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附录A复杂矿井相关参数的敏感性分析摘要基于5个矿井通风系统对分枝数，节点数，计算精度，气流速度，迭代初步价值等参数关系的研究，应用计算机数值试验方法分析矿井通风网络收敛性。结果表明，较高的计算精度大大影响了迭代次数。当解决一个复杂矿井的通风网络的精度高达10-6m3/s时，虽然运用高性能计算机但运行时间却很长。气流初始值在1-1000m3/s时，对迭代次数的影响很小。除此之外，网络结构对于迭代次序也有很小的影响。关键词：矿井通风；敏感性分析；数值试验；参数调整引言经过几十年的发展和应用，矿井通风网络分析已成为一项成熟可靠的技术。然而，在矿井通风系统中，一些重要参数的定量分析仍处于极端而没有被解决。例如，当给出了计算的硬件、软件和它的计算方法时，改变一些参数如准确性，气流速度，树枝，节点数量和分支的阻值，并让它们处于最高和最低之间，其中像迭代次数，计算时间和网络分析这些参数之间的关系衔接方面都没有发现系统性的文献检索。解决这些问题对于网络分析，网络优化设计及矿井通风网络系统的调整无论在理论上还是在实践上都有重要的意义。一方面，如果初始的气流速度值的大小对网络分析影响不大，那么网络分析之前的工作可以简化。另一方面，在矿井通风的数字模型中，如果充分的重视分支阻力，而且网络分析可以照常工作，那么有可能把所有不确定的数据（包括一些未被发掘的不确定数据）放入电子文件中而且能够充分重视到未被发掘的分支阻力。当这些不确定的因素被发掘，就有必要去修改他们以减少其在电子文件中的抗性。1 方法和调查事实1.1 计算条件为了探讨上述问题，选择了五个矿井的通风网络作为分析对象。在数字测试中，计算机、软件和计算方法的条件如下：(1)电脑和作业系统：普通的能兼容IBM的电脑，windows98系统。(2)迭代算法：哈代-交叉迭代。在哈代克洛斯的算术方法中，一些基本规律例如节点流量平衡、路端失衡、阿特金森定律等呗应用。迭代的运算公式可以写成如下形式：(1)这里Qk是每个封闭回路分支的风流速度误差值，单位为m/s；Ri是每个封闭回路分支的风阻，单位为NS2m-8；Qai是每个封闭回路中分支的风流流量，单位为m3/s；Pfk是每个回路中的风压值（当风流方向为顺时针时为正值，否则为负值），单位为Pa；pvpk是一个封闭回路的自然风压，单位为Pa。ak是风流速率，经过对风机特性曲线求导而得出，k=1,2，M。M是独立回路的个数。b是一个封闭回路中的分支数目。1.2 网络分析软件及案例矿井网络分析软件是由笔者开发的。程序是用C+语言编写的。它的功能如下：数据处理、模拟风机特性曲线、错误信息提示、标明每个分支的风速、选择最小阻力路线、形成独立回路、进行风流速率迭代、计算每条分支的最大损失、处理漏风量、输出所有的计算结果和形成通风系统图。测试了五个实际的矿井通风网络技术参数，如表1。2测试数据结果影响通风网络计算过程中迭代次数的因素有很多，如精度要求、网络的复杂程度、分之阻力的大小和已知的风速值。下面是主要数值测试结果的说明。表1 五个矿井通风网络参数的实测值Tab.1 Parameters of 5 mine ventilation networks for numerical test矿名分支个数节点数独立回路个数风机个数主扇压力/pa主扇风量/m3s-1等积孔面积/m2铜绿山矿417244174288471.32.85凤山铜矿189144762204659.11.55唐家湾矿12870591111796.53.44安庆铜矿100633832338131.73.24凡口矿102384547931602186.25.542.1 计算精度对迭代次数的影响因素凤山矿以通风网络数据为基础，通过改变计算精度，可以得到最小迭代次数。在计算过程，分析对象作为单一参数，试结果见表2，从中可以看出最大和最小的分支阻力分别为20和0.0056 NS2m-8。表2 风流量计算的准确性和迭代次数的关系Tab.2 Relationship between computation accuracy of airflow rate and iteration numberQ/m3s-1节点实际风流误差/m3s-1回路风流实际误差/m3s-1实际风压误差/pa实际迭代次数1.0000000.9809000.8914006.551000190.1000000.0976600.0937603.390000440.0100000.0097620.0093040.036370720.0010000.0007100.0009660.0223501000.0001000.0000880.0001000.0006791420.0000100.0000100.0000100.000081830.0000010.0000040.0000180.00004710000从表2中可以得出以下结论：当风速度的精度要求不是太严格时，随着迭代次数的增加，风流速度的计算误差和压力损失随之减小。但是，当风流流速精度要求非常高(高达10-6m3s-1)时，一个不寻常的现象就发生了，每个回路的迭代次数将会急剧增加（高达1000次）。对于非常复杂的通风网络，运行时间就会变得特别长，令人难以接受。与此同时，当Q10-5m3s-1时，所有节点的风流流量误差满足精度要求。根据实际需求，当实际风流流量的计算精度等于10-5m3s-1时，是一个考虑的误差传递合适的选择。它可以满足实际需求并且确保整个网络分析的运行速度。压力损失误差是所有参数中最大的，这是由于误差的传递和积累造成的。根据实验数值结果显示，Q对迭代次数的影响是显而易见的。2.2 气流速度对迭代次数的影响通过对网络计算的数值测试，不同气流速度的迭代次数列于表3。从表3中可以看出，起初的风流速率对迭代次数的影响是非常微弱的。因此，任何给定的风流值除零之外，都可以应用，没有必要对风流的起初值进行谨慎的选择。2.3 通风网络复杂程度对迭代次数的影响通风系统的复杂程度可以表现为一些参数，例如节点数、分枝数、独立回路数、主扇数和矿井通风系统的构建情况。一个红系统中，节点数越多那么分支和独立回路数就越多，这个系统就越复杂。于此同时，随着限制条件的增加，迭代次数也随之增加。为了明确节点数、分支数和迭代次数之间的关系，进行了大量的数值测试（见表一）。表3 风流速度的初始值和迭代次数的关系Tab.3 Relationship between preliminary value of airflow rate and iteration number风流初始值/m3s-1-5-1015100迭代次数187192无意义188180211为了比较实验结果中的所有元素，在数值测试中每个参数分别给出相同的数值。在给定的条件下（迭代次数为1000、迭代精度为10-5m3/s、初始气流速度为10.0m3/s）计算结果列于表4通过分析表4中的数据，我们可以得出一些结论。在给定参数条件下，网络计算结果满足的计算精度的要求，这表明该网络的计算是可行的，其结果满足工程要求。从迭代次数的观点，结果几乎与设计值相同，这表明同一给定参数，网络越复杂，迭代次数越多。凡口铅锌矿的通风网络是最复杂的，分枝数超过了1000。实际节点风流误差仍然满足要求，但是实际回路风流速率和压力误差要比实际节点气流速率的误差要小。表4 5个矿的矿井通风网络计算Tab.4 Computation results of 5 mines ventilation networks矿名分支个数节点数实际迭代次数实际节点风流误/m3s-1回路风流误差/m3s-1回路压力损失误差/Pa安庆矿100631740.858 310-50.976 710-50.152 610-4铜绿山矿4172449720.953 710-50.986 810-50.207 310-3凤山矿1891441860.953 710-50.953 410-50.115 410-3唐家湾矿128701330.882 110-50.971 310-50.118 010-4凡口矿132384520000.953 710-50.221 510-20.456 710-2通过对表4中的数据的进一步分析，可以发现，对于一个实际的通风系统，网络里面的节点和分枝数越多，系统中的独立回路数就越多。然而，有一个异常情况，安庆矿的节点和分支数比唐家湾的要少，但是其迭代次数要多于后者。它可以由网络拓扑关系来解释。拥有相同的节点和分支数，而网络拓扑关系不同，那么网络的差别是巨大的。这无疑影响了网络计算的迭代次数。图一中给出了由六个分支和五个节点组成的几种不同形式的网络结构。从图1中可以看出，对于一个只有六个分支和五个节点的简单的网络图，只对一个分支进行修改便派生出九个不同的网络图。随着分支和节点数目的增加，出现数以千计的网络结构，这将不可避免的影响到网络计算的迭代次数。图1 六个分支和五个节点组成的网络形式Fig.1 Patterns of network with 6 branches and 5 nodes3结论1)在做矿井通风网络分析时，每个分支的气流初始值（除零之外）对计算迭代次数的影响不大，通常情况下推荐的数值为10 m3s-1。2)在矿井通风网络分析中，给定的风流速率的计算精度对迭代次数影响比较大。当计算精度高达10-6m3s-1时，即使使用高配置个人电脑，计算过程也无法再短时间内完成。推荐的气流速度是10-5m3/s。附录BSensitivity analysis of relevant parameters in complicated mine ventilation network by numerical testAbstractDepending on the numerical test approach on a computer, the relationships among relevant parameters,eg branch number, node number, mesh number, computation accuracy,preliminary value of airflow rate, iterationnumber, computation time and convergence in a mine ventilation network analysis, were investigated based on 5mine ventilation systems. The results show that a higher computation accuracy greatly influences the iteration num-ber. Whe n the accuracy reaches 10-6m3s-1for solving a complicated mine ventilation network, the running timeis too long though a high-speed computer is used. The preliminary value of airflow rate in the range of 1100 m3s-1has little effects the iteration number. The structure of network also has some effect on the iteration number.Key words:mine ventilation; sensitivity analysis; numerical test; parameters adjustmentIntrodouctionAfter several decades of development and application, the mine ventilation network analysishas become a mature and useful technology. However the quantitative analysis of important parameters in the extreme in a mine ventilation system hasnot been conducted1 10. For example, when the hardware of computer, the method of computationand software are given, changing those parame-ters, such as the accuracy, the preliminary value ofairflow rate, the number of branch, the number ofnode and the resistance of a branch, and lettingthem stand on critical status of the maximum andminimum, the relationships among those parameters like the iteration number, calculation time andconvergence of the network analysis are not found in a systemic literature search10 17. Tackling those problems is important both in theory and in practice to network analysis, network optimization design and network adjustment in a mine ventilation.For instance, if the size of the preliminary value of airflow rate has little effect on network analysis,the work before network analysis can be simplified. For another instance, in the digital model of a mine ventilation, if an extremely big value is given to the resistance of a branch and the network analysis can work as usual, it is possible to put the data of all drifts (including some drifts that is not ex-cavated) into the digital file and give an extremely large value to the resistance of a branch which is not excavated. When the drifts are dug, there isneed to modify the resistances of the drifts in the digital file.1Approach and cases of investigation1.1Computation conditionIn order to investigate the problems above, 5 mine ventilation networks were selected as theanalysis objects. In the numeral test, the conditions of computer, software and computation approaches are as follows.1) Computer and operating system: commoncompactable IBM-PC, Windows98.2) Iteration arithmetic: Hardy-Cross iteration.In the arithmetic of Hardy-Cross, some basiclaws, such as the conservation of airflow at node,the loss balance of circuit head and Atkinson laws in a ventilation network were used. The formula ofiteration arithmetic is written as follows. (1)whereQk is the error value of airflow rate for each branch in a close mesh, m3s-1;Riis the resistance of a branch in a close mesh, Ns2m-8; Qaiis the airflow rate of a branch in a close mesh,m3s-1; pfk is the fan pressure in a close mesh(when the action direction is clock wise, it is assumed as positive, otherwise negative), Pa;pvpk is the natural ventilation pressure in a close mesh,Pa;ak is the derivation of the characteristic curve of the fan pressure the airflow rate,k=1,2,M; M is the number of independent mesh in the networks;b is the number of branch in the independent mesb. 2.2 software of network analysis and cases The software applied in the mine network analysis was developed by the authors. The code was written by visual C+ language. Its functions are as follows:organizing data, managing characteristic curves of fans, hinting error informations, marking a fixed airflow rate in a branch, sorting the minimum path of resistance, forming independent meshes, conducting the iteration of airflow rate, calculating the head loss of each branch, disposing the value of air leakage, outputting all results of calculation, and forming the chart of ventilation system.The main parameters of 5 practical mine ventilation networks for the numerical test are listed in Tab.1.Tab.1Parameters of 5 mine ventilation networks for numerical testMine namBranchnumberNodenumbeIndependencemesh numberFan numberPressure headof mainfan/PaAirflowRate of main fan/m3s-1Area ofequivalenthole/m2Tonglushan coppemine417244174288471.32.85Fengshancopper min189144762204659.11.55Kangjiawanlead & zinc mine12870591111796.53.44Anqingcopper mine100633832338131.73.24Fankoulead&zinc mine102384547931602186.25.542results of numerical testThere are a lot of factors infecting the iteration number in the course of ventilation network computation, such as the required accuracy, the complex degree of network, the resistance size of a branch, and the given value of airflow rate. The main numerical test results are described as follows.2.1Influence of computation accuracy on iterationnumberBased on the ventilation network data Fengshan copper mine, by changing the value computation accuracy, the minimum iteration nuber can be gotten. In the course of computatio the analysis object is single parameter, and the sults of test are listed in Table 2, where the mimum and minimum resistance values of a braare 20 and 0.0056 Ns2m-8, respectively.From Table 2, some conclusions can be drawn as follows: the computation error of airflow rate and pressure loss decrease with increasing the iteration number when the demand of airflow rate accuracy is not too strict. But when the airflow rate accuracy is very high (up to 10-6m3s-1), an unusual phenomenon takes place, that is, the factualiteration number of a mesh increases sharply (morethan 10000 times). For a very complicated ventilation network, the whole running time becomes too long to be accepted. At the same time, factual node airflow rate error of all nodes meets the need of accuracy whenQ10-5m3s-1. According to the practical requirement, when the computation accuracy of factual airflow rate is equal to 10-5m3s-1, it is a suitable choice for considering the error transfer. It can meet factual need and ensure the running speed of the whole network analysis. The error of pressure loss is the biggest among all the parameters, which is caused by the transfer and accumulation of error. According to the results of numerical test, the influence of Q on the iteration number is obvious.Tab.2Relationship between computation accuracy of airflow rate and iteration numberQ/m3s-1Factualnode airflow/m3s-1Factual mesh air flowrate error/m3s-1Factual pressure head error/PaFactual Iteration number1.0000000.9809000.8914006.551000190.1000000.0976600.0937603.390000440.0100000.0097620.0093040.036370720.0010000.0007100.0009660.0223501000.0001000.0000880.0001000.0006791420.0000100.0000100.0000100.000081830.0000010.0000040.0000180.000047100002.2Influence of airflow rate on iteration numberBy the numerical test of network computation, the results of iteration number at various airflow rates are listed in Table 3. From Table 3, it can be seen that the influence of the preliminaryairflow rate on the iteration number is very weak.Accordingly, any given value of fairflow rate canbe applied except zero. Therefore it is not necessaryto choose carefully a preliminary value of airflow rate.Tab.3Relationship between preliminary value of airflow rate and iteration numberPreliminary value of airflow rate/m3s-1-5-1015100The complex degree of ventilation network can be representedIteration number187192unless1881802112.3Influence of complex degree of ventilation network on iteration number by the parameters, such as the node number, the branch number, the independent mesh number, the main fan number and the situation of the construction in the mine ventilation system. The more nodes a system has, the more branches and independence meshes the system has and the more complex the system is. At the same time, the iteration number increases with the increase of number of restriction condition. In order to make clear the relationships among the node number, the branch number and the iteration num ber, a lot of numerical tests were done (see Tab.1). In order to compare all characters of experimen results, all parameters in the numerical test were given as the same value respectively. Under thgiven conditions (the iteration number is 1000,the iteration accuracy is 10-5m3s-1, and the preliminary value of airflow rate is 10.0 m3s-1),the computation results are listed in Tabl.4.By analyzing the data in Tab.4, we can draw some conclusions. Under the condition of given parameters, the result of network computation meets the need of computation accuracy, which shows that network computation is feasible and the results meet the requirement of engineering. From the viewpoint of iteration number, the results are almost the same as the design value, indicating that for the same given parameters, the more complex the network is, the more times the iterationis. The network of Fankou lead & zinc mine is the most complex, and the branch number is more than 1000. The factual node airflow rate error still meets the requirement of accuracy, but the accuracy of mesh airflow rate error and actual mesh pressure error are smaller than those of the factual node airflow.By further analyzing the data in Tab.4, it is found that for a factual ventilation system, the larger the number of branches and nodes in a network are, the larger the number of independent meshes in the system is. However, there is an exceptionalcase. The number of branches and nodes of Anqing copper mine is less than that of Kangjiawan lead & zinc mine, but the factual iteration number of the former is larger than that of the latter.It can be exwith the topological structure of network. With the same number of branches and nodes and the different topological structures, the difference of networks is tremendous. And this definitely affects the iteration number of network computation. A simple chart and its various patterns of a network with 6 branches and 5 nodes are given in Fig.1. From Fig.1 it can be seen that 9 different patterns are derived from a simple network with 6 branches and 5 nodes by modifying only one branch.When the number of branch and node is increased, the network has thousands of structure, which will ,inevitably affect the iteration number of network computation.Fig.1 Patterns of network with 6 branches and 5 nodes3conclusion1) When making the analysis of mine ventilation network, the preliminary value of airflow rate in each branch has little effects on the iteration number of computation, except zero. Usually, the recommendation value is 10 m3s-1.2) A given compution accuracy of airflow rate in the mine ventilation network analysis has important effect on the iteration number. When the accuracy is up to 10-6m3s-1, the iteration number is too large to be finished in a short time, though a high speed personal computer is used. The recommendation value of the airflow rate is 10-5m3/s.REFERENCES 1JIA Jin-zhang, WEI Shi-chuan, LIU Jian. Network simplification technology on mine ventilation simulation systemJ. Journal of Liaoning Technical University(NaturalScience),2004, 23(4): 433 437. (inChinese)2Dalgic A, Karakus A. A computerized study on the natural ventilation characteristics of the Guleman Kef chromium mineJ. Transactions of the Institution of Mining and Metallurgy A, 2004, 113(3): 153 162.3WEI Jian-ping, HE Xue-qiu, WANG En-yuan. Convergence analysis on numerical solution of non-steady flow for mine ventilation networkJ. Journal of China University of Mining and Technology, 2004, 33(3):295 297.(in Chinese)4 Wala A, Jacob J, Brown J, et al. New approaches to mine-face ventilationJ. Mining Engineering, 2003,55(3): 25 30.5Vasilchuk M P, Zimich V S, Popov V B. On rating the ventilation parameters of minesJ. Bezopastnost Truda Promyshlennosti, 2003, 5: 45 47
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