Doctoral Dissertation
Civil Engineering - Earthquake
Summer 2013
Abstract
One of the appropriate tools to know the state of the network As one of the vital artery systems, water distribution is an indicator of reliability. A bunch of methods Another one, which is more suitable due to the existence of many parameters of vital artery systems, is to use the concept of Shannon's information entropy theory and determine the network redundancy index. In the works done on the redundancy of water distribution networks, the simultaneous effect of hydraulic and mechanical parameters is usually not considered. For this purpose, in this study, a modified criterion based on the concept of information entropy is presented to evaluate the service level of water distribution networks. So that in this regard, the effect of hydraulic uncertainties (such as the flow rate in pipes) and mechanical uncertainties (such as the possibility of flow lines breaking) are taken into account at the same time.
For this purpose, after examining the effect of various methods of weighting the entropy function on the behavior of the function, a coefficient has been defined as the ratio of the demand of the consumption node to the flow rate of all network links. With proper weighting of the hydraulic entropy function available in the technical literature, the effect of the sequence and the way of connecting the consumption nodes to the spring nodes has been seen in the proposed relationship. The correctness of the behavior of the proposed function has been evaluated with the help of examples with different configurations. The concept of conditional entropy has also been used to consider the effect of the link's non-serviceability. In this way, a penalty function is defined based on the probability of each link breaking under a specific risk scenario, and this penalty function is appropriately applied to the hydraulic entropy function. In this case, by considering different limit states and comparing the results with the expected results, the correctness of the behavior of the proposed entropy function has been checked.
With the help of the proposed entropy relation, the functioning of a number of sample water distribution networks, from simple tree networks to complex ring networks, has been checked, so that the correctness of the results of the proposed relation in evaluating the overall performance of the networks has also been investigated. In the following, the results of the proposed entropy relationship are compared with the results of the classical relationships of calculating the reliability of water distribution networks for a number of networks with the same consumption nodes and springs but with different configurations, and the effectiveness of the proposed index is shown both to achieve the optimal hydraulic configuration for a new water network and to choose the best plan to reduce damage in an existing network against various natural or man-made hazards. As a real example, the behavior of the water distribution network of Kobe city has also been evaluated based on the proposed relationship. One of the most important advantages of the proposed method is the much greater simplicity of this method compared to other existing methods for determining the reliability of networks and determining the best configuration. Meanwhile, in this proposed method, hydraulic and mechanical uncertainties are simultaneously included.
Since the characteristic parameters of the network, such as the level of demand of consumption nodes or the probability of link unavailability, etc., also have uncertainty, in the final part of the thesis, with the help of fuzzy mathematics and the concept of Fuzzy-entropy has been used to investigate the sensitivity of the results to such uncertainties. In this section, it has been shown that the presence of uncertainty in some parameters, such as the amount of demand of some consumption nodes, can have a significant effect on the level of confidence in the results, while the presence of uncertainty in some other parameters does not have much effect on the changes in the results. As a result, with the help of this method, sensitive parameters on network performance can also be identified. Chapter 1: Introduction 1-1- Research Background: To systems such as water distribution networks that are affected during natural disasters such as earthquakes. They have great sensitivity and importance, and in fact, saving human lives, reducing financial losses, and returning to normal life and serving the society is highly dependent on them, they are called the vital artery.. Returning vital arteries to normal as soon as possible requires careful planning. Accurate planning in critical conditions requires sufficient knowledge of the system's status, system analysis, determining the parameters of healthy or damaged system components. Repairs and reconstruction can be done based on the results of a comprehensive analysis of the system and by observing the priorities, which is very important in the quick return of society to normal. Therefore, it is very important to determine the current status of vital arteries and express it in a tangible way for the decision makers of the country so that they can make a correct, quick and economical decision. The reliability index is one of the best tools for this purpose. But calculating the reliability of large-scale systems such as vital arteries is a very difficult task, so many researchers seek to find a way to simplify this problem, and one of these methods to evaluate the safety level of vital artery systems is an uncertain index. In the technical literature, a mathematical concept called information entropy is used to express the uncertain index.
For the network Reliability of water distribution systems is usually calculated in two ways: mechanical reliability and hydraulic reliability. In mechanical reliability, the probability of demand nodes staying connected It is checked to the spring node. In hydraulic reliability, the probability is estimated that each of the demand nodes in the network will receive water at a predetermined pressure, even if some of the pipelines are also out of operation. In the technical literature, hydraulic and mechanical reliability have been studied at the same time. In this project, the aim is to determine the reliability of the water distribution network using the concept of information entropy theory, which simultaneously considers hydraulic and mechanical parameters. One of the most important branches of research on water distribution networks in recent decades has been to quantify the reliability of these networks in different conditions. One of the accepted methods to study the reliability of these networks is to use the information entropy theory and determine the degree of redundancy of these networks. The works done in the technical literature on the reliability of water distribution networks usually either only examine the hydraulic reliability of the network or examine the mechanical reliability of the system, and hydraulic and mechanical parameters are not taken into account at the same time. Simultaneous examination of hydraulic and mechanical parameters is important to determine the level of network risk after an accident such as an earthquake. Examining the hydraulic reliability of a network without considering the fact that some lines are out of service after the accident and some of their water is wasted, cannot give us a comprehensive picture of the network's condition. On the other hand, checking the reliability of the network mechanically without taking into account the hydraulic demand of the nodes, which is obviously different before, during and after the accident, cannot give a proper view to the decision makers to manage the critical situation. Determining the reliability of the network with a mechanical-hydraulic approach allows us to identify high-risk parts in the network and strengthen them, and if necessary, even by adding redundancy to these areas, reduce the risk of the network for events such as earthquakes. Among the expected achievements of this project is the development of a method to calculate the reliability of the water distribution network by considering the effects of hydraulic and mechanical parameters to evaluate the urban network covered by a reservoir in its current state and in The situation after the accident as well as the use of this method for the development of new networks.
1-2- Statement of the problem
Reports from the occurrence of unexpected accidents show that vital arteries are exposed to dangers caused by underground and supra-terrestrial phenomena. Due to the vastness of the vital arteries and their impact on the urban complex, the two basic criteria of their safety and reliability against unexpected events are of great importance.