Generalized inverses of nonlinear mappings and the nonlinear geodetic datum problem

Motivated by the existing theory of the geometric characteristics of linear generalized inverses of linear mappings, an attempt is made to establish a corresponding mathematical theory for nonlinear generalized inverses of nonlinear mappings in finite- dimensional spaces. The theory relies on the concept of fiberings consisting of disjoint manifolds (fibers) in which the domain and range spaces of the mappings are partitioned. Fiberings replace the quotient spaces generated by some characteristic subspaces in the linear case. In addition to the simple generalized inverse, the minimum-distance and the x ₀-nearest generalized inverse are introduced and characterized, in analogy with the least-squares and the minimum-norm generalized inverses of the linear case. The theory is specialized to the geodetic mapping from network coordinates to observables and the nonlinear transformations (Baarda's S-transformations) between different solutions are defined with the help of transformation parameters obtained from the solution of nonlinear equations. In particular, the transformations from any solution to an x ₀-nearest solution (corresponding to Meissl's inner solution) are given for two- and three-dimensional networks for both the similarity and the rigid transformation case. Finally the nonlinear theory is specialized to the linear case with the help of the singular-value decomposition and algebraic expressions with specific geometric meaning are given for all possible types of generalized inverses. Received: 11 April 1996 / Accepted: 19 April 1997     

滤管两端均不在含水层层面的承压不完整井近似计算方法研究

不完整井在实际工程中应用广泛,且存在某些承压不完整井,其滤管顶、底均不在含水层层面,不能直接按常规的方法进行计算。可根据流线图中的水平流线对渗流场分层后进行简化计算,但分层位置的确定非常困难。因此,提出了简便可行的渗流场分层方法,包括假设上下部渗流场渗径相等的等渗径改进方法、假设上下部渗流场中井滤管长度与其含水层厚度比值相等的等比例改进方法和以等比例方法为基础的等效阻力法,并以此为基础对计算简便、精度较高的沙金煊公式进行完善,得到了适用于滤管顶、底均不在含水层层面的承压不完整井近似计算方法。经过算例验证和与有限元比较,该方法计算精度较高,实用性较强。     

基于两种插值算法的三维地质建模对比

三维地质建模过程中,插值算法对模型准确性具有显著影响。为评价不同插值算法对三维建模准确性的影响,本文选取反距离权重插值法和自然邻域插值法开展对比研究。通过理论分析和案例研究,从统计学原理、插值误差和可视化效果等三方面进行了对比分析。结果表明：反距离权重插值法在建模中精度较高,适应面更广。与自然邻域插值法相比,反距离权重插值法更加适用于地层缺失严重的层位,能够更好地保留地层缺失的特征;同时,反距离权重插值法能够更好地处理断层构造,对于地层的错断起伏情况表现效果更好;反距离权重插值法在沉积地层中误差更小,与实际情况更接近。     

Inference of in situ stress from thermoporoelastic borehole breakouts based on artificial neural network

The determination of in situ stresses is very important in petroleum engineering. Hydraulic fracturing is a widely accepted technique for the determination of in situ stresses nowadays. Unfortunately, the hydraulic fracturing test is time-consuming and expensive. Taking advantage of the shape of borehole breakouts measured from widely available caliper and image logs to determine in situ stress in petroleum engineering is highly attractive. By finite element modeling of borehole breakouts considering thermoporoelasticity, the authors simulate the process of borehole breakouts in terms of initiation, development, and stabilization under Mogi-Coulomb criterion and end up with the shape of borehole breakouts. Artificial neural network provides such a tool to establish the relationship between in situ stress and shape of borehole breakouts, which can be used to determine in situ stress based on different shape of borehole breakouts by inverse analysis. In this paper, two steps are taken to determine in situ stress by inverse analysis. First, sets of finite element modeling provide sets of data on in situ stress and borehole breakout measures considering the influence of drilling fluid temperature and pore pressure, which will be used to train an artificial neural network that can eventually represent the relationship between the in situ stress and borehole breakout measures. Second, for a given measure of borehole breakouts in a certain drilling fluid temperature, the trained artificial neural network will be used to predict the corresponding in situ stress. Results of numerical experiments show that the inverse analysis based on finite element modeling of borehole breakouts and artificial neural network is a promising method to determine in situ stress.     

黄土高原草地和农田生态系统碳滞留时间及固碳潜力

采用概率反演分析法估算黄土高原草地和农田生态系统各碳库滞留时间及固碳潜力。结果表明:除农田植物地上部分外,植物地上部分、地下部分、代谢性凋落物及土壤活性有机碳库滞留时间最短,为25~203d;惰性凋落物碳库滞留时间为2.4~3a;慢性有机碳库和惰性有机碳库滞留时间最长,分别为57.4~79.6a和593~598a。多年生草地的根系滞留时间显著高于农田;而农田代谢性凋落物碳库和慢性有机碳库的滞留时间显著高于草地。根据反演所得参数模拟,在当前气候和土壤条件下,农田和草地系统土壤有机碳在250a左右时达稳定状态,农田系统固碳潜力约为2 680g C·m^-2,草地约为3 130g C·m^-2。农田有机肥的输入能使土壤有机碳多固定4 000g C·m^-2。有机肥的输入及土壤有机碳周转缓慢使耕作农田比草地更有利于土壤有机碳积累。     

Comparison of temperature extremes between Zhongshan Station and Great Wall Station in Antarctica

Although temperature extremes have led to more and more disasters, there are as yet few studies on the extremes and many disagreements on temperature changes in Antarctica. Based on daily minimum, maximum, and mean air temperatures(Tmin, Tmax, Tmean) at Great Wall Station(GW) and Zhongshan Station(ZS), we compared the temperature extremes and revealed a strong warming trend in Tmin, a slight warming trend in Tmean, cooling in Tmax, a decreasing trend in the daily temperature range, and the typical characteristic of coreless winter temperature. There are different seasonal variabilities, with the least in summer. The continentality index and seasonality show that the marine air mass has more effect on GW than ZS. Following the terminology of the Fifth Assessment Report of the Intergovernmental Panel on Climate Change(IPCC AR5), we defined nine indices of temperature extremes, based on the Antarctic geographical environment. Extreme-warm days have decreased, while extreme-warm nights have shown a nonsignificant trend. The number of melting days has increased at GW, while little change at ZS. More importantly, we have found inverse variations in temperature patterns between the two stations, which need further investigation into the dynamics of climate change in Antarctica.     

电力系统元件非线性微分-代数子系统模型的逆系统控制:一种新算法

针对电力系统元件非线性微分-代数子系统模型,本文提出一种新算法研究其逆系统控制问题.所提出的新算法不需要对控制输出及其高阶导数做复杂的变换,具有更好的应用性.本文的逆系统控制方法主要分为两步：第1步,利用所提出的新算法来判断被控元件的可逆性,若可逆,则基于状态反馈与动态补偿,构造出元件的α阶积分右逆系统,实现复合系统的线性化和解耦;第2步,利用线性控制的理论和方法设计闭环控制器,使得元件被控对象满足期望的性能指标.最后按照本文所提出的方法,研究了多机电力系统的分散非线性汽门控制问题.仿真结果验证了本文所提方法的有效性.     

The Kuroshio East of Taiwan and in the East China Sea and the currents East of Ryukyu Islands during early summer of 1996

Using hydrographic data and moored current meter records and the ADCP observed current data during May–June 1996, a modified inverse method is applied to calculate the Kuroshio east of Taiwan and in the East China Sea and the currents east of Ryukyu Islands. There are three branches of the Kuroshio east of Taiwan. The Kuroshio in the East China Sea comes from the main (first) and second branches of the Kuroshio east of Taiwan. The easternmost (third) branch of the Kuroshio flows northeastward to the region east of Ryukyu Islands. The net northward volume transports of the Kuroshio through Section K₂ southeast of Taiwan and Section PN in the East China Sea are 44.4×10⁶ and 27.2×10⁶ m³s⁻¹, respectively. The western boundary current east of Ryukyu Islands comes from the easternmost branch of the Kuroshio east of Taiwan and an anticyclonic recirculating gyre more east, making volume transports of 10 to 15×10⁶ m³s⁻¹. At about 21°N, 127°E southeast of Taiwan, there is a cold eddy which causes branching of the Kuroshio there.     

概略坐标对GPS PWV解算的影响

利用GAMIT 10.6和2016年第101天至第160天南昌站的GPS观测资料,开展了13组概略坐标变化对GPS PWV解算的影响研究试验(南昌站概略坐标设置以10 m等间距从0~120 m逐渐向西偏移真实坐标)。其结果发现:当概略坐标与实际坐标偏离在60 m以内时,概略坐标的变化对GPSPWV的解算影响不大(长基线的相对误差和均方根残差NRMS分别维持在5.7×10~(-9)和0.24附近);但当概略坐标与真实坐标偏离超过60 m后,概略坐标的变化对GPS PWV的解算有着显著的影响,其中基线相对误差和GPS PWV与探空PWV的标准偏差随概略坐标偏离的增加而快速增大,NRMS和GPS PWV与探空PWV的相关系数也有明显的增加和减小,GPSPWV的成功解算日数则随概略坐标偏离的增加而快速减小(当偏离≥120 m时南昌无GPS PWV生成);概略坐标变化对基线相对误差、GPS PWV精度以及GPS PWV能否被成功解算的影响仅限于本站,某站概略坐标的偏离不会对其他站GPS PWV解算造成明显的影响。