P(zs,t?k|ms,t?n,Z?(s,t),s)?KTCkn?β?Cn'?1T?SKCsk?αKTkn'?Tβ?Cs'?1SSKs'k?Sα
Among them，
Z?(s,t)is the current distribution of the dam group with the
SKCskexception of the s condition type。is the number of times the sample s is assigned KTCknto the kth dam group, excluding the current state。is excluded from the current
state, whether more than warning water level type n is assigned to the kth dam。K is
the number of implicit variables in the reservoir group, and S is the total number of condition types.
4.2.5 Analysis of the Result
Improved (maximum precipitation) Normal probability Probability of failure total Pre-improvement (maximum precipitation) Normal probability Probability of failure total
771 229 1,000 765 235 1,000 77.10% 22.90% 76.50% 23.50% Consistency of model results before and after improvement Consistent 856 85.60% Inconsistent 144 14.40% total 1,000 In order to facilitate the analysis of the state of the dam B and the profit and loss value, the actual water quantity of the dam B after precipitation is shown in the following table.
TableActual amount of water in dam B BWater quantity AIncoming water 0V 0.25V 0.95V 0Vflood discharge 0V 0.4V 1.3V 1.7V 1.55V 1.95V 2.25V 2.65V 0.4Vflood discharge 0V 0.4V 0.9V 1.3V 1.15V 1.55V 1.85V 2.25V It can be seen that after optimization model analysis, dam A adopts 0.25V flood discharge, dam B takes 0.4V flood as the optimal decision, the expected risk value is 0.024591V. Therefore, the dam group can resist flood and drought through optimal decision-making.
4.3 Model Validation
4.3.1 Author topic model
This paper applies ATM to the optimal decision of dam group. The method also uses a variety of information sources: water flow, reservoir capacity, rainfall, warning water level, total storage capacity, regulating storage capacity. In this model, the dam system corresponds to the Authors, the words of the dam, the corresponding documents of the meteorological conditions, and the topics of the water storage and discharge decision. This method can effectively obtain the optimal decision of dam group.
In the rainy season: the red dam that super-warning level, the need for early decision-making flood, green dam that did not exceed the warning level, do not need flood. In the dry season: Red Dam said the lack of water, need to advance the water, green dam that adequate water, do not need to advance storage.Each circle represents a dam, and arrows indicate the relationship between the dams controlling water volume.
4.3.2 BP network
Artificial neural network is a kind of mathematical model of information processing which is similar to the structure of brain synaptic connection. In engineering and academia also often referred to directly as neural network or neural network. Neural network is a computing model, which consists of a large number of nodes connected with each other. Each node represents a specific output function,
called the activation function. The connection between every two nodes represents a weighted value of the signal passing through the connection, called the weight, which is equivalent to the memory of the artificial neural network. The output of the network depends on how the network is connected, the weights, and the incentive functions. The network itself is usually a natural algorithm or function approximation, it may be a logical expression.
Suppose there are s1 neurons in the hidden layer, the excitation function is F1, and there are s2 neurons in the output layer, and the corresponding activation function is F2, which is the input data of the dam. The output is Y and the target vector is T.
（1） The positive transfer of information
① The output of the neuron in the hidden layer is：
y1i?f1(?w1ijxj?b1i),i?1,2,Ls1 (4-3)
j?1r② The output of the k-th neuron in the output layer is：
y2k?f2(?w2kiy1i?b2k),k?1,2,Ls2 (4-4)
i?1s1③ The error function is defined as：
1s2E(W,B)??(tk?y2k)2 (4-5)
2k?1（2） The Change of Weight and the Back Propagation of Error
① The weight of the output layer changes
The weight change from the first input to the first output is：
?w2ki????E?E?y2k?????(tk?y2k)f2?y1i???kiy1i (4-6) ?w2ki?y2k?w2ki(4.18)，?ki?(tk?y2k)f2??ekf2?；ek?tk?y2k。
Similarly available：
?b2k????E?E?y2k??????(tk?y2k)?f2?????ki (4-7) ?b2ki?y2k?b2ki② Implied layer weight changes
For the weights from the ith input to the jth output, the change is：
?w1ij???s2?E?E?y2k?y1i??????w1ij?y2k?y1i?w1ij (4-8)
???(tk?y2k)f2??w2kif1??xj????ij?xjk?1?ei?(4-8)，?ij?eif1,??k?1s2kiw2ki
Similarly available：?b1i???ij。
This can be obtained for the output of the dam spillway, water storage value.
4.4 Model Error Analysis
In this paper, the mean square error and the absolute error are used to evaluate
the prediction results.
4.4.1 ABS
Absolute error (ABS) is the difference between the exact value x and its approximate value x *, denoted as e (x *) = x * -x, abbreviated as e *.However, in general, the size of e (x *) can not be known accurately. The upper bound of the absolute value can be estimated by measuring or calculating | e (x *) | = | x * -x | ≤ε (x * (X *) is called the approximate absolute error of the number x * limit, referred to as the error limit, abbreviated as ε *.
?Absolute Error Formula：ABS?yi?yi
Note: where yiandyi represent true and predicted values
When selecting dam monitoring indicators for testing, the error is shown in the following table.
Tab Model error comparison LSSVM ATM BP LDA MSE 624.4849 443.2745 160.9934 50.9441 ABS 20.8579 15.2839 10.9251 5.7826 ?Therefore, using this method, we can get a better monitoring of the dam to make the best decision.
V. Conclusions
5.1 Conclusions of the problem
ZRA management requires a brief assessment of the three options listed, with sufficient detail to provide an overview of potential costs and benefits associated with each option.
The annual economic benefits of the dam are made up of a number of benefits. These include power generation benefits, water supply benefits, irrigation benefits, shipping benefits, the value of flood storage, cultural tourism value, biological benefits, environmental benefits and so on. As a result of the various benefits, especially the power generation efficiency is changing year by year.
The annual economic losses caused by the dam include food production, fishery production, organic matter production, soil erosion control, ecological restoration, dam maintenance, reservoir dredging, water treatment, species loss, loss of cultural relics.
According to the relationship between the size of the dam can be taken to repair, reconstruction, reconstruction and other measures. In this study, the economic benefit model, economic loss model, comprehensive benefit model, absolute return model after repair, investment payback period model, the reconstruction of 10 to 20 dam groups after the demolition of Kaliba dam will bring the best Cost and benefit.
Removing the Kariba Dam and replacing it with a series of ten to twenty smaller dams along the Zambezi river. This new system of dams should have the same overall water management capabilities as the existing Kariba Dam while providing the same or greater levels of protection and water management options for Lake Kariba that are in place with the existing dam. This result support the location and number of the new dam.
5.2 Applications of our models
In this paper, the optimal decision-making model based on probability topic and Gibbs algorithm is established. All the models are of high accuracy and can provide decision-making basis for the water conservancy department and have generalization ability.
If this paper can further study the location and capacity of the dam group, it will have more practical significance.
VI. Future Work
In this paper, a mathematical model based on comprehensive benefits is established, and a probability topic model based on Gibbs sampling algorithm is established. Although the above model has high accuracy, it is worthy to further study the location, capacity, meteorological factors and ecological factors of the dam group. In addition, models such as topic model and LDA model should be compared in order to better serve decision-making bodies.
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