Adaptive anomaly detection in time-series data

An anomaly detection and control system comprising at least one processor, a memory, and a plurality of programming instructions, the plurality of programming instructions when executed by the at least one processor cause the processor to:

• receive uniformly spaced clean digital data from a plurality of sensors, monitoring equipment components of a monitored physical system, the plurality of sensors comprising at least vibration, flow rate, pressure, power meters, pH, torque or acoustic sensors that generate signals representative of operating conditions of the equipment components;
• receive, from a database, physical model parameters derived from a composite physical model of the monitored physical system, wherein the composite physical model comprises individual component physical models of sensors and equipment components, and wherein each individual component physical model is based on manufacturer design specifications, analyzed physical defects, and associated remediation measures and further includes process parameters, operating thresholds, component status and condition, and failure modes, in order to construct an accurate physical model for each monitored equipment component;
• generate, by an orthogonal function processor, a set of orthogonal kernel basis functions defined by a native sample interval and gaussian distribution parameters derived from the composite physical model;
• correlate the uniformly spaced clean digital data with the set of orthogonal kernel basis functions implemented by the orthogonal function processor to extract a plurality of feature components representing correlation between measured sensor data and modeled system responses, and generate a three-dimensional energy map across phase, frequency, and amplitude domains that is dynamically updated in real time for signature anomaly detection and visualization;
• detect a set of signature anomalies in the three-dimensional energy map by identifying non-uniform energy distributions or discontinuities relative to a predefined spectral baseline derived from the composite physical model, each detected signature anomaly being associated with at least one monitored equipment component of the physical system;
• for each detected signature anomaly of the set of signature anomalies:
• determine a number and corresponding width of each feature component associated with the detected signature anomaly;
• while the number of orthogonal kernel basis functions within the set of orthogonal kernel basis functions is less than the number of feature components indicating that the current precision of analysis is insufficient to fully characterize the detected signature anomaly:
• update at least a portion of the set of orthogonal kernel basis functions, wherein the updated set of orthogonal kernel basis functions has increased precision by increasing the number of orthogonal kernel basis functions relative to the immediately preceding set of orthogonal kernel basis functions;
• correlate the uniformly spaced clean digital data with the updated set of orthogonal kernel basis functions using the orthogonal function processor to extract additional feature components corresponding to newly generated basis functions, thereby adaptively increasing analysis precision of the detected signature anomaly;
• and
• determine whether the number of feature components extracted from correlation with the updated set of orthogonal kernel basis functions has converged or changed relative to the prior iteration, thereby assessing whether further refinement of the basis functions is required;
• determine the width of each feature component by measuring native sample interval of each feature component within the three-dimensional energy map;
• while the width of each feature component is less than a width of a corresponding orthogonal kernel basis function of the updated set of orthogonal kernel basis functions, indicating that the existing basis-function resolution is coarser than the observed signature anomaly feature and additional refinement is required:
• modify the updated set of orthogonal kernel basis functions by narrowing each orthogonal-kernel-basis-function width parameter in relation to the measured widths of the feature components, thereby generating a modified set of orthogonal kernel basis functions having increased resolution that is quantitatively defined by the reduced width parameters of the updated set of orthogonal kernel basis functions;
• correlate the uniformly spaced clean digital data with the modified set of orthogonal kernel basis functions using the orthogonal function processor to re-analyze the same uniformly spaced clean digital data with the modified basis-function set, thereby adaptively increasing resolution and improving localization accuracy of the detected signature anomaly;
• and
• determine the width of each feature component based on correlation results obtained using the modified set of orthogonal kernel basis functions;
• determine whether the correlation results obtained using the modified set of orthogonal kernel basis functions have converged or changed relative to a prior iteration, thereby assessing whether further narrowing of the orthogonal kernel basis functions is required;
• determine the width represents a refined sample rate of the corresponding signature anomaly feature within the three-dimensional energy map;
• perform an adaptive dynamic-range adjustment on the generated three-dimensional energy-map, the adaptive dynamic-range adjustment being executed by a spectral display compander to produce an non-linear representation of the set of signature anomalies to fit a constraint associated with the spectral display compander and optimize visual contrast for increased detection precision and improved feature extraction characterization,
• store, in the memory, coefficients, parameters, and metadata defining the modified set of orthogonal kernel basis functions and the spectral display compander for subsequent anomaly detection and tracking system calibration, or physical model adjustment or computational resource optimization;
• and
• transmit, to a damage detector, data associated with the set of signature anomalies together with control parameters derived from the modified set of orthogonal kernel basis functions for initiating or adjusting at least one maintenance or process-control operation associated with the monitored physical system;
• upon receiving confirmation of the process-control operation, update the composite physical model to include data representative of the corresponding set of signature anomalies.