# US 9,518,839 B2 · Wavelet based monitoring of system parameters > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 9,518,839 B2 - Document ID: US9518839B2 - Status: Granted - Kind: B2 - Application number: 14/090,865 - Filed: 2013-11-26 - Published: 2015-05-28 - Granted: 2016-12-13 - Earliest claimed: 2013-11-26 - Assignees: Northrop Grumman Systems Corporation - Applicants: Aaron A. D. Fansler - Inventors: Aaron A. D. Fansler - Web page: https://patentgrep.com/patent/US9518839B2 ## CPC - G01D 5/00: Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable (G01D3/00 takes precedence; specially adapted for apparatus giving results other than momentary value of variable G01D1/00) - G01D 7/00: Indicating measured values - G05B 23/0221: {Preprocessing measurements, e.g. data collection rate adjustment; Standardization of measurements; Time series or signal analysis, e.g. frequency analysis or wavelets; Trustworthiness of measurements; Indexes therefor; Measurements using easily measured parameters to estimate parameters difficult to measure; Virtual sensor creation; De-noising; Sensor fusion; Unconventional preprocessing inherently present in specific fault detection methods like PCA-based methods} - G05B 23/0235: {based on a comparison with predetermined threshold or range, e.g. "classical methods", carried out during normal operation; threshold adaptation or choice; when or how to compare with the threshold} - G05B 23/0281: {Quantitative, e.g. mathematical distance; Clustering; Neural networks; Statistical analysis} - G01D: MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR - G05B: CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (systems for controlling or regulating non-electric variables G05D; systems for regulating electric or magnetic variables G05F; control devices or systems insofar as characterised by mechanical features only G05G) ## Abstract Systems and methods are provided for monitoring parameters within a system. A plurality of sensors each monitor at least one parameter associated with the system. A controller is configured to receive a signal representing the monitored at least one parameter from each of the plurality of sensors and adjust a function of the system based on the received signal. Respective discrete wavelet transform components are associated with each of the plurality of sensors. Each of the discrete wavelet transform components is configured to provide a set of discrete wavelet transform coefficients, representing a content of the signal for its associated sensor, to a discrete wavelet transform monitoring component. ## Claims ### Claim 1 A system comprising: a plurality of sensors, each monitoring at least one parameter associated with the system; a controller configured to receive a signal representing the monitored at least one parameter from each of the plurality of sensors and adjust a function of the system based on the received signals; and respective discrete wavelet transform components associated with each of the plurality of sensors, each of the discrete wavelet transform components configured to provide a set of discrete wavelet transform coefficients representing a content of the signal for its associated sensor to a discrete wavelet transform monitoring component; a signal reconstruction component configured to reconstruct a portion of the signal only from a set of discrete wavelet transform coefficients that fall outside of associated defined range of values; and a fault analysis component configured to evaluate the reconstructed portion of the signal to identify an anomaly that is represented by the set of discrete wavelet transform coefficient falling outside of the defined range of values. ### Claim 2 (depends on 1) The system of claim 1, the discrete wavelet transform monitoring component being configured to alert a user when a discrete wavelet transform coefficient falls outside of a defined range of values. ### Claim 3 (depends on 2) The system of claim 2, further comprising a signal reconstruction component configured to reconstruct at least a portion of the signal in response to an alert. ### Claim 4 (depends on 2) The system of claim 2, wherein the defined range of values for each discrete wavelet transform coefficient is determined from a historical behavior of the system. ### Claim 5 (depends on 4) The system of claim 4, wherein the defined range of values for each discrete wavelet transform coefficient is determined as a range include all values within three standard deviations from a mean value associated with the discrete wavelet transform coefficient. ### Claim 6 (depends on 1) The system of claim 1, wherein each sensor includes a processor and a nontransitory computer readable medium, and the discrete wavelet transform component corresponding to each sensor is implemented as machine readable instructions stored on the non-transitory computer readable medium. ### Claim 7 (depends on 1) The system of claim 1, wherein the controller includes a processor and a nontransitory computer readable medium, and discrete wavelet transform monitoring component is implemented as machine readable instructions stored on the nontransitory computer readable medium. ### Claim 8 (depends on 1) The system of claim 1, wherein each of the discrete wavelet transform components is configured to apply a dyadic scale discrete wavelet transform to its associated signal to provide an associated set of approximation and detail coefficients. ### Claim 9 (depends on 1) The system of claim 1, further comprising a user interface to communicate the anomaly to the operator. ### Claim 10 A method comprising: monitoring a parameter associated with a system at each of a plurality of sensors to provide respective sensor signals representing the parameter; decomposing each of the plurality of sensor signals via an inverse wavelet transform by inserting zeros into coefficients representing the sensor signal to provide a set of wavelet transform coefficients for each signal; convolving the decomposed sensor signals with low-pass and high-pass filters; monitoring the sets of wavelet transform coefficients for aberrant coefficients; and alerting an operator via a user interface if an aberrant coefficient is detected. ### Claim 11 (depends on 10) The method of claim 10, wherein decomposing each of the plurality of sensor signals via the wavelet transform comprises applying a dyadic scale discrete wavelet transform to each signal to provide an associated set of approximation and detail coefficients. ### Claim 12 (depends on 10) The method of claim 10, wherein monitoring the sets of wavelet transform coefficients for aberrant coefficients comprises comparing each wavelet transform coefficient to an associated range of values. ### Claim 13 (depends on 12) The method of claim 12, further comprising determining the range of values associated with each wavelet transform coefficient from historical values of the wavelet transform coefficient. ### Claim 14 (depends on 13) The method of claim 13, wherein determining the range of values associated with each wavelet transform coefficient from historical values of the wavelet transform component comprises: determining an average value of the wavelet transform coefficient over a specified time period; and defining the range of values as a confidence interval around the average value according to an acceptable error rate for the system. ### Claim 15 (depends on 10) The method of claim 10, further comprising: reconstructing a signal associated with an aberrant coefficient from at least a portion of the set of wavelet transform coefficients associated with the signal; and identifying an anomaly within the system from the reconstructed signal. ### Claim 16 An industrial control system comprising: a plurality of sensors, each located at a specific point in the industrial control system and configured to monitor at least one of a power, voltage, current, flow rate, pressure, temperature, humidity, and chemical concentration associated with the industrial control system; a controller configured to receive a signal representing the monitored at least one parameter from each of the plurality of sensors and adjust a function of the system based on the received signals; respective discrete wavelet transform components associated with each of the plurality of sensors, each of the discrete wavelet transform components configured to provide a set of discrete wavelet transform coefficients representing a content of the signal for its associated sensor to a discrete wavelet transform monitoring component associated with the controller; a signal reconstruction component configured to reconstruct a portion of the signal if a discrete wavelet transform coefficients of the sets of discrete wavelet transform coefficients provided by the discrete wavelet transform components departs from a defined range of values associated with the coefficient; and a fault analysis component configured to evaluate the reconstructed the portion of the signal to identify an anomaly represented by the coefficient falling outside of the defined range of values.