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目 錄
1概述 1
2大氣污染預(yù)測方法 1
2.1空氣質(zhì)量模型 2
2.1.1箱模型 2
2.1.2高斯模型 2
2.1.3 K模型 2
2.2灰色理論模型 3
2.2.1 GM(1,1)模型 3
2.2.2 GM(1,N)模型 4
2.3投影尋蹤回歸模型 5
2.4模糊理論模型 6
2.5環(huán)境質(zhì)量計算模型 6
2.6統(tǒng)計理論方法 7
3大氣污染預(yù)測中應(yīng)注意的幾個問題 7
4結(jié)論 8
參 考 文 獻 8
1 Overview 10
2 Air Pollution Forecast Method 11
2.1 Air Quality Model 11
2.1.1 A Box Model 11
2.1.2 Gaussian Model 12
2.1.3 K Model 12
2.2 Gray Theory Model 13
2.2.1 GM(1,1) Model 13
2.2.2 GM(1,N)Model 14
2.3 Projection Pursuit Regression Model 15
2.4 Fuzzy Theory Model 16
2.5 Environmental Quality Measurement Model 17
2.6 Statistical Theory Method 17
3 Some Problems Must be paid Attention To In Air Pollution Forecast 18
4 Conclusion 19
References 20
大氣污染預(yù)測方法探討
鄭博福 游海 弓曉峰 齊美富
(南昌大學(xué)環(huán)境與化學(xué)工程學(xué)院,江西南昌 330029)
摘要 綜述當前常用的大氣污染預(yù)測方法,對空氣質(zhì)量模型、灰色理論模型、投影尋蹤回歸模型等3種主要的大氣污染預(yù)測方法進行了詳細介紹,重點分析討論了這些方法的實用性和局限性,闡述了進行大氣污染預(yù)測時應(yīng)注意的幾個問題。
關(guān)鍵詞 大氣污染, 預(yù)測, 模型
1 概 述
預(yù)測就是根據(jù)主觀的經(jīng)驗和教訓(xùn)、客觀的資料與條件和演變的邏輯與推斷,尋求事物的發(fā)展規(guī)律,對事物未來發(fā)展趨勢和可能達到的水平做出估計和推斷。環(huán)境預(yù)測是以人口為中心,以社會經(jīng)濟預(yù)測和科學(xué)技術(shù)預(yù)測為基礎(chǔ),預(yù)計和推測隨著人口、經(jīng)濟、政策等社會因素的發(fā)展環(huán)境的變化趨勢，提出防止環(huán)境質(zhì)量惡化和改善環(huán)境質(zhì)量的對策,達到社會的發(fā)展與環(huán)境保護之間的協(xié)調(diào)與統(tǒng)一。
污染預(yù)測是環(huán)境預(yù)測的基礎(chǔ)和重要組成部分,污染預(yù)測的誤差大小直接影響著環(huán)境預(yù)測質(zhì)量。污染預(yù)測根據(jù)預(yù)測對象可以分大氣污染預(yù)測、水污染預(yù)測、土壤污染預(yù)測、噪聲污染預(yù)測等。大氣污染預(yù)測就是預(yù)測某一特定區(qū)域的大氣污染的未來變化趨勢,并提出改善大氣環(huán)境質(zhì)量的對策,為決策部門在制定該區(qū)域大氣污染防治規(guī)劃與經(jīng)濟發(fā)展規(guī)劃時提供參考和依據(jù)。
2 大氣污染預(yù)測方法
目前,國內(nèi)外學(xué)者用于大氣污染預(yù)測的方法模型主要有:空氣質(zhì)量模型、灰色理論模型、投影尋蹤回歸模型、模糊理論模型、線型系統(tǒng)分析模型、環(huán)境質(zhì)量計量模型、統(tǒng)計理論方法等預(yù)測模型和方法。
2.1空氣質(zhì)量模型
常用于大氣污染預(yù)測的空氣質(zhì)量模型有:箱模型、高斯模型及K理論模型。
2.1.1箱模型
箱模型是一種最簡單的城市空氣質(zhì)量模型。它把整個城市空間看作為一個或多個矩形的箱形式,其主要假設(shè)條件為:1)在一個箱體內(nèi),污染源(看作面源)的源強是一個常數(shù);2)污染物進入箱體(大氣)后,立即在鉛直方向均勻分布。由于城市污染源分布比較均勻,鉛直擴散速率較快,上述假設(shè)有一定的合理性。但是箱模型的假定與實際情況有很大差異,對近地面的濃度估算偏低。
2.1.2高斯模型
高斯模型是城市空氣質(zhì)量模型中最主要的應(yīng)用模型,因為:1)大多數(shù)平原城市及郊區(qū)的范圍在20～30km以內(nèi),流場并不十分復(fù)雜;2)城市空氣質(zhì)量模型的誤差主要來源于模型輸入?yún)?shù),尤其是污染源資料并不可能十分準確、精細,使對模型本身的改進歸于徒勞,從應(yīng)用的效果看,復(fù)雜數(shù)值模型并不優(yōu)于高斯模型;3)高斯模型對氣象資料的需求比其它空氣質(zhì)量模型對氣象資料的需求更低,而運算效果卻明顯提高。
高斯模型具有簡單實用、空間分辨率高的優(yōu)點,但它有以下不足之處:1) 當模擬的尺度達到幾十公里,或者因下墊面不均勻,使流場比較復(fù)雜時,高斯煙流模型的精度就難以滿足要求;2)高斯模型的沉積和化學(xué)轉(zhuǎn)化過程只能十分粗略的處理,當這些過程已相當重要或者作為研究對象時,高斯模型不適用。
2.1.3 K模型
該模型是由平流擴散方程式經(jīng)各種簡化假設(shè)而推導(dǎo)得出的,它具有如下效能:1)能夠模擬三維非定常流場中的輸送和擴散,因此可以模擬復(fù)雜下墊面和較大的尺度范圍內(nèi)的空氣污染;2)污染源場可以任意給定,即Q=Q(x,y,z,t),3)邊界可以反射、吸收和穿透污染物質(zhì),其濃度在邊界上可變;4)可以模擬包括非線型化學(xué)反應(yīng)引起的濃度變化;5)可以模擬干、濕沉積引起的濃度的變化。
因為K模型來源于模仿分子擴散的梯度輸送假設(shè),它具有一定的局限性;1)梯度輸送假設(shè)要求滿足一定的尺度條件,使擴散方程僅僅在煙流尺度大于占優(yōu)勢的湍渦尺度時才是正確的;2)對流條件下梯度-輸送關(guān)系不成立,可能出現(xiàn)反梯度輸送的現(xiàn)象,不能應(yīng)用K模型;3)K模型對基礎(chǔ)資料及輸入?yún)?shù)的要求很高。
空氣質(zhì)量模型的預(yù)測精度在很大程度上依賴于對污染源和氣象條件的預(yù)測精度,因此,比較適用于短時污染預(yù)測,一般不用于長期污染預(yù)測。
2.2灰色理論模型
由于灰色理論模型在建模、預(yù)測、控制等方面的獨到性,十多年來已在氣象、生態(tài)、環(huán)境、社會經(jīng)濟等領(lǐng)域得了廣泛應(yīng)用,常用于環(huán)境污染預(yù)測得灰色理論模型主要有:GM(1,1)模型和GM(1,N)模型。
2.2.1 GM(1,1)模型
該模型是對原始數(shù)據(jù)列|}作累加生成,弱化隨機性后建立的時間連續(xù)性微分方程,一般形式為
+ χ =μ (1)
式中: ,μ為參數(shù),可由最小二乘法解得。
離散響應(yīng)值為
(2)
此時是累加值,可以還原成預(yù)測值模型:
(3)
式中
(4)
模型建立后,k為定值
該模型相當于指數(shù)模型y=aebx,是特定的指數(shù)曲線,形狀簡單,具有單調(diào)性,其特點是能反映事物發(fā)展的趨勢,但不能很好地擬合擺動過程,對變化幅度大、起伏大地數(shù)據(jù)顯得無能為力。因而,該模型對數(shù)據(jù)的分布有一定的要求。
2.2.2 GM(1,N)模型
該模型是由N個變量組成的一階線型動態(tài)時間連續(xù)微分方程,一般形式為
其中,是對原始數(shù)列作最后一次累加生成,即
記系數(shù)向量為,可由最小二乘求得,由此可得離散響應(yīng)值為
最后,對作一次還原生成,即
則就是未來預(yù)測值。
在用該模型進行環(huán)境污染的預(yù)測時,首先需要確定出與要預(yù)測的因子相關(guān)性較大的影響因子(如社會、經(jīng)濟因子等),在選取主要影響因子時,一般要采用灰色關(guān)聯(lián)分析方法。由于該模型采用了影響因子的篩選,使環(huán)境預(yù)測與社會、經(jīng)濟等因素預(yù)測相結(jié)合,從而提高了預(yù)測的精確度和可信度。
2.3投影尋蹤回歸模型
投影尋蹤回歸模型是用來處理和分析高維非正態(tài)觀測數(shù)據(jù)的一種探索數(shù)據(jù)分析新方法。其基本思想是:把高維數(shù)據(jù)投影到低維空間上,通過極小化某個投影指標,尋找出能反映原高維數(shù)據(jù)結(jié)構(gòu)或特征的投影,以達到研究、分析高維數(shù)據(jù)的目的。
K階投影尋蹤自回歸(PPAR(k))模型的一般形式為
式中: xi為時間序列{x|在t時刻估計值,xi-1,xi-2…,xi-k為k個時序預(yù)測因子,其選取最終由數(shù)據(jù)結(jié)構(gòu)決定,為第m 個投影方向含量,滿足||||=1,是的最優(yōu)分段線性函數(shù),稱為嶺函數(shù),它是一個數(shù)值函數(shù), 表示第m個嶺函數(shù)對xi的貢獻大小的權(quán)重系數(shù)。
尋找xi的表示方法是逐次找出最優(yōu)的:
模型的最小準則是選取適當?shù)膮?shù)求滿足下式的解：
該式中“E”為運算符,表示“誤差的平方和的均值”。
K 階自回歸實際上是一個多變量輸入、單變量輸出的問題。為了適合xi與 xi-1,xi-2…,xi-k不呈線性關(guān)系的特點．PPAR(k)模型選取一系列嶺函數(shù)的“和”來逼近目標函數(shù)的方法，即用增大 M 的方法來減少模型誤差，并且采用遙段線性函數(shù)在相應(yīng)各投影方向上不斷對觀測數(shù)據(jù)平滑逼近得到的數(shù)值函數(shù)。能使模型更客觀地反映數(shù)據(jù)本身的內(nèi)在結(jié)構(gòu)。從而增強預(yù)測結(jié)果的穩(wěn)定性。
2.4模糊理論模型
模糊理論知識特別是模糊聚類分析、系統(tǒng)模型參數(shù)辨識以及模糊模型識別等知識廣泛用于環(huán)境預(yù)測中。
在大氣污染預(yù)測中,由于影響大氣污染物濃度的因素是多方面的,大氣污染物濃度的高低沒有明確的界限,具有模糊性,一般的單變量統(tǒng)計方法難以客觀反映各指標與污染物濃度間的相關(guān)關(guān)系。而運用模糊識別理論法,可以利用已有的實測資料,能計算得到相應(yīng)的最優(yōu)模糊分類中心矩陣、最優(yōu)模糊劃分矩陣和指標綜合權(quán)重矩陣等有用參數(shù),然后應(yīng)用最優(yōu)模糊識別理論進行預(yù)測,且可以隨著實測資料的增多和變化不斷進行參數(shù)調(diào)整,使其能夠貼切地反映實際情況。
在進行環(huán)境污染預(yù)測時,模糊理論知識一般情況下都和其它預(yù)測模型結(jié)合使用,這樣能取得更好的預(yù)測效果。因為用模糊聚類分析可以較好地把影響環(huán)境質(zhì)量的各種因素按主次區(qū)分開來,預(yù)測環(huán)境污染只需考慮必要的影響因素(主因素)而將次要因素略去,如果考慮的影響因素過多,不僅使計算量增大,還會得不到好的預(yù)測效果;如果考慮的影響因素過少,沒有把主要因素考慮進去,則預(yù)測的結(jié)果是不可信的。
2.5環(huán)境質(zhì)量計算模型
環(huán)境質(zhì)量計量模型是通過對環(huán)境系統(tǒng)中大量隨機現(xiàn)象的研究，確定環(huán)境質(zhì)量與環(huán)境系統(tǒng)中各因素之間的相互作用形式，以數(shù)學(xué)模型來預(yù)測環(huán)境質(zhì)量變化趨勢，主要有回歸分析模型和 投入產(chǎn)出模型等幾種模型?；貧w分析所研究的數(shù)學(xué)模型主要是線性回歸和多項式回歸模型。對于環(huán)境質(zhì)量和影響環(huán)境質(zhì)量的幾個參數(shù)它們的k次觀察(試驗)數(shù)據(jù)是( )，x=1，2，…,k,那么，它們之間的關(guān)系可用下式表示：
式中是n+1個待估計的未知效，即回歸系數(shù)，可以用最小二乘法求得。在求線性回歸方程前，線性回歸模型只是一種假設(shè)，盡管這種假設(shè)常常不是沒有根據(jù)的，但在求出線性回歸方程后，還是需要對其進行統(tǒng)計檢驗，以給出肯定或者否定的結(jié)論。在模型的準確性經(jīng)核實后,即可進行預(yù)測和控制。
環(huán)境質(zhì)量計量模型中的投入產(chǎn)出法預(yù)測環(huán)境污染狀況是根據(jù)國家和各部門經(jīng)濟發(fā)展的規(guī)劃,結(jié)合環(huán)境可以忍受的污染水平來預(yù)測未來的環(huán)境狀況的。
2.6統(tǒng)計理論方法
用與環(huán)境預(yù)測的統(tǒng)計理論方法有時間序列法、自回歸分析法、多元線型回歸法、多元統(tǒng)計分析法、概率統(tǒng)計法、神經(jīng)網(wǎng)絡(luò)法、遞推預(yù)測法等,時間序列法和自回歸分析法是最常用的兩種統(tǒng)計理論預(yù)測方法。
時間序列法就是把說明某一環(huán)境現(xiàn)象各個時期的統(tǒng)計資料,按時間先后進行排列,從而得到這一環(huán)境現(xiàn)象依時間變化的動態(tài)數(shù)列,通過對數(shù)列的變化分析,來預(yù)計未來,這種方法比較簡單易行,但由于它只依據(jù)過去資料,對環(huán)境變化有關(guān)的因素及未來可能的影響考慮較少,因此預(yù)測的精度會隨著預(yù)測時間的增長而下降,在環(huán)境污染的中長期很少使用這一預(yù)測方法。
自回歸分析法就是把給出的測量數(shù)據(jù)x1,x2,…,xn看作隨機過程x(t)的一個樣本函數(shù),通過對現(xiàn)實xi的分析,估計過程x(t)的總體特征,預(yù)測x(t)未來取值的概率分布,從而給出t>tn時x(t)的預(yù)報值。由于環(huán)境問題中時間序列的復(fù)雜性,一般來說,質(zhì)量因素或污染因素不可能用一個完全的數(shù)學(xué)函數(shù)給出來,但可以用一個概率分布函數(shù)組給出x(t)未來取值狀況的統(tǒng)計描述,因此適于這種描述的自回歸分析法也可以用于環(huán)境預(yù)測。
3大氣污染預(yù)測中應(yīng)注意的幾個問題
1) 在進行大氣污染預(yù)測時,由于污染源數(shù)量多、排放方式不同,且污染物擴散、遷移的影響因素較多,大氣污染狀況的各種影響因素之間又相互聯(lián)系和制約,作用機理不十分清楚;由于客觀環(huán)境是一個復(fù)雜的系統(tǒng),在目前,任何計算模型和計算方法都不能把所有的影響因素反映出來,因此,如何確定不同類型污染源及大氣污染狀況的主要影響因素,是大氣污染源預(yù)測中必需要注意的問題。
2) 要進行區(qū)域大氣污染的長期預(yù)測,人口、資源、經(jīng)濟、技術(shù)等因素對環(huán)境質(zhì)量的影響是不可忽略的[9]。環(huán)境預(yù)測應(yīng)以人口預(yù)測為中心,以社會經(jīng)濟預(yù)測和科學(xué)技術(shù)預(yù)測為基礎(chǔ),如果單純以污染物濃度的原始資料來預(yù)測環(huán)境的未來發(fā)展趨勢，不考慮社會、經(jīng)濟、政策等影響因素，是不現(xiàn)實、不可信的。所以，必須重視分析社會、經(jīng)濟、政策等因素的發(fā)展趨勢以及它們對 環(huán)境質(zhì)量的影響。
3) 當前，對大氣污染進行預(yù)測的一些方法還未擺脫 “從某些假定出發(fā)，按照一定的準則,進行模擬，作出預(yù)測”這種格式，它們在環(huán)境預(yù)測中的應(yīng)用受到一定的限制。對于不同的實際情況，一定要選取適合該情況的預(yù)測模型，以充分利用這些預(yù)測模型的優(yōu)點，克服它們的缺點，提高預(yù)測的精度和可信度。所以，如何針對不同情況，科學(xué)地選取預(yù)測模型和建立新的預(yù)測模型是值得重視和迫切需要解決的問題。
4結(jié)論
近些年來，環(huán)境預(yù)測正由單目標向多目標、單環(huán)境要素向多環(huán)境要素、靜態(tài)影響向動態(tài)影響的方向發(fā)展，進行預(yù)測時不再是僅僅考慮污染源、氣象條件等歷史資料，而是要同時考慮預(yù)測區(qū)域內(nèi)人口、經(jīng)濟、技術(shù)、政策等在內(nèi)的宏觀影響因素的變化對環(huán)境質(zhì)量的影響。環(huán)境預(yù)測正向科學(xué)化、系統(tǒng)化、計算機化、精確度高、可信度高的方向發(fā)展。
在區(qū)域大氣污染長期預(yù)測方面，目前還缺乏系統(tǒng)、可靠、成熟的頂級測試方法。由于環(huán)境質(zhì)量狀況與人口、經(jīng)濟、技術(shù)、政策等因素密切相關(guān)，它們之間相互作用的機理非常復(fù)雜，人們在進行區(qū)域環(huán)境長期預(yù)測時．往往只對這些影響因素和環(huán)境質(zhì)量的關(guān)系進行定性的分析和描述，因而,預(yù)測效果一般都不太令人滿意。所以，在進行區(qū)域大氣污染長期預(yù)測時．在污染源、 氣象條件、人口、經(jīng)濟等歷史資料調(diào)查和現(xiàn)狀調(diào)查的基礎(chǔ)上，認真考慮人口、經(jīng)濟、技術(shù)、政策等社會因素對大氣污染狀況的影響并定量地分析這種關(guān)系是非常重要的。
參 考 文 獻
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An Approach on the Models for Air Pollution Forecast
Bofu Zheng Hai You Xiaofeng Gong Meifu Qi
(Environmental and Chemical Engineering School，Nanchang University, Nanchang
330029, China)
ABSTRACT This paper summarized some methods which were often applied in air pollution forceast，introduced three mainly used models of air pollution forecast in detail, such as air quality model, gray theory model and projection pursuit regression model，analysed the practice and limitness of those models，formulated some problems which would be paid attention to on forecasting air pollution.
KEY WORDS air pollution, forecast，model
1 Overview
Forecast is based on subjective experience, lessons and objective information on conditions with the evolution of the logic and inference. Seek the law of the things. Make estimates and assumptions to the things for the development of the future development trend and a level may reach．Environment forecasts is based on population projections for the center, and socio-economic forecasts and projections for the science and technology infrastructure. Forecasting and concluding the trend of environment as population, economic, social factors developing, bringing forward the policies to prevent deterioration of environmental quality and improve environmental quality measures, making social development and environmental protection harmonization and unification.
Pollution forecast is the basis and an important component of the Environmental forecast, pollution prediction errors have a direct impact on the environmental forecast quality.According to forecasts pollution target, we can divided pollution forecasts into air pollution forecasts, water pollution, soil pollution forecasts, noise pollution forecast．Atmospheric pollution is forecasting air pollution trends for the future in a particular area, and bringing forward some strategies to improve air quality, also providing a reference basis. to decision makers to work out the regional air pollution control planning and economic development planning.
2 Air Pollution Forecast Method
At present, what domestic and foreign scholars use for air pollution prediction models approach are : air quality model, a gray model, projection pursuit regression model, fuzzy model, linear model analysis, environmental quality measurement model methods of statistical theory and methods of forecasting model.
2.1 Air Quality Model
What are commonly used in atmospheric pollution forecast models are : a box model, Gaussian model and K model.
2.1.1 A Box Model
A box model is the simplest model of urban air quality. It look the entire space as the city of one or more rectangular box form, the main assumptions are: 1) in a box, sources of pollution (as sources) is a constant; 2) If went into the box , pollutants (air) immediately distribute in the vertical direction. Because urban sources of pollution distributed more equitably and vertically proliferate at a faster rate, the above assumptions are certainly reasonable. However, there is a big difference between a box model assumptions and the actual situation, as in the near ground the concentration estimates is low.
2.1.2 Gaussian Model
Gaussian model of urban air quality is the most important model for the application model because : 1) Areas of most of the plains cities and suburbs is within the 20 ~30km,and the flow field is not very complicated; 2) Errors of urban air quality model mainly come from the model input parameters, especially sources of information may not be very accurate, precise, so that the improvement of model itself is attributable to in vain, from the effects of application , complex numerical model is not better than the Gaussian model; 3) Gaussian model needs little weather information than other air quality model, but the result was markedly improved.
Gaussian model is simple and practical, high spatial resolution of the merits, but it has the following shortcomings : 1) When the simulation scale reaches tens of kilometers, or has an uneven surface, more complex flow field, precision of Gaussian plume model will be difficult to meet the requirements; 2) Gaussian model for the deposition and chemical transformation process is very rough, When these processes are important or as a research object, the Gaussian model is not applicable.
2.1.3 K Model
The model consists of advection - diffusion equation is simplified by various assumptions derivation, it has the following performance : 1)It can simulate transmission and proliferation in three-dimensional unsteady flow field, so it can simulate complex surface and larger scale of air pollution;2) Pollution sources fields can be given arbitrarily, that is Q=Q (x, y, z, t); 3) Borders have reflection, absorption and penetration of pollutants, its concentration on the border can change; 4) It can simulate non-linear chemical reaction caused by the concentration; 5) It can simulate dry and wet deposition of concentration changes.
Because K model for molecular diffusion copied from the gradient transfer assumption, it has certain limitations; 1) gradient carrier must meet the requirements of the assumption that the standard conditions diffusion equation so only smoke scale is dominant at the eddy scale that it is correct; 2)When convection conditions gradient-carrier relationship is not established, it may appear counter - gradient transport phenomena .It will be not applied to K model; 3) K model has a high demand of basic information and input parameters .
Prediction accuracy of air quality model is largely dependent on the sources of pollution and forecast accuracy of weather conditions, therefore, it is more applicable to short-term pollution forecasts generally than forecast for the long-term contamination.
2.2 Gray Theory Model
Gray theory model is unique as theoretical model in modeling, forecasting, and control ect. For this 10 years ,it is widely used in meteorology, ecology, the environment, social and economic fields , gray model which are commonly used in the pollution forecast are : GM (1,1) and GM (1, N) model.
2.2.1 GM(1,1) Model
The model is result of the cumulative production for the original data presentation |}, weakening the randomness of time after the establishment of continuity equation, and the general form is:
+ χ =μ (1)
in the formula: ,μ is parameters,which can be soluted by Least Square.
Discrete Response Value is
(2)
Here is accumulated value,which can be revert predictive value Model.
(3)
in the formula
(4)
After the model, the fixed value is k .
The model is equivalent to exponential model y = aebx ,which has a specific exponential curve, and the shape is simple and monotonous. Its characteristics is able to reflect the trend of development of things, but not a good fit for a Swing process of the magnitude of changes, it is powerless undulating land data. Thus, the model of data distribution have certain requirements.
2.2.2 GM(1,N)Model
The model consists of N variables in a dynamic time-continuous linear differential equations, the general form is
Thereinto, is the original series for a final cumulative production, that is
Modulus vetor is ,which can be soluted by Least Square.Thus,
Discrete Response Value is
At last, makea revert building, that is
So is the future forecast value.
Using the model of pollution prediction, firstly,we need to identify and predict the factors associated with greater impact factor (such as social and economic factors, etc.) When choosing the main factor affecting the selection, generally using gray relational analysis. As the model uses an impact factor screening, environmental prediction and social and economic factors combine forecast, enhances the result accuracy and credibility.
2.3 Projection Pursuit Regression Model
Projection pursuit regression model is used for the processing and analysis of high dimensional non-normal data to explore a new method for data analysis. The basic idea is : Make high-dimensional data projection to the low-dimensional space, through a projection of a very small target .Find out the projection which would reflect the original high-dimensional data structures or features of the projector to achieve the purposes for studying and analysising high-dimensional data.
The general form of k rank projection pursuit regression model (PPAR(k))model is
in the formula:xi is Time series {x| estimated value when the time is t , xi-1,xi-2…,xi-k is the k predictors factor of timing, its final selection by the data structure, is the m content in the direction of the projector to meet||||=1. is the optimal piecewise linear function of , known as Ling function, and it is a numerical function, and shows that is the m Ling-function,which has an contribution to xi of the size of the weight coefficients.
Find the method of showing xi is to find out the optimal :
The least model selection criteria is to select appropriate parameters to
work out the following formula:
"E" in the formula is the operator, said the "error of the mean square."
K- factorial autoregressive is actually problem with a multi - variable input, single-output variables . To be fit for not linear characteristics of xi and xi-1,xi-2…,xi-k., PPAR (k) model selectes a series of ridge function " summation " to make a approximation to objective function, that is, increase M to reduce the amount of the model errors. Also use linear function of the distance to make a constant observation data on the projection right direction to get the numerical approximation functions smoothly. It can reflect the internal data structure of itself more objectively. Thereby enhance the stability of the results of forecasts.
2.4 Fuzzy Theory Model
Fuzzy theory, especially fuzzy clustering analysis, Parameter identification system model and fuzzy model identification extensive knowledge is used widely in the environment forecast.
In atmospheric pollution forecast, because the concentration of air pollutants are affected by many factors, there is no clear boundaries in atmospheric concentrations of the pollutants level, and it is blurred. General univariate statistical methods is hard to reflect the objective correlated relation between indicators and the pollutant concentration. When recognizing and using fuzzy theory, we can utilize the existing datas to calculate the optimal fuzzy classification center matrix, Optimal fuzzy partition matrix indicators and comprehensive weight matrix and other useful parameters, then use the optimal fuzzy recognition theory to forecast ,also with the measured data increased and the ongoing changes in parameter adjustment, it can precisely reflect the actual situation.
When making an environmental pollution forecast, fuzzy theoretical knowledge is used under normal circumstances by combining other forecasting models, which will achieve a better prediction. Because fuzzy clustering analysis can be used to reduce the impact of environmental quality to prioritize factors.When making an environmental pollution forecast we only consider the necessary environmental impact factor (the main factors) not a secondary factor. If considering the impact of too many factors, not only increase the amount of calculation, but also be not a good forecast results. If the consideration of factors is too few, not only the main factors is taken into account, but also the projected results are unbelievable.
2.5 Environmental Quality Measurement Model
Environmental quality measurement model studys large of random phenomenon in environment system to identify environmental quality and environmental system interaction factors forms by a mathematical model to predict the trend of the environment quality changes, and there are mainly regression analysis model and the input-output model and other models. The mathematical model which Regression analysis study is mainly the linear and polynomial regression model. Some parameters of environmental quality and environmental quality isand their k observations (test) data is (), x = 1, 2, ..., k ,so that the relationship between them can be given by :
In the formule, is n+1 yet to be the unknown effect, that is the regression coefficient which can be worked out by using the method of least squares. Before working out linear regression equation, the linear regression model is only a hypothesis, although this assumption is often not unfounded. When the linear regression equation is worked out, we need to make statistical tests to give a positive or negative conclusion. If the accuracy of the model is verified, we can predict and control it.
The method input and output forecasting the contaminated status about Environmental quality measurement model is based on the environmental situation of countries and sectors of economic development planning, integrating environment can tolerate pollution levels to predict the future state of the environment.