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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (10): 1470-1476, 1519.  DOI: 10.11908/j.issn.0253-374x.2019.10.012 0

### 引用本文

CHEN Zhang, LIANG Yuanlu, SUN Lijun. Effect of Vibration Timeliness on Road Riding Quality Evaluation[J]. Journal of Tongji University (Natural Science), 2019, 47(10): 1470-1476, 1519. DOI: 10.11908/j.issn.0253-374x.2019.10.012

### 文章历史

Effect of Vibration Timeliness on Road Riding Quality Evaluation
CHEN Zhang , LIANG Yuanlu , SUN Lijun
Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai 201804, China
Abstract: The many-to-one situation that each vibration moment corresponded to the scoring moment for a time lag was transformed to a one-to-one situation that each vibration process had only one representative time lag. The effect of the time lag on subjective scorings was tested and regressed. A fractional order calculus was then introduced to capture the effect of vibration history and the order that gave the best prediction precision for subjective scorings was chosen as the best order. Test results revealed that a short time lag does not influence the subjective scorings, while a longer time lag can have a significant effect. A structural behavior function was then adopted to arrive at a better description of the relationship between the time lags and the subjective scorings. If 0.7 and 0.3 order integration are used for the frequency weighted principle acceleration and angular velocity respectively, an 11.9% improvement can be achieved in the precision error. It reflects that humans are sensitive to cumulative vibration.
Key words: road riding quality    subjective scoring    time lag    historical process

1 数据采集系统 1.1 需要采集的数据

1.2 主观评分标尺定义

 图 1 评分标尺 Fig.1 Rating scale
1.3 系统布设方案

 图 2 坐标系、传感器与人员的设置 Fig.2 Setting of coordinate system, sensors and crew
2 时滞对评分结果的影响 2.1 代表时滞的定义

 ${\alpha _{{\rm{VDV}}, i}} = {\left( {\int_0^T {Y_i^4} (t){\rm{d}}t} \right)^{\frac{1}{4}}}$ (1)

2.2 代表时滞对评分结果的影响显著性检验

 图 3 试验环道中的沥青路面局部异常凸起 Fig.3 Abrupt bulge in the test loop road

 图 4 环道试验评分结果箱线图 Fig.4 Boxplot of the rating results

2.3 不同刺激下代表时滞对评分结果影响的量化

 图 5 新增加的两类不同刺激 Fig.5 Newly added two types of road stimuli
 图 6 三条试验路上的z轴加速度时间历程曲线 Fig.6 z axis acceleration history of three test roads
 图 7 三条试验路上的主观评分结果与代表时滞关系散点图 Fig.7 Scatter plot of subjective scorings to rep-resentative time lags of three test roads

2.4 将代表时滞对人体主观感受的影响考虑到物理量中

 $R \propto B\log \frac{A}{{{A_0}}}$ (2)

 $R \propto B\log \left( {1 + \left| A \right|} \right)$ (3)

 ${\mathop{\rm sgn}} \left( A \right)\left( {{{\left( {1 + \left| A \right|} \right)}^y} - 1} \right)$ (4)

3 历史振动过程对人的影响

Wikström等[21]的研究表明，人连续经历两个同样的路面刺激，第二个刺激会被评价为更不舒适，相较于它被放在第一个位置的时候.因此，人对振动的历史过程可能是敏感的，需要对其进行量化考虑，以增加客观评价指标与主观评分之间的一致性.对历史过程进行描述，可以考虑使用分数阶微积分，对于离散系统，可以使用最直接的Grünwald-Letnikov型分数阶微积分[22]，如下所示：

 $\begin{array}{*{20}{c}} {\mathop {{\mathop{\rm GL}\nolimits} }\limits_l D_u^kf(t) = \mathop {\lim }\limits_{h \to 0} \frac{1}{{{h^k}}}\sum\limits_{j = 0}^{(l - u)/h} {{{( - 1)}^j}} \left( {\begin{array}{*{20}{l}} k\\ j \end{array}} \right)f(t - jh) \cong }\\ {\frac{1}{{{h^k}}}\sum\limits_{j = 0}^{(l - u)/h} {w_j^k} f(t - jh)} \end{array}$ (5)

 $w_{0}^{k}=1, w_{j}^{k}=\left(1-\frac{k+1}{j}\right) w_{j-1}^{k}, j=1, 2, \cdots$ (6)

 图 8 新增试验场景 Fig.8 Newly added testing scenarios

 $\begin{array}{l} Y_i^k(t) = \mathop l\limits^{{\rm{GL}}} D_u^k\left( {\sum\limits_m {\left( {{\beta _{{\rm{IMF}}, m}}({\mathop{\rm sgn}} (A(t)))(1 + } \right.} } \right.\\ \;\;\;\;\;\;\;\;\;\;\;\left. {\left. {\left. {|A(t){|^y} - 1} \right)} \right){w_i}\left( {{f_m}(t)} \right)} \right) \end{array}$ (7)
 图 9 模型预测精度分布 Fig.9 Distribution of model precisions

4 结语