Sensitivity analysis of parameters influencing the ice–seabed interaction in sand by using extreme learning machine

Abstract

Ice gouging problem is a significant challenge threatening the integrity of subsea pipelines in the Arctic (e.g., Beaufort Sea) and even non-Arctic (e.g., Caspian Sea) offshore regions. Determining the seabed response to ice scour through the subgouge soil deformations and the keel reaction forces are important aspects for a safe and cost-effective design. In this study, the subgouge soil deformations and the keel reaction forces were simulated by the extreme learning machine (ELM) for the first time. Nine ELM models (ELM 1–ELM 9) were developed using the key parameters governing the ice–seabed interaction. The number of neurons in the hidden layer was optimized and the best activation function for the ELM network was identified. The premium ELM model, resulting in the lowest level of inaccuracy and complexity and the highest level of correlation with experimental values was identified by performing a sensitivity analysis. The gouge depth ratio and the shear strength of the seabed soil were found to be the most influential input parameters affecting the subgouge soil deformations and the keel reaction forces. A set of the ELM-based equations were proposed to approximate the ice gouging parameters. The uncertainty analysis showed that the premium ELM model slightly underestimated the subgouge soil deformation.

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Correspondence to Hodjat Shiri.

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Appendices

Appendix

ELM-based equations

ELM 1 was considered as the premium ELM model to simulate the subgouge sand parameters \(\left(\eta \right)\) comprising the subgouge deformations (dh/W & dv/W) and the subgouge forces (Fh/W & Fv/W). Among all ELM models, ELM 1 had reasonable accuracy, correlation and complexity. It is worth mentioning that ELM 1 estimated the subgouge sand parameters by using all input parameters and the general format of the extreme learning machine-based formula was as the following form:

$$\eta = \left[ {\frac{1}{{1 + exp\left( {InW \times InV \times BHI} \right)}}} \right]^{T} \times OutW,$$
(23)

where \(InW\) is the matrix of input weight, \(InV\) is the matrix of input parameters, \(BHI\) is the matrix of bias of hidden layer and \(OutW\) is the matrix of output weights. As shown, ELM 1 had a good performance to estimate the horizontal ice-induced deformations (dh/W) in the sand. Thus, matrices of ELM 1 to estimate the horizontal deformations were presented as below:

$$\begin{gathered} InV = \left[ {\begin{array}{*{20}c} \frac{y}{w} \\ {\frac{{D_{s} }}{W}} \\ \varphi \\ \alpha \\ {\frac{h^{\prime}}{W}} \\ {\frac{{L_{h} }}{{\gamma_{s} W{}^{3}}}} \\ {\frac{{L_{v} }}{{\gamma_{s} W{}^{3}}}} \\ {\frac{{V^{2} }}{gW}} \\ \end{array} } \right],BHI = \left[ {\begin{array}{*{20}c} {0.108} \\ {0.212} \\ {0.181} \\ {0.091} \\ {0.160} \\ {0.274} \\ {0.173} \\ {0.038} \\ {0.263} \\ {0.285} \\ {0.233} \\ {0.159} \\ {0.151} \\ {0.117} \\ {0.015} \\ {0.122} \\ {0.066} \\ {0.261} \\ {0.036} \\ {0.182} \\ {0.253} \\ {0.183} \\ {0.179} \\ {0.299} \\ {0.104} \\ {0.319} \\ {0.019} \\ {0.213} \\ \end{array} } \right], \hfill \\ InW = \left[ {\begin{array}{*{20}c} {0.076} & {0.053} & {0.231} & {0.351} & {0.091} & {0.039} & {0.224} & {0.113} \\ {0.122} & {0.190} & {0.258} & {0.168} & {0.473} & {0.003} & {0.234} & {0.094} \\ {0.353} & {0.072} & {0.025} & {0.032} & {0.173} & {0.305} & {0.047} & {0.183} \\ {0.180} & {0.082} & {0.456} & {0.019} & {0.103} & {0.237} & {0.104} & {0.006} \\ {0.016} & {0.291} & {0.021} & {0.103} & {0.301} & {0.002} & {0.132} & {0.185} \\ {0.046} & {0.182} & {0.093} & {0.317} & {0.171} & {0.231} & {0.135} & {0.109} \\ {0.335} & {0.052} & {0.088} & {0.245} & {0.026} & {0.083} & {0.101} & {0.309} \\ {0.261} & {0.144} & {0.017} & {0.092} & {0.167} & {0.118} & {0.124} & {0.303} \\ {0.028} & {0.291} & {0.367} & {0.307} & {0.154} & {0.092} & {0.009} & {0.009} \\ {0.063} & {0.254} & {0.131} & {0.117} & {0.201} & {0.140} & {0.003} & {0.095} \\ {0.249} & {0.100} & {0.136} & {0.122} & {0.166} & {0.038} & {0.309} & {0.212} \\ {0.174} & {0.072} & {0.117} & {0.159} & {0.227} & {0.067} & {0.243} & {0.438} \\ {0.164} & {0.183} & {0.106} & {0.029} & {0.012} & {0.243} & {0.242} & {0.057} \\ {0.265} & {0.144} & {0.054} & {0.118} & {0.054} & {0.043} & {0.025} & {0.103} \\ {0.081} & {0.266} & {0.228} & {0.122} & {0.119} & {0.195} & {0.069} & {0.339} \\ {0.176} & {0.167} & {0.098} & {0.388} & {0.082} & {0.392} & {0.013} & {0.080} \\ {0.213} & {0.164} & {0.076} & {0.007} & {0.073} & {0.123} & {0.229} & {0.219} \\ {0.010} & {0.090} & {0.079} & {0.220} & {0.044} & {0.058} & {0.061} & {0.459} \\ {0.135} & {0.321} & {0.120} & {0.038} & {0.241} & {0.059} & {0.105} & {0.002} \\ {0.050} & {0.217} & {0.314} & {0.468} & {0.283} & {0.139} & {0.187} & {0.032} \\ {0.200} & {0.150} & {0.052} & {0.049} & {0.072} & {0.136} & {0.376} & {0.090} \\ {0.361} & {0.218} & {0.104} & {0.042} & {0.100} & {0.418} & {0.067} & {0.070} \\ {0.260} & {0.039} & {0.015} & {0.050} & {0.112} & {0.216} & {0.150} & {0.101} \\ {0.042} & {0.141} & {0.303} & {0.114} & {0.098} & {0.399} & {0.410} & {0.060} \\ {0.002} & {0.315} & {0.315} & {0.036} & {0.057} & {0.039} & {0.167} & {0.041} \\ {0.150} & {0.045} & {0.038} & {0.186} & {0.191} & {0.172} & {0.260} & {0.135} \\ {0.111} & {0.326} & {0.185} & {0.047} & {0.224} & {0.049} & {0.140} & {0.138} \\ {0.252} & {0.051} & {0.026} & {0.086} & {0.367} & {0.123} & {0.212} & {0.031} \\ \end{array} } \right], \hfill \\ OutW = \left[ {\begin{array}{*{20}c} {29.275} \\ {72.459} \\ {165.167} \\ {2160.705} \\ {596.242} \\ {35395.487} \\ {2167.263} \\ {22.303} \\ {17132.658} \\ {75.972} \\ {62.933} \\ {4.386} \\ {866.932} \\ {311.317} \\ {594.914} \\ {42.614} \\ {703.678} \\ {129.912} \\ {775.673} \\ {17100.189} \\ {168.320} \\ {1054.218} \\ {54.598} \\ {292.875} \\ {23846.632} \\ {30.669} \\ {2671.287} \\ {130.130} \\ \end{array} } \right] \hfill \\ \end{gathered}$$
(24)

Moreover, the matrices of ELM 1 to estimate the vertical sand deformations (dv/W) were provided as follows:

$$\begin{gathered} InV = \left[ {\begin{array}{*{20}c} \frac{y}{w} \\ {\frac{{D_{s} }}{W}} \\ \varphi \\ \alpha \\ {\frac{h^{\prime}}{W}} \\ {\frac{{L_{h} }}{{\gamma_{s} W{}^{3}}}} \\ {\frac{{L_{v} }}{{\gamma_{s} W{}^{3}}}} \\ {\frac{{V^{2} }}{gW}} \\ \end{array} } \right],BHI = \left[ {\begin{array}{*{20}c} {0.007} \\ {0.081} \\ {0.077} \\ {0.169} \\ {0.217} \\ {0.218} \\ {0.130} \\ {0.112} \\ {0.298} \\ {0.113} \\ {0.060} \\ {0.166} \\ {0.155} \\ {0.015} \\ {0.285} \\ {0.298} \\ {0.212} \\ {0.030} \\ {0.140} \\ {0.162} \\ {0.277} \\ {0.143} \\ {0.048} \\ {0.175} \\ {0.292} \\ {0.291} \\ {0.167} \\ {0.289} \\ \end{array} } \right], \hfill \\ InW = \left[ {\begin{array}{*{20}c} {0.352} & {0.139} & {0.018} & {0.165} & {0.031} & {0.084} & {0.013} & {0.026} \\ {0.223} & {0.157} & {0.193} & {0.048} & {0.004} & {0.573} & {0.026} & {0.174} \\ {0.020} & {0.103} & {0.058} & {0.001} & {0.001} & {0.293} & {0.064} & {0.242} \\ {0.113} & {0.048} & {0.451} & {0.200} & {0.086} & {0.022} & {0.138} & {0.136} \\ {0.006} & {0.399} & {0.243} & {0.023} & {0.259} & {0.254} & {0.296} & {0.121} \\ {0.140} & {0.018} & {0.115} & {0.153} & {0.222} & {0.258} & {0.028} & {0.184} \\ {0.098} & {0.011} & {0.420} & {0.200} & {0.222} & {0.070} & {0.001} & {0.206} \\ {0.026} & {0.045} & {0.118} & {0.361} & {0.182} & {0.016} & {0.222} & {0.032} \\ {0.229} & {0.106} & {0.122} & {0.335} & {0.326} & {0.166} & {0.166} & {0.001} \\ {0.274} & {0.161} & {0.106} & {0.124} & {0.097} & {0.079} & {0.276} & {0.225} \\ {0.442} & {0.059} & {0.108} & {0.160} & {0.002} & {0.132} & {0.381} & {0.057} \\ {0.309} & {0.003} & {0.228} & {0.348} & {0.258} & {0.056} & {0.278} & {0.277} \\ {0.099} & {0.064} & {0.142} & {0.144} & {0.047} & {0.341} & {0.064} & {0.075} \\ {0.118} & {0.280} & {0.229} & {0.011} & {0.254} & {0.012} & {0.277} & {0.632} \\ {0.060} & {0.047} & {0.194} & {0.248} & {0.382} & {0.085} & {0.148} & {0.252} \\ {0.108} & {0.335} & {0.073} & {0.044} & {0.114} & {0.066} & {0.009} & {0.047} \\ {0.096} & {0.313} & {0.023} & {0.089} & {0.213} & {0.136} & {0.356} & {0.083} \\ {0.050} & {0.307} & {0.090} & {0.263} & {0.152} & {0.175} & {0.067} & {0.034} \\ {0.025} & {0.286} & {0.088} & {0.001} & {0.144} & {0.037} & {0.158} & {0.036} \\ {0.107} & {0.024} & {0.101} & {0.087} & {0.188} & {0.092} & {0.098} & {0.039} \\ {0.141} & {1.098} & {0.006} & {0.259} & {0.241} & {0.048} & {0.001} & {0.045} \\ {0.126} & {0.134} & {0.244} & {0.085} & {0.183} & {0.159} & {0.082} & {0.012} \\ {0.227} & {0.117} & {0.015} & {0.146} & {0.102} & {0.036} & {0.286} & {0.360} \\ {0.034} & {0.010} & {0.129} & {0.435} & {0.154} & {0.061} & {0.213} & {0.090} \\ {0.330} & {0.212} & {0.126} & {0.038} & {0.147} & {0.111} & {0.047} & {0.046} \\ {0.135} & {0.247} & {0.306} & {0.056} & {0.189} & {0.127} & {0.220} & {0.097} \\ {0.278} & {0.264} & {0.263} & {0.015} & {0.124} & {0.194} & {0.198} & {0.178} \\ {0.066} & {0.218} & {0.037} & {0.003} & {0.237} & {0.313} & {0.123} & {0.004} \\ \end{array} } \right], \hfill \\ OutW = \left[ {\begin{array}{*{20}c} {6.367} \\ {129.078} \\ {13.435} \\ {734.438} \\ {1073.040} \\ {1914.414} \\ {3822.172} \\ {137.341} \\ {28.803} \\ {24.231} \\ {412.769} \\ {736.786} \\ {11.185} \\ {3327.398} \\ {385.798} \\ {4.120} \\ {9.616} \\ {43.026} \\ {300.883} \\ {74.807} \\ {342.412} \\ {750.359} \\ {18.367} \\ {124.443} \\ {336.378} \\ {305.840} \\ {78.977} \\ {31.751} \\ \end{array} } \right] \hfill \\ \end{gathered}$$
(25)

Besides, the matrices of ELM 1 to estimate the ice-induced horizontal forces (Fh/W) in sand were written as below:

$$\begin{gathered} InV = \left[ {\begin{array}{*{20}c} \frac{x}{w} \\ {\frac{{D_{s} }}{W}} \\ \varphi \\ \alpha \\ {\frac{h^{\prime}}{W}} \\ {\frac{{L_{h} }}{{\gamma_{s} W{}^{3}}}} \\ {\frac{{L_{v} }}{{\gamma_{s} W{}^{3}}}} \\ {\frac{{V^{2} }}{gW}} \\ \end{array} } \right],BHI = \left[ {\begin{array}{*{20}c} { - 0.173} \\ { - 0.218} \\ { - 0.337} \\ {0.036} \\ { - 0.026} \\ {0.113} \\ { - 0.077} \\ { - 0.133} \\ { - 0.026} \\ {0.295} \\ { - 0.052} \\ {0.321} \\ {0.331} \\ {0.233} \\ { - 0.014} \\ { - 0.101} \\ { - 0.023} \\ { - 0.117} \\ { - 0.020} \\ { - 0.281} \\ { - 0.244} \\ { - 0.235} \\ { - 0.023} \\ {0.083} \\ { - 0.162} \\ { - 0.342} \\ { - 0.095} \\ {0.177} \\ \end{array} } \right], \hfill \\ InW = \left[ {\begin{array}{*{20}c} { - 0.158} & {0.154} & { - 0.294} & { - 0.299} & {0.018} & {0.032} & { - 0.197} & {0.258} \\ {0.340} & { - 0.035} & { - 0.082} & { - 0.268} & { - 0.013} & { - 0.158} & {0.098} & { - 0.434} \\ { - 0.050} & {0.200} & {0.160} & {0.287} & { - 0.250} & { - 0.034} & {0.046} & { - 0.161} \\ {0.177} & {0.119} & {0.061} & {0.252} & { - 0.122} & {0.222} & {0.264} & { - 0.023} \\ {0.278} & { - 0.153} & {0.073} & { - 0.149} & { - 0.090} & {0.211} & { - 0.003} & {0.327} \\ {0.002} & {0.197} & { - 0.269} & { - 0.134} & {0.214} & {0.254} & { - 0.262} & { - 0.179} \\ {0.264} & { - 0.012} & { - 0.045} & { - 0.233} & { - 0.232} & {0.128} & { - 0.222} & { - 0.042} \\ {0.033} & {0.445} & {0.018} & {0.089} & {0.029} & { - 0.082} & {0.203} & {0.282} \\ { - 0.095} & { - 0.260} & { - 0.093} & { - 0.128} & { - 0.269} & { - 0.142} & {0.003} & { - 0.011} \\ { - 0.163} & { - 0.220} & { - 0.006} & {0.121} & { - 0.364} & {0.232} & { - 0.033} & {0.312} \\ {0.233} & { - 0.101} & {0.260} & {0.091} & {0.022} & { - 0.085} & { - 0.311} & { - 0.044} \\ { - 0.202} & { - 0.113} & {0.019} & { - 0.056} & { - 0.172} & { - 0.240} & { - 0.058} & { - 0.023} \\ { - 0.279} & { - 0.097} & {0.178} & { - 0.188} & { - 0.197} & {0.190} & { - 0.082} & { - 0.102} \\ { - 0.216} & { - 0.019} & { - 0.038} & { - 0.043} & { - 0.052} & {0.115} & { - 0.413} & { - 0.229} \\ { - 0.103} & { - 0.033} & { - 0.292} & {0.342} & { - 0.192} & { - 0.200} & { - 0.232} & {0.131} \\ { - 0.101} & {0.023} & {0.174} & {0.198} & {0.212} & {0.184} & { - 0.217} & { - 0.052} \\ {0.046} & { - 0.171} & { - 0.367} & {0.320} & { - 0.136} & { - 0.024} & {0.147} & { - 0.194} \\ {0.098} & {0.346} & { - 0.134} & {0.056} & { - 0.109} & {0.214} & {0.048} & { - 0.053} \\ {0.075} & { - 0.021} & { - 0.234} & { - 0.340} & { - 0.267} & {0.038} & {0.171} & {0.053} \\ {0.098} & { - 0.097} & { - 0.320} & {0.256} & {0.328} & { - 0.147} & {0.024} & {0.217} \\ { - 0.071} & {0.385} & {0.190} & { - 0.024} & { - 0.163} & { - 0.059} & { - 0.033} & {0.243} \\ {0.382} & { - 0.213} & { - 0.030} & {0.045} & {0.037} & {0.043} & { - 0.263} & {0.186} \\ {0.002} & { - 0.151} & { - 0.116} & { - 0.106} & {0.320} & {0.289} & {0.172} & { - 0.055} \\ { - 0.292} & { - 0.088} & {0.079} & {0.023} & {0.131} & {0.356} & {0.171} & { - 0.202} \\ {0.064} & { - 0.281} & {0.192} & { - 0.035} & { - 0.061} & {0.064} & {0.339} & {0.033} \\ {0.356} & {0.114} & {0.152} & {0.173} & { - 0.172} & {0.229} & { - 0.175} & { - 0.084} \\ { - 0.018} & {0.006} & { - 0.302} & {0.140} & { - 0.151} & {0.418} & {0.0431} & {0.036} \\ { - 0.051} & { - 0.177} & {0.224} & { - 0.001} & {0.196} & {0.099} & { - 0.084} & {0.272} \\ \end{array} } \right], \hfill \\ OutW = \left[ {\begin{array}{*{20}c} { - 57904382.543} \\ {11327617709.333} \\ {25804356551.036} \\ {23880116986.524} \\ {49235561.598} \\ { - 2107351719.547} \\ { - 6133664925.287} \\ { - 324830407.099} \\ {14514446831.585} \\ { - 691139063.538} \\ {69679699824.426} \\ { - 270014640.236} \\ { - 180938532.185} \\ {5203121750} \\ {16177672.834} \\ { - 45918830515.734} \\ {86028151.093} \\ { - 641785582.707} \\ {914415067.981} \\ {444471868.539} \\ {23259646121.250} \\ { - 118218046.915} \\ {4266202972.363} \\ {109167304.838} \\ {7941707982.082} \\ {9530629767.052} \\ {2019320579.769} \\ { - 113281225148.813} \\ \end{array} } \right] \hfill \\ \end{gathered}$$
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Furthermore, the matrices of this ELM model to surmise the ice-induced vertical reaction forces (Fv/W) in a sandy seabed were suggested as follows:

$$\begin{gathered} InV = \left[ {\begin{array}{*{20}c} \frac{x}{w} \\ {\frac{{D_{s} }}{W}} \\ \varphi \\ \alpha \\ {\frac{h^{\prime}}{W}} \\ {\frac{{L_{h} }}{{\gamma_{s} W{}^{3}}}} \\ {\frac{{L_{v} }}{{\gamma_{s} W{}^{3}}}} \\ {\frac{{V^{2} }}{gW}} \\ \end{array} } \right],BHI = \left[ {\begin{array}{*{20}c} { - 0.256} \\ {0.079} \\ {0.091} \\ { - 0.278} \\ {0.127} \\ { - 0.222} \\ { - 0.338} \\ {0.336} \\ { - 0.215} \\ { - 0.119} \\ {0.311} \\ {0.097} \\ {0.326} \\ {0.152} \\ { - 0.042} \\ { - 0.159} \\ { - 0.083} \\ {0.003} \\ { - 0.140} \\ { - 0.106} \\ { - 0.045} \\ {0.135} \\ {0.138} \\ { - 0.104} \\ {0.037} \\ {0.129} \\ {0.029} \\ {0.341} \\ \end{array} } \right], \hfill \\ InW = \left[ {\begin{array}{*{20}c} { - 0.045} & { - 0.358} & {0.040} & {0.217} & { - 0.267} & {0.029} & {0.051} & { - 0.338} \\ {0.020} & {0.120} & {0.061} & {0.146} & { - 0.123} & { - 0.137} & {0.232} & {0.254} \\ {0.009} & {0.371} & {0.027} & {0.181} & {0.115} & { - 0.013} & { - 0.055} & { - 0.284} \\ {0.300} & { - 0.042} & { - 0.015} & {0.086} & { - 0.045} & {0.032} & { - 0.185} & { - 0.208} \\ { - 0.293} & { - 0.060} & { - 0.118} & {0.273} & {0.029} & { - 0.231} & { - 0.196} & {0.283} \\ { - 0.107} & {0.386} & {0.208} & { - 0.028} & { - 0.351} & {0.136} & {0.236} & { - 0.132} \\ { - 0.259} & { - 0.235} & { - 0.155} & {0.220} & { - 0.044} & { - 0.001} & { - 0.018} & {0.167} \\ { - 0.324} & {0.014} & {0.166} & { - 0.165} & { - 0.013} & { - 0.336} & {0.347} & {0.253} \\ {0.317} & {0.153} & {0.149} & { - 0.209} & {0.012} & { - 0.338} & { - 0.056} & { - 0.043} \\ {0.139} & {0.155} & { - 0.012} & {0.223} & {0.454} & {0.389} & { - 0.001} & {0.269} \\ { - 0.059} & {0.146} & { - 0.012} & { - 0.122} & { - 0.077} & {0.163} & { - 0.101} & {0.109} \\ { - 0.278} & {0.050} & { - 0.093} & { - 0.032} & {0.198} & { - 0.106} & {0.218} & { - 0.326} \\ { - 0.107} & {0.401} & {0.031} & {0.125} & { - 0.210} & {0.018} & { - 0.084} & { - 0.015} \\ {0.070} & {0.113} & {0.259} & { - 0.188} & {0.110} & { - 0.071} & { - 0.161} & {0.055} \\ { - 0.084} & { - 0.079} & {0.095} & { - 0.296} & { - 0.046} & {0.160} & {0.028} & { - 0.046} \\ {0.251} & { - 0.106} & {0.191} & {0.115} & { - 0.183} & {0.111} & {0.194} & {0.169} \\ { - 0.272} & { - 0.154} & {0.267} & { - 0.277} & {0.241} & {0.182} & {0.225} & {0.050} \\ {0.091} & { - 0.156} & { - 0.031} & {0.138} & {0.234} & { - 0.167} & {0.107} & { - 0.129} \\ { - 0.186} & { - 0.020} & {0.057} & {0.180} & { - 0.425} & {0.014} & { - 0.239} & {0.043} \\ {0.257} & { - 0.036} & {0.141} & {0.077} & { - 0.183} & {0.064} & {0.086} & {0.440} \\ {0.211} & {0.088} & { - 0.285} & { - 0.164} & { - 0.033} & { - 0.052} & {0.224} & {0.046} \\ {0.001} & {0.248} & {0.064} & {0.033} & {0.056} & {0.162} & {0.079} & {0.006} \\ { - 0.055} & { - 0.079} & { - 0.233} & { - 0.254} & { - 0.203} & {0.307} & {0.024} & { - 0.096} \\ { - 0.146} & {0.175} & { - 0.149} & { - 0.257} & {0.039} & { - 0.271} & { - 0.437} & {0.127} \\ { - 0.191} & {0.066} & {0.320} & {0.237} & {0.068} & {0.010} & {0.084} & { - 0.138} \\ {0.061} & {0.158} & { - 0.431} & { - 0.206} & { - 0.193} & { - 0.057} & {0.247} & {0.048} \\ {0.013} & {0.229} & { - 0.387} & {0.281} & {0.087} & { - 0.087} & {0.311} & { - 0.005} \\ { - 0.233} & {0.072} & { - 0.203} & { - 0.064} & {0.039} & {0.413} & { - 0.125} & {0.114} \\ \end{array} } \right] \hfill \\ OutW = \left[ {\begin{array}{*{20}c} { - 9846993.568} \\ { - 3754470.686} \\ { - 57306.747} \\ {739540.221} \\ {567279.640} \\ {4111811.376} \\ {115947.041} \\ {776649.753} \\ { - 101460.754} \\ { - 3108267.921} \\ { - 412567.206} \\ {528094.443} \\ { - 4728862.345} \\ {896003.104} \\ {592571.805} \\ {6710766.618} \\ { - 571166.680} \\ { - 287955.147} \\ { - 5324488.298} \\ { - 1195984.731} \\ {37129.165} \\ {6906839.302} \\ {61221.738} \\ {625421.204} \\ {8430674.410} \\ {70.211} \\ {1328898.924} \\ {555030.486} \\ \end{array} } \right] \hfill \\ \end{gathered}$$
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Azimi, H., Shiri, H. Sensitivity analysis of parameters influencing the ice–seabed interaction in sand by using extreme learning machine. Nat Hazards (2021). https://doi.org/10.1007/s11069-021-04544-9

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Keywords

  • Ice–seabed interaction
  • Sandy seabed
  • Extreme learning machine
  • Sensitivity analysis
  • Uncertainty analysis