Similar to many fields of sciences,recent deep learning advances have been applied extensively in geosciences for both small-and large-scale problems.However,the necessity of using large training data and the’black ...Similar to many fields of sciences,recent deep learning advances have been applied extensively in geosciences for both small-and large-scale problems.However,the necessity of using large training data and the’black box’nature of learning have limited them in practice and difficult to interpret.Furthermore,including the governing equations and physical facts in such methods is also another challenge,which entails either ignoring the physics or simplifying them using unrealistic data.To address such issues,physics informed machine learning methods have been developed which can integrate the governing physics law into the learning process.In this work,a 1-dimensional(1 D)time-dependent seismic wave equation is considered and solved using two methods,namely Gaussian process(GP)and physics informed neural networks.We show that these meshless methods are trained by smaller amount of data and can predict the solution of the equation with even high accuracy.They are also capable of inverting any parameter involved in the governing equation such as wave velocity in our case.Results show that the GP can predict the solution of the seismic wave equation with a lower level of error,while our developed neural network is more accurate for velocity(P-and S-wave)and density inversion.展开更多
Cracks are accounted as the most destructive discontinuity in rock, soil, and concrete. Enhancing our knowledge from their properties such as crack distribution, density, and/or aspect ratio is crucial in geo-systems....Cracks are accounted as the most destructive discontinuity in rock, soil, and concrete. Enhancing our knowledge from their properties such as crack distribution, density, and/or aspect ratio is crucial in geo-systems. The most well-known mechanical parameter for such an evaluation is wave velocity through which one can qualitatively or quantitatively characterize the porous media. In small scales, such information is obtained using the ultrasonic pulse velocity(UPV) technique as a non-destructive test. In large-scale geo-systems, however, it is inverted from seismic data. In this paper, we take advantage of the recent advancements in machine learning(ML) for analyzing wave signals and predict rock properties such as crack density(CD) – the number of cracks per unit volume. To this end, we designed numerical models with different CDs and, using the rotated staggered finite-difference grid(RSG) technique, simulated wave propagation. Two ML networks, namely Convolutional Neural Networks(CNN) and Long Short-Term Memory(LSTM), are then used to predict CD values. Results show that, by selecting an optimum value for wavelength to crack length ratio, the accuracy of predictions of test data can reach R2> 96% with mean square error(MSE) < 25e-4(normalized values). Overall, we found that:(i) performance of both CNN and LSTM is highly promising,(ii) accuracy of the transmitted signals is slightly higher than the reflected signals,(iii) accuracy of 2D signals is marginally higher than 1D signals,(iv)accuracy of horizontal and vertical component signals are comparable,(v) accuracy of coda signals is less when the whole signals are used. Our results, thus, reveal that the ML methods can provide rapid solutions and estimations for crack density, without the necessity of further modeling.展开更多
Crack growth modeling has always been one of the major challenges in fracture mechanics.Among all numerical methods,the extended finite element method(XFEM)has recently attracted much attention due to its ability to e...Crack growth modeling has always been one of the major challenges in fracture mechanics.Among all numerical methods,the extended finite element method(XFEM)has recently attracted much attention due to its ability to estimate the discontinuous deformation field.However,XFEM modeling does not directly lead to reliable results,and choosing a strategy of implementation is inevitable,especially in porous media.In this study,two prevalent XFEM strategies are evaluated:a)applying reduced Young’s modulus to pores and b)using different partitions to the model and enriching each part individually.We mention the advantages and limitations of each strategy via both analytical and experimental validations.Finally,the crack growth is modeled in a natural porous media(Fontainebleau sandstone).Our investigations proved that although both strategies can identically predict the stress distribution in the sample,the first strategy simulates only the initial crack propagation,while the second strategy could model multiple cracks growths.Both strategies are reliable and highly accurate in calculating the stress intensity factor,but the second strategy can compute a more reliable reaction force.Experimental tests showed that the second strategy is a more accurate strategy in predicting the preferred crack growth path and determining the maximum strength of the sample.展开更多
文摘Similar to many fields of sciences,recent deep learning advances have been applied extensively in geosciences for both small-and large-scale problems.However,the necessity of using large training data and the’black box’nature of learning have limited them in practice and difficult to interpret.Furthermore,including the governing equations and physical facts in such methods is also another challenge,which entails either ignoring the physics or simplifying them using unrealistic data.To address such issues,physics informed machine learning methods have been developed which can integrate the governing physics law into the learning process.In this work,a 1-dimensional(1 D)time-dependent seismic wave equation is considered and solved using two methods,namely Gaussian process(GP)and physics informed neural networks.We show that these meshless methods are trained by smaller amount of data and can predict the solution of the equation with even high accuracy.They are also capable of inverting any parameter involved in the governing equation such as wave velocity in our case.Results show that the GP can predict the solution of the seismic wave equation with a lower level of error,while our developed neural network is more accurate for velocity(P-and S-wave)and density inversion.
基金the Deutsche Forschungsgemeinschaft (DFG) for financial support of the CODA-project (FOR 2825)。
文摘Cracks are accounted as the most destructive discontinuity in rock, soil, and concrete. Enhancing our knowledge from their properties such as crack distribution, density, and/or aspect ratio is crucial in geo-systems. The most well-known mechanical parameter for such an evaluation is wave velocity through which one can qualitatively or quantitatively characterize the porous media. In small scales, such information is obtained using the ultrasonic pulse velocity(UPV) technique as a non-destructive test. In large-scale geo-systems, however, it is inverted from seismic data. In this paper, we take advantage of the recent advancements in machine learning(ML) for analyzing wave signals and predict rock properties such as crack density(CD) – the number of cracks per unit volume. To this end, we designed numerical models with different CDs and, using the rotated staggered finite-difference grid(RSG) technique, simulated wave propagation. Two ML networks, namely Convolutional Neural Networks(CNN) and Long Short-Term Memory(LSTM), are then used to predict CD values. Results show that, by selecting an optimum value for wavelength to crack length ratio, the accuracy of predictions of test data can reach R2> 96% with mean square error(MSE) < 25e-4(normalized values). Overall, we found that:(i) performance of both CNN and LSTM is highly promising,(ii) accuracy of the transmitted signals is slightly higher than the reflected signals,(iii) accuracy of 2D signals is marginally higher than 1D signals,(iv)accuracy of horizontal and vertical component signals are comparable,(v) accuracy of coda signals is less when the whole signals are used. Our results, thus, reveal that the ML methods can provide rapid solutions and estimations for crack density, without the necessity of further modeling.
文摘Crack growth modeling has always been one of the major challenges in fracture mechanics.Among all numerical methods,the extended finite element method(XFEM)has recently attracted much attention due to its ability to estimate the discontinuous deformation field.However,XFEM modeling does not directly lead to reliable results,and choosing a strategy of implementation is inevitable,especially in porous media.In this study,two prevalent XFEM strategies are evaluated:a)applying reduced Young’s modulus to pores and b)using different partitions to the model and enriching each part individually.We mention the advantages and limitations of each strategy via both analytical and experimental validations.Finally,the crack growth is modeled in a natural porous media(Fontainebleau sandstone).Our investigations proved that although both strategies can identically predict the stress distribution in the sample,the first strategy simulates only the initial crack propagation,while the second strategy could model multiple cracks growths.Both strategies are reliable and highly accurate in calculating the stress intensity factor,but the second strategy can compute a more reliable reaction force.Experimental tests showed that the second strategy is a more accurate strategy in predicting the preferred crack growth path and determining the maximum strength of the sample.
