Mountain permafrost distribution modeling using Multivariate Adaptive Regression Spline (MARS) in the Wenquan area over the Qinghai-Tibet Plateau

In high mountainous areas, the development and distribution of alpine permafrost is greatly affected by macro- and mi- cro-topographic factors. The effects of latitude, altitude, slope, and aspect on the distribution of permafrost were studied to under- stand the dislribution patterns of permafrost in Wenquan on the Qinghai-Tibet Plateau. Cluster and correlation analysis were per- formed based on 30 m Global Digital Elevation Model （GDEM） data and field data obtained using geophysical exploration and borehole drilling methods. A Multivariate Adaptive Regression Spline model （MARS） was developed to simulate permafrost spa- tial distribution over the studied area. A validation was followed by comparing to 201 geophysical exploration sites, as well as by comparing to two other models, i.e., a binary logistic regression model and the Mean Annual Ground Temperature model （IVlAGT）. The MARS model provides a better simulation than the other two models. Besides the control effect of elevation on permafrost distribution, the MARS model also takes into account the impact of direct solar radiation on permafrost distribution.

Multivariate adaptive regression splines based simulation optimization using move-limit strategy

This paper makes an approach to the approximate optimum in structural design,which combines the global response surface（GRS） based multivariate adaptive regression splines（MARS） with Move-Limit strategy（MLS）.MARS is an adaptive regression process,which fits in with the multidimensional problems.It adopts a modified recursive partitioning strategy to simplify high-dimensional problems into smaller highly accurate models.MLS for moving and resizing the search sub-regions is employed in the space of design variables.The quality of the approximation functions and the convergence history of the optimization process are reflected in MLS.The disadvantages of the conventional response surface method（RSM） have been avoided,specifically,highly nonlinear high-dimensional problems.The GRS/MARS with MLS is applied to a high-dimensional test function and an engineering problem to demonstrate its feasibility and convergence,and compared with quadratic response surface（QRS） models in terms of computational efficiency and accuracy.

Multivariate adaptive regression splines and neural network models for prediction of pile drivability

Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and tension stresses in the piles. Hence, an important design consideration is to check that the strength of the pile is sufficient to resist the stresses caused by the impact of the pile hammer. Due to its complexity, pile drivability lacks a precise analytical solution with regard to the phenomena involved.In situations where measured data or numerical hypothetical results are available, neural networks stand out in mapping the nonlinear interactions and relationships between the system’s predictors and dependent responses. In addition, unlike most computational tools, no mathematical relationship assumption between the dependent and independent variables has to be made. Nevertheless, neural networks have been criticized for their long trial-and-error training process since the optimal configuration is not known a priori. This paper investigates the use of a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines（MARS）, as an alternative to neural networks, to approximate the relationship between the inputs and dependent response, and to mathematically interpret the relationship between the various parameters. In this paper, the Back propagation neural network（BPNN） and MARS models are developed for assessing pile drivability in relation to the prediction of the Maximum compressive stresses（MCS）, Maximum tensile stresses（MTS）, and Blow per foot（BPF）. A database of more than four thousand piles is utilized for model development and comparative performance between BPNN and MARS predictions.

Advanced reliability analysis of slopes in spatially variable soils using multivariate adaptive regression splines

This study aims to extend the multivariate adaptive regression splines(MARS)-Monte Carlo simulation(MCS) method for reliability analysis of slopes in spatially variable soils. This approach is used to explore the influences of the multiscale spatial variability of soil properties on the probability of failure(P_f) of the slopes. In the proposed approach, the relationship between the factor of safety and the soil strength parameters characterized with spatial variability is approximated by the MARS, with the aid of Karhunen-Loeve expansion. MCS is subsequently performed on the established MARS model to evaluate Pf.Finally, a nominally homogeneous cohesive-frictional slope and a heterogeneous cohesive slope, which are both characterized with different spatial variabilities, are utilized to illustrate the proposed approach.Results showed that the proposed approach can estimate the P_f of the slopes efficiently in spatially variable soils with sufficient accuracy. Moreover, the approach is relatively robust to the influence of different statistics of soil properties, thereby making it an effective and practical tool for addressing slope reliability problems concerning time-consuming deterministic stability models with low levels of P_f.Furthermore, disregarding the multiscale spatial variability of soil properties can overestimate or underestimate the P_f. Although the difference is small in general, the multiscale spatial variability of the soil properties must still be considered in the reliability analysis of heterogeneous slopes, especially for those highly related to cost effective and accurate designs.

Using multivariate adaptive regression splines to develop relationship between rock quality designation and permeability

The assessment of in situ permeability of rock mass is challenging for large-scale projects such as reservoirs created by dams,where water tightness issues are of prime importance.The in situ permeability is strongly related to the frequency and distribution of discontinuities in the rock mass and quantified by rock quality designation(RQD).This paper analyzes the data of hydraulic conductivity and discontinuities sampled at different depths during the borehole investigations in the limestone and sandstone formations for the construction of hydraulic structures in Oman.Cores recovered from boreholes provide RQD data,and in situ Lugeon tests elucidate the permeability.A modern technique of multivariate adaptive regression splines(MARS)assisted in correlating permeability and RQD along with the depth.In situ permeability shows a declining trend with increasing RQD,and the depth of investigation is within 50 m.This type of relationship can be developed based on detailed initial investigations at the site where the hydraulic conductivity of discontinuous rocks is required to be delineated.The relationship can approximate the permeability by only measuring the RQD in later investigations on the same site,thus saving the time and cost of the site investigations.The applicability of the relationship developed in this study to another location requires a lithological similarity of the rock mass that can be verified through preliminary investigation at the site.

基于MARS的岩石抗拉强度预测模型

将无损检测技术与机器学习相结合,通过建立预测模型来快速确定岩石抗拉强度已经成为热门研究方向之一。为了建立预测模型,提出一种基于多元自适应回归样条(MARS)的数据驱动建模技术,用于岩石抗拉强度预测。共收集了80组试验数据,包括施密特回弹数、干密度、点荷载强度指数以及巴西抗拉强度。所有数据被随机分为2个部分,其中70%的数据用于训练模型,剩余30%的数据用于测试模型性能。同时开发了人工神经网络、支持向量机和决策树3种数据驱动模型。选择了4种常用的模型性能评价指标,分别为均方根误差、平均绝对误差、相关系数和决定系数,以此来对所开发模型的预测性能进行比较。结果表明:所开发的智能模型均能够提供较高的预测精度,其中MARS模型性能优于其他3种模型,支持向量机和人工神经网络模型次之,决策树模型相对较差。值得一提的是,MARS模型能够通过方差分析来评估每个变量的相对重要性。研究成果有助于快速确定岩石抗拉强度。

基于MARS的银行信用风险压力测试实证研究——以招商银行为例

压力测试是商业银行信用风险管理的一种常用手段,在进行压力测试时,对测试方法的选择是一个不容忽视的问题,就测试方法的选择来说,目前银行所使用的方法有其各自的优缺点。本文对压力测试方法进行分析,并将多元自适应回归样条(MARS)方法引入该研究中,在通过实证分析后,最终发现在使用MARS方法进行商业银行信用风险压力测试时,该方法表现优越,尤其是其样条函数模型对于现象的解释能力强于一般的线性回归模型。

A nonparametric regression method for multiple longitudinal phenotypes using multivariate adaptive splines

In genetic studies of complex diseases, particularly mental illnesses, and behavior disorders, two distinct characteristics have emerged in some data sets. First, genetic data sets are collected with a large number of phenotypes that are potentially related to the complex disease under study. Second, each phenotype is collected from the same subject repeatedly over time. In this study, we present a nonparametric regression approach to study multivariate and time-repeated phenotypes together by using the technique of the multivariate adaptive regression splines for analysis of longitudinal data （MASAL）, which makes it possible to identify genes, gene-gene and gene-environment, including time, interactions associated with the phenotypes of interest. Furthermore, we propose a permutation test to assess the associations between the phenotypes and selected markers. Through simulation, we demonstrate that our proposed approach has advantages over the existing methods that examine each longitudinal phenotype separately or analyze the summarized values of phenotypes by compressing them into one-time-point phenotypes. Application of the proposed method to the Framingham Heart Study illustrates that the use of multivariate longitudinal phenotypes enhanced the significance of the association test.

Downscaling Landsat-8 land surface temperature maps in diverse urban landscapes using multivariate adaptive regression splines and very high resolution auxiliary data

We propose a method for spatial downscaling of Landsat 8-derived LST maps from 100(30 m)resolution down to 2–4 m with the use of the Multiple Adaptive Regression Splines(MARS)models coupled with very high resolution auxiliary data derived from hyperspectral aerial imagery and large-scale topographic maps.We applied the method to four Landsat 8 scenes,two collected in summer and two in winter,for three British towns collectively representing a variety of urban form.We used several spectral indices as well as fractional coverage of water and paved surfaces as LST predictors,and applied a novel method for the correction of temporal mismatch between spectral indices derived from aerial and satellite imagery captured at different dates,allowing for the application of the downscaling method for multiple dates without the need for repeating the aerial survey.Our results suggest that the method performed well for the summer dates,achieving RMSE of 1.40–1.83 K prior to and 0.76–1.21 K after correction for residuals.We conclude that the MARS models,by addressing the non-linear relationship of LST at coarse and fine spatial resolutions,can be successfully applied to produce high resolution LST maps suitable for studies of urban thermal environment at local scales.

Prediction of interfaces of geological formations using the multivariate adaptive regression spline method

The design and construction of underground structures are significantly affected by the distribution of geological formations.Prediction of the geological interfaces using limited data has been a difficult task.A multivariate adaptive regression spline(MARS)method capable of modeling nonlinearities automatically was used in this study to spatially predict the elevations of geological interfaces.Borehole data from two sites in Singapore were used to evaluate the capability of the MARS method for predicting geological interfaces.By comparing the predicted values with the borehole data,it is shown that the MARS method has a mean of root mean square error of 4.4 m for the predicted elevations of the Kallang Formation–Old Alluvium interface.In addition,the MARS method is able to produce reasonable prediction intervals in the sense that the percentage of testing data covered by 95% prediction intervals was close to the associated confidence level,95%.More importantly,the prediction interval evaluated by the MARS method had a non-constant width that appropriately reflected the data density and geological complexity.

Modeling of unconfined compressive strength of soil-RAP blend stabilized with Portland cement using multivariate adaptive regression spline

The recycled layer in full-depth reclamation (FDR) method is a mixture of coarse aggregates and reclaimed asphalt pavement (RAP) which is stabilized by a stabilizer agent. For design and quality control of the final product in FDR method, the unconfined compressive strength of stabilized material should be known. This paper aims to develop a mathematical model for predicting the unconfined compressive strength (UCS) of soil-RAP blend stabilized with Portland cement based on multivariate adaptive regression spline (MARS). To this end, two different aggregate materials were mixed with different percentages of RAP and then stabilized by different percentages of Portland cement. For training and testing of MARS model, total of 64 experimental UCS data were employed. Predictors or independent variables in the developed model are percentage of RAP, percentage of cement, optimum moisture content, percent passing of #200 sieve, and curing time. The results demonstrate that MARS has a great ability for prediction of the UCS in case of soil-RAP blend stabilized with Portland cement (R2 is more than 0.97). Sensitivity analysis of the proposed model showed that the cement, optimum moisture content, and percent passing of #200 sieve are the most influential parameters on the UCS of FDR layer.

基于MARS的语音清晰度客观评价

提出了基于多元自适应回归样条法(Multivariate adaptive regression spline,MARS)的语音清晰度客观评价方法。该方法提取语音信号的Mel倒谱系数作为评估语音清晰度的候选特征参数。在Mel倒谱系数的失真距离基础上,利用MARS方法选出对语音清晰度影响较大的特征参数,并结合主观DRT分建立最佳客观预测模型,实现特征参数失真距离到客观DR∧T分的映射。仿真结果表明,分别采用训练集合样本和测试集合样本进行测试时,使用该方法评价的客观DR∧T分与主观DRT分的相关度,分别达到0.958和0.9102。

基于MARS模拟鄱阳湖地区参考作物蒸散量

为了寻找最适宜的鄱阳湖作物蒸散量替代计算方法,文中以FAO Penman-Monteith模型参考作物蒸散量计算结果(ET0)为标准值,使用江西省南昌站1966—2015年逐日最高温度、最低温度、日照时数、风速和相对湿度数据(其中1966—1990年数据用于建立模型,1991—2015年数据用于验证模型),建立12种不同气象要素组合条件下的多元自适应回归样条(MARS)ET0计算模型,并将计算结果与广义回归神经网络(GRNN)、支持向量机(SVM)和经验模型(Hargreaves法、Irmak-Allen法、Makkink法、Pristley-Taylor法)的计算结果相比较.结果表明:3种人工智能算法的ET0计算结果精度均优于相同输入数据下的经验模型.3种人工智能算法中MARS的精度最高,在全参数组合下RMSE为0.227mm/d,R^2为0.982,NRMSE为0.086,其次是支持向量机,其在全参数组合下RMSE为0.266mm/d,R^2为0.978,NRMSE为0.101,GRNN排第三,其在全参数组合下RMSE为0.323mm/d,R^2为0.962,NRMSE为0.123.缺少温度参数时,模型精度总体较差,3种人工智能算法下R^2仅为0.800左右.MARS法不但精度更高,而且具有明确的数学表达式,是鄱阳湖地区适宜的ET0计算方法.

基于LZW算法和贝叶斯MARS的入侵检测研究

提出了一种基于LZW算法的入侵检测算法。使用系统调用序列作为特征数据,采用LZW算法对系统调用序列数据进行变长短序列划分,同时对短序列进行压缩,并在应用的过程中对LZW算法进行适当调整以适应序列的划分。通过贝叶斯多元自适应回归样条(贝叶斯MARS)模型,对正常和异常序列进行分类并标识入侵。实验结果表明,基于LZW变长序列划分方法符合系统调用序列的内在规律,在较高压缩比的情况下,获得了很好的检测性能。LZW算法与贝叶斯MARS相结合的入侵检测算法,对各种数据表现稳定,具有一定可行性和实用性。

基于K/N系统和MARS算法的长区段路基边坡稳定可靠性评价

针对路基边坡土体空间变异导致有限宽度失稳的特征,将路基长边坡划分为彼此相邻的独立单元;运用适应高维非线性的MARS算法,基于少量代表性边坡样本,建立单元边坡几何、材料参数与可靠指标β的显性表达式;采用可接受部分单元边坡失稳的K/N(F)系统模型,开展长区段路基边坡系统安全性的概率评价.结果表明:长区段路基边坡沿线路纵向的潜在失稳长度主要受土性水平相关距离影响,路基边坡系统宜按50 m进行单元划分;基于MARS算法的预测方程可实现众多单元边坡β的高效计算,验证误差不超过±10%;路基边坡系统失效的发生概率随单元失稳个数增加而快速降低,研究区段内路基单元长度取50 m时,边坡累积失稳个数占比大于0.149%(即4个)的发生概率不大于3%,为偶然事件.

基于模糊MARS的入侵检测系统

多元自适应样条回归是一种有效的针对高维数据回归建模方法,将该算法应用于入侵检测系统,根据入侵检测中存在的噪声数据和异常数据问题,提出了基于模糊算法的多元自适应样条回归方法。通过基于KDD1999数据集的训练和测试,与SVM在数据集上的测试结果进行对比,得出结论:该算法在入侵检测应用方面优于SVM算法。

多疾病共同危险因素挖掘与MARS预测模型研究

针对高血压和高血脂危险因素的相关性,集成多种数据挖掘模型分析获得两种疾病的共同危险因素,使用多元自适应回归样条(MARS)的方法建立高血压和高血脂疾病的预测模型。通过与BP神经网络预测方法相比较,表明多元自适应回归样条方法能够很好地反映疾病的危险因素与患病的关系,具有更高的稳定性,是很好的建立预测多种疾病模型的方法。

基于黄金分割法的加速MARS研究

多元自适应回归样条法(Multivariate adaptive regression spline,MARS)是一种专门针对高维数据拟合的回归方法。该方法以样条函数的张量积作为基函数,以样本数据坐标作为可选的节点矢量值,算法过程以失拟度(Lack of fit,LOF)最小为目标优化选择基函数和节点矢量。提出了基于黄金分割的加速MARS算法,引入一维黄金分割搜索算法及计算子区间概念,以提高算法节点矢量和基函数的优化选择效率。最后,四个典型的测试算例验证了所提出的方法在保证模型近似精度的前提下可大幅节省模型构造时间。

基于MARS的电池荷电状态估计

将多元自适应回归样条估算方法应用于大容量磷酸铁锂电池组的SOC估计,将电压、电流和温度共同作为输入变量。对实验所得数据进行标准化处理,将处理后的数据进行训练,得到SOC估计的精简数学模型,并对模型进行了验证。仿真实验结果表明该方法可以提高SOC估算精度。

基于MARS的卷烟吸阻和通风预测模型

通过对卷烟吸阻、通风率的原理分析找出相关的影响因子,结合大量丰富的不同规格和原辅料特性的卷烟数据,利用多元自适应回归样条(MARS)方法建立了卷烟吸阻、通风预测模型。结果表明,吸阻预测模型的标准化均方误差为0.276,绝对误差平均值为37.5Pa;纸通风预测模型的标准化均方误差为0.184,绝对误差平均值为0.91%;滤嘴通风预测模型的标准化均方误差为0.044,绝对误差平均值为1.27%,模型预测效果较好。