تجزیه و تحلیل حساسیت، واسنجی و اعتبارسنجی از مدل تورفتگی برف

Quantification of the mechanical behavior of snow in response to loading is of importance in vehicle-terrain interaction studies. Snow, like other engineering materials, may be studied using indentation tests. However, unlike engineered materials with targeted and repeatable material properties, snow is a naturally-occurring, heterogeneous material whose mechanical properties display a statistical distribution. This study accounts for the statistical nature of snow behavior that is calculated from the pressure-sinkage curves from indentation tests. Recent developments in the field of statistics were used in conjunction with experimental results to calibrate, validate, and study the sensitivity of the plasticity-based snow indentation model. It was found that for material properties, in the semi-infinite zone of indentation, the cohesion has the largest influence on indentation pressure, followed by one of the the hardening coefficients. In the finite depth zone, the friction angle has the largest influence on the indentation pressure. A Bayesian metamodel was developed, and model parameters were calibrated by maximizing a Gaussian likelihood function. The calibrated model was validated using three local and global confidence-interval based metrics with good results.

A key component in the modeling of vehicle-terrain interactions for soils and snow [1], [2] and [3] is the pressure-sinkage relationship of terrain material obtained using indentation testing. Naturally occurring terrain materials have been categorized as random heterogeneous materials [4] such that their properties should be treated statistically. Recent efforts in statistical modeling of vehicle-snow interaction include the interval analysis approach in [5], a metamodeling approach in [6], and a polynomial chaos approach in [7]. The pressure-sinkage relationship used in these efforts were, however, empirically-based. Recently, a snow indentation model in [8] was developed based on plasticity theory such that pressure-sinkage curves have a physical basis, which gives an improvement over the empirical nature of previous research work. The model uses only a few fundamental material properties such as the cohesion, friction angle and hardening parameters. However, due to limited test data, the material properties of the model were assumed in an ad hoc fashion without consideration of the statistical variations of the pressure-sinkage curves of natural snow. Estimating parameters of a physical model against test data is a statistical process that is usually difficult since it belongs to the class of inverse problems. Indeed, estimating mechanical properties from indentation tests for engineering materials in general poses as an inverse problem. Parameter estimation is also called calibration and is intimately related to the validation of the model. Validation of engineering and scientific models has drawn much attention from academia and industry in recent years resulting in common terminology (e.g., [9]) for validation and related statistical frameworks [10] and [11]. One accepted definition of validation is ‘the process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model’ [9]. Characterization of uncertainties of model and data is an integral part of the validation process. Toward this end, advancement of flexible and reasonably rigorous statistical frameworks such as [10] and [11] has been made to address the issues of sensitivity, calibration of parameters and validation of models including many applications to road-load interaction in automotive engineering [11], [12] and [13]. In addition, quantitative validation metrics have been an active research area that provide a more rigorous statistical assessment of the agreement between test results and model predictions [14]. Although headway has been made in the statistical modeling of vehicle-snow interaction, no statistically rigorous efforts have been made to validate the various models developed recently. This paper applies recent results in the field of statistics, to study the sensitivity of the snow indentation model, to calibrate fundamental material properties of the model using newly obtained experimental results, and to validate the model using calibrated material properties and several validation metrics. The paper is organized as follows. Section 2 discusses background in the snow indentation model, statistical methodology in global sensitivity analysis, Bayesian metamodel, calibration, and confidence-interval based validation metrics. Section 3 presents new snow indentation tests. Section 4 discusses results, and Section 5 follows with discussion and conclusions.

In this paper, we used a few interrelated statistical methods to calibrate parameters of the snow indentation model, and infer statistically the pressure-sinkage relationship based on new test data with replications. The Bayesian metamodel is a key component of the methodology serving the following roles: (1) an efficient emulator of the physical model for the calibration, prediction and validation of the model, and (2) as a non-intrusive stochastic model of the physical model such that statistical inference can be made. Global sensitivity analysis was conducted rigorously and efficiently for several purposes: (1) to gain physical insight of the influence of the multidimensional parameters to model output, (2) to select only influential parameters for calibration which utilizes the Bayesian metamodel, (3) to avoid the possibility of getting physically unreasonable results for the calibration process [13]. The results presented here are from the slightly-modified indentation model, as a consequence of applying the statistical methodology during the design of experiment stage, and before the validation metrics were applied, demonstrating another aspect of the usefulness of the methodology employed. In summary, our results indicated that, in terms of material properties, pd, c2 influence significantly the pressure-sinkage relationship for zone II (semi-infinite hardening), whereas β has the most important contribution for zone III (finite-depth). The three interval-based validation metrics used indicated that the calibrated model is quite adequate for the two snows used in the paper.