond to a processor with associated physical memory. The node may alternatively correspond to a processor with shared memory and/or resources. Further, software instructions to perform embodiments of the invention may be stored on a computer readable medium such as a compact disc (CD), a diskette, a tape, a file, or any other computer readable storage device.

Illustrative Embodiments:

[00118] In one embodiment, there is disclosed a system comprising a piece of equipment; a sensor adapted to measure an operating parameter of the equipment; a database adapted to store the operating parameter of the equipment; a model to approximate future operation of the equipment; and a modeling engine adapted to take an input of the current and past operating parameters of the equipment and predict future operations. In some embodiments, the modeling engine is adapted to predict future process trends of the equipment. In some embodiments, the modeling engine is adapted to output alerts regarding future operation of the equipment. In some embodiments, the modeling engine is adapted to prioritize the alerts according to severity.

[00119] In one embodiment, there is disclosed a method comprising operating a piece of equipment; collecting operating data from the equipment; selecting a model to approximate the equipment; and calculating future key performance indicators for the equipment using the model. In some embodiments, the method also includes observing trends in the future key performance indicators. In some embodiments, the method also includes adjusting operations of the equipment based on the future key performance indicators. In some embodiments, the method also includes de-noising the operating data.

[00120] While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments may be devised which do not depart from the scope of the invention as disclosed herein. Accordingly, the scope of the invention should be limited only by the attached claims.

Claims

C L A I M S

1. A system comprising: a piece of equipment; a sensor adapted to measure an operating parameter of the equipment; a database adapted to store the operating parameter of the equipment; a model to approximate future operation of the equipment; and a modeling engine adapted to take an input of the current and past operating parameters of the equipment and predict future operations.

2. The system of claim 1, wherein the modeling engine is adapted to predict future process trends of the equipment.

3. The system of one or more of claims 1-2, wherein the modeling engine is adapted to output alerts regarding future operation of the equipment.

4. The system of claim 3, wherein the modeling engine is adapted to prioritize the alerts according to severity.

5. A method comprising: operating a piece of equipment; collecting operating data from the equipment; selecting a model to approximate the equipment; and calculating future key performance indicators for the equipment using the model.

6. The method of claim 5, further comprising observing trends in the future key performance indicators.

7. The method of one or more of claims 5-6, further comprising adjusting operations of the equipment based on the future key performance indicators.

8. The method of one or more of claims 5-6, further comprising de -noising the operating data.