Sensitivity and regression analysis of acoustic parameters for determining physical properties of frozen fine sand with ultrasonic test

(1) Three-factor analysis of variance (ANOVA) Orthogonal tests are an effective means of multi-factor analysis and lend themselves to assessing the impact of relevant factors (Li Y. et al., 2010; Liu Y.Q. et al., 2016). An orthogonal experiment consisting of nine groups—L9(34)—selected three physical properties of frozen fine sand (temperature, density and water content) as factors to study the sensitivity of three acoustic parameters (wave velocity, attenuation coefficient and dominant frequency) to the physical properties. The values of the factors used for the orthogonal test are given in Table 2. Position for Table 2 (2) Control variable test The control variable test included two types of experiment. One had 16 groups of different levels of water content (4.31, 7.31, 10.31 and 13.31%) at a single level of density (1.87g/cm3) to study the relationships between sensitive acoustic parameters and physical properties (water content and temperature). The other had 16 groups of different levels of density (1.87, 1.8, 1.76 and 1.73g/cm3) under a single level of water content (7.31%) to study the relationships between sensitive acoustic parameters and density. Each group was evaluated three times at four levels of temperature (–5, –10, –15 and –20°C), and the results are mean values of repeated tests.(1) 三因素方差分析（Analysis of Variance, ANOVA）与正交试验是多因素分析的有效手段，可用于评估相关因素的影响效应（Li Y.等，2010；Liu Y.Q.等，2016）。本研究采用含9组试验的L9(34)正交试验方案，以冻结细砂的三项物理特性——温度、密度与含水率——作为试验因素，探究三项声学参数（波速、衰减系数、主频）对该类物理特性的敏感性。正交试验各因素的取值详见表2，表2位置见标注。 (2) 控制变量试验：本控制变量试验包含两类试验：其一为固定密度为单水平（1.87g/cm³），设置16组不同含水率水平（4.31%、7.31%、10.31%、13.31%），以探究敏感声学参数与物理特性（含水率、温度）之间的关联；其二为固定含水率为单水平（7.31%），设置16组不同密度水平（1.87、1.8、1.76、1.73g/cm³），以探究敏感声学参数与密度之间的关联。每组均在4个温度水平（-5、-10、-15、-20℃）下重复测试3次，试验结果取重复测试的平均值。