Multivariate Adaptive Regression Research Articles

Radial basis functions with a priori bias as surrogate models:A comparative study

Radial basis functions are augmented with a posteriori bias in order to perform robustly when used as metamodels. Recently, it has been proposed that the bias can simply be set a priori by using the normal equation, i.e., the bias becomes the corresponding regression model. In this study, we demonstrate the performance of the suggested approach (RBFpri) with four other well-known metamodeling methods; Kriging, support vector regression, neural network and multivariate adaptive regression. The performance of the five methods is investigated by a comparative study, using 19 mathematical test functions, with five different degrees of dimensionality and sampling size for each function. The performance is evaluated by root mean squared error representing the accuracy, rank error representing the suitability of metamodels when coupled with evolutionary optimization algorithms, training time representing the efficiency and variation of root mean squared error representing the robustness. Furthermore, a rigorous statistical analysis of performance metrics is performed. The results show that the proposed radial basis function with a priori bias achieved the best performance in most of the experiments in terms of all three metrics. When considering the statistical analysis results, the proposed approach again behaved the best, while Kriging was relatively as accurate and support vector regression was almost as fast as RBFpri. The proposed RBF is proven to be the most suitable method in predicting the ranking among pairs of solutions utilized in evolutionary algorithms. Finally, the comparison study is carried out on a real-world engineering optimization problem.

A performance comparison between the subjective workload analysis technique and the NASA-TLX in a healthcare setting

ABSTRACTIn recent years, healthcare organizations in the United States have been looking for methods to improve the efficiency of their processes and use of human resources. Many organizations have adapted tools and concepts to understand and evaluate nurses' performance and workload. Workload is defined as a dynamic balance between task demands and the individual's response. Two notable perceptual workload measuring tools, the NASA Task Load Index (NASA-TLX) and Subjective Workload Analysis Technique (SWAT), were used to assess workload of nurses at an infusion area of a cancer clinic. The objective was to compare the performance of both tools in this setting. Given that both tools were developed under different constructs, this research also explored nonlinear relationships between the dimensions of NASA-TLX with respect to the total score of SWAT and vice versa. Multi Adaptive Regression Spines (MARS) was used for nonparametric and nonlinear regression analysis method. The results show that, for this setting, NASA-TLX can be used to predict the result of the C-SWAT; however, the reverse is not true. The results show that C-SWAT fails to include the dimensions of performance and frustration. This research will improve the process of selecting an appropriate workload measuring tool in healthcare settings.

Soft computing-based slope stability assessment: A comparative study

Analysis of slope stability failures, as one of the complex natural hazards, is one of the important research issues in the field of civil engineering. Present paper adopts and investigates four soft computing-based techniques for this problem: Patient Rule-Induction Method (PRIM), M5\' algorithm, Group Method of data Handling (GMDH) and Multivariate Adaptive Regression Splines (MARS). A comprehensive database consisting of 168 case histories is used to calibrate and test the developed models. Six predictive variables including slope height, slope angle, bulk density, cohesion, angle of internal friction, and pore water pressure ratio were considered to generate new models. The results of test studies are used for feasibility, effectiveness and practicality comparison of techniques with each other, and with the other available well-known methods in the literature. Results show that all methods not only are feasible but also result in better performance than previously developed soft computing based predictive models and tools. It is shown that M5\' and PRIM algorithms are the most effective and practical prediction models.

A multivariate adaptive regression splines model for estimation of maximum wall deflections induced by braced excavation

With rapid economic growth, numerous deep excavation projects for high-rise buildings and subway transportation networks have been constructed in the past two decades. Deep excavations particularly in thick deposits of soft clay may cause excessive ground movements and thus result in potential damage to adjacent buildings and supporting utilities. Extensive plane strain finite element analyses considering small strain effect have been carried out to examine the wall deflections for excavations in soft clay deposits supported by diaphragm walls and bracings. The excavation geometrical parameters, soil strength and stiffness properties, soil unit weight, the strut stiffness and wall stiffness were varied to study the wall deflection behaviour. Based on these results, a multivariate adaptive regression splines model was developed for estimating the maximum wall deflection. Parametric analyses were also performed to investigate the influence of the various design variables on wall deflections.

Static crushing of aluminium tubes filled with PET foam and a GFRP skeleton. Numerical modelling and multiobjective optimization

This investigation focuses on the multiobjective optimization of a crash box subjected to static loading by using a validated numerical model and an analytical approach. The crash box is made with a unique combination of three materials: an aluminium tube filled with polyethylene terephthalate (PET) foam and a glass-fibre reinforced polymer (GFRP) skeleton. A finite element model was calibrated based on the results obtained in a material testing campaign using appropriate constitutive equations. A J2–plasticity model was used for the material behaviour of the aluminium alloy, and the PET foam was modelled using Deshpande and Fleck’s model. Regarding the short-fibres GFRP, a Voce plasticity model was fitted to the experimental data. After a successful validation of the finite element model, the filled aluminium tube was subjected to a structural optimization to achieve the best crash performance. Three relevant design variables were selected: the thickness of the outer aluminium cylinder, the thickness of the GFRP and the density of the PET foam, the last being related to the crushing strength of the foam. Given the high computational cost of each finite element model, a multi-adaptive regression splines metamodel was fitted to a large-scale sampling. Optimum pairs were obtained for the absorbed energy, the specific energy absorption, the peak load and the mass of the component; stating the relative contribution of each design variable to the crashworthiness of the crash box and enabling the choice of a balanced optimum design. A semi-empirical model based on Hanssen’s interaction formula was calibrated with the data from a validated finite element model. This analytical model was able to reproduce the behaviour of the component over the design region selected for the optimization, and was also used for its optimization with satisfactory results.

Assessment of Machine Learning Approaches for Bathymetry Mapping in Shallow Water Environments using Multispectral Satellite Images

This paper evaluates the performance of two proposed empirical approaches—random forest (RF) and multi-adaptive regression spline (MARS)—for bathymetry calculations in three diverse areas: the Alexandria harbor shallow coastal area, Egypt, as an example of a low-turbidity, silt-sand bottom water area with depths ranging from 4 m to 10.5 m; the Lake Nubia entrance zone, Sudan, which is considered a high-turbidity, unstable, clay bottom area with a depth of 6 m; and Shiraho, Ishigaki Island, Japan, a coral reef area with a depth of 14 m. Data from Landsat 8 and Spot 6 satellite images were used to evaluate the performance of the proposed models. The bathymetry results of the proposed models were compared with the corresponding results yielded from two conventional empirical methods: the neural network (NN) model and the Lyzenga generalized linear model (GLM). When compared with echo sounder data, the RF and MARS results outperformed Lyzenga GLM results. Moreover, the RF method produced more accurate results with average 0.25 m RMSE improvements range than the NN model. The RF algorithm produced the most accurate results proved to be a preferable algorithm for bathymetry mapping in the shallow water context.

Design of explicit models for estimating efficiency characteristics of microbial fuel cells

Recent years have seen the use of microbial fuel cells for the generation of electricity from wastewater and renewable biomass. The efficiency characteristics (power density and voltage output) of fuel cells depend highly on their operating conditions such as current density, chemical oxygen demand concentration and anolyte concentration. Computational intelligence methods based on genetic programming and multi-adaptive regression splines are proposed in design of explicit models for estimating efficiency characteristics of microfluidic microbial fuel cells based on the operating conditions. Performance of the models evaluated against the actual data reveals that the models formulated from genetic programming outperform the multi-adaptive regression splines models. The robustness in the best models is validated by performing simulation of the models over 8000 runs based on the normal distribution of the operating conditions. 2-D and 3-D surface analysis conducted on the models reveals that the power density of the fuel cell increases with an increase in values of chemical oxygen demand concentration and current density till a certain value and then decreases. The voltage output decreases with an increase in values of current density while increases with an increase in values of chemical oxygen demand concentration to a certain limit.

Estimating future cyanobacterial occurrence and importance in lakes: a case study with Planktothrix rubescens in Lake Geneva

Among the multiple forms of freshwater pelagic cyanobacteria, the phycoerythrin-rich species Planktothrix rubescens is well adapted to temperate, deep and large lakes. In Lake Geneva, this filamentous and microcystin-producing species has been the dominant cyanobacterial species observed since the early years of this century. In addition to the trophic state (e.g., the phosphorus level), the influences of air and water temperature on the occurrence and development of cyanobacteria are particularly relevant in the context of global climate change. The latter may indeed be particularly marked for lakes in the Alpine region, with a rate of warming that may be twice as large as the global average. The impact of climate change on P. rubescens is thus an important challenge and it has been analysed in this study through two different approaches: (1) the extreme air temperature events as a proxy for future climate and (2) the multi adaptive regression splines (MARS) model to predict future P. rubescens biomass. These methods allowed us to determine whether Lake Geneva will still sustain an important biomass of P. rubescens in forthcoming years, provided there is no severe over-enrichment with nutrients in the future. The outcomes strongly suggest that the fraction of cyanobacterium could increase with respect to the total phytoplankton community by as much as 34 % by the end of this century and induce a significant change in the microalgal composition. Additionally, the results point to the fact that spring is a key period during which air temperature and nutrients become the determinant factors for outbreaks of this species in the subsequent seasons.

Computational model for predicting the effect of process parameters on surface characteristics of mass finished components

Purpose Mass finishing is a commonly employed surface finishing process for improving surface characteristics of aerospace engineering components. Optimization of surface characteristics of such critical components require an explicit computational model that can describe the surface characteristics of the finished component. This paper aims to develop an explicit computational model that can describe the surface roughness as a function of various process parameters which influence the mass finishing process. Design/methodology/approach In the present work, the authors propose to study the roughness characteristics using a combined evolutionary computing approach based on Multi-Adaptive Regression Splines (MARS) and Genetic Programming (GP) techniques. Findings The authors conducted sensitivity and parametric analysis to capture the dynamics of surface characteristics by unveiling dominant input variables and hidden non-linear relationships. It is found that by regulating the process time and media size, a greatest variation in surface finish reduction can be achieved in mass finishing process. Originality/value To the best of authors knowledge, for the first time a hybrid evolutionary computational technique has been proposed in this work. The authors combined two powerful evolutionary techniques, namely Multi-variate Adaptive Regressive Splines and Genetic Programming approach. The proposed approach was able to capture the dynamics of surface roughness with higher accuracy as comparable to that of the experiments.

Power consumption and tool life models for the production process

For achieving the multi-objective optimization of product quality and power consumption of any production process, the formulation of generalized models is essential. Extensive research has been done on applying the traditional statistical methods (analysis of variance, response surface methodology, grey relational analysis, Taguchi method) in formulation of these models for the processes. In the present work, a detailed survey on the applications of these methods in modelling of power consumption for the production operations specifically machining is conducted. Critical issues arising from the survey are highlighted and hence form the motivation of this study. Further, three advanced soft computing methods, namely evolutionary-based genetic programming (GP), support vector regression, and multi-adaptive regression splines are proposed in predictive modelling of tool life and power consumption of a turning phenomenon in machining. Statistical comparison based on the five error metrics and hypothesis tests for the goodness of the fit reveals that the GP model outperforms the other two models. The hidden relationships between the process parameters are unveiled from the formulated models. It is found that the cutting speed parameter is the most influential input for power consumption and tool life in the turning phenomenon. The future scope comprising of the challenges in predictive modelling of production processes is highlighted in the end.

Multivariate adaptive regression splines based prediction of peak expiratory flow with spirometric data.

Spirometry evaluates the integrated function of lung capacity and chest wall mechanics measuring the total volume of air forcefully exhaled from a fully inflated lung. This non-invasive, informative technique for characterizing pulmonary function has an important role in clinical trials to narrow the differential diagnosis of subjects being assessed for pulmonary disorders. The test however requires patient co-operation and sometimes sub maximal effort affects the results potentially thereby leading to incomplete test and misdiagnosis. The aim of this work is to develop a prediction model based on Multivariate adaptive regression splines (MARS) technique to estimate the spirometric parameter Peak Expiratory Flow (PEF) volume. In the present study, flow-volume data from N = 220 subjects are considered. Model performances are evaluated statistically with coefficient of determination (R2) and Root Mean Squared Error (RMSE). The significant spirometric features captured in the model were FEV1, FEF50, FEF25 and the demographic parameter weight. Bland-Altman plots for the estimated PEF values showed a minimal bias. The MARS model successfully adopted the important features for prediction of PEF parameter with overall good fit and these findings can assist clinicians with enhanced spirometric investigations on respiratory disorders.

Development of energy consumption model of abrasive machining process by a combined evolutionary computing approach

Abrasive machining is employed for improving surface characteristics of components used in oil and gas applications. Optimization of power consumed in abrasive machining process is vital from environmental standpoint that requires the formulation of the generalized and an explicit mathematical model. In the present work, we propose to study the power consumption in abrasive machining process using a combined evolutionary computing approach based on Multi-Adaptive Regression Splines (MARS) and Genetic Programming (GP) techniques. Sensitivity and parametric analysis have also been conducted to capture the dynamics of process by unveiling dominant input variables and hidden non-linear relationships. It is concluded that selection of optimal machining time and abrasive is necessary for achieving better environmental performance of abrasive machining process.

A multi-objective reliability-based optimization of the crashworthiness of a metallic-GFRP impact absorber using hybrid approximations

In the field of automotive safety, the lightweight design of crash absorbers is an important research topic with a direct effect on the occupant safety levels. The design of these absorbers usually requires an optimization of their crashworthiness, which can include multi-objective and reliability-based optimization techniques. This process is very time-consuming, and in spite of the continuous growing of computational power, the problem needs a reliable solving scheme. The use of surrogate models and parallel computing are suitable alternatives to deal with this issue. However, the strongly non-linear response functions obtained from the finite element simulations need careful treatment. This work contributes with the application of a surrogate-based reliability-based design optimization method to an original design of a crash absorber made of metal and a glass-fiber reinforced polymer which is subjected to a frontal impact. Multi-adaptive regression splines models are employed to emulate the original responses, and three different approaches in the sampling stage of the method are compared. The absorbed energy and the mass of the element are considered as objective functions, while the peak value of the force transmitted to the occupants of the vehicle is the design constraint. A discussion of the employed materials is presented and the proposed approaches are compared. Finally, several Pareto fronts are obtained as a solution to the probabilistic problem. Results show that a combination of aluminum and glass fiber reinforced polymer is optimum for this problem, and some design rules are offered.

Application of the Multi-Adaptive Regression Splines to Integrate Sea Level Data from Altimetry and Tide Gauges for Monitoring Extreme Sea Level Events

This article determines sea level fields with nonlinear components along the northern coast of Australia using a state-of-the-art approach of the Multi-Adaptive Regression Splines (MARS). The 20 years of data from multi-missions of satellite altimetry (e.g., Topex, Jason-1, Jason-2) and 14 tide gauges are combined to provide a consistent view of sea levels. The MARS is chosen because it is capable of dividing measured sea levels into distinct time intervals where different linear relationships can be identified, and of weighting individual tide gauge according to the importance of their contributions to predicted sea levels. In the study area, the mean R-squared (R2) of 0.62 and Root Mean Squared (RMS) error of 6.73 cm are obtained from modelling sea levels by MARS. The comparison of the MARS with the multiple-regression shows an improved sea level prediction, as MARS can explain 62% of sea level variance while multiple-regression only accounts for 44% of variance. The predicted sea levels during six tropical cyclones are validated against sea level observations at three independent tide-gauge sites. The comparison results show a strong correlation (˜99%) between modelled and observed sea levels, suggesting that the MARS can be used for efficiently monitoring sea level extremes.

Spatial variability of rock depth using adaptive neuro-fuzzy inference system (ANFIS) and multivariate adaptive regression spline (MARS)

This article adopts adaptive neuro-fuzzy inference system (ANFIS) and multi adaptive regression spline (MARS) for prediction of spatial variability of reduced level of rock depth (d) in Bangalore. The database consists of 652 d values spread over a 220 km2 area of Bangalore. In two-dimensional analysis, the function \(d = f (x_{\text{1}} ,x_{\text{2}} )\), where x1, and x2 are the latitude and longitude of a point corresponding to d value, is to be approximated with which d value at any half space point in Bangalore can be determined. The input variables of ANFIS and MARS are x1 and x2. Map of d has been also produced by developed ANFIS and MARS models. The comparison between the MARS and ANFIS models demonstrates that the MARS model is superior to the ANFIS model.

Fine-scale selection of nesting habitat in Little Crake Porzana parva and Water Rail Rallus aquaticus in small ponds

Capsule The most important factor determining fine-scale selection of nesting habitat in Little Crake and Water Rail is water depth.Aims To evaluate factors affecting nest-site selection and relative inter-specific differences in two poorly studied Rallidae species, the Little Crake and Water Rail.Methods Habitat variables describing water depth, water cover, as well as vegetation type and structure were measured within 3-m radius plots around birds' nests and random points, located in small ponds scattered within a largely cultivated landscape in north-eastern Poland. Descriptive statistics and multi-adaptive regression splines were used to describe nesting habitat and to model nest-site selection in the study species.Results Little Crake nested in sites with deeper water and lower percentage of vegetation cover than Water Rail. Both species chose nest sites according to water depth (probability of Little Crake nests occurrence was the highest around 40 cm and of Water Rail below 12 cm) and vegetation stage in which nests were build (old vegetation was preferred). Little Crake nests were also associated with vegetation height lower than 1.5 m and high percentage cover of old vegetation within a 3-m radius around nests, whereas Water Rail preferred Carex spp. and Juncus effusus for nesting.Conclusion For both species, water depth was the main driver of nest-site selection, followed by vegetation traits. Water depth was also the variable most important in discriminating between the nesting sites of the two species. The different patterns of habitat selection showed by the two species are likely to be due to different morphology and nest characteristics, and are probably driven by the need to maximize both nest and adult safety.

Relationship between acid-base status and inflammation in the critically ill.

IntroductionThere is a complex interplay between changes in acid–base components and inflammation. This manuscript aims to explore associations between plasma cytokines and chemokines and acid–base status on admission to intensive care.MethodsWe conducted a prospective cohort study in a 13-bed ICU in a tertiary-care center in Brazil. 87 unselected patients admitted to the ICU during a 2-year period were included. We measured multiple inflammatory mediators in plasma using multiplex assays and evaluated the association between mediator concentrations and acid–base variables using a variety of statistical modeling approaches, including generalized linear models, multiadaptive regression splines and principal component analysis.ResultsWe found a positive association between strong ion gap (SIG) and plasma concentrations of interleukin (IL)6, 8, 10 and tumor necrosis factor (TNF); whereas albumin was negatively associated with IL6, IL7, IL8, IL10, TNF and interferon (IFN)α. Apparent strong ion difference (SIDa) was negatively associated with IL10 and IL17. A principal component analysis including SAPS 3 indicated that the association between acid–base components and inflammatory status was largely independent of illness severity, with both increased SIG and decreased SIDa (both drivers of acidosis) associated with increased inflammation.ConclusionAcid–base variables (especially increased SIG, decreased albumin and decreased SIDa) on admission to ICU are associated with immunological activation. These findings should encourage new research into the effects of acid–base status on inflammation.

Comparison of Machine Learning Regression Methods to Simulate NO<sub>3</sub> Flux in Soil Solution under Potato Crops

Nitrate (NO3) leaching is a major issue in sandy soils intensively cropped to potato. Modelling could test the effect of management practices on nitrate leaching, particularly with regard to optimal N application rates. The NO3 concentration in the soil solution is well known for its local heterogeneity and hence represents a major challenge for modeling. The objective of this 2-year-study was to evaluate machine learning regression methods to simulate seasonal NO3 concentration dynamics in suction lysimeters in potato plots receiving different N application rates. Four machine learning function approximation methods were compared: multiple linear regressions, multivariate adaptive regression splines, multiple-layer perceptrons, and least squares support vector machines. Input candidates were chosen for known relationships with NO3 concentration. The best regression model was obtained with a 6-inputs least squares support vector machine combining cumulative rainfall, cumulative temperature, day of the year, N fertilisation rate, soil texture, and depth.

Habitat preferences of the threatened Black-eared Wheatear Oenanthe hispanica in southern Italy

Capsule We analysed habitat preferences of Black-eared Wheatear Oenanthe hispanica of the eastern subspecies (O. hispanica melanoleuca) in South Italy, considering 1-ha (coinciding with territory size) square plots (49 occupied and 49 unoccupied). We used multi-adaptive regression splines to model habitat preferences. Black-eared Wheatear occurrence was positively associated with three factors: aspect (a SE orientation was preferred), cover of grazed grassland and cover of bare ground. Species conservation should be based on the maintenance of grazed grasslands, especially on SE-facing slopes, and including at least 2500 m2 of bare ground per ha.

Forecasting fish distribution along stream networks: brown trout (Salmo trutta) in Europe

AbstractAimSpecies inhabiting fresh waters are severely affected by climate change and other anthropogenic stressors. Effective management and conservation plans require advances in the accuracy and reliability of species distribution forecasts. Here, we forecast distribution shifts of Salmo trutta based on environmental predictors and examine the effect of using different statistical techniques and varying geographical extents on the performance and extrapolation of the models obtained.LocationWatercourses of Ebro, Elbe and Danube river basins (c. 1,041,000 km2; Mediterranean and temperate climates, Europe).MethodsThe occurrence of S. trutta and variables of climate, land cover and stream topography were assigned to stream reaches. Data obtained were used to build correlative species distribution models (SDMs) and forecasts for future decades (2020s, 2050s and 2080s) under the A1b emissions scenario, using four statistical techniques (generalised linear models, generalised additive models, random forest, and multivariate adaptive regression).ResultsThe SDMs showed an excellent performance. Climate was a better predictor than stream topography, while land cover characteristics were not necessary to improve performance. Forecasts predict the distribution of S. trutta to become increasingly restricted over time. The geographical extent of data had a weak impact on model performance and gain/loss values, but better species response curves were generated using data from all three basins collectively. By 2080, 64% of the stream reaches sampled will be unsuitable habitats for S. trutta, with Elbe basin being the most affected, and virtually no new habitats will be gained in any basin.Main conclusionsMore reliable predictions are obtained when the geographical data used for modelling approximate the environmental range where the species is present. Future research incorporating both correlative and mechanistic approaches may increase robustness and accuracy of predictions.