تجزیه و تحلیل حساسیت بر روی مدل پرسپترون چند لایه برای شناسایی موارد مایع سازی

In this paper, a new approach is presented for quantifying the system sensitivity of key parameters influencing the recognition of field liquefaction cases in a multilayer perceptron neural network (MLP model). A novel index, the average sensitivity factor, SFi , derived from the mathematical formulation of neural network is proposed to quantify the result of the sensitivity analysis. The SFi is a robust index of sensitivity analysis for the MLP model and can be used in the other problems not just in the recognition of field liquefaction problem. A well-trained MLP model is first developed to discriminate between the cases of liquefaction and non-liquefaction. Excellent performance and good generalization is achieved, with the higher recognition rate 98.9% in the training phase, 91.2% in testing phase and 96.6% on the overall cases. Using this model, the SFi values are then calculated and reveal that peak ground acceleration (PGA ) is the most sensitive factor in both the liquefaction and non-liquefaction cases. Earthquake parameters (Mw and PGA ), the stress state parameters of the soil layer (rd , σV and View the MathML sourceσv′), and the soil resistance parameters (SPT-N , CN , CE and FC ) play approximately equal roles. The seismic demand factors (Mw , PGA , rd , σV , and View the MathML sourceσv′) is more sensitive than the liquefaction resistance capacity factors (SPT-N, CN, CE, and FC) in the two-class liquefaction recognition problem.

Soil liquefaction is known to be one of the most severe seismic hazards, causing damage to structures founded on both shallow and deep foundations, harbor structures, and disrupting buried infrastructure such as communication lines [1], [2] and [3]. In engineering practice, it is essential to identify those sites vulnerable to liquefaction-induced damage and to then mitigate possible damage by taking appropriate measures in advance of a seismic event. Seed and Idriss’s [4] “simplified procedure” methodology has evolved as standard practice in evaluating liquefaction potential. Various simplified methods (the SPT-based, CPT-based, and Vs-based methods) have been proposed and have become standard practice throughout the world because of the difficulty and cost involved in obtaining high-quality undisturbed samples of saturated sandy soils to be tested in the laboratory [5] and [6]. These three simplified methods generally involve the presentation of data in a chart that defines the boundary between liquefaction and non-liquefaction in an empirical plot of cyclic resistance ratio (CRR) versus corrected SPT-N values, the normalized CPT tip resistance, and the normalized Vs, respectively. Liquefaction cases arising from the Taiwan Chi-Chi Earthquake have recently become available for calibrating and modifying the boundary between liquefaction and non-liquefaction cases in these empirical plots [1]. Cetin et al. [7] also presented improved correlations for assessment of the likelihood of initiation of soil liquefaction. These new correlations can eliminate several sources of bias intrinsic to previous similar correlations and provide greatly reduced overall uncertainty and variance. In recent years, a useful and powerful computation tool, Artificial Neural Networks (ANNs), has been introduced for solving the problem of recognizing liquefaction cases (two-class pattern recognition). Many researchers have reported similar or superior accuracy to that of simplified methods using ANNs in discriminating between liquefaction and non-liquefaction cases. Goh [8], [9] and [10] and Juang and Chen [11] adopted different types of neural networks and various combinations of input variables in assessing liquefaction potential from actual field records (both CPT-qc and SPT-N datasets), concluding that neural networks are simpler than and as reliable as conventional simplified methods. Baziar and Nilipour [12] used CPT dataset to analyze the occurrence of liquefaction using a multilayer perceptron network and the back-propagation algorithm. Again, the authors concluded that the neural network provided a more accurate prediction of liquefaction than the conventional CPT-based method. Lee and Hsiung [13] adopted both a probabilistic neural network (PNN) and multilayer perceptron model (MLP model) to identify liquefaction and non-liquefaction cases; both approaches provided nearly perfect performance in terms of classifying liquefaction potential. The MLP model achieved a slightly higher rate of recognition; however, longer searching time was required to overcome the local minima problem that potentially interrupts the process that corrects for the back-propagation error in obtaining the optimal result. A cyclic resistance ratio limit state curve established from the successfully trained and tested neural network was proposed by Juang et al. [14] and it can accurately predict the occurrence of liquefaction and non-liquefaction cases. The shortcoming of the ANN approach is the difficulty involved in interpreting the knowledge gained by “black-box” type models. The evaluation of liquefaction potential is a complicated multivariable problem with non-linear input and output relationships. It is necessary to examine not only the predictive power of liquefaction potential but also the key parameters that control liquefaction occurrence, and to evaluate the relative importance of the parameters. In the liquefaction problem, both the simplified procedures and the existing ANN models are unable to provide information regarding the degree to which the model output (liquefaction or non-liquefaction occurrence) is sensitive to changes in the key parameters. Sensitivity analysis of a neural network is an important tool in solving engineering problems, especially when non-linearity is involved. It is possible to infer the behavior of the system faces in response to variations in parameters without the need to solve complex non-linear relations. Sensitivity analysis is therefore required to identify those input variables that are important in terms of contributing to predicting the output variable and in quantifying how changes in the values of the input parameters alter the value of the outcome variable. Baziar and Nilipour [12] and Goh [8] and [9] considered the relative importance of effective parameters in liquefaction assessments using the concept proposed by Garson [15], however, this index cannot give clear physical meanings on justifying the contribution of each input variable. In the present study, a total of 644 SPT-based cases of liquefaction and non-liquefaction were compiled and used to train and test a MLP model with nine input parameters. The final optimal architecture of the MLP model, with the optimal interconnection weights and threshold values, was attained via repeated trial-and-error. A novel index, the average sensitivity factor, was first derived to calculate the degree of variation in the output subject in response to a small change in the input in the architecture of the MLP model. The average sensitivity factor for the well-trained MLP model with the best performance was then calculated to quantify the relative importance of each input parameter used in the liquefaction identification of the 644 SPT-N based field cases. Moreover, the effect of uncertainty and noise in the case dataset and the robustness of the average sensitivity factor (SFi) were also discussed.

In this study, a new approach to sensitivity analysis of the well-trained MLP model was presented for quantifying the key parameters influencing the field liquefaction recognition. A novel index, the average sensitivity factor that derived from mathematical formulation and the framework of MLP neural network is proposed. A well-trained MLP model was first developed to recognize liquefaction and non-liquefaction cases, achieving a high rate of successful recognition (96.6%). Then calculation of the average sensitivity factor can provide a measurement of the relative contributions of the input parameters influencing the two-class liquefaction recognition problem. Also, it can capture the hierarchy characteristics of the relative importance of those parameters. The average sensitivity factor permits the possible input noise or implicit uncertainty. For both liquefaction and non-liquefaction cases, PGA is the most sensitive factor in evaluation of liquefaction. In evaluating the relative importance of earthquake parameters (Mw and PGA ), the stress states of the soil layer (rd , σV , and View the MathML sourceσv′), and soil resistance (SPT-N, CN, CE, and FC), we found that the average sensitivity factors for these three groups are 34%, 30.4%, and 35.6%, respectively. These three groups of parameters play approximately equal roles. From the viewpoint of the soil strength and earthquake excitation the seismic demand factors are more sensitive than the liquefaction resistance capacity factors in the evaluation of liquefaction.