CN105389638A - Retired uranium tailing impoundment environment stability analysis and prediction method based on uncertainty theory - Google Patents

Abstract

The present invention discloses a retired uranium tailing impoundment environment stability analysis and prediction method based on an uncertainty theory. Stability analysis comprises establishment of a uranium tailing impoundment environment stability index system, calculation of each index stable interval, and analysis of an environment stability of each dam section of a uranium tailing impoundment; and environment stability prediction comprises prediction on time required for converting to an unstable state from a stable state, and prediction on time required for converting to the stable state from the unstable state. The stable intervals of main environment pollution indexes of the uranium tailing impoundment are obtained, the environment stabilities of the uranium tailing impoundment at different time points are calculated, and the fuzzy conception of the uranium tailing impoundment environment stability is defined by the accurate mathematical language, so that organic combination of qualitative analysis and quantitative calculation on the uranium tailing impoundment environment stability is implemented and the theoretical basis is provided for safety management and decision analysis on the retired uranium tailing impoundment.

Description

Retired uranium tailings pond environmental stability based on uncertain theory is analyzed and Forecasting Methodology

Technical field

The invention belongs to the energy and technical field of information processing, relate to a kind of retired uranium tailings pond environmental stability analysis based on uncertain theory and Forecasting Methodology.

Background technology

Along with China is to the demand of the energy, by a large amount of Uranium tailings of generation and barren rock, for the uranium tailings pond that stores Uranium tailings and the barren rock potential safety problem to environment and the public very outstanding (uranium tailings pond refers to what build a dam the interception mouth of a valley or exclosure were formed, in order to store up the industrial site of uranium ore barren rock, tailings).Although its surrounding enviroment quality and ecologic regime obtain obvious improvement after Remediation, but due to its radioactive nuclide and other chemical toxic elements cover administer and in long duration after closing hole still by number of ways diffusion, migration, the accident such as dam break, landslide happens occasionally, the serious threat public security of the lives and property; On the other hand because land resource is deficient, the ecologic environment level before adopting smelting need be returned to as early as possible, guarantee the sustainable development of retired Uranium facility region, therefore, the safety and stability process accelerating uranium tailings pond becomes the important subject of Decommissioning of Uranium Mining/milling Facilities.

No matter from preserving the ecological environment or ensureing the angle of public's security of the lives and property, to retired uranium tailings pond stabilization process carry out research and analysis all tool be of great significance.But; at present the analysis of uranium tailings pond stability only be only considered to the mechanical stability of tailing dam, only cannot meet the needs of retired uranium tailings pond ecological environmental protection and sustainable development using the mechanical stability index of dam body as the evaluation index that whether safe retired uranium tailings pond is.For the Environmental Status of the problems referred to above and uranium tailings pond, this research proposes a kind of analysis and Forecasting Methodology of retired uranium tailings pond environmental stability based on uncertain theory, further abundant and improve retired uranium tailings pond Comprehensive Assessment Technology, there are positive meaning and impact to the Remediation of uranium tailings pond and environmental effect.Wherein, uncertain theory is from measure theory viewpoint, has the mathematic system of standardization, self-duality, monotonicity, subadditivity and product measure axiom.Prior art is adopted with the following method:

1. the analysis of uranium tailings pond environmental stability.

Utilize in theory of probability and expect to show that each index Asymptotic Stability is interval with the theory of variance, use the Chebyshev inequality in probability statistics, the probability of stability that finding out affects each environmental index is more than or equal to stable region during α.

Definition 1: set stochastic variable X as the observed value of certain index, the value of X is x ₁, x ₂, L, x _n, Y _k(k=1,2, Λ, n) is for certain index is at time [t ₁, t ₂] in the sequence of random variables of continuous k observed value formation, if Y _kmathematical expectation EY _kwith variance DY _kall exist, and to arbitrary α ∈ [0,1], there is ε >0, make inequality

P (| Y _k-EY _k| < ε)>=α sets up,

Then claim this index at [t ₁, t ₂] upper (α, ε) stablize, and claims [EY _k-ε, EY _k+ ε] be that this index is at time [t ₁, t ₂] in corresponding probability be the stable region of α.In conjunction with Chebyshev inequality and index v _istable definition, can show that the pass between α, ε is $\mathrm{\&alpha;}=1-\frac{D\left(Y_k\right)}{{\mathrm{\&epsiv;}}^2},$ Namely $\mathrm{\&epsiv;}=\sqrt{\frac{D\left(Y_k\right)}{1-\mathrm{\&alpha;}}}.$

In order to carry out quantitative test to the environmental stability of uranium tailings pond, give definition and the computing method of ambient stable rate.

Definition 2: establish x _ifor each index observed value at a time, w _ifor the weight of each environmental index, for the indicative function of each index stable region, for index A _ithe lower limit of stable region, for index A _ithe higher limit of stable region, ambient stable rate ρ is the extent of stability of a certain moment Tailings Dam environment, and

$\mathrm{\&rho;}=w_1{\mathrm{\&chi;}}_{A_1}\left(x_1\right)+w_2{\mathrm{\&chi;}}_{A_2}\left(x_2\right)+\mathrm{\&Lambda;}+w_m{\mathrm{\&chi;}}_{A_m}\left(x_m\right)=\underset{i=1}{\overset{m}{\&Sigma;}}{w}_i\&CenterDot;{\mathrm{\&chi;}}_{A_i}\left(x_i\right)$

Wherein, indicative function can be expressed as

Definition 3: establish the time [t ₁, t _k] interior certain environmental index sequence of random variables Y _kcorresponding stable region $\&lsqb;a,b\&rsqb;=\underset{i=1}{\overset{k}{I}}\&lsqb;{\mathrm{EY}}_i-{\mathrm{\&epsiv;}}_i,{\mathrm{EY}}_i+{\mathrm{\&epsiv;}}_i\&rsqb;,$ If interval $\&lsqb;a^{*},b^{*}\&rsqb;=\&lsqb;a-\frac{b-a}{l},b+\frac{b-a}{l}\&rsqb;$ Make

$\underset{i=1}{\overset{k}{I}}\&lsqb;{\mathrm{EY}}_i-{\mathrm{\&epsiv;}}_i,{\mathrm{EY}}_i+{\mathrm{\&epsiv;}}_i\&rsqb;\&Subset;\&lsqb;a^{*},b^{*}\&rsqb;\&Subset;\underset{i=1}{\overset{k}{Y}}\&lsqb;{\mathrm{EY}}_i-{\mathrm{\&epsiv;}}_i,{\mathrm{EY}}_i+{\mathrm{\&epsiv;}}_i\&rsqb;$ Set up,

Then claim interval [a ^*, b ^*] between elastic region for this index stability.

2. the prediction of uranium tailings pond environmental stability

The ambient stable process of retired uranium tailings pond is predicted, exactly the stabilization trend of each environmental index is predicted, the stable region of each index is obtained by structure random sum sequence of random variables, structure forecast function calculates new stable region and original stable region is made comparisons, and prediction environmental index is converted into non-steady state by steady state (SS) and is converted into the time needed for steady state (SS) by non-steady state.The anticipation function being converted into non-steady state by steady state (SS) only considers straight line growth form, exponential increase type and mechanical periodicity type, if new stable region is contained in original stable region, then this index is still in steady state (SS), if new stable region breaches original stable region, then this index is converted into non-steady state; The anticipation function being converted into steady state (SS) by non-steady state only considers exponential damping type, if stable region is originally contained in new stable region, then this index still plays pendulum, if new stable region enters original stable region, then this index is converted into steady state (SS).In two kinds of situations, index breaks through or enters the relational expression that the time s needed for stable region need meet and is respectively:

$\underset{i=1}{\overset{k}{I}}\&lsqb;{\mathrm{EY}}_i-{\mathrm{\&epsiv;}}_i-\frac{b-a}{l},{\mathrm{EY}}_i+{\mathrm{\&epsiv;}}_i+\frac{b-a}{l}\&rsqb;\&Subset;\underset{i=1}{\overset{k+s}{I}}\&lsqb;{\mathrm{EY}}_i-{\mathrm{\&epsiv;}}_i,{\mathrm{EY}}_i+{\mathrm{\&epsiv;}}_i\&rsqb;$

Or $\underset{i=1}{\overset{k+s}{I}}\&lsqb;{\mathrm{EY}}_i-{\mathrm{\&epsiv;}}_i,{\mathrm{EY}}_i+{\mathrm{\&epsiv;}}_i\&rsqb;\&Subset;\underset{i=1}{\overset{k}{I}}\&lsqb;{\mathrm{EY}}_i-{\mathrm{\&epsiv;}}_i-\frac{b-a}{l},{\mathrm{EY}}_i+{\mathrm{\&epsiv;}}_i+\frac{b-a}{l}\&rsqb;$

Wherein: EY _ithe mathematical expectation of i month monitor value before expression environmental index, k represents a kth month of environment Monitoring Indexes, is also the starting point moment of environmental stability prediction simultaneously, represent the elastic range of index stable region, corresponding interval $\underset{i=1}{\overset{k}{I}}\&lsqb;{\mathrm{EY}}_i-{\mathrm{\&epsiv;}}_i-\frac{b-a}{l},{\mathrm{EY}}_i+{\mathrm{\&epsiv;}}_1+\frac{b-a}{l}\&rsqb;$ Between the stable elastic region being called index.

The existing research relevant for uranium tailings pond environment aspect only considers some environmental factor mostly, not yet carry out the analysis of system comprehensively from a large angle, and sizable blank out is also existed to the analysis of uranium tailings pond environmental stability and research, some current evaluation methods and theory also cannot solve this technical matters.

The application of uncertain theory in Tailings Dam field is also just confined to tailing dam body slope stability, the environmental problem increasingly serious in the face of uranium tailings pond and influence factor complicated and changeable, obviously this cannot meet ecological, environmental protective and the sustainable development demand of uranium tailings pond Remediation, and how to carry out effective analysis and prediction to its steady state (SS) is also current research bottleneck.

Summary of the invention

The object of this invention is to provide a kind of retired uranium tailings pond environmental stability analysis based on uncertain theory and Forecasting Methodology, solve problems of the prior art, achieve the qualitative analysis of uranium tailings pond environmental stability and the combination that quantitatively calculates, uranium tailings pond environmental index is converted into non-steady state by steady state (SS) and is converted into steady state (SS) required time by non-steady state and predicts.

The technical solution adopted in the present invention is, a kind of retired uranium tailings pond environmental stability based on uncertain theory is analyzed and Forecasting Methodology, it is characterized in that, carries out according to following steps:

Step one, environmental stability analysis;

1) foundation of uranium tailings pond environmental stability index system;

2) calculating of each index stable region;

3) analysis of uranium tailings pond each monolith ambient stable rate;

Step 2, environmental stability are predicted;

1) be converted into non-steady state required time by steady state (SS) to predict;

2) be converted into steady state (SS) required time by non-steady state to predict.

Feature of the present invention is also, further, in described step one, the foundation of uranium tailings pond environmental stability index system, utilizes analytical hierarchy process to ask the weight of each environmental index, specifically carry out according to following steps:

Step 1: Judgement Matricies;

Element value in judgment matrix is the quantitative indices that each element relative importance judges, the judgment matrix C=(C of structure _ij) _{n × n}as shown shown in a;

Table a

Criterion B k	C 1	C 2	Λ	C n
					C 1	C 11	C 12	Λ	C 1n
C 2	C 21	C 22	Λ	C 2n
					Μ	Μ	Μ	Λ	Μ
C n	C n1	C n2	Λ	C nn

Judgment matrix C has following character: (1) C _ij>0; (2) C _ij=1/C _ji(i ≠ j); (3) C _ii=1 (i, j=1,2, Λ, n); In judgment matrix, the numerical value of each element judges each factor relative importance, then will judge that quantification obtains according to ratio scale, and adopt 1 ~ 9 method of scales, judgment matrix scale and implication thereof are in Table b;

Table b

Sequence number	Importance rate	C ijAssignment
			1	I, j two elements are of equal importance	1
2	I element is slightly more important than j element	3
			3	I element is obviously more important than j element	5
4	I element is strongly more important than j element	7
			5	I element is extremely more important than j element	9
6	I element is slightly more inessential than j element	1/3
			7	I element is obviously more inessential than j element	1/5
8	I element is strongly more inessential than j element	1/7
			9	I element is extremely more inessential than j element	1/9

M _ifor the product of each row element, if a _ijfor the element value of the i-th row jth row in judgment matrix, then

$M_i=\underset{j=1}{\overset{n}{\&Pi;}}{a}_{ij}$

Wherein, i=1,2 ... n;

Step 2: calculate M _in th Root

${\stackrel{\&OverBar;}{w}}_i=\sqrt[n]{M_i}$

Step 3: to vector normalized, normalization formula is

$w_i=\frac{{\stackrel{\&OverBar;}{w}}_i}{\underset{j=1}{\overset{n}{\&Sigma;}}{\stackrel{\&OverBar;}{w}}_j}$

W _ifor the weight of each index, then w=[w ₁, w ₂, Λ, w _n] ^tbe required proper vector;

Step 4: the Maximum characteristic root λ calculating judgment matrix _max, (if Cw) _irepresent i-th element of vectorial Cw, then

${\mathrm{\&lambda;}}_{max}=\underset{i=1}{\overset{n}{\&Sigma;}}\frac{{\left(Cw\right)}_i}{{\mathrm{nw}}_i}.$

Further, consistency check step carried out to judgment matrix as follows:

Step 1: calculate consistency check index CI;

If λ _maxjudgment matrix eigenvalue of maximum, then

$CI=\frac{{\mathrm{\&lambda;}}_{max}-n}{n-1}$

Step 2: search corresponding Aver-age Random Consistency Index RI according to table 1, wherein n represents the exponent number of judgment matrix;

Table 1

n	1	2	3	4	5	6	7	8	9	10	11
												RI	0	0	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.49	1.51

Step 3: calculate random Consistency Ratio CR, computing formula is

$CR=\frac{CI}{RI}$

As CR<0.10, namely think that judgment matrix has satisfied consistance, otherwise just need the element value adjusting judgment matrix, make it that there is satisfied consistance.

Further, in described step one, the calculating of each index stable region is carried out according to following steps:

Algorithm 1.1: the algorithm of stable region;

Step 1: input X=[x ₁, x ₂, Λ, x _k], stochastic variable X is the monitor value of certain index, x _k>=0, x _krepresent the monitor value in certain index kth month, α=0.95;

Step 2: calculate EY _kand DY _k, wherein ${\mathrm{EY}}_k=\frac{1}{k}\underset{i=1}{\overset{k}{\&Sigma;}}{x}_i,{\mathrm{DY}}_k=\frac{1}{k}\underset{i=1}{\overset{k}{\&Sigma;}}{(L-{\mathrm{EY}}_k)}^2;$

Wherein: EY _kfor environmental index sequence of random variables Y _kmathematical expectation, DY _kfor environmental index sequence of random variables Y _kvariance, k represents a kth month of environment Monitoring Indexes, is also simultaneously the starting point moment of environmental stability prediction;

Step 3: calculate ε _k, ε _kbe the intermediate variable of parameter stable region, reacted the degree that different monitoring moment stable region departs from sequence of random variables expectation value, wherein

Step 4: calculate a _k, b _k; a _k, b _kthe lower limit of the stable region before representing respectively corresponding to k month index and the upper limit, wherein a _k=EY _k-ε _k, b _k=EY _k+ ε _k;

Step 5: export [a _k, b _k]; Calculate $\underset{i=1}{\overset{k}{I}}\&lsqb;a_k,b_k\&rsqb;=\&lsqb;a,b\&rsqb;;$

Then result of calculation [a, b] is the stable region of required front k month.

Further, the analysis of uranium tailings pond each monolith ambient stable rate adopts following steps to carry out:

The environmental monitoring data in multiple for each monolith month is substituted into the algorithm of stable region, obtain the stable region of each index, then the computing formula of combining environmental coefficient of stabilization, obtain each monolith ambient stable rate ρ curve over time;

Wherein, the definition of ambient stable rate and computing formula as follows:

If x _ifor each index observed value at a time, w _ifor the weight of each environmental index, for the indicative function of each index stable region, for index A _ithe lower limit of stable region, for index A _ithe higher limit of stable region, ambient stable rate ρ is the extent of stability of a certain moment Tailings Dam environment, and

$\mathrm{\&rho;}=w_1{\mathrm{\&chi;}}_{A_1}\left(x_1\right)+w_2{\mathrm{\&chi;}}_{A_2}\left(x_2\right)+\mathrm{\&Lambda;}+w_m{\mathrm{\&chi;}}_{A_m}\left(x_m\right)=\underset{i=1}{\overset{m}{\&Sigma;}}{w}_i\&CenterDot;{\mathrm{\&chi;}}_{A_i}\left(x_i\right)$

Wherein, indicative function can be expressed as

Further, described step 2, is converted into the prediction of non-steady state required time by steady state (SS) and specifically carries out according to following steps:

Suppose t _kthe initial value a of moment index ₀for the average of stable region, i.e. a ₀=EY _k, predict that monitor value presses straight line change respectively, when index variation and mechanical periodicity, break through the time needed for stable region;

Be converted into non-steady state by steady state (SS), new stable region is broken through and to be needed the relational expression met to be between original stable elastic region:

$\frac{\underset{i=1}{\overset{k+s}{\&Sigma;}}{y}_i}{k+s}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{k+s}{\&Sigma;}}{(y_i-\frac{\underset{i=1}{\overset{k+s}{\&Sigma;}}{y}_i}{k+s})}^2}{k+s}}\&GreaterEqual;\frac{\underset{i=1}{\overset{k}{\&Sigma;}}{y}_i}{k}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{k}{\&Sigma;}}{(y_i-\frac{\underset{i=1}{\overset{k}{\&Sigma;}}{y}_i}{k})}^2}{k}}+\frac{b-a}{l}$

Wherein: yi represents the monitor value in this index each month, as 1≤i≤k, yi equals the monitor value in a front k month, as i>k, and y _icorresponding three kinds of Growth Function respectively, and

Between the elastic region of algorithm for design 1.2 parameter, algorithm 1.3 parameter is converted into the time needed for non-steady state by steady state (SS);

Algorithm 1.2: the algorithm between index elastic region;

Step 1-1: input ε _k, a, b, l; Wherein, a, b represent lower limit and the higher limit of index stable region respectively, and l is the elasticity coefficient between elastic region;

Step 1-2: calculate a ^*, b ^*, wherein i=1,2, Λ, k; a ^*, b ^*represent the lower limit between index elastic region and higher limit respectively;

Step 1-3: export [a ^*, b ^*];

Wherein [a ^*, b ^*] be front k month between certain elastic region corresponding to index stable region;

Algorithm 1.3: steady state (SS) is to the algorithm of non-steady state required time;

Step 2-1: input X=[x ₁, x ₂, Λ, x _k] and the front k stable region [a of individual month _k, b _k]; X represent front k month Monitoring Indexes value form set;

Step 2-2: calculate x (n+1)=f (t _n+1), x=f (t) is the concentration change function of structure; Upgrade X=[x ₁, x ₂, Λ, x _k, x _k+1];

Step 2-3: utilize algorithm 1.1 to calculate corresponding stable region [a _k+1, b _k+1], if then calculate and terminate and export kth+1 to start unstable; Otherwise, then export kth and stablize for+1 month, and upgrade k=k+1, get back to step 2-2 cycle calculations, until export crank-up time;

Described step 2, is converted into the prediction of steady state (SS) required time by non-steady state and specifically carries out according to following steps:

Suppose the initial value a of certain index ₀for the maximal value y of Historical Monitoring data _max, when prediction index monitor value is exponentially decayed on this basis, enter the time needed for stable region;

Be converted into steady state (SS) by non-steady state, new stable region reenters and to need the relational expression met to be between original stable elastic region:

$\frac{\underset{i=1}{\overset{k+s}{\&Sigma;}}{y}_i}{k+s}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{k+s}{\&Sigma;}}{(y_i-\frac{\underset{i=1}{\overset{k+s}{\&Sigma;}}{y}_i}{k+s})}^2}{k+s}}\&le;\frac{\underset{i=1}{\overset{k}{\&Sigma;}}{y}_i}{k}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{k}{\&Sigma;}}{(y_i-\frac{\underset{i=1}{\overset{k}{\&Sigma;}}{y}_i}{k})}^2}{k}}+\frac{b-a}{l}$

Wherein, y _irepresent the observed reading in this index each month; As 1≤i≤k, y _iequal the monitor value of front k month; As i>k, y _i=EY _k+ (a ₀-EY _k) e ^-mi, wherein m>=0; I=0,1,2 ... s; E represents natural logarithm; a ₀represent the initial monitor value of certain index; M is the damped expoential of anticipation function.

The invention has the beneficial effects as follows, uncertain theory is applied to the environmental stability analysis and prediction of uranium tailings pond, achieve the quantitative test to uranium tailings pond environmental stability on the one hand, obtain the environmental stability dynamic rule of each moment Tailings Dam, overcome the defect of traditional evaluation analysis method, make the stable calculation analysis of uranium tailings pond more reasonable; On the other hand, by indetermination theory the environmental stability of uranium tailings pond is predicted, and taken into full account the multiple situation of change from steady state (SS) to non-steady state and from unsure state to steady state (SS), and programming has shown that environmental index breaks through steady state (SS) in varied situations and comes back to the time needed for steady state (SS), thus the prediction achieved uranium tailings pond environmental stability, more science and analyze the stability of Tailings Dam accurately.

Accompanying drawing explanation

Fig. 1 is uranium tailings pond environmental stability index system figure.

Fig. 2 is leap dam ambient stable rate Changing Pattern figure.

Fig. 3 is Nan Po dam ambient stable rate Changing Pattern figure.

Fig. 4 is pine forest dam ambient stable rate Changing Pattern figure.

Fig. 5 is western eyebrow dam ambient stable rate Changing Pattern figure.

Fig. 6 is the time diagram that straight line growth form breaks through needed for stable region.

Fig. 7 is the time diagram that index growth form breaks through needed for stable region.

Fig. 8 is the time diagram that mechanical periodicity type breaks through needed for stable region.

Fig. 9 is the time diagram that index attenuation type enters needed for stable region.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

Retired uranium tailings pond environmental stability based on uncertain theory is analyzed and a Forecasting Methodology, comprises environmental stability analysis and environmental stability is predicted.

Step one, environmental stability analysis.

1) foundation of uranium tailings pond environmental stability index system;

The flowing of environmental contaminants mainly through water of uranium tailings pond and the diffusive migration of air, affect the pool of periphery, Stream Systems of The Xiang Jiang River and soil and air, the leading indicator affecting environment has been drawn according to principal component analysis (PCA) and correlation technique, and in conjunction with the actual conditions of Uranium tailings, seep water from Tailings Dam, Tailings Dam atmospheric environment, radioactive contamination three aspects have chosen 12 environmental impact indicators, as shown in Figure 1, reach national limit standard through Remediation atmospheric environment index in earlier stage and radioactive contamination index and substantially tended towards stability, therefore the index of uranium tailings pond infiltration is the principal element affecting environmental stability.

Because retired uranium tailings pond stabilization evaluating data is limited, the regularity of distribution of each factor index weight of methods analyst of objective mathematical statistics cannot be adopted, the weight of each index can only be determined according to artificial subjective judgement, and analytical hierarchy process just (AHP) overcome well that these are not enough, various shortage Data support can be applicable to, index system complicated situation, and there is the advantage that qualitative and quantitative analysis combines, result can be judged to be expressed by the form of quantity and to carry out scientific disposal analysis artificial, problem can be reflected all sidedly, therefore determine to adopt analytical hierarchy process to carry out weight assignment.

Utilize analytical hierarchy process to ask the weight of each environmental index, its concrete steps are as follows:

Step 1: Judgement Matricies.(definition of judgment matrix: the judged result numeric representation of the relative importance of each factor of each level in system out, being write as matrix form is exactly judgment matrix).Element value in judgment matrix is the quantitative indices that each element relative importance judges, the judgment matrix C=(C of structure _ij) _{n × n}as shown shown in a.

Table a judgment matrix general type

Criterion B k	C 1	C 2	Λ	C n
					C 1	C 11	C 12	Λ	C 1n
C 2	C 21	C 22	Λ	C 2n
					Μ	Μ	Μ	Λ	Μ
C n	C n1	C n2	Λ	C nn

Judgment matrix C has following character: (1) C _ij>0; (2) C _ij=1/C _ji(i ≠ j); (3) C _ii=1 (i, j=1,2, Λ, n).

In judgment matrix, the numerical value of each element is judged each factor relative importance by expert group, then will judge that quantification obtains according to certain ratio scale.General employing 1 ~ 9 method of scales, judgment matrix scale and implication thereof are in Table b.

Table b judgment matrix scale and implication thereof

Sequence number	Importance rate	C ijAssignment
			1	I, j two elements are of equal importance	1
2	I element is slightly more important than j element	3
			3	I element is obviously more important than j element	5
4	I element is strongly more important than j element	7
			5	I element is extremely more important than j element	9
6	I element is slightly more inessential than j element	1/3
			7	I element is obviously more inessential than j element	1/5
8	I element is strongly more inessential than j element	1/7
			9	I element is extremely more inessential than j element	1/9

The product M of each row element _iif, a _ijfor the element value of the i-th row jth row in judgment matrix, then

$M_i=\underset{j=1}{\overset{n}{\&Pi;}}{a}_{ij}$

Wherein, i=1,2 ... n;

Step 2: calculate M _in th Root

${\stackrel{\&OverBar;}{w}}_i=\sqrt[n]{M_i}$

Step 3: to vector normalized, normalization formula is

$w_i=\frac{{\stackrel{\&OverBar;}{w}}_i}{\underset{j=1}{\overset{n}{\&Sigma;}}{\stackrel{\&OverBar;}{w}}_j}$

W _ifor the weight of each index, then w=[w ₁, w ₂, Λ, w _n] ^tbe required proper vector;

Step 4: the Maximum characteristic root λ calculating judgment matrix _max, (if Cw) _irepresent i-th element of vectorial Cw, then

${\mathrm{\&lambda;}}_{max}=\underset{i=1}{\overset{n}{\&Sigma;}}\frac{{\left(Cw\right)}_i}{{\mathrm{nw}}_i}$

Consistency check: in order to ensure the rationality of conclusion, needs to carry out consistency check to judgment matrix.Consistency check step carried out to judgment matrix as follows:

Step 1: calculate consistency check index CI;

If λ _maxjudgment matrix eigenvalue of maximum, then

$CI=\frac{{\mathrm{\&lambda;}}_{max}-n}{n-1}$

Step 2: search corresponding Aver-age Random Consistency Index RI according to table 1 (note: table 1 is existing public technology, and all RI are unified), wherein n represents the exponent number of judgment matrix.

Table 1 Aver-age Random Consistency Index

n	1	2	3	4	5	6	7	8	9	10	11
												RI	0	0	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.49	1.51

Step 3: calculate random Consistency Ratio CR, computing formula is

$CR=\frac{CI}{RI}$

As CR<0.10, namely think that judgment matrix has satisfied consistance, otherwise just need the element value (namely needing to rethink model or re-construct the larger pairwise comparison matrix of those Consistency Ratios CR) adjusting judgment matrix, make it that there is satisfied consistance.

Through expert group (being made up of the scientific research personnel in this field and staff) environmental index of uranium tailings pond is compared between two, the judgment matrix A of final structure is as follows:

$\left[\begin{array}{cccccc}1& 3/4& 3/2& 3& 5/2& 2\\ 4/3& 1& 2& 4& 7/2& 8/3\\ 2/3& 1/2& 1& 2& 5/3& 4/3\\ 1/3& 1/4& 1/2& 1& 5/6& 2/3\\ 2/5& 1/3& 3/5& 6/5& 1& 4/5\\ 1/2& 3/8& 3/4& 3/2& 5/4& 1\end{array}\right]$

Consistency check is carried out: CR=0.0044 < 0.1 meets the demands according to above step.

Finally obtain the weight vectors of each index: w=(0.23520.31620.15680.07840.09580.1176).

2) calculating of each index stable region;

According to definition and the algorithm 1.1 of stable region, the fetching target probability of stability is 0.95, i.e. α=0.95, then can calculate the stable region of leap dam, Nan Poba, pine forest dam and each index of Xi Meiba, be shown in Table 2.

Algorithm 1.1: the algorithm of stable region

Step 1: input X=[x ₁, x ₂, Λ, x _k], (note: stochastic variable X is the monitor value of certain index, with above) x _k>=0 (x _krepresent the monitor value in certain index kth month), α=0.95;

Step 2: calculate EY _kand DY _k, wherein ${\mathrm{EY}}_k=\frac{1}{k}\underset{i=1}{\overset{k}{\&Sigma;}}{x}_i,{\mathrm{DY}}_k=\frac{1}{k}\underset{i=1}{\overset{k}{\&Sigma;}}{(x_i-{\mathrm{EY}}_k)}^2;$

Wherein: EY _kfor environmental index sequence of random variables Y _kmathematical expectation, DY _kfor environmental index sequence of random variables Y _kvariance, k represents a kth month of environment Monitoring Indexes, is also simultaneously the starting point moment of environmental stability prediction;

Step 3: calculate ε _k(ε _kbe the intermediate variable of parameter stable region, reacted the degree that different monitoring moment stable region departs from sequence of random variables expectation value), wherein

Step 4: calculate a _k, b _k(a _k, b _kthe lower limit of the stable region before representing respectively corresponding to k month index and the upper limit), wherein a _k=EY _k-ε _k, b _k=EY _k+ ε _k;

Step 5: export [a _k, b _k]; Calculate $\underset{i=1}{\overset{k}{I}}\&lsqb;a_k,b_k\&rsqb;=\&lsqb;a,b\&rsqb;.$

Then result of calculation [a, b] is the stable region of required front k month.

The stable region of table 2 each monolith main environment index

3) analysis of uranium tailings pond each monolith ambient stable rate;

2010-2012 leap dam, Nan Po dam, pine forest dam, the western eyebrow dam environmental monitoring data of 36 months are substituted into the stable region that algorithm 1.1 obtains each index, can obtain each monolith ambient stable rate ρ curve over time in conjunction with the computing formula of ambient stable rate in definition 2 again, result of calculation as Figure 2-Figure 5.

Dam total environment steadiness of leaping as shown in Figure 2 is better, except 12nd month, beyond the 30th month and 33rd month, the ambient stable rate in all the other months is 1, illustrate that the main environment Monitoring Indexes value in leap dam major part month is all in steady state (SS) thus, environmental stability is better.

Nan Po dam total environment steadiness is poor as shown in Figure 3,36 middle of the month only have 13 months ambient stable rates to equal 1, all the other, ambient stable rate was all less than 1 in month, and the fluctuation of coefficient of stabilization curve is larger, illustrate that the main environment Monitoring Indexes value in Nan Po dam major part month is all beyond steady state (SS) thus, environmental stability is poor.

Pine forest dam total environment steadiness is better as shown in Figure 4,36 middle of the month have 29 months ambient stable rates to equal 1, the ambient stable rate in all the other months is less than 1, fluctuation within a narrow range is there is in coefficient of stabilization curve in some month, but general status is better, illustrate that pine forest dam environment is in steady state (SS) substantially thus.

Western eyebrow dam total environment steadiness is very poor as shown in Figure 5,36 middle of the month only have 6 months ambient stable rates to equal 1, all the other, ambient stable rate was all less than 1 in month, the coefficient of stabilization in some month is even less than 0.5, and the amplitude of coefficient of stabilization curve fluctuation and scope are all very large, illustrate that leap dam environment is in extremely unstable state.

Step 2, environmental stability are predicted;

1) be converted into non-steady state required time by steady state (SS) to predict;

Become non-steady state mainly because the monitor value of uranium tailings pond following a period of time accumulates contribution break through original stable region from steady state (SS), suppose t _kthe initial value a of moment index ₀for the average of stable region, i.e. a ₀=EY _k, predict that monitor value presses straight line change, breaks through the time needed for stable region when index variation and mechanical periodicity on this basis respectively.The corresponding stable emissions of actual cathetus growth form, exponential increase correspondence accelerates discharge, the corresponding regular discharge of mechanical periodicity type etc., its Growth Function y _irespectively as shown in figs 6-8.

Be converted into non-steady state by steady state (SS), new stable region is broken through and to be needed the relational expression met to be between original stable elastic region:

$\frac{\underset{i=1}{\overset{k+s}{\&Sigma;}}{y}_i}{k+s}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{k+s}{\&Sigma;}}{(y_i-\frac{\underset{i=1}{\overset{k+s}{\&Sigma;}}{y}_i}{k+s})}^2}{k+s}}\&GreaterEqual;\frac{\underset{i=1}{\overset{k}{\&Sigma;}}{y}_i}{k}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{k}{\&Sigma;}}{(y_i-\frac{\underset{i=1}{\overset{k}{\&Sigma;}}{y}_i}{k})}^2}{k}}+\frac{b-a}{l}$

Wherein: y _irepresent the monitor value in this index each month, as 1≤i≤k, y _iequal the monitor value in a front k month, as i>k, y _icorresponding three kinds of Growth Function respectively, and k=36 in this test case.

According to analytic method process, between the elastic region devising algorithm 1.2 parameter, algorithm 1.3 parameter is converted into the time needed for non-steady state by steady state (SS).

Algorithm between algorithm 1.2 index elastic region;

Step 1: input ε _k, a, b, l; (a, b represent lower limit and the higher limit of index stable region respectively, and l is the elasticity coefficient between elastic region)

Step 2: calculate a ^*, b ^*, wherein i=1,2, Λ, k; (a ^*, b ^*represent the lower limit between index elastic region and higher limit respectively)

Step 3: export [a ^*, b ^*].

Wherein [a ^*, b ^*] be front k month between certain elastic region corresponding to index stable region.

Algorithm 1.3 steady state (SS) is to the algorithm of non-steady state required time;

Step 1: input X=[x ₁, x ₂, Λ, x _k] and the front k stable region [a of individual month _k, b _k];

(X is consistent with the X implication in algorithm 1.1 herein, all represent before k month Monitoring Indexes value formation set)

Step 2: calculate x (n+1)=f (t _n+1), x=f (t) is the concentration change function of structure; Upgrade X=[x ₁, x ₂, Λ, x _k, x _k+1];

Step 3: utilize algorithm 1.1 to calculate corresponding stable region [a _k+1, b _k+1], if then calculate and terminate and export kth+1 to start unstable; Otherwise, then export kth and stablize for+1 month, and upgrade k=k+1, get back to second step cycle calculations, until export crank-up time.

Now to leap dam F ion for 2010-2012, detailed data is listed by table 3, becomes the time needed for non-steady state, then initial time t when changing by Fig. 6-8 according to the Monitoring Data prediction F ion monitor value of 36 months in table 3 from steady state (SS) _k=t ₃₆, calculate [t ₁, t ₃₆] stable region of F ion in the time according to the scope of the condition determination F ion l in definition 3, because after stable region determines, [a between the average area zone of approach of known first 36 months ₃₆, b ₃₆], make so choose l $a^{*}=a_{36}-\frac{b_{36}-a_{36}}{20}$ Or $b^{*}=b_{36}-\frac{b_{36}-a_{36}}{20},$ Utilize [a between the elastic region corresponding to algorithm 1.2 calculation stability interval ^*, b ^*].

Table 32010-2012 leap dam F ion Monitoring Data

Sequence of random variables Y is calculated by 36 Monitoring Data of F ion in table 3 ₃₆mathematical expectation EY ₃₆with variance DY ₃₆, and a ₀initial value be respectively:

EY ₃₆＝1.6295，DY ₃₆＝1.0759，a ₀＝1.6295.

The stable region that after supposing s month, F ion is new breaches the stable region of original 36 months monitor values just, then have

$\frac{\underset{i=1}{\overset{36+s}{\&Sigma;}}{y}_i}{36+s}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{36+s}{\&Sigma;}}{(y_i-\frac{\underset{i=1}{\overset{36+s}{\&Sigma;}}{y}_i}{36+s})}^2}{36+s}}\&GreaterEqual;\frac{\underset{i=1}{\overset{36}{\&Sigma;}}{y}_i}{36}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{36}{\&Sigma;}}{(y_i-\frac{\underset{i=1}{\overset{36}{\&Sigma;}}{y}_i}{36})}^2}{36}}+\frac{b-a}{20}$

Wherein, y _irepresent the observed reading in F ion each month, when 1≤i≤36, y _iequal the monitor value of first 36 months, as i>36, y _ican be tried to achieve by Growth Function, and

According to the Monitoring Data in algorithm 1.3 and table 3, utilize C ⁺⁺language is programmed, with dam of leaping for example, the time that F ion in three kinds of situations is become required for non-steady state from steady state (SS) is predicted, detailed results is in shown in Table 4-6, in like manner other indexs of measurable leap dam press the time of breakthrough needed for stable region when straight line increases, and just do not list one by one herein.

Table 4 is leaped and is broken through the time prediction of stable region when dam F ion increases by straight line

M value	Predicted time (moon)	M value	Predicted time (moon)
				≤0.01	157	0.13～0.14	12
0.02	75	0.14～0.15	11
				0.03	47	0.16～0.17	10
0.04	37	0.18～0.20	9
				0.05	29	0.21～0.23	8
0.06	25	0.24～0.28	7
				0.07	21	0.29～0.35	6
0.08	19	0.36～0.47	5
				0.09	17	0.48～0.67	4
0.10	15	0.68～1.09	3
				0.11	14	1.10～2.43	2
0.12	13	≥2.44	1

Table 5 is leaped and is broken through the time prediction of stable region when dam F ion exponentially increases

Table 6 leaps dam F ion by the time prediction breaking through stable region during mechanical periodicity

M value	Predicted time (moon)	M value	Predicted time (moon)
				0.01	17	0.88～1.30	8
0.02	15	1.31～1.43	7
				0.03～0.04	14	＝1.44	6
0.05～0.06	13	1.45～1.50	5
				0.07～0.11	12	1.51～1.74	4
0.12～0.21	11	1.75～2.44	3
				0.22～0.44	10	2.45～4.87	2
0.45～0.87	9	＝4.88	1

2) be converted into steady state (SS) required time by non-steady state to predict;

Become steady state (SS) from non-steady state to need monitor value constantly to accumulate minimizing just to enter original stable region, suppose the initial value a of certain index ₀for the maximal value y of Historical Monitoring data _max, enter the time needed for stable region when prediction index monitor value is exponentially decayed on this basis, actual Exponential attenuation type corresponding natural purification and manual intervention etc., its attenuation function y _ias shown in Figure 9.

Be converted into steady state (SS) by non-steady state, new stable region reenters and to need the relational expression met to be between original stable elastic region:

$\frac{\underset{i=1}{\overset{k+s}{\&Sigma;}}{y}_i}{k+s}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{k+s}{\&Sigma;}}{(y_i-\frac{\underset{i=1}{\overset{k+s}{\&Sigma;}}{y}_i}{k+s})}^2}{k+s}}\&le;\frac{\underset{i=1}{\overset{k}{\&Sigma;}}{y}_i}{k}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{k}{\&Sigma;}}{(y_i-\frac{\underset{i=1}{\overset{k}{\&Sigma;}}{y}_i}{k})}^2}{k}}+\frac{b-a}{l}$

Wherein, y _irepresent the observed reading in this index each month.As 1≤i≤k, y _iequal the monitor value of front k month; As i>k, y _i=EY _k+ (a ₀-EY _k) e ^-mi, wherein m>=0; I=0,1,2 ... s; (e represents natural logarithm, approximates 2.72; a ₀represent the initial monitor value of certain index; M is the damped expoential of anticipation function), k=36 in test, y in instance analysis _i=EY _k+ (y _max-EY _k) e ^-mi, and wherein, 1≤i≤k.Y _maxfor the maximal value of certain index Historical Monitoring data.

For 2010-2012 western eyebrow dam F ion, when exponentially decaying according to the Monitoring Data prediction F ion of 36 months in table 7, become time needed for steady state (SS), then initial time t from non-steady state _k=t ₃₆, calculate [t ₁, t ₃₆] stable region of F ion in the time the scope of l is determined, line-like according to definition

Growth form, [a between the elastic region utilizing algorithm 1.2 to calculate F ion stability ^*, b ^*].

Table 72010-2012 western eyebrow dam F ion Monitoring Data

Sequence of random variables Y is calculated by 36 Monitoring Data of F ion in table 7 ₃₆mathematical expectation EY ₃₆with variance DY ₃₆, and a ₀initial value be respectively

EY ₃₆＝3.64，DY ₃₆＝16.89，a ₀＝25.25.

The stable region that after supposing s month, F ion is new enters the stable region of 36 months original monitor values just, can obtain as lower inequality according to previous analysis

$\frac{\underset{i=1}{\overset{36+s}{\&Sigma;}}{y}_i}{36+s}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{36+s}{\&Sigma;}}{(y_i-\frac{\underset{i=1}{\overset{36+s}{\&Sigma;}}{y}_i}{36+s})}^2}{36+s}}\&le;\frac{\underset{i=1}{\overset{36}{\&Sigma;}}{y}_i}{36}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{36}{\&Sigma;}}{(y_i-\frac{\underset{i=1}{\overset{36}{\&Sigma;}}{y}_i}{36})}^2}{36}}+\frac{b-a}{20}$

Wherein, y _irepresent the observed reading in F ion each month.When 1≤i≤36, y _iequal the monitor value in front 36 month, as i>36, y _i=3.64+21.61e ^-mi, and

According to the primary monitoring data in algorithm 1.3 and table 7, utilize C ⁺⁺language is programmed, to the west of eyebrow dam be example, predict the time that F ion is become required for steady state (SS) from non-steady state, detailed results is in table 8, enter the time needed for stable region when in like manner other indexs of measurable Xi Meiba exponentially decay, just do not list one by one herein.

Table 8 western eyebrow dam F ion enters the time prediction of stable region when exponentially decaying

M value	Predicted time (moon)	M value	Predicted time (moon)
				0.15	149	＝0.80	47
0.20	117	＝0.85	46
				0.25	98	＝0.90	45
0.30	85	＝0.95	44
				0.35	76	＝1.00	43
0.40	70	1.05～1.10	42
				0.45	64	＝1.15	41
0.50	60	1.20～1.30	40
				0.55	57	1.35～1.45	39
0.60	54	1.50～1.65	38
				0.65	52	1.70～1.95	37
0.70	50	2.00～2.75	36
				0.75	48	＝2.80	35

Key point of the present invention is the quantitative test of uncertain theory to retired uranium tailings pond environmental stability, and retired uranium tailings pond environmental index stablizes the prediction with the non-steady state time.Environmental index is mainly contained to the prediction of the ambient stable process of retired uranium tailings pond and is converted into by steady state (SS) two kinds of prediction theory methods that non-steady state and non-steady state are converted into steady state (SS), the index that can dope under the steady state (SS) index entered under time of non-steady state and non-steady state enters the time of steady state (SS), for Tailings Dam environmental improvement provides theoretical foundation.

The present invention utilizes the correlation techniques such as probability analysis, draw the stable region of uranium tailings pond Environmental Pollution index, and calculate the ambient stable rate of uranium tailings pond in different time points, define the fuzzy conception of uranium tailings pond environmental stability with accurate mathematical linguistics, achieve the combination to the qualitative analysis of uranium tailings pond environmental stability and quantitatively calculating.Be converted into non-steady state required time to uranium tailings pond environmental index by steady state (SS) to predict, and consider that environmental index monitor value increases by straight line, exponential increase and mechanical periodicity time break through time needed for stable region; Simultaneously, also be converted into steady state (SS) required time to uranium tailings pond environmental index by non-steady state to predict, and consider environmental index monitor value exponentially attenuation change time enter time needed for stable region, for retired uranium tailings pond safety management and decision analysis provide theoretical foundation.

Claims (6)

1. the retired uranium tailings pond environmental stability based on uncertain theory is analyzed and a Forecasting Methodology, it is characterized in that, carries out according to following steps:

Step one, environmental stability analysis;

1) foundation of uranium tailings pond environmental stability index system;

2) calculating of each index stable region;

3) analysis of uranium tailings pond each monolith ambient stable rate;

Step 2, environmental stability are predicted;

1) be converted into non-steady state required time by steady state (SS) to predict;

2) be converted into steady state (SS) required time by non-steady state to predict.

2. a kind of retired uranium tailings pond environmental stability based on uncertain theory according to claim 1 is analyzed and Forecasting Methodology, it is characterized in that, in described step one, the foundation of uranium tailings pond environmental stability index system, utilize analytical hierarchy process to ask the weight of each environmental index, specifically carry out according to following steps:

Step 1: Judgement Matricies;

Element value in judgment matrix is the quantitative indices that each element relative importance judges, the judgment matrix C=(C of structure _ij) _{n × n}as shown shown in a;

Table a

Criterion B _k C ₁ C ₂ Λ C _n C ₁ C ₁₁ C ₁₂ Λ C _1n C ₂ C ₂₁ C ₂₂ Λ C _2n Μ Μ Μ Λ Μ C _n C _n1 C _n2 Λ C _nn

Judgment matrix C has following character: (1) C _ij>0; (2) C _ij=1/C _ji(i ≠ j); (3) C _ii=1 (i, j=1,2, Λ, n);

In judgment matrix, the numerical value of each element judges each factor relative importance, then will judge that quantification obtains according to ratio scale, and adopt 1 ~ 9 method of scales, judgment matrix scale and implication thereof are in Table b;

Table b

Sequence number Importance rate C _ijAssignment 1 I, j two elements are of equal importance 1 2 I element is slightly more important than j element 3 3 I element is obviously more important than j element 5 4 I element is strongly more important than j element 7 5 I element is extremely more important than j element 9 6 I element is slightly more inessential than j element 1/3 7 I element is obviously more inessential than j element 1/5 8 I element is strongly more inessential than j element 1/7 9 I element is extremely more inessential than j element 1/9

M _ifor the product of each row element, if a _ijfor the element value of the i-th row jth row in judgment matrix, then

$M_i=\underset{j=1}{\overset{n}{\mathrm{\&Pi;}}}{a}_{ij}$

Wherein, i=1,2 ... n;

Step 2: calculate M _in th Root

$\stackrel{\&OverBar;}{w_i}=\sqrt[n]{M_i}$

Step 3: to vector normalized, normalization formula is

$w_i=\frac{{\stackrel{\&OverBar;}{w}}_i}{\underset{j=1}{\overset{n}{\&Sigma;}}{\stackrel{\&OverBar;}{w}}_j}$

W _ifor the weight of each index, then w=[w ₁, w ₂, Λ, w _n] ^tbe required proper vector;

Step 4: the Maximum characteristic root λ calculating judgment matrix _max, (if Cw) _irepresent i-th element of vectorial Cw, then

${\mathrm{\&lambda;}}_{max}=\underset{i=1}{\overset{n}{\&Sigma;}}\frac{{\left(Cw\right)}_i}{{\mathrm{nw}}_i}.$

3. a kind of retired uranium tailings pond environmental stability based on uncertain theory according to claim 2 is analyzed and Forecasting Methodology, it is characterized in that, carries out consistency check step as follows to judgment matrix:

Step 1: calculate consistency check index CI;

If λ _maxjudgment matrix eigenvalue of maximum, then

$CI=\frac{{\mathrm{\&lambda;}}_{max}-n}{n-1}$

Step 2: search corresponding Aver-age Random Consistency Index RI according to table 1, wherein n represents the exponent number of judgment matrix;

Table 1

n 1 2 3 4 5 6 7 8 9 10 11 RI 0 0 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49 1.51

Step 3: calculate random Consistency Ratio CR, computing formula is

$CR=\frac{CI}{RI}$

As CR<0.10, namely think that judgment matrix has satisfied consistance, otherwise just need the element value adjusting judgment matrix, make it that there is satisfied consistance.

4. a kind of retired uranium tailings pond environmental stability based on uncertain theory according to claim 1 is analyzed and Forecasting Methodology, and it is characterized in that, in described step one, the calculating of each index stable region is carried out according to following steps:

Algorithm 1.1: the algorithm of stable region;

Step 1: input X=[x ₁, x ₂, Λ, x _k], stochastic variable X is the monitor value of certain index, x _k>=0, x _krepresent the monitor value in certain index kth month, α=0.95;

Step 2: calculate EY _kand DY _k, wherein ${\mathrm{EY}}_k=\frac{1}{k}\underset{i=1}{\overset{k}{\&Sigma;}}{x}_i,{\mathrm{DY}}_k=\frac{1}{k}\underset{i=1}{\overset{k}{\&Sigma;}}{(x_i-{\mathrm{EY}}_k)}^2;$

Wherein: EY _kfor environmental index sequence of random variables Y _kmathematical expectation, DY _kfor environmental index sequence of random variables Y _kvariance, k represents a kth month of environment Monitoring Indexes, is also simultaneously the starting point moment of environmental stability prediction;

Step 3: calculate ε _k, ε _kbe the intermediate variable of parameter stable region, reacted the degree that different monitoring moment stable region departs from sequence of random variables expectation value, wherein

Step 4: calculate a _k, b _k; a _k, b _kthe lower limit of the stable region before representing respectively corresponding to k month index and the upper limit, wherein a _k=EY _k-ε _k, b _k=EY _k+ ε _k;

Step 5: export [a _k, b _k]; Calculate $\underset{i=1}{\overset{k}{I}}\&lsqb;a_k,b_k\&rsqb;=\&lsqb;a,b\&rsqb;;$

Then result of calculation [a, b] is the stable region of required front k month.

5. a kind of retired uranium tailings pond environmental stability based on uncertain theory according to claim 4 is analyzed and Forecasting Methodology, it is characterized in that, the analysis of uranium tailings pond each monolith ambient stable rate adopts following steps to carry out:

The environmental monitoring data in multiple for each monolith month is substituted into the algorithm of stable region, obtain the stable region of each index, then the computing formula of combining environmental coefficient of stabilization, obtain each monolith ambient stable rate ρ curve over time;

Wherein, the definition of ambient stable rate and computing formula as follows:

If x _ifor each index observed value at a time, w _ifor the weight of each environmental index, for the indicative function of each index stable region, for index A _ithe lower limit of stable region, for index A _ithe higher limit of stable region, ambient stable rate ρ is the extent of stability of a certain moment Tailings Dam environment, and

$\mathrm{\&rho;}=w_1{\mathrm{\&chi;}}_{A_1}\left(x_1\right)+w_2{\mathrm{\&chi;}}_{A_2}\left(x_2\right)+\mathrm{\&Lambda;}+w_m{\mathrm{\&chi;}}_{A_m}\left(x_m\right)=\underset{i=1}{\overset{m}{\&Sigma;}}{w}_i\&CenterDot;{\mathrm{\&chi;}}_{A_i}\left(x_i\right)$

Wherein, indicative function can be expressed as

6. a kind of retired uranium tailings pond environmental stability based on uncertain theory according to claim 4 is analyzed and Forecasting Methodology, it is characterized in that, described step 2, is converted into the prediction of non-steady state required time by steady state (SS) and specifically carries out according to following steps:

Suppose t _kthe initial value a of moment index ₀for the average of stable region, i.e. a ₀=EY _k, predict that monitor value presses straight line change respectively, when index variation and mechanical periodicity, break through the time needed for stable region;

Be converted into non-steady state by steady state (SS), new stable region is broken through and to be needed the relational expression met to be between original stable elastic region:

$\frac{\underset{i=1}{\overset{k+s}{\mathrm{\&Sigma;}}}{y}_i}{k+s}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{k+s}{\mathrm{\&Sigma;}}}{(y_i-\frac{\underset{i=1}{\overset{k+s}{\mathrm{\&Sigma;}}}{y}_i}{k+s})}^2}{k+s}}\&GreaterEqual;\frac{\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{y}_i}{k}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{(y_i-\frac{\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{y}_i}{k})}^2}{k}}+\frac{b-a}{l}$

Wherein: yi represents the monitor value in this index each month, as 1≤i≤k, yi equals the monitor value in a front k month, as i>k, and y _icorresponding three kinds of Growth Function respectively, and

Between the elastic region of algorithm for design 1.2 parameter, algorithm 1.3 parameter is converted into the time needed for non-steady state by steady state (SS);

Algorithm 1.2: the algorithm between index elastic region;

Step 1-1: input ε _k, a, b, l; Wherein, a, b represent lower limit and the higher limit of index stable region respectively, and l is the elasticity coefficient between elastic region;

Step 1-2: calculate a ^*, b ^*, wherein i=1,2, Λ, k; a ^*, b ^*represent the lower limit between index elastic region and higher limit respectively;

Step 1-3: export [a ^*, b ^*];

Wherein [a ^*, b ^*] be front k month between certain elastic region corresponding to index stable region;

Algorithm 1.3: steady state (SS) is to the algorithm of non-steady state required time;

Step 2-1: input X=[x ₁, x ₂, Λ, x _k] and the front k stable region [a of individual month _k, b _k]; X represent front k month Monitoring Indexes value form set;

Step 2-2: calculate x (n+1)=f (t _n+1), x=f (t) is the concentration change function of structure; Upgrade X=[x ₁, x ₂, Λ, x _k, x _k+1];

Step 2-3: utilize algorithm 1.1 to calculate corresponding stable region [a _k+1, b _k+1], if then calculate and terminate and export kth+1 to start unstable; Otherwise, then export kth and stablize for+1 month, and upgrade k=k+1, get back to step 2-2 cycle calculations, until export crank-up time;

Described step 2, is converted into the prediction of steady state (SS) required time by non-steady state and specifically carries out according to following steps:

Suppose the initial value a of certain index ₀for the maximal value y of Historical Monitoring data _max, when prediction index monitor value is exponentially decayed on this basis, enter the time needed for stable region;

Be converted into steady state (SS) by non-steady state, new stable region reenters and to need the relational expression met to be between original stable elastic region:

$\frac{\underset{i=1}{\overset{k+s}{\mathrm{\&Sigma;}}}{y}_i}{k+s}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{k+s}{\mathrm{\&Sigma;}}}{(y_i-\frac{\underset{i=1}{\overset{k+s}{\mathrm{\&Sigma;}}}{y}_i}{k+s})}^2}{k+s}}\&le;\frac{\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{y}_i}{k}+\sqrt{20\&times;\frac{\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{(y_i-\frac{\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{y}_i}{k})}^2}{k}}+\frac{b-a}{l}$

Wherein, y _irepresent the observed reading in this index each month; As 1≤i≤k, y _iequal the monitor value of front k month; As i>k, y _i=EY _k+ (a ₀-EY _k) e ^-mi, wherein m>=0; I=0,1,2 ... s; E represents natural logarithm; a ₀represent the initial monitor value of certain index; M is the damped expoential of anticipation function.