In mathematics, space encompasses various structured sets such as Euclidean, metric, or vector space. This article introduces temporal space—a novel concept independent of traditional spatial dimensions and frames of...In mathematics, space encompasses various structured sets such as Euclidean, metric, or vector space. This article introduces temporal space—a novel concept independent of traditional spatial dimensions and frames of reference, accommodating multiple object-oriented durations in a dynamical system. The novelty of building temporal space using finite geometry is rooted in recent advancements in the theory of relationalism which utilizes Euclidean geometry, set theory, dimensional analysis, and a causal signal system. Multiple independent and co-existing cyclic durations are measurable as a network of finite one-dimensional timelines. The work aligns with Leibniz’s comments on relational measures of duration with the addition of using discrete cyclic relational events that define these finite temporal spaces, applicable to quantum and classical physics. Ancient formulas have symmetry along with divisional and subdivisional orders of operations that create discrete and ordered temporal geometric elements. Elements have cyclically conserved symmetry but unique cyclic dimensional quantities applicable for anchoring temporal equivalence relations in linear time. We present both fixed equivalences and expanded periods of temporal space offering a non-Greek calendar methodology consistent with ancient global timekeeping descriptions. Novel applications of Euclid’s division algorithm and Cantor’s pairing function introduce a novel paired function equation. The mathematical description of finite temporal space within relationalism theory offers an alternative discrete geometric methodology for examining ancient timekeeping with new hypotheses for Egyptian calendars.展开更多
为有效识别桥梁健康监测数据的异常,减少误预警、漏预警现象,保障桥梁监测数据的质量和有效性,针对大跨度斜拉桥长期监测数据的缺失、离群和漂移3类异常数据,提出基于时间序列压缩分割的监测数据异常识别算法。该算法将原始监测数据时...为有效识别桥梁健康监测数据的异常,减少误预警、漏预警现象,保障桥梁监测数据的质量和有效性,针对大跨度斜拉桥长期监测数据的缺失、离群和漂移3类异常数据,提出基于时间序列压缩分割的监测数据异常识别算法。该算法将原始监测数据时间序列通过基于序列重要点(Series Importance Point, SIP)的时间序列线性分段(Piecewise Linear Represent, PLR)算法(PLR_SIP)得到数条时间子序列;然后采用欧氏距离进行时间子序列的相似性分析,并基于改进的局部离群因子(Local Outlier Factor, LOF)算法计算每条时间子序列的局部离群因子;最后将其与设定的阈值相比较,从而识别出监测数据的异常。为验证该算法的准确性与工程实用性,对某公路大跨度斜拉桥健康监测数据进行异常识别。结果表明:采用PLR_SIP算法对原始时间序列压缩分割得到的时间子序列能够准确地反映原序列的变化趋势和范围;改进的LOF算法突破了传统LOF算法仅能识别离群值这类无持续时间异常的局限性,能够排除噪声的干扰,实现对离群、缺失和漂移3种异常的识别。该算法无需定义训练集,直接以原始监测数据作为算法的输入,同时能够自适应调整阈值参数,具有良好的可扩展性、实时性、准确性和高效性,适用于处理实时、大量的桥梁健康监测数据。展开更多
文摘In mathematics, space encompasses various structured sets such as Euclidean, metric, or vector space. This article introduces temporal space—a novel concept independent of traditional spatial dimensions and frames of reference, accommodating multiple object-oriented durations in a dynamical system. The novelty of building temporal space using finite geometry is rooted in recent advancements in the theory of relationalism which utilizes Euclidean geometry, set theory, dimensional analysis, and a causal signal system. Multiple independent and co-existing cyclic durations are measurable as a network of finite one-dimensional timelines. The work aligns with Leibniz’s comments on relational measures of duration with the addition of using discrete cyclic relational events that define these finite temporal spaces, applicable to quantum and classical physics. Ancient formulas have symmetry along with divisional and subdivisional orders of operations that create discrete and ordered temporal geometric elements. Elements have cyclically conserved symmetry but unique cyclic dimensional quantities applicable for anchoring temporal equivalence relations in linear time. We present both fixed equivalences and expanded periods of temporal space offering a non-Greek calendar methodology consistent with ancient global timekeeping descriptions. Novel applications of Euclid’s division algorithm and Cantor’s pairing function introduce a novel paired function equation. The mathematical description of finite temporal space within relationalism theory offers an alternative discrete geometric methodology for examining ancient timekeeping with new hypotheses for Egyptian calendars.
文摘为有效识别桥梁健康监测数据的异常,减少误预警、漏预警现象,保障桥梁监测数据的质量和有效性,针对大跨度斜拉桥长期监测数据的缺失、离群和漂移3类异常数据,提出基于时间序列压缩分割的监测数据异常识别算法。该算法将原始监测数据时间序列通过基于序列重要点(Series Importance Point, SIP)的时间序列线性分段(Piecewise Linear Represent, PLR)算法(PLR_SIP)得到数条时间子序列;然后采用欧氏距离进行时间子序列的相似性分析,并基于改进的局部离群因子(Local Outlier Factor, LOF)算法计算每条时间子序列的局部离群因子;最后将其与设定的阈值相比较,从而识别出监测数据的异常。为验证该算法的准确性与工程实用性,对某公路大跨度斜拉桥健康监测数据进行异常识别。结果表明:采用PLR_SIP算法对原始时间序列压缩分割得到的时间子序列能够准确地反映原序列的变化趋势和范围;改进的LOF算法突破了传统LOF算法仅能识别离群值这类无持续时间异常的局限性,能够排除噪声的干扰,实现对离群、缺失和漂移3种异常的识别。该算法无需定义训练集,直接以原始监测数据作为算法的输入,同时能够自适应调整阈值参数,具有良好的可扩展性、实时性、准确性和高效性,适用于处理实时、大量的桥梁健康监测数据。
