Systems And Methods For Estimating Remaining Useful Life Of Cutting Tools In Cnc Machines
Abstract:
Industrial machines are equipped with many internal sensors. Gleaning information from these to ascertain state of a process or a subsystem as well as to predict any relevant failures in the manufacturing is important. Getting robust estimation of requisite quantities as a function of the available measurements is a highly challenging task due to the interplay of many factors. Embodiments of the present disclosure implement systems and methods that enable understanding and modeling underlying machining phenomena to help detect change which are correlated to different events (for example, maintenance activity, tool wear, alarms, etc.) and using this as a feature for cutting tool condition monitoring (e.g., tool wear). Given the tool change records, this change feature is augmented with Singular Spectrum Analysis (SSA) and Graph Total Variation (GTV) based features which are extracted raw sensor data to estimate remaining useful life of cutting tools used in the machining process.
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Notices, Deadlines & Correspondence
Nirmal Building, 9th Floor,
Nariman Point, Mumbai - 400021, Maharashtra, India
Inventors
1. KUMAR, Kriti
Tata Consultancy Services Limited, #152, Gopalan Global Axis H - Block, Opposite Satya Sai Hospital, ITPL Main road, EPIP Zone, Whitefield, Bangalore - 560066, Karnataka, India
2. BAPNA, Aakanksha
Tata Consultancy Services Limited, #152, Gopalan Global Axis H - Block, Opposite Satya Sai Hospital, ITPL Main road, EPIP Zone, Whitefield, Bangalore - 560066, Karnataka, India
3. THOKALA, Naveen Kumar
Tata Consultancy Services Limited, #152, Gopalan Global Axis H - Block, Opposite Satya Sai Hospital, ITPL Main road, EPIP Zone, Whitefield, Bangalore - 560066, Karnataka, India
4. CHANDRA, Girish Mariswamy
Tata Consultancy Services Limited, #152, Gopalan Global Axis H - Block, Opposite Satya Sai Hospital, ITPL Main road, EPIP Zone, Whitefield, Bangalore - 560066, Karnataka, India
Specification
Claims:1. A processor implemented method, comprising:
receiving raw sensor data pertaining to one or more internal sensors integrated in a Computer Numerical Control (CNC) machine (202), wherein the raw sensor data comprises an actual spindle load signal, spindle speed, cutting tool axes positions, cutting tool axes servo loads, and feed rate for estimating condition of a cutting tool comprised in the CNC machine;
learning one or more machine learning (ML) models using the raw sensor data (204);
estimating a spindle load using the learned one or more ML models based on the raw sensor data (206);
determining a change metric pertaining to behavior of the cutting tool based on a comparison of the estimated spindle load signal and the actual spindle load signal (208);
extracting (i) magnitude, (ii) Singular Spectrum Analysis (SSA) based features, and (iii) a Graph Total Variation (GTV) based feature from the actual spindle load signal (210); and
estimating a Remaining Useful Life (RUL) of the cutting tool as a function of the change metric, the extracted magnitude, SSA based features and GTV based feature (212).
2. The processor implemented method of claim 1, wherein the SSA based features are extracted by:
generating a transition matrix using the actual spindle load signal;
applying a Singular Value Decomposition (SVD) technique on the transition matrix to obtain a set of Eigen modes;
learning a contribution of each Eigen mode from the set of Eigen modes extracted from the actual spindle load signal; and
identifying, based on the contribution, one or more dominant Eigen modes from the set of Eigen modes, wherein the one or more dominant Eigen modes are indicative of the SSA based features.
3. The processor implemented method of claim 1, wherein the GTV based feature is extracted by:
computing an adjacency matrix using the actual spindle load signal, wherein the adjacency matrix comprises correlation between a plurality of samples from a reference spindle load signal that correspond to a normal operation of the CNC machine;
generating a graph using the adjacency matrix, wherein the graph comprises a plurality of nodes having length of the reference spindle load signal; and
projecting the actual spindle load signal on the graph to obtain the GTV based feature.
4. The processor implemented method of claim 1, wherein the RUL of cutting tool is estimated using a machine learning based regression model trained on previously recorded cutting tool information pertaining to the cutting tool of the CNC machine, and wherein the previously recorded cutting tool information comprises raw sensor data and tool change information.
5. A system (100), comprising:
a memory (102) storing instructions;
one or more communication interfaces (106); and
one or more hardware processors (104) coupled to the memory (102) via the one or more communication interfaces (106), wherein the one or more hardware processors (104) are configured by the instructions to:
receive raw sensor data pertaining to one or more internal sensors integrated in a Computer Numerical Control (CNC) machine, wherein the raw sensor data comprises an actual spindle load signal, spindle speed, cutting tool axes positions, cutting tool axes servo loads, and feed rate for estimating condition of a cutting tool comprised in the CNC machine;
learn one or more machine learning (ML) models using the raw sensor data;
estimate a spindle load signal using the learned one or more ML models based on the raw sensor data;
determine a change metric pertaining to behavior of the cutting tool based on a comparison of the estimated spindle load signal and the actual spindle load signal;
extract (i) magnitude, (ii) Singular Spectrum Analysis (SSA) based features, and (iii) a Graph Total Variation (GTV) based feature from the actual spindle load signal; and
estimate a Remaining Useful Life (RUL) of the cutting tool as a function of the change metric, the extracted magnitude, SSA based features and GTV based feature.
6. The system of claim 5, wherein the SSA based features are extracted by:
generating a transition matrix using the actual spindle load signal;
applying a Singular Value Decomposition (SVD) technique on the transition matrix to obtain a set of Eigen modes;
learning a contribution of each Eigen mode from the set of Eigen modes extracted from the actual spindle load signal; and
identifying, based on the contribution, one or more dominant Eigen modes from the set of Eigen modes, wherein the one or more dominant Eigen modes are indicative of the SSA based features.
7. The system of claim 5, wherein the GTV based feature is extracted by:
computing an adjacency matrix using the actual spindle load signal, wherein the adjacency matrix comprises correlation between a plurality of samples from a reference spindle load signal that correspond to a normal operation of the CNC machine;
generating a graph using the adjacency matrix, wherein the graph comprises a plurality of nodes having length of the reference spindle load signal; and
projecting the actual spindle load signal on the graph to obtain the GTV based feature.
8. The system of claim 5, wherein the RUL of cutting tool is estimated using a machine learning based regression model trained on previously recorded cutting tool information pertaining to the cutting tool of the CNC machine, and wherein the previously recorded cutting tool information comprises raw sensor data and tool change information.
, Description:FORM 2
THE PATENTS ACT, 1970
(39 of 1970)
&
THE PATENT RULES, 2003
COMPLETE SPECIFICATION
(See Section 10 and Rule 13)
Title of invention:
SYSTEMS AND METHODS FOR ESTIMATING REMAINING USEFUL LIFE OF CUTTING TOOLS IN CNC MACHINES
Applicant
Tata Consultancy Services Limited
A company Incorporated in India under the Companies Act, 1956
Having address:
Nirmal Building, 9th floor,
Nariman point, Mumbai 400021,
Maharashtra, India
The following specification particularly describes the invention and the manner in which it is to be performed.
TECHNICAL FIELD
The disclosure herein generally relates to tool wear prediction, and, more particularly, to systems and methods for estimating remaining useful life of cutting tools in Computer Numerical Control (CNC) machines.
BACKGROUND
Present day industrial machines are equipped with many internal sensors- both physical and virtual. Gleaning the information from these to ascertain the state of a process or a subsystem as well as to predict any relevant failures in the manufacturing is all the more important in the envisaged fourth industrial revolution. Getting the robust estimation of the requisite quantities as a function of the available measurements is a highly challenging task due to the interplay of many factors. The problem is further aggravated when the data is both limited and poorly annotated.
Further, health of any manufacturing industry, particularly for the contract manufactures who have invested heavily on high end machines are mainly depending on the availability, performance and quality of the equipment. One of the challenging tasks in the manufacturing industry is to maintain the high productivity and quality with less operating cost, due to the multiple reasons for example, change in machine, material, cutting tools condition over time. Therefore, improving the overall equipment effectiveness of the plant or machines still remains a challenge.
SUMMARY
Embodiments of the present disclosure present technological improvements as solutions to one or more of the above-mentioned technical problems recognized by the inventors in conventional systems. For example, in one aspect, there is provided a processor implemented method for health monitoring of the cutting tools of CNC machines. The method comprises receiving raw sensor data pertaining to one or more internal sensors integrated in a Computer Numerical Control (CNC) machine, wherein the raw sensor data comprises an actual spindle load signal, spindle speed, cutting tool axes positions, cutting tool axes servo loads, and feed rate for estimating condition of a cutting tool comprised in the CNC machine; learning one or more machine learning (ML) models using the raw sensor data; estimating spindle load signal using the learned one or more ML models based on the raw sensor data; determining a change metric pertaining to behavior of the cutting tool based on a comparison of the estimated a spindle load signal and the actual spindle load signal; extracting (i) magnitude, (ii) Singular Spectrum Analysis (SSA) based features, and (iii) a Graph Total Variation (GTV) based feature from the actual spindle load signal; and estimating a Remaining Useful Life (RUL) of the cutting tool as a function of the change metric, the extracted magnitude, SSA based features and GTV based feature. In an embodiment, in addition to estimating the RUL of the cutting tool as a function of the change metric, the extracted magnitude, SSA based features and GTV based feature, the RUL of cutting tool is also estimated using a machine learning based regression model trained on previously recorded cutting tool information pertaining to the cutting tool of the CNC machine, and wherein the previously recorded cutting tool information comprises raw sensor data and tool change information.
In an embodiment, the SSA based features are extracted by: generating a transition matrix using the actual spindle load signal; applying a Singular Value Decomposition (SVD) technique on the transition matrix to obtain a set of Eigen modes; learning a contribution of each Eigen mode from the set of Eigen modes extracted from the actual spindle load signal; and identifying, based on the contribution, one or more dominant Eigen modes from the set of Eigen modes, wherein the one or more dominant Eigen modes are indicative of the SSA based features.
In an embodiment, the GTV based feature is extracted by: computing an adjacency matrix using the actual spindle load signal, wherein the adjacency matrix comprises correlation between a plurality of samples from a reference spindle load signal that correspond to a normal operation of the CNC machine; generating a graph using the adjacency matrix, wherein the graph comprises a plurality of nodes having length of the reference spindle load signal; and projecting the actual spindle load signal on the graph to obtain the GTV based feature.
In another aspect there is provided a system for health monitoring of the cutting tools of CNC machines. The system comprises: a memory storing instructions; one or more communication interfaces; and one or more hardware processors coupled to the memory via the one or more communication interfaces, wherein the one or more hardware processors are configured by the instructions to: receive raw sensor data pertaining to one or more internal sensors integrated in a Computer Numerical Control (CNC) machine, wherein the raw sensor data comprises an actual spindle load signal, spindle speed, cutting tool axes positions, cutting tool axes servo loads, and feed rate for estimating condition of a cutting tool comprised in the CNC machine; learn one or more machine learning (ML) models using the raw sensor data; estimate a spindle load signal using the learned one or more ML models based on the raw sensor data; determine a change metric pertaining to behavior of the cutting tool based on a comparison of the estimated spindle load signal and the actual spindle load signal; extract (i) magnitude, (ii) Singular Spectrum Analysis (SSA) based features, and (iii) a Graph Total Variation (GTV) based feature from the actual spindle load signal; and estimate a Remaining Useful Life (RUL) of the cutting tool as a function of the change metric, the extracted magnitude, SSA based features and GTV based feature. In an embodiment, in addition to estimating the RUL of the cutting tool as a function of the change metric, the extracted magnitude, SSA based features and GTV based feature, the RUL of cutting tool is also estimated using a machine learning based regression model trained on previously recorded cutting tool information pertaining to the cutting tool of the CNC machine, and wherein the previously recorded cutting tool information comprises raw sensor data and tool change information.
In an embodiment, the SSA based features are extracted by: generating a transition matrix using the actual spindle load signal; applying a Singular Value Decomposition (SVD) technique on the transition matrix to obtain a set of Eigen modes; learning a contribution of each Eigen mode from the set of Eigen modes extracted from the actual spindle load signal; and identifying, based on the contribution, one or more dominant Eigen modes from the set of Eigen modes, wherein the one or more dominant Eigen modes are indicative of the SSA based features.
In an embodiment, the GTV based feature is extracted by: computing an adjacency matrix using the actual spindle load signal, wherein the adjacency matrix comprises correlation between a plurality of samples from a reference spindle load signal that correspond to a normal operation of the CNC machine; generating a graph using the adjacency matrix, wherein the graph comprises a plurality of nodes having length of the reference spindle load signal; and projecting the actual spindle load signal on the graph to obtain the GTV based feature.
In yet another aspect, there are provided one or more non-transitory machine readable information storage mediums comprising one or more instructions which when executed by one or more hardware processors causes health monitoring of the cutting tools of CNC machines. The instructions comprise receiving raw sensor data pertaining to one or more internal sensors integrated in a Computer Numerical Control (CNC) machine, wherein the raw sensor data comprises an actual spindle load signal, spindle speed, cutting tool axes positions, cutting tool axes servo loads, and feed rate for estimating condition of a cutting tool comprised in the CNC machine; learning one or more machine learning (ML) models using the raw sensor data; estimating a spindle load signal using the learned one or more ML models based on the raw sensor data; determining a change metric pertaining to behavior of the cutting tool based on a comparison of the estimated spindle load signal and the actual spindle load signal; extracting (i) magnitude, (ii) Singular Spectrum Analysis (SSA) based features, and (iii) a Graph Total Variation (GTV) based feature from the actual spindle load signal; and estimating a Remaining Useful Life (RUL) of the cutting tool as a function of the change metric, the extracted magnitude, SSA based features and GTV based feature. In an embodiment, in addition to estimating the RUL of the cutting tool as a function of the change metric, the extracted magnitude, SSA based features and GTV based feature, the RUL of cutting tool is also estimated using a machine learning based regression model trained on previously recorded cutting tool information pertaining to the cutting tool of the CNC machine, and wherein the previously recorded cutting tool information comprises raw sensor data and tool change information.
In an embodiment, the SSA based features are extracted by: generating a transition matrix using the actual spindle load signal; applying a Singular Value Decomposition (SVD) technique on the transition matrix to obtain a set of Eigen modes; learning a contribution of each Eigen mode from the set of Eigen modes extracted from the actual spindle load signal; and identifying, based on the contribution, one or more dominant Eigen modes from the set of Eigen modes, wherein the one or more dominant Eigen modes are indicative of the SSA based features.
In an embodiment, the GTV based feature is extracted by: computing an adjacency matrix using the actual spindle load signal, wherein the adjacency matrix comprises correlation between a plurality of samples from a reference spindle load signal that correspond to a normal operation of the CNC machine; generating a graph using the adjacency matrix, wherein the graph comprises a plurality of nodes having length of the reference spindle load signal; and projecting the actual spindle load signal on the graph to obtain the GTV based feature.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, serve to explain the disclosed principles:
FIG. 1 illustrates an exemplary block diagram of a system for estimating Remaining Useful Life (RUL) of a cutting tool in Computer Numerical Control (CNC) machines in accordance with an embodiment of the present disclosure.
FIG. 2 illustrates an exemplary flow diagram of a method of estimating the Remaining Useful Life (RUL) of a cutting tool in the CNC machines using the system of FIG. 1 in accordance with an embodiment of the present disclosure.
FIG. 3 depicts a graphical representation illustrating change detection based feature with tool change in accordance with an example embodiment of the present disclosure.
FIG. 4 depict a graphical representation illustrating magnitude based features with tool change in accordance with an example embodiment of the present disclosure.
FIG. 5 depict a graphical representation illustrating Singular Spectrum Analysis (SSA) based features with tool change in accordance with an example embodiment of the present disclosure.
FIG. 6 depicts a graphical representation illustrating Graph Total Variation (GTV) based features with tool change in accordance with an embodiment of the present disclosure.
FIG. 7 depicts a graphical representation illustrating RUL Estimation with magnitude and change metric based features in accordance with an embodiment of the present disclosure.
FIG. 8 depicts a graphical representation illustrating RUL estimation with SSA and GTV based features in accordance with an embodiment of the present disclosure.
DETAILED DESCRIPTION OF EMBODIMENTS
Exemplary embodiments are described with reference to the accompanying drawings. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. Wherever convenient, the same reference numbers are used throughout the drawings to refer to the same or like parts. While examples and features of disclosed principles are described herein, modifications, adaptations, and other implementations are possible without departing from the spirit and scope of the disclosed embodiments. It is intended that the following detailed description be considered as exemplary only, with the true scope and spirit being indicated by the following claims.
Since the commencement of Industry 4.0, there has been a surge in use of technology for industrial transformation. Artificial Intelligence (AI) assists in autonomous production, Internet of Things (IOT) based platforms facilitate capturing and exchange of the machine data and cloud computing enables provision of services and analytics. One of the important services that can be offered via IOT and cloud is Machine Health Monitoring for Smart Factories. Machine health monitoring encompasses many tasks, for example, inspecting the condition(s) of different parts of the machine(s), assessing quality of the finished workpiece(s), keeping a check on the temperature(s), power consumption(s), vibration(s), etc. of the machine(s) which can be used to prevent serious downtime of machine(s) and loss to the industry.
The health of any manufacturing industry, particularly for the contract manufacturers, who have invested heavily on high end machines are mainly depending on the availability, performance and quality of the equipment. One of the challenging tasks in the manufacturing industry is to maintain the high productivity and quality with less operating cost, as the raw material and the condition of the machine and cutting tools change over time. Hence, it is important to continuously monitor and control the machine elements and the health of the cutting tools, to improve the overall effectiveness of the plant. This work is more focused towards tool condition monitoring with reference to Computer Numerical Control (CNC) machines. Tool condition monitoring gives information about optimal replacement time of the tool such that the tool is effectively utilized at the same time it does not impact the quality of the end workpiece. It also helps in reducing the time required for tool replacement and need of manual inspection.
Existing technology makes use of both external and internal sensors to carry out tool condition monitoring. External sensors namely, dynamo-meters to measure cutting force, accelerometers to measure vibration, sound from machining process and cameras to monitor tool condition are used. However, they are not practical to use as they hinder with the machining process, and further add to the complexity and cost of the machining process.
Internal sensors like, spindle speed, spindle load, axis drive currents and axis positions on the other hand, directly tapped from the machines are more robust and do not incur any additional cost. They have been used to understand the dynamics of the machining process and give deeper insights to the machine performance on tool wear. There are few works which make use of the spindle load signal alone for characterizing tool wear. Although spindle load signal serves as a good measure of tool condition, the tool health is also affected by a number of factors namely, difference in raw material, cutting conditions and complex relationship of machining process to tool wear. This makes the problem of designing a reliable tool condition monitoring system more challenging. To address this problem, a different methodology is proposed in this disclosure which makes use of novel features based on Singular Spectrum Analysis (SSA) and Graph Total Variation (GTV) as input arguments of a (learnt) regression function. Deep learning techniques have also been used in the existing literature to predict tool wear. But, with limited and poorly annotated data, as in the case of industrial machinery data, deep learning based techniques fail to provide satisfactory results.
The present disclosure presents systems and methods for monitoring health of the cutting tools and machining process and estimating the Remaining Useful Life (RUL) of the tool using the change detection feature in addition to other novel features which are extracted from the spindle load signal. The change detection feature is worked out by modeling the spindle load signal as a function of cutting conditions and raw material of the workpiece and then observing the change between the predicted and actuals. It is focused at understanding and modeling the underlying machining phenomena to help detect change from the normal behaviour which can be correlated to some event (like, maintenance activity, tool wear, alarms, etc.). The other features explored here are based on Singular Spectrum Analysis (SSA) and Graph Total Variation (GTV).
Referring now to the drawings, and more particularly to FIG. 1 through 8, where similar reference characters denote corresponding features consistently throughout the figures, there are shown preferred embodiments and these embodiments are described in the context of the following exemplary system and/or method.
FIG. 1 illustrates an exemplary block diagram of a system 100 for estimating Remaining Useful Life (RUL) of a cutting tool in CNC machines in accordance with an embodiment of the present disclosure. The system 100 may also be referred as ‘a Remaining Useful Life (RUL) system’ and interchangeably used hereinafter. In an embodiment, the system 100 includes one or more processors 104, communication interface device(s) or input/output (I/O) interface(s) 106, and one or more data storage devices or memory 102 operatively coupled to the one or more processors 104. The one or more processors 104 may be one or more software processing modules and/or hardware processors. In an embodiment, the hardware processors can be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the processor(s) is configured to fetch and execute computer-readable instructions stored in the memory. In an embodiment, the device 100 can be implemented in a variety of computing systems, such as laptop computers, notebooks, hand-held devices, workstations, mainframe computers, servers, a network cloud and the like.
The I/O interface device(s) 106 can include a variety of software and hardware interfaces, for example, a web interface, a graphical user interface, and the like and can facilitate multiple communications within a wide variety of networks N/W and protocol types, including wired networks, for example, LAN, cable, etc., and wireless networks, such as WLAN, cellular, or satellite. In an embodiment, the I/O interface device(s) can include one or more ports for connecting a number of devices to one another or to another server.
The memory 102 may include any computer-readable medium known in the art including, for example, volatile memory, such as static random access memory (SRAM) and dynamic random access memory (DRAM), and/or non-volatile memory, such as read only memory (ROM), erasable programmable ROM, flash memories, hard disks, optical disks, and magnetic tapes. In an embodiment a database 108 can be stored in the memory 102, wherein the database 108 may comprise, but are not limited to information pertaining to tools of CNC machine under consideration. More specifically, information pertaining to the tool may comprise operation information pertaining to tool, features, RUL information, and the like. In an embodiment, the memory 102 may store one or more technique(s) (e.g., machine learning models for regression, and the like) which when executed by the one or more hardware processors 104 to perform the methodology described herein. The memory 102 may further comprise information pertaining to input(s)/output(s) of each step performed by the systems and methods of the present disclosure.
FIG. 2, with reference to FIG. 1, illustrates an exemplary flow diagram of a method of estimating Remaining Useful Life (RUL) of a cutting tool in CNC machines using the system 100 of FIG. 1 in accordance with an embodiment of the present disclosure. In an embodiment, the system(s) 100 comprises one or more data storage devices or the memory 102 operatively coupled to the one or more hardware processors 104 and is configured to store instructions for execution of steps of the method by the one or more processors 104. The steps of the method of the present disclosure will now be explained with reference to the components of the system 100 as depicted in FIG. 1, and the flow diagram. In an embodiment of the present disclosure, at step 202, the one or more hardware processors 104 receive raw sensor data pertaining to one or more internal sensors integrated in a Computer Numerical Control (CNC) machine. In an embodiment, the raw sensor data comprises an actual spindle load signal, spindle speed, cutting tool axes positions, cutting tool axes servo loads, and feed rate for estimating condition of a cutting tool comprised in the CNC machine. Internal sensors may comprise for example but are not limited to, linear position sensor, proximity sensor, current sensor, rotary encoder, and the like. In another embodiment, upon processing the above example sensors, other derived data can be obtained. In an embodiment of the present disclosure, at step 204, the one or more hardware processors 104 learn one or more machine learning (ML) models using the raw sensor data. In an embodiment, the one or more ML models comprise, but are not limited to, Random Forest, Neural Network, Support Vector Regression (SVR), and the like.
In an embodiment of the present disclosure, at step 206, the one or more hardware processors 104 estimate a spindle load signal using the learned one or more ML models based on the raw sensor data and a change metric pertaining to behavior of the cutting tool is determined based on a comparison of the estimated spindle load signal and the actual spindle load signal at step 208.
In an embodiment of the present disclosure, at step 210, the one or more hardware processors 104 extract (i) magnitude, (ii) Singular Spectrum Analysis (SSA) based features, and (iii) a Graph Total Variation (GTV) based feature from the actual spindle load signal. The SSA based features are extracted from the actual spindle load signal by: generating a transition matrix using the actual spindle load signal; applying a Singular Value Decomposition (SVD) technique on the transition matrix to obtain a set of Eigen modes; learning a contribution of each Eigen mode from the set of Eigen modes extracted from the actual spindle load signal; and identifying, based on the contribution, one or more dominant Eigen modes from the set of Eigen modes, wherein the one or more dominant Eigen modes are indicative of the SSA based features. In an embodiment of the present disclosure, contribution of each Eigen mode refers to amount of variance in the actual spindle load signal captured by each Eigen mode. The above SSA based features extraction is better understood by way of following exemplary description and an implementation of the Singular Spectrum Analysis (SSA) by the present disclosure.
SSA is a non-parametric technique of time series analysis, used for extracting information from the covariance structure of the time series. It is found to work well in the area of nonlinear and non-stationary time series analysis and can be applied to both univariate and multivariate signals as known in the art. This method consists of two stages: (i) embedding, and (ii) reconstruction. In the present disclosure, during the embedding stage, the original signal is decomposed into Eigen modes by constructing a time delayed embedding matrix or the trajectory matrix. Restricting to the univariate case, given a uniformly sampled signal x=[x_1,x_2,x_3,…,x_N ], of length N, a time-delayed embedding of x is created using a window size M(1
Documents
Application Documents
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Name
Date
1
201821040502-STATEMENT OF UNDERTAKING (FORM 3) [26-10-2018(online)].pdf
2018-10-26
2
201821040502-REQUEST FOR EXAMINATION (FORM-18) [26-10-2018(online)].pdf
2018-10-26
3
201821040502-FORM 18 [26-10-2018(online)].pdf
2018-10-26
4
201821040502-FORM 1 [26-10-2018(online)].pdf
2018-10-26
5
201821040502-FIGURE OF ABSTRACT [26-10-2018(online)].jpg