# US 2019/0318251 A1 · Using the barycentric coordinate technique to determine optimal sensor locations > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2019/0318251 A1 - Document ID: US20190318251A1 - Status: Published application - Kind: A1 - Application number: 15/951,996 - Filed: 2018-04-12 - Published: 2019-10-17 - Earliest claimed: 2018-04-12 - Assignees: Oracle International Corporation - Applicants: Oracle International Corporation - Inventors: Kenny C. Gross; Aleksey M. Urmanov - Web page: https://patentgrep.com/patent/US20190318251A1 ## CPC - G06N 5/04: Inference or reasoning models - G01M 99/00: Subject matter not provided for in other groups of this subclass - G06N 20/00: Machine learning - G06N 7/01: Probabilistic graphical models, e.g. probabilistic networks - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS - G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR ## Abstract After sensors are placed at three or more non-collinear locations on a surface of the component, the system receives time-series signals from the sensors while the component operates on a representative workload. The system then defines one or more triangles on the surface of the component, wherein each triangle is defined by three vertices, which coincide with different sensor locations on the surface of the component. For each triangle, the system applies a barycentric coordinate technique (BCT) to time-series signals received from sensors located at the vertices of the triangle to determine a candidate location within the triangle to place an additional sensor. The system then compares the candidate locations for each of the one or more triangles to determine a globally optimal location for the additional sensor, and a new sensor is placed at this location. This process is repeated until a desired number of sensors are placed. ## Claims ### Claim 1 A method for determining sensor locations for a component to be monitored, comprising: after sensors are placed at three or more non-collinear locations on a surface of the component, receiving time-series signals from the sensors while the component operates on a representative workload; defining one or more triangles on the surface of the component, wherein each triangle is defined by three vertices, which coincide with three different sensor locations on the surface of the component; for each triangle, applying a barycentric coordinate technique (BCT) to time-series signals received from sensors located at the vertices of the triangle to determine a candidate location within the triangle to place an additional sensor; comparing the candidate locations for each of the one or more triangles to determine a globally optimal location for the additional sensor; and indicating that the additional sensor needs to be placed at the globally optimal location. ### Claim 2 (depends on 1) The method of claim 1, wherein after the additional sensor is placed at the globally optimal location, the method is repeated to determine a location for another additional sensor. ### Claim 3 (depends on 2) The method of claim 2, wherein the method is repeated until the location of the additional sensor moves less than a predefined distance from the location of a preceding additional sensor. ### Claim 4 (depends on 1) The method of claim 1, wherein the sensors are initially placed at extrema points on the surface of the component. ### Claim 5 (depends on 1) The method of claim 1, wherein while comparing the candidate locations for the one or more triangles, the method compares residuals produced by the MSET technique to determine how well time-series signals originating from other sensors will predict a signal originating from an additional sensor at each of the candidate locations. ### Claim 6 (depends on 1) The method of claim 1, wherein the component comprises one of: an electronic device; a mechanical device, an electro-mechanical device; or a hydraulic-flow system. ### Claim 7 (depends on 1) The method of claim 1, wherein the optimal location for the new sensor maximizes one or more of the following for a time-series signal received from the additional sensor: information content; sensitivity to changes in operational parameters of the component; and correlation with time-series signals from other sensors. ### Claim 8 (depends on 1) The method of claim 1, wherein after the method completes and one or more additional sensors are placed on the component, the method further comprises: receiving time-series signals from the sensors while the component operates on a real workload; and analyzing the time-series signals using a prognostic-surveillance system to detect incipient anomalies that arise during execution of the component. ### Claim 9 (depends on 8) The method of claim 8, wherein analyzing the time-series signals using the prognostic-surveillance system comprises: using an inferential model trained on previously received time-series signals from the component to generate estimated values for the time-series signals based on correlations between the time-series signals; performing a pairwise differencing operation between actual values and the estimated values for the time-series signals to produce residuals; and performing a sequential probability ratio test (SPRT) on the residuals to detect incipient anomalies that arise during operation of the monitored system. ### Claim 10 (depends on 9) The method of claim 9, wherein the inferential model is trained using a Multivariate State Estimation Technique (MSET). ### Claim 11 (depends on 1) The method of claim 1, wherein after the one or more additional sensors are placed, the method further comprises using the BCT to refine locations for one or more of the initially placed sensors. ### Claim 12 A non-transitory computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for determining sensor locations for a component to be monitored, the method comprising: after sensors are placed at three or more non-collinear locations on a surface of the component, receiving time-series signals from the sensors while the component operates on a representative workload; defining one or more triangles on the surface of the component, wherein each triangle is defined by three vertices, which coincide with three different sensor locations on the surface of the component; for each triangle, applying a barycentric coordinate technique (BCT) to time-series signals received from sensors located at the vertices of the triangle to determine a candidate location within the triangle to place an additional sensor; comparing the candidate locations for each of the one or more triangles to determine a globally optimal location for the additional sensor; and indicating that the additional sensor needs to be placed at the globally optimal location. ### Claim 13 (depends on 12) The non-transitory computer-readable storage medium of claim 12, wherein after the additional sensor is placed at the globally optimal location, the method is repeated to determine a location for another additional sensor. ### Claim 14 (depends on 13) The non-transitory computer-readable storage medium of claim 13, wherein the method is repeated until the location of the additional sensor moves less than a predefined distance from the location of a preceding additional sensor. ### Claim 15 (depends on 12) The non-transitory computer-readable storage medium of claim 12, wherein the sensors are initially placed at extrema points on the surface of the component. ### Claim 16 (depends on 12) The non-transitory computer-readable storage medium of claim 12, wherein while comparing the candidate locations for the one or more triangles, the method compares residuals produced by the MSET technique to determine how well time-series signals originating from other sensors will predict a signal originating from an additional sensor at each of the candidate locations. ### Claim 17 (depends on 12) The non-transitory computer-readable storage medium of claim 12, wherein the component comprises one of: an electronic device; a mechanical device; an electro-mechanical device; or a hydraulic-flow system. ### Claim 18 (depends on 12) The non-transitory computer-readable storage medium of claim 12, wherein after the method completes and one or more additional sensors are placed on the component, the method further comprises: receiving time-series signals from the sensors while the component operates on a real workload; and analyzing the time-series signals using a prognostic-surveillance system to detect incipient anomalies that arise during execution of the component. ### Claim 19 (depends on 18) The non-transitory computer-readable storage medium of claim 18, wherein analyzing the time-series signals using the prognostic-surveillance system comprises: using an inferential model trained on previously received time-series signals from the component to generate estimated values for the time-series signals based on correlations between the time-series signals; performing a pairwise differencing operation between actual values and the estimated values for the time-series signals to produce residuals; and performing a sequential probability ratio test (SPRT) on the residuals to detect incipient anomalies that arise during operation of the monitored system. ### Claim 20 A method for determining sensor locations for a component to be monitored, comprising: after sensors are placed at four or more non-collinear locations in a volume within the component, receiving time-series signals from the sensors while the component operates on a representative workload; defining one or more tetrahedra within the volume of the component, wherein each tetrahedron is defined by four vertices, which coincide with different sensor locations within the volume of the component; for each tetrahedron, applying a three-dimensional barycentric coordinate technique (BCT) to time-series signals received from sensors located at the vertices of the tetrahedron to determine a candidate location within the tetrahedron to place an additional sensor; comparing the candidate locations for each of the one or more tetrahedra to determine a globally optimal location for the additional sensor; and indicating that the additional sensor needs to be placed at the globally optimal location.