Adaptive anomaly detection in time-series data

1 . 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.

2 . The anomaly detection and control system of claim 1 , wherein the damage detector comprises a plurality of programming instructions when further executed by the processor cause the processor to:

for each detected signature anomaly:

calculate an associated volume of energy spectrum;

compare the volume of energy spectrum against predefined equipment component fault thresholds associated with the monitored physical system;

upon the volume of energy spectrum exceeding a predefined equipment component fault threshold, generate and display a real-time instantaneous alert to a network-connected graphical user interface;

wherein the alert comprises, information associated with at least a portion of set of signature anomalies, the information comprising, at least, anomaly type, criticality level, and timestamp.

3 . The anomaly detection and control system of claim 1 , wherein the plurality of programming instructions when further executed by the processor cause the processor to:

acquire, by a data manager, time-series analog raw sensor data from the plurality of sensors coupled to the monitored physical system via data acquisition systems;

convert, by the data manager, raw sensor data to digital data continuously storing the incoming data into a central database for subsequent processing and historical access;

retrieve, by the data manager, digital data from the database, wherein the data may include recent samples and historical records, potentially exhibiting irregular sampling intervals or data compression artifacts;

standardize, by a data manager, the retrieved digital data;

estimate, by the data manager, the data compression factor of data stored in database;

detect, by a sample rate detector, the conditioned signal to determine a native sample interval and assess whether the data exhibits uniform or non-uniform sampling behavior across multiple sensor sources;

resample, by a resampler, the conditioned signal using the effective sampling interval to generate uniformly spaced clean digital data, when a non-uniform sampling is detected, ensuring compatibility with orthogonal kernel-based transformations.

4 . The anomaly detection and control system of claim 1 , wherein to detect a signature anomaly, the plurality of programming instructions when further executed by the processor cause the processor to:

generate the three-dimensional energy map based on the plurality of feature components extracted by correlating the uniformly spaced clean digital data with the modified set of orthogonal kernel basis functions, wherein the three-dimensional energy map represents the distribution of energy across the phase, frequency, and amplitude domains for real-time or iterative analysis of the uniformly spaced clean digital data;

detect the set of signature anomalies by analyzing deviations in the three-dimensional energy map relative to a predefined flat spectral threshold associated with the monitored physical system;

identify non-uniform energy distributions that are correlated with a fault associated with at least one monitored equipment component by comparing the detected spectral energy to a fundamental frequency signature from the composite physical model;

extract localized energy discontinuities, associated with the set of signature anomalies;

define the set of signature anomalies based on the extracted discontinuities and identify associated features components, the set of signature anomalies comprising, at least, specific sizes, volumes, shapes, amplitudes, frequencies, phases and temporal patterns.

5 . The anomaly detection and control system of claim 4 , wherein the plurality of programming instructions when further executed by the processor cause the processor to:

apply a signal enhancement module comprising a spectral display compander to compress broadband noise components in processed spectral data, by attenuating high-amplitude regions using non-linear transformations wherein the processed spectral data is associated with the three-dimensional energy map;

apply a signal enhancement module comprising the spectral display compander to amplify low-amplitude, feature components of diagnostic relevance using an adaptive gain function to improve anomaly visibility and detection;

adjust the dynamic range of the signature anomalies to fit the spectral display constraints and optimize visual contrast;

display the enhanced signature anomalies on a spectral display for operator interpretation and diagnostics of one or more equipment components of a monitored physical system.

6 . The anomaly detection and control system of claim 1 , wherein the damage detector comprises a plurality of programming instructions when further executed by the processor cause the processor to:

transform processed spectral features from the set of signature anomalies into a one-dimensional parameter representing the cumulative impact of the set of signature anomalies on condition indicators associated with the monitored physical system;

identify long-term cumulative damage patterns using a damage detector configured to track progressive anomaly effects over time associated with the monitored physical system;

analyze health degradation parameters associated with the monitored physical system, including estimated wear rates and efficiency loss indicators, based on the identified accumulated damage patterns;

evaluate the severity of the cumulative damage using the analyzed degradation parameters; and

generate a list of possible actions to rectify the anomalies based on the severity;

generate and display, to a network-connected graphical user interface, a real-time alert notification, using the accumulated damage alert generator wherein the accumulated real-time alert comprises wear rates, early warning indicators, part replacement schedules, and prioritized maintenance actions based on historical anomaly progression.

7 . The anomaly detection and control system of claim 1 , wherein the plurality of programming instructions when further executed by the processor cause the processor to:

receive uniformly spaced clean digital data from the resampler and perform multivariate time-domain correlation analysis including one or more of autocorrelation, cross-correlation, or correlation coefficient computations, to identify relationships between anomalies across different time periods or across different monitored equipment components, sensors, and other data sets in the database;

receive spectral data from the adaptive anomaly analyzer and perform multivariate frequency-domain correlation analysis, including one or more of autocorrelation, cross-correlation, or correlation coefficient computations, to identify relationships between anomalies across different time periods or across different monitored equipment components, sensors, and other data sets in the database;

reduce the dimensionality of the temporal and spectral data based on an optimal linear transformation to enhance the separation of anomaly-related features from noise to identify one or more equipment components closest to the source of an anomaly by evaluating anomalous signal energy levels and at least one correlation metric between monitored equipment components;

process the results of the correlation and dimensionality reduction analysis using an interpreter module, wherein the interpreter module assesses, at least, the amplitude and the characteristics of correlated signature anomalies of the set of signature anomalies; and

compare signature anomaly characteristics with stored reference patterns indicative of specific equipment component faults, thereby facilitating identification of potential causes or sources of the anomalies and possible corrective actions to extend the life of the equipment component of the monitored physical system.

8 . The anomaly detection and control system of claim 7 , wherein the plurality of programming instructions when further executed by the processor cause the processor to:

receive data from the interpreter module comprising correlated signature anomaly data, including at least one of identified signature anomalies, potential signature anomaly sources, and recommended corrective actions to rectify the anomalies;

compare time-series data against a composite physical model of the monitored physical system, and compute a divergence metric;

classify, by a classifier, the correlated signature anomaly data representative of a normal or anomalous condition by applying one or more signal processing-based classification techniques, comprising divergence measures, hypothesis testing methods, or graph processing techniques;

compute a confidence level in the classification based on a deviation from a pre-defined threshold; and

transmit the confidence level to a network-connected graphical user interface.

9 . The anomaly detection and control system of claim 1 , wherein the orthogonal kernel basis functions comprise Gaussian distributions defined by a width, a height, and offset parameters, each multiplied by a complex exponential term that comprises a native sample interval that defines a width of an orthogonal kernel basis function or feature component, wherein the Gaussian parameters and native sample interval are derived from the composite physical model of the monitored physical system.

10 . The anomaly detection system of claim 1 , wherein the manufacturer design specifications include characteristics comprising at least one of: rotational speed, balance parameters, alignment specifications, fluid flow rates, mechanical pressures ranges, temperature ranges, electrical characteristics, and equipment process specifications, wherein the anomaly detection is dynamically adapted to the operational behavior of each type of monitored equipment component.

11 . The anomaly detection and control system of claim 1 ,

wherein the construction of each individual component physical model comprises analyzing underlying physics of the monitored physical system, process parameters, operating thresholds, equipment component status and condition, and failure modes; and

wherein the composite physical model establishes a mapping between energy of the detected signature anomalies and conditions associated with specific equipment components, and supports the maintenance or process control operation of the monitored physical system.

12 . The anomaly detection and control system of claim 1 , wherein the monitored physical system comprises at least one of:

rotating equipment comprising pumps, compressors, generators, turbines, or motors;

flow equipment comprising valves, pipelines, or fittings;

electrical equipment comprising transformers, switchgear or uninterruptible power supply; and

process equipment comprising heat exchangers, separators or extraction units.

13 . The anomaly detection and control system of claim 1 , wherein the plurality of sensors include a combination of specific sensors selected according to the monitored physical system mechanisms, the sensors comprising at least one of:

voltage sensors for measuring electrical potential differences;

current sensors for measuring current flow;

phase sensors for measuring electrical phase relationships;

flow rate sensors for measuring fluid flow;

piezoelectric transducers for measuring mechanical stress;

accelerometers for measuring vibration;

temperature sensors for measuring thermal conditions;

optical sensors for measuring position; and

capacitive sensors for measuring process parameters.