Claims:
1. A processor-implemented method (800) for forecasting outcome of a fatigue testing of atleast one material specimen under test comprising:
receiving (802), via one or more input/output (I/O) interfaces, a plurality of real-time signal data of a fatigue test of at least one material specimen under test from a plurality of physical sensors, one or more ground truth crack lengths and a plurality of historical signal data of at least one historical fatigue test from a historical information database;
pre-processing (804), via one or more hardware processors, the received plurality of signal data of fatigue testing according to one or more predefined formats of the signal data;
extracting (806), via the one or more hardware processors, one or more features from one or more domains from the pre-processed plurality of signal data;
estimating (808), via the one or more hardware processors, crack lengths of the atleast one specimen for a first set of stress-loading cycles using a data-driven model based on the extracted one or more features and the pre-processed signal data;
inferencing (810), via the one or more hardware processors, a crack length propagation, and a fatigue behavior of the at least one material specimen using a Paris-Erdogan equation for a variable amplitude stress-loading based on the one or more ground truth crack lengths to obtain prior distributions of model parameters;
updating (812), via the one or more hardware processors, prior distributions of model parameters based on the estimated crack lengths of the at least one material specimen to obtain posterior distributions of model parameters; and
forecasting (814), via the one or more hardware processors, crack lengths for second set of stress-loading cycles based on the obtained posterior distributions of model parameters and using the Paris-Erdogan equation for the variable amplitude stress loading.
2. The processor-implemented method (800) of claim 1, further comprising:
comparing, via the one or more hardware processors, the estimated crack lengths with the one or more ground truth crack lengths to learn one or more parameters of a data-driven regression model.
3. The processor-implemented method (800) of claim 1, wherein the plurality of physical sensors comprising:
a plurality of load cells of the fatigue testing apparatus;
one or more actuators and one or more receivers mounted on the material specimen; and
a plurality of thermocouples attached to the material specimen.
4. The processor-implemented method (800) of claim 1, wherein pre-processing comprising:
removing, via the one or more hardware processors, noise, and outliers from the received plurality of signal data;
achieving, via the one or more hardware processors, uniform sampling frequency of the received plurality of signal data;
imputing, via the one or more hardware processors, missing values of the received plurality of signal data;
synchronizing, via the one or more hardware processors, signal data by incorporating appropriate lags; and
integrating, via the one or more hardware processors, plurality of signal data from various data sources.
5. The processor-implemented method (800) of claim 1, wherein the one or more domains from which features are extracted include time-domain, frequency-domain, wavelet-domain, and neural networks.
6. A system (100) for forecasting outcome of a fatigue testing of atleast one material specimen under test comprising:
a plurality of physical sensors (128) comprising at least one actuator sensor and at least one receiver sensor, wherein the at least one actuator sensor and at least one receiver sensor mounted on either side of the at least one material specimen;
one or more input/output (I/O) interfaces (104) to receive a plurality of real-time signal data of a fatigue testing of at least one material specimen undergoing testing and a plurality of historical signal data of at least one historical fatigue test from a historical information database;
one or more hardware processors (108);
at least one memory in communication with the one or more hardware processors (108), wherein the one or more hardware processors (108) are configured to execute programmed instructions stored in the at least one memory, to:
pre-process the received plurality of signal data of fatigue testing according to one or more predefined formats of the signal data;
extract one or more features from one or more domains from the pre-processed plurality of signal data;
estimate crack lengths of the atleast one specimen for a first set of stress-loading cycles using a data-driven model based on the extracted one or more features and the pre-processed signal data;
infer a crack length propagation, and a fatigue behavior of the at least one material specimen using a Paris-Erdogan equation for a variable amplitude stress-loading based on the one or more ground truth crack lengths to obtain prior distributions of model parameters;
update prior distributions of model parameters based on the estimated crack lengths of the at least one material specimen to obtain posterior distributions of model parameters; and
forecast crack lengths for second set of stress-loading cycles based on the obtained posterior distributions of model parameters and using the Paris-Erdogan equation for the variable amplitude stress loading.
7. The system (100) of claim 6, wherein the estimated crack lengths are compared with the one or more ground truth crack lengths to learn one or more model parameters of the data-driven regression model.
8. A non-transitory computer readable medium storing one or more instructions which when executed by one or more processors on a system, cause the one or more processors to perform method for forecasting outcome of a fatigue testing of atleast one material specimen under test comprising:
receiving, via one or more input/output (I/O) interfaces, a plurality of real-time signal data of a fatigue test of at least one material specimen under test from a plurality of physical sensors, one or more ground truth crack lengths and a plurality of historical signal data of at least one historical fatigue test from a historical information database;
pre-processing, via one or more hardware processors, the received plurality of signal data of fatigue testing according to one or more predefined formats of the signal data;
extracting, via the one or more hardware processors, one or more features from one or more domains from the pre-processed plurality of signal data;
estimating, via the one or more hardware processors, crack lengths of the atleast one specimen for a first set of stress-loading cycles using a data-driven model based on the extracted one or more features and the pre-processed signal data;
inferencing, via the one or more hardware processors, a crack length propagation, and a fatigue behavior of the at least one material specimen using a Paris-Erdogan equation for a variable amplitude stress-loading based on the one or more ground truth crack lengths to obtain prior distributions of model parameters;
updating, via the one or more hardware processors, prior distributions of model parameters based on the estimated crack lengths of the at least one material specimen to obtain posterior distributions of model parameters; and
forecasting, via the one or more hardware processors, crack lengths for second set of stress-loading cycles based on the obtained posterior distributions of model parameters and using the Paris-Erdogan equation for the variable amplitude stress loading.
, 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:
METHOD AND SYSTEM FOR FORECASTING OUTCOME OF FATIGUE TESTING

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 the field of fatigue testing of materials and specifically, to a method and system for forecasting outcome of a fatigue testing of atleast one material specimen under test.

BACKGROUND
Several quality assurance tests are conducted in manufacturing and process industries such as iron and steel making, power generation, pharma-manufacturing, refineries, cement making, oil and gas production, etc. to ensure the quality of products from these industries. Fatigue testing of objects/specimens made up of metals, alloys, polymers, etc. is one such quality assurance test. Fatigue is the weakening of a material due to repeated load and leads to cracks in materials. Fatigue testing is done to determine how much of mechanical stress a manufactured material specimen can withstand. During fatigue testing, continuous repetitive cycles of mechanical stress are applied to the specimen and its response in terms of crack initiation, crack length propagation, yield stress, etc. is studied. For example, fatigue tests are conducted on aircraft-grade aluminum structures by aircraft OEMs (original equipment manufacturers) as part of mandatory quality assurance to meet rigorous quality and safety standards. These aluminum specimens develop cracks when subjected to mechanical stress and the crack length behavior of the specimen with respect to the stress is investigated. This exercise is continued until the material specimen reaches its breaking point. These tests require sophisticated equipment and experienced manpower and are lengthy (6-24 hours) and expensive to perform. It will be helpful for product manufacturers and end-users (e.g. airline OEMs) to reduce the duration of fatigue tests carried out on aluminum specimens.
The duration/effort required for conducting fatigue tests could be reduced by capturing the pattern/behavior of the response of the material specimen to the fatigue test from the initial few stress cycles and using this to forecast the response of the specimen to subsequent stress cycles, instead of taking the fatigue test to completion, i.e. till the specimen yields or breaks. For example, for aluminum specimens, the fatigue testing could be conducted for only initial few stress-loading cycles (e.g. 20000 cycles) using which the behavior of the crack length propagation could be learnt. The learnt crack length propagation behavior could be used to forecast the crack lengths of subsequent cycles. This method of fatigue testing carried out only for initial few cycles is also known as ‘truncated fatigue testing’. There are two types of fatigue loadings used in fatigue testing i.e. constant and variable amplitude loading. Constant amplitude loading means the stress amplitude applied in each stress cycle is the same. Whereas in variable amplitude loading, the stress amplitudes vary from cycle to cycle. Variable amplitude loading mimics the real-world stress patterns experienced by material specimen more closely. Fatigue test forecasting for constant amplitude loading is relatively easier compared to variable amplitude loading.

SUMMARY
Embodiments of the 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 embodiment, a method and system for forecasting outcome of fatigue testing of atleast one material specimen undergoing testing is provided.
In one aspect, a processor-implemented method for forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing is provided. The method includes one or more steps such as receiving a plurality of real-time signal data of a fatigue test of at least one material specimen under test and a plurality of historical signal data of at least one historical fatigue test from a historical information database, and pre-processing the received plurality of signal data of the fatigue testing according to one or more predefined formats of the signal data. Further, the method includes extracting one or more features from one or more domains from the pre-processed plurality of signal data and estimating one or more crack lengths for a first set of stress-loading cycles using a data-driven model based on the pre-processed signal data and the extracted one or more features.
Furthermore, the method includes inferencing a crack length propagation, and a fatigue behavior of the at least one material specimen using a Paris-Erdogan equation for variable amplitude stress-loading based on the one or more estimated crack lengths and with the at least one measured crack length to obtain prior distributions of model parameters, updating prior distributions based on the estimated crack lengths of the at least one material specimen to obtain posterior distributions of model parameters, and forecasting at least one crack length for second set of stress-loading cycles based on the obtained posterior distribution of model parameters and using Paris-Erdogan equation for variable amplitude stress-loading.
In another aspect, a system for forecasting outcome of a fatigue testing of atleast one material specimen under test is provided. The system includes at least one actuator sensor and at least one receiver sensor mounted on either side of the at least one material specimen, an input/output interface configured to a plurality of real-time signal data of a fatigue test of at least one material specimen under test and a plurality of historical signal data of at least one historical fatigue test from a historical information database, one or more hardware processors and at least one memory storing a plurality of instructions, wherein the one or more hardware processors are configured to execute the plurality of instructions stored in the at least one memory.
Further, the system is configured to pre-process the received plurality of signal data according to one or more predefined formats of the signal data, extract one or more features from one or more domains from the pre-processed plurality of signal data, and estimate one or more crack lengths for a first set of stress-loading cycles using a data-driven model based on the pre-processed signal data and the extracted one or more features.
Furthermore, the system is configured to infer a crack length propagation, and a fatigue behavior of the at least one material specimen using a Paris-Erdogan equation for variable amplitude stress-loading based on the one or more estimated crack lengths and with the at least one measured crack length to obtain prior distributions of model parameters, update prior distributions based on the estimated crack lengths of the at least one material specimen to obtain posterior distributions of model parameters, and to forecast at least one crack length for second set of stress-loading cycles based on the obtained posterior distribution of parameters and using a Paris-Erdogan equation for variable amplitude stress-loading.
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 a method for forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing is provided. The method includes one or more steps such as receiving a plurality of real-time signal data of a fatigue test of at least one material specimen under test and a plurality of historical signal data of at least one historical fatigue test from a historical information database, and pre-processing the received plurality of signal data of the fatigue testing according to one or more predefined formats of the signal data. Further, the method includes extracting one or more features from one or more domains from the pre-processed plurality of signal data and estimated one or more crack lengths for a first set of stress-loading cycles using a data-driven model based on the pre-processed signal data and the extracted one or more features. Furthermore, the method includes inferencing a crack length propagation, and a fatigue behavior of the at least one material specimen using a Paris-Erdogan equation for variable amplitude stress-loading based on the one or more estimated crack lengths and with the at least one measured crack length to obtain prior distributions of model parameters, updating prior distributions based on the estimated crack lengths of the at least one material specimen to obtain posterior distributions of model parameters, and forecasting at least one crack length for second set of stress-loading cycles based on the obtained posterior distributions of parameters and using a Paris-Erdogan equation for variable amplitude stress-loading.
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 system for forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing, according to an embodiment of the present disclosure.
FIG. 2 illustrates an architectural diagram of a system for forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing, according to an embodiment of the present disclosure.
FIG. 3 is a functional block diagram to illustrate forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing, according to an embodiment of the present disclosure.
FIG. 4 is a schematic diagram to illustrate crack sensing mechanism, according to an embodiment of the present disclosure.
FIG. 5 is a schematic diagram to illustrate the types of stress loading cycles, according to an embodiment of the present disclosure.
FIG. 6 is a schematic diagram to illustrate prior and posterior distributions of parameters obtained from a Bayesian inference, according to an embodiment of the present disclosure.
FIG. 7 is a schematic diagram to illustrate crack length propagation with respect to the stress loading cycles for the atleast one material specimen undergoing testing, according to an embodiment of the present disclosure.
FIG. 8 is a flow diagram to illustrate a method for forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing, in accordance with some embodiments of the present disclosure.
FIG. 9 is a flow chart to illustrate forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing, in accordance with some embodiments of the present disclosure.
It should be appreciated by those skilled in the art that any block diagrams herein represent conceptual views of illustrative systems and devices embodying the principles of the present subject matter. Similarly, it will be appreciated that any flow charts, flow diagrams, and the like represent various processes, which may be substantially represented in computer readable medium and so executed by a computer or processor, whether or not such computer or processor is explicitly shown.

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 scope of the disclosed embodiments.
The embodiments herein provide a method and system for forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing. It would be appreciated that fatigue testing is carried out to test the durability or reliability of a material, by repeatedly applying mechanical load to the industrial material samples and recording its response. The duration/effort required for conducting fatigue tests could be reduced by capturing the crack length pattern/behavior of the material sample to the fatigue tests from initial few stress cycles. Herein, the captured crack length behavior is used to forecast the crack length of subsequent stress-loading cycles instead of completing the fatigue test cycles and noting the specimen’s response. The stress-loading used in truncated fatigue testing could be constant or variable amplitude loading. The present disclosure provides the system and method for forecasting the crack lengths in truncated fatigue tests under variable amplitude loading conditions and any number of cycles by utilizing data science, physics-based modeling, and engineering expertise.
Referring now to the drawings, and more particularly to FIG. 1 through 9, 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 a block diagram of a system (100) for forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing, in accordance with an example embodiment. Although the present disclosure is explained considering that the system (100) is implemented on a server, it may be understood that the system (100) may comprise one or more computing devices (102), such as a laptop computer, a desktop computer, a notebook, a workstation, a cloud-based computing environment and the like. It will be understood that the system 100 may be accessed through one or more input/output interfaces 104-1, 104-2... 104-N, collectively referred to as I/O interface (104). Examples of the I/O interface (104) may include, but are not limited to, a user interface, a portable computer, a personal digital assistant, a handheld device, a smartphone, a tablet computer, a workstation, and the like. The I/O interface (104) are communicatively coupled to the system (100) through a network (106).
In an embodiment, the network (106) may be a wireless or a wired network, or a combination thereof. In an example, the network (106) can be implemented as a computer network, as one of the different types of networks, such as virtual private network (VPN), intranet, local area network (LAN), wide area network (WAN), the internet, and such. The network 106 may either be a dedicated network or a shared network, which represents an association of the different types of networks that use a variety of protocols, for example, Hypertext Transfer Protocol (HTTP), Transmission Control Protocol/Internet Protocol (TCP/IP), and Wireless Application Protocol (WAP), to communicate with each other. Further, the network (106) may include a variety of network devices, including routers, bridges, servers, computing devices, storage devices. The network devices within the network (106) may interact with the system (100) through communication links.
The system (100) supports various connectivity options such as BLUETOOTH®, USB, ZigBee and other cellular services. The network environment enables connection of various components of the system (100) using any communication link including Internet, WAN, MAN, and so on. In an exemplary embodiment, the system (100) is implemented to operate as a stand-alone device. In another embodiment, the system (100) may be implemented to work as a loosely coupled device to a smart computing environment. The components and functionalities of the system (100) are described further in detail.
Referring FIG. 2, illustrates an exemplary system (100) for forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing. It would be appreciated that there are usually two types of mechanical loading applied to the material specimens being tested viz. constant amplitude loading and variable amplitude loading. The constant amplitude loading means the stress amplitude applied in each stress-loading cycle is the same. Whereas, in variable amplitude loading, the stress amplitudes vary from one stress-loading cycle to another. The variable amplitude loading mimics real-world stress patterns experienced by material specimens more closely. Hence, fatigue test forecasting for variable amplitude loading is more challenging compared to constant amplitude loading and is more sought after for quality assurance purposes in various industries.
Referring FIG. 3, a functional flow diagram (300) of the system (100) to illustrate forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing, wherein a system (100) is configured for forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing. The system (100) comprises at least one memory with a plurality of instructions, one or more databases (112), one or more input/output (I/O) interfaces (104) and one or more hardware processors (108) which are communicatively coupled with the at least one memory to execute a plurality of modules (114) therein. Further, the system (100) comprises a plurality of physical sensors (128), a pre-processing module (116), a feature extraction module (118), a prediction module (120), an inferencing module (122), an updation module (124), and a forecasting module (126).
The one or more I/O interfaces (104) are configured to receive a plurality of real-time signal data of a fatigue testing of at least one material specimen undergoing testing and a plurality of historical signal data of at least one historical fatigue test from a historical information database. The one or more I/O interfaces (104) are configured to convey the estimated and forecasted crack lengths from the system (100) back to the user.
It is to be noted that the input to the system (100) comprising a real-time signal data and a historical signal data of at least one historical fatigue test from a historical information database. The real-time signal data comprises of (a) signal data (e.g. ultrasonic wave data) that captures the crack length from ongoing fatigue test (b) number of stress cycles data of the specimens. The I/O interfaces (104) are configured to receive data from ongoing fatigue experiments and the historical experiment database and send the received data to the pre-processing module (116). The historical experiment database maintains the physical sensors data and outcomes from historical fatigue tests along with the metadata of the materials on which fatigue tests were conducted. Metadata of the material includes the dimensions and weights of the specimens, and material properties such as chemical composition, microstructure, density, etc.
Referring FIG. 4, wherein a schematic diagram (400) to illustrate crack sensing mechanism is provided. Herein, the hydraulic material testing machine, working at a given frequency, is used to apply continuous and repetitive mechanical stress load on a material specimen being tested. This continuous application of stress-loading cycles causes the material specimen to develop cracks. The crack length increases as the test progresses and the number of stress-loading cycles increases. The number of stress-loading cycles are applied until the specimen reaches its breaking point i.e. the crack becomes too large for the specimen to maintain integrity.
It would be appreciated that the plurality of physical sensors (128) includes a plurality of load cells of the fatigue testing apparatus, one or more actuators and one or more receivers mounted on the material specimen and a plurality of thermocouples attached to the material specimen, Herein, the actuator and receiver sensors, are mounted on either side of the material specimen along to the direction in which cracks are likely to be generated. The actuator sensor sends out ultrasonic lamb waves which are recorded by the receiver. If there is a crack along the wave propagation path, the crack will distort and disperse some of the energy of the wave being transmitted. Hence, the wave signal received at the receiver sensor will be distorted and lesser in amplitude (energy) compared to the transmitted signal. As the crack length increases, more will be the difference in amplitude between transmitted and received signals. Further, the actuator and receiver signal differences have to be mapped to corresponding crack lengths. For this purpose, for few specimens, the crack lengths are measured manually using an optical microscope along with the ultrasonic wave sensor measurements. The measured crack lengths are directly mapped to the ultrasonic wave signal differences using data-driven regression models that are then used to estimate crack lengths without having to measure them manually.
In the preferred embodiment, the pre-processing module (116) of the system (100) is configured to perform pre-processing of the received plurality of signal data according to one or more predefined formats of the signal data. The pre-processing involves removal of redundant data, unification of sampling frequency, filtering of data, outlier identification & removal, imputation of missing data, synchronization of data by incorporating appropriate lags, and integration of variables from various data sources.
In the preferred embodiment, the feature extraction module (118) of the system (100) is configured to extract one or more time-domain features from the pre-processed plurality of signal data. It would be appreciated that the differences in ultrasonic wave signals of actuator and receiver is mapped to the crack length. The differences in ultrasonic wave signals are quantified by extracted time domain features such as mean, root mean square (RMS), maximum value, minimum value, kurtosis, etc. Apart from time-domain features, other features such as frequency-domain features, wavelet-domain features, neural network-based features, etc. which may bring out the differences in data signals could also be used.
Further, it is to be noted that performing the fatigue test, the ultrasonic wave sensor measurements, and microscopic measurement to obtain the crack lengths after the first set of stress-loading cycles until the material specimen reaches its breaking point, is time consuming. Hence, a truncated fatigue test is performed, wherein the ultrasonic wave signal measurements are taken, and the crack lengths are obtained using the data-driven regression model for the first set of stress-loading cycles.
In the preferred embodiment, the prediction module (120) of the system (100) is configured to estimate one or more crack lengths for a first set of stress loading cycles in which one or more variable loads are applied on the at least one material specimen, using the data-driven regression model based on the extracted one or more time-domain or other domain features and the pre-processed signal data. It is to be noted that the prediction module (120) comprises of data-driven regression model of the form:
y = f(x, m, ?) (1)
wherein, “y” is crack length (usually in mm), “x” are the extracted features, “m” is the metadata of the material specimen and “?” are the model parameters.
The techniques used for data-driven models include variants of regression (multiple linear regression, stepwise regression, forward regression, backward regression, partial least squares regression, principal component regression, Gaussian process regression, polynomial regression, etc.), decision tree and it’s variants (random forest, bagging, boosting, bootstrapping), support vector regression, k-nearest neighbors regression, spline fitting or its variants (e.g. multi adaptive regression splines), artificial neural networks and its variants (multi-layer perceptron, recurrent neural networks & its variants e.g. long short term memory networks), and time series regression models. These models are trained in order to optimize a cost function. The cost function can be mean squared error (MSE), root mean squared error (RMSE) or mean absolute error (MAE). The crack length prediction models developed for material specimens with different metadata are stored in the models database and appropriate models are chosen for prediction based on the material specimen being tested.
In the preferred embodiment, the system (100) is configured to map the estimated crack length with at least one ground truth crack length for the data driven regression model to learn one or more model parameters.
In the preferred embodiment, the inferencing module (122) of the system (100) is configured to infer the crack length propagation, and a fatigue behavior of the at least one material specimen based on the estimated crack lengths and with the at least one measured crack length by learning the model parameters of a Paris-Erdogan equation. It is to be noted that the crack growth against number of cycles data is modelled using a physics-based mathematical model. The crack propagation behavior in material and alloy specimens typically follows Paris' Law (also known as the Paris–Erdogan equation). The Paris' law is a crack growth equation that gives the rate of growth of a fatigue crack. In particular, it helps to obtain crack length as a mathematical function of number of load cycles.
In yet another embodiment, wherein the crack length equation as a function of number of cycles for variable amplitude loading is derived. According to Paris’ Law, the rate of change of crack length a with respect to loading cycle N is given by:

da/dN=C??K?^n (2)

Where stress intensity factor ?K=Y ?s vpa

da/dN=CY^n p^(n/2) a^(n/2) ??s?^n (3)

Where C,Y,n "are material parameters/properties,?s - stress level" applied during fatigue testing. Let ?_1=CY^n p^(n/2) and, substituting ?_1 "in eq (3)" ,

da/dN=?_1 a^(n/2) ??s?^n (4)

da= a^(n/2) ??s?^n dN (5)

?_(a_0)^a¦?da/a^(n/2) = ?_1 ?_0^N¦???s?^n dN? ? (6)

wherein, a- "final crack length,"
a_0- "initial crack length,"
N-n"umber of cycles for which load is applied."

In a block variable loading, there are (N1 + N2) block loading cycles, in which the stress level ?s1 applied for N1 cycles and ?s2 for N2 cycles. Let N in the equation (6) be:
N=N_1+N_2 (7)

Substituting (7) in (6),

?_(a_0)^a¦?da/a^(n/2) = ?_1 [?_0^(N_1)¦???s?_1^n dN?+ ?_(N_1)^(N_1+N_2)¦???s?_2^n dN?] ? (8)

?_(a_0)^a¦?da/a^(n/2) = ?_1 [??s?_1^n ?_0^(N_1)¦dN+ ??s?_2^n ?_(N_1)^(N_1+N_2)¦dN] ? (9)

?_(a_0)^a¦?da/a^(n/2) = ?_1 [??s?_1^n N_1+ ??s?_2^n ? N?_2 ] ? (10)

Evaluating the left integral in (10),

(a^((-n)/2+1)-a_0^((-n)/2+1))/((-n)/2+1)= ?_1 [??s?_1^n N_1+ ??s?_2^n ? N?_2 ] (11)

Let ?_2=n/2-1 (12)

Substituting ?_2 " in (11),"

1/a^(?_2 ) -1/(a_0^(?_2 ) ) ?=-??_1 ?_2 [??s?_1^n N_1+ ??s?_2^n ? N?_2 ]

1/a^(?_2 ) = (1-?_1 ?_2 [??s?_1^n N_1+ ??s?_2^n ? N?_2 ] a_0^(?_2 ))/(a_0^(?_2 ) )

a= a_0/[1- a_0^(?_2 ) ?_1 ?_2 [??s?_1^n N_1+ ??s?_2^n ? N?_2 ]]^(1/?_2 ) (13)

From (12), n=2(?_2+1) (14)

Substituting (14) in (13),

a= a_0/[1- a_0^(?_2 ) ?_1 ?_2 [??s?_1^(2(?_2+1)) N_1+ ??s?_2^(2(?_2+1)) ? N?_2 ]]^(1/?_2 ) (15)

In general, (15) could be extended to ‘m’ stress levels,

a= a_0/[1- a_0^(?_2 ) ?_1 ?_(2 ) ?_1^m¦???s?_m^2(?_2+1) ? N_m ]^(1/?_2 ) (16)

Considering the special case of constant amplitude loading as below:

Then, ?s_1= ?s_2= ?s and (15) becomes,

a= a_0/[1- a_0^(?_2 ) ?_1 ?_2 [ ??s?^(2(?_2+1)) N_1+ ? ??s?^(2(?_2+1)) N?_2 ]]^(1/?_2 )

a= a_0/[1- a_0^(?_2 ) ?_1 ?_2 ??s?^(2(?_2+1)) [N_1+N_2 ]]^(1/?_2 )

We know that N=N_1+N_2,

a= a_0/[1- a_0^(?_2 ) ?_1 ?_2 ??s?^(2(?_2+1)) N]^(1/?_2 ) (17)

wherein, equation (17) resembles the crack length equation for constant amplitude loading. In equation (16), the model parameters ?_1 "and " ?_2 indirectly relate to the fatigue behavior of the material specimen. Hence, learning the probable values of the model parameters helps in forecasting the crack lengths in the specimens being testing. Methods such as Bayesian inference, Frequentist inference, etc. can be used for learning the values or distributions of the model parameters. Herein, a Bayesian inference model is used to learn the probability distributions of ?_1 "and " ?_2 from the crack lengths against the number of cycles data. It is to be noted that the probability distributions are assumed to follow Gaussian distribution. So, the Bayesian inference model learns the mean and standard deviation of the distribution known as prior distribution. Furthermore, it is noted that the equation (16) works even when stress level varies randomly and there is no periodic pattern in the stress levels, as is the case with practical situations. Hence, the equation (16) model can be used for practical scenarios.
Referring FIG. 5, as an example, a schematic diagram (500) illustrating the types of stress loading cycles used in fatigue tests is provided. In constant amplitude loading, the stress amplitude is same for all stress loading cycles. In variable amplitude loading, the stress amplitude varies for the stress loading cycles.
In the preferred embodiment, the updation module (124) of the system (100) is configured to update a prior distribution of model parameters using a Bayesian inference model based on the inferenced crack length propagation and the fatigue behavior of the at least one material specimen to obtain a posterior distribution of model parameters of the Bayesian model. It would be appreciated that the fatigue test is carried out and crack lengths are estimated for the first set of stress-loading cycles from the prediction module (120). The estimated crack lengths are used to update the values of the model parameters, originally learnt from the inferencing module (122) and then forecast the crack lengths for the second set of stress-loading cycles in the fatigue test.
Referring FIG. 6, a schematic diagram (600) to illustrate prior and posterior distributions of the model parameters (?_1 "and " ?_2) is provided. Herein, the Bayesian inference model is used in inferencing module (122), to obtain the prior distributions of the model parameters using crack length behavior of material specimens from historical fatigue tests. The updation module (124) is used to update the prior distributions to obtain the posterior distributions of model parameters ?_1 "and " ?_2 by using the crack length predicted by the prediction module (120). These updated distributions better represent the crack length propagation behavior of the current material specimen that is undergoing the fatigue test.
In the preferred embodiment, the forecasting module (126) of the system (100) is configured to forecast the crack lengths for a second set of stress-loading cycles based on the obtained updated posterior distribution parameters. Herein, the updated values of model parameters, ?_1 "and " ?_2, obtained from the updation module (124) are used by the forecasting module (126) to predict the crack length of the second set of stress-loading cycles using the Paris’ Erdogan equation derived for variable amplitude stress-loading cycles.
Herein, the posterior distributions from the updation module are used to obtain the values of ?_1 "and " ?_2. Since ?_1 "and " ?_2 are assumed to follow a Gaussian distribution, the means of the distributions give the values of ?_1 "and " ?_2. These values are used in the Paris Erdogan equation for variable amplitude loading (equation 16) to forecast the crack lengths, as a function of number of second set of stress-loading cycles. The estimated crack lengths for the first set of stress-loading cycles and forecasted crack lengths for the second set of stress-loading cycles for a material specimen are shown in FIG. 7. It would be appreciated that the forecasted crack lengths are stored in a crack length database and reported to the user via the I/O interface.
Referring FIG. 8, to illustrate a processor-implemented method (800) for forecasting outcome of a fatigue testing of atleast one material specimen undergoing testing.
Herein, the fatigue testing is carried out to test the durability or reliability of a material specimen, by repeatedly applying mechanical load to the industrial material specimens and recording its response as explained in a flowchart (900) of FIG. 9. The duration/effort required for conducting fatigue testing could be reduced by capturing the crack length pattern/behavior of the material specimen to the fatigue testing from the first set of stress-loading cycles and using it to forecast the crack lengths for the second set of stress-loading cycles. It would be appreciated that there are usually two types of mechanical loading applied to the material specimens being tested i.e. constant amplitude loading and variable amplitude loading. The constant amplitude loading means the stress amplitude applied in each stress-loading cycle is the same. Whereas, in variable amplitude loading, the stress amplitudes vary from one stress-loading cycle to another. The variable amplitude loading mimics real-world stress patterns experienced by material specimen more closely. Hence, fatigue test forecasting for variable amplitude loading is more challenging compared to constant amplitude loading and is more sought after for quality assurance purposes in various industries.
Initially, at the step (802), receiving a plurality of real-time signal data of a fatigue testing of at least one material specimen undergoing testing and a plurality of historical signal data of at least one historical fatigue test from a historical information database. The historical experiment database maintains the data from physical sensors (128) and outcomes from historical fatigue tests along with the metadata of the materials on which fatigue tests were conducted. Metadata of the material includes the dimensions and weights of the specimens, and material properties such as chemical composition, microstructure, density, etc.
At the next step (804), the received plurality of signal data is pre-processed according to one or more predefined formats of the signal data. Herein, the signal data is pre-processed for verification of availability of received plurality of data, removal of redundant data, unification of sampling frequency, filtering of data, identification and removal of outliers, imputation of missing data, and synchronization by incorporating appropriate lags and integration of a plurality of variables from one or more databases.
At the next step (806), extracting one or more features using one or more domains such as time-domain, frequency-domain, wavelet-domain, and the like from the pre-processed plurality of signal data.
At the next step (808), estimating crack lengths for a first set of stress-loading cycles using a data-driven model based on the extracted one or more features and the pre-processed signal data. The crack length prediction models developed for material specimens with different metadata are stored in the models database and appropriate models are chosen for prediction based on the material specimen being tested.
At the next step (810), inferencing a crack length propagation, and a fatigue behavior of the at least one material specimen using a Paris-Erdogan equation based on the estimated crack lengths and at least one measured crack length. The crack propagation behavior in metal and alloy specimens typically follows Paris' Law (also known as the Paris–Erdogan equation). The Paris' law is a crack growth equation that gives the rate of growth of a fatigue crack.
At the next step (812), updating a prior distribution of model parameters using a Bayesian model based on the inferenced crack length propagation, and the fatigue behavior of the at least one material specimen to obtain posterior distribution of model parameters. It would be appreciated that the fatigue test is carried out and crack lengths are estimated for the first set of stress-loading cycles from the prediction module (120). The crack lengths are used to update the distribution of the model parameters learnt from the inferencing module (122) and then forecast the crack lengths for the second set of stress-loading cycles in the fatigue test.
At the last step (814), forecasting crack lengths for the second set of stress-loading cycles based on the obtained posterior distribution of model parameters and the Paris-Erdogan equation for variable amplitude stress-loading. It would be appreciated that the forecasted crack lengths are stored in a crack length database and reported to the user via the I/O interface.
The written description describes the subject matter herein to enable any person skilled in the art to make and use the embodiments. The scope of the subject matter embodiments is defined by the claims and may include other modifications that occur to those skilled in the art. Such other modifications are intended to be within the scope of the claims if they have similar elements that do not differ from the literal language of the claims or if they include equivalent elements with insubstantial differences from the literal language of the claims.
The embodiments of present disclosure herein address unresolved problem of reliably forecasting the outcome of fatigue testing of material (metals, alloys, plastic, polymers, etc.) specimens for quality assurance. Therefore, embodiments herein provide a system and method for forecasting outcome of fatigue testing of material specimens. The duration/effort required for conducting fatigue testing could be reduced by capturing the pattern/behavior of the response of the material sample to the fatigue testing from initial few stress-loading cycles. This captured pattern could be used to forecast the response of the sample to subsequent stress cycles, instead of conducting the fatigue tests till the specimens yield or break. For example, for aluminum samples, the fatigue testing could be conducted for only initial few stress cycles (e.g. 20000 cycles) and the behavior of the crack length propagation behavior could be learnt. This learnt crack length propagation behavior could then be used to forecast the crack lengths due to subsequent load cycles.
It is to be understood that the scope of the protection is extended to such a program and in addition to a computer-readable means having a message therein; such computer-readable storage means contain program-code means for implementation of one or more steps of the method, when the program runs on a server or mobile device or any suitable programmable device. The hardware device can be any kind of device which can be programmed including e.g. any kind of computer like a server or a personal computer, or the like, or any combination thereof. The device may also include means which could be e.g. hardware means like e.g. an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a combination of hardware and software means, e.g. an ASIC and an FPGA, or at least one microprocessor and at least one memory with software modules located therein. Thus, the means can include both hardware means, and software means. The method embodiments described herein could be implemented in hardware and software. The device may also include software means. Alternatively, the embodiments may be implemented on different hardware devices, e.g. using a plurality of CPUs.
The embodiments herein can comprise hardware and software elements. The embodiments that are implemented in software include but are not limited to, firmware, resident software, microcode, etc. The functions performed by various modules described herein may be implemented in other modules or combinations of other modules. For the purposes of this description, a computer-usable or computer readable medium can be any apparatus that can comprise, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
The illustrated steps are set out to explain the exemplary embodiments shown, and it should be anticipated that ongoing technological development will change the manner in which particular functions are performed. These examples are presented herein for purposes of illustration, and not limitation. Further, the boundaries of the functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternative boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. Alternatives (including equivalents, extensions, variations, deviations, etc., of those described herein) will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein. Such alternatives fall within the scope of the disclosed embodiments. Also, the words “comprising,” “having,” “containing,” and “including,” and other similar forms are intended to be equivalent in meaning and be open ended in that an item or items following any one of these words is not meant to be an exhaustive listing of such item or items, or meant to be limited to only the listed item or items. It must also be noted that as used herein and in the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise.
Furthermore, one or more computer-readable storage media may be utilized in implementing embodiments consistent with the present disclosure. A computer-readable storage medium refers to any type of physical memory on which information or data readable by a processor may be stored. Thus, a computer-readable storage medium may store instructions for execution by one or more processors, including instructions for causing the processor(s) to perform steps or stages consistent with the embodiments described herein. The term “computer-readable medium” should be understood to include tangible items and exclude carrier waves and transient signals, i.e., be non-transitory. Examples include random access memory (RAM), read-only memory (ROM), volatile memory, nonvolatile memory, hard drives, CD ROMs, DVDs, flash drives, disks, and any other known physical storage media.