IV. Based on Gibbs sampling algorithm of probability
model of the topic（Requirement 2）
4.1 Basic Model
1) Removing the Kariba Dam and replacing it with a series of ten to twenty smaller dams along the Zambezi river.
2) 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.
3) This result support the location and number of the new dam.
4) Establish a probability topic model based on Gibbs sampling algorithm, and analyze the optimal decision problem of water storage and flood in drought, large, medium and light rainfall.
5) Using MATLAB and SPSS MODELER software to establish Author Topic Model, BP network and LS-SVM model to verify the LDA model.
6) Using MSE and ABS method to carry on the error analysis to the LDA model. 4.1.1 Terms, Definitions and Symbols
In the case of several dams connected to a cascade system, two dams are selected for modeling discussion, namely, dam A and dam B, and the decision of dam B is obviously affected by upstream A dam decision；Hydrologic station forecast reservoirA rainfall and the probability of rainfall QA is PA，Hydrologic station forecast reservoir Brainfall and the probability of rainfallQB is PB，the decision of QA (QB) for non-flood discharge and pre-flood can be selected。
A, B reservoirs in the normal water level to the warning level, warning water level to the highest water level, the maximum water level than the probability of safety were: PA?,PA??,PA???,PB?,PB??,PB???。
In the actual situation, due to the capacity of the reservoir flood discharge
capacity, emergency flood will bring high risk, should be avoided, so here we do not consider the status of emergency flood, so A dam on the B dam is mainly reflected in the if Dam A dam, and A dam flooding to reach the dam leading to the water B to bring a greater risk.
In all the components of the system, the failure of any one unit will affect the entire system, such a system is called a tandem system. Tandem systems are the most common and simplest models, as shown in the following figure. In this paper, only two dam A and dam B are calculated for simplified calculation.
DAM-A DAM-B DAM-C DAM-E DAM-D Figure Dam in series diagram
4.1.2 Assumptions
1) Assuming that the design parameters, site selection and construction of the dam (dam group) after restoration, reconstruction and reconstruction are in
accordance with the requirements of water conservancy and hydropower projects. The number and location of the dam groups are in line with the requirements of water conservancy and hydropower projects. Therefore, the research problems are: a) Comparing the comprehensive benefits of the dams after restoration, reconstruction and reconstruction, establishing the mathematical model, and expounding the costs and benefits of each case; b) Reconstructing the dams (rebuilding the existing dams 10-20 A little dam), in the case of drought, heavy rain, moderate rain and light rain, when the impoundment and flood discharge can ensure the probability of dam break, the risk decision of dam group is optimized.
2) Assuming that the probability of dam break after rainfall to a certain water level is fixed.
3) Assume that the rainfall is a continuous variable, obeying the normal distribution.
4) Assuming that the dam group is a series model, do not consider the parallel and mixed.
5) Suppose the head of each dam in the dam group is the same.
6) Assuming that the dam group is designed to regulate the amount of water, generating capacity of not less than the original dam.
7) The risk of flood discharge in emergencies is high, and this study does not consider the situation of emergency flood discharge.
8) Assuming that the ecological restoration of the water-level drawdown area after the demolition of the dam, construction waste transport, sediment deposition are ideal.
9) Assume that the accuracy of weather forecasting is custom. 4.1.3 The Foundation of Model
'SGiven a sample containing, each dam has its rating in a given condition,
which is likely to be associated with the dam as a whole.Therefore, each dam can be
represented by a vector of the corresponding evaluation values，Recorded as
?????g?{g1?,g2,...,gS?1,gS}.Here，{g2s?1,g2s}indicates that the dam group exceeded the
warning level in the sample s（Over-expressed）and less than the warning level
's?{1,...,S},ThusS?2S'。In order to obtain these complex （Under-expressed）,
integer number of times sample s as follows,
(?2s?1,i,?2s,i),We normalize a dam evaluation value in
σ2s-1,i,σ2s,i?c?????|v|?,0,????0,??c?|v|??,s,is,ivs,i?meds
Which is the expression of
vs,i dam in the s-th sample，medsrepresents the
mean value of the water masses in the s-th sample for all dam groups，An evaluation value greater than or equal to meds is considered to be the dam's super-warning water level in the s-th sample, otherwise it is less than the warning water level and c is
a calibration constant.
?s,kαzs,tβ?k,nms,tKTsS
Fig Probability Topic Model Relation of Dam Group
DALADBFlood AALBBFlood B Fig Probabilistic Topic Model for Series Dam Group
4.1.4 Analysis of the Result
FigProbabilistic Topic Modeling
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 0Vflood discharge 0.4Vflood discharge quantity AIncoming 0V 0.4V 0V 0.4V water 0V 1.3V 1.7V 0.9V 1.3V 0.25V 1.55V 1.95V 1.15V 1.55V 0.95V 2.25V 2.65V 1.85V 2.25V It can be seen that dam A adopts 0.25V flood discharge, dam B takes 0.4V flood discharge as the optimal decision, the expected risk value is 0.025301V. Therefore, the dam group can resist flood and drought through optimal decision-making. 4.1.5 Strength and Weakness
? Strength: In despite of this, the model has proved that the 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.
? Weakness: This model as we have stated,the same or greater levels of
protection and water management options for Lake Kariba. The parameter of the model can be optimized. That’s just what we should do in the improved model.
4.2 Improved Model
In this paper, we use the Gibbs algorithm to optimize the parameters in the probability topic model to improve the model accuracy.
In this paper, a kind of folded Gibbs sampling method is used to estimate these parameters. The Monte Carlo method is used to sample the posterior probability of parameters.
Folded Gibbs Sampling
zs,tand
ms,tare marginalized in each state sample by
co-sampling the implicit variablesvariable t, samples of
?s,kand?k,n. For the s-th sample of a dam group
zs,tand
ms,tcan be expressed as a conditional probability：