系統(tǒng)動(dòng)力學(xué)及其在環(huán)境水利方面的應(yīng)用

1、系統(tǒng)動(dòng)力學(xué)及其在環(huán)境水利方面的應(yīng)用,2011-4-23,雷宏軍 13460323316，69127405，leihongjun@ncwu.edu.cn,系統(tǒng)的定義 從組成角度看，系統(tǒng)由兩個(gè)或兩個(gè)以上相互聯(lián)系的要素組成的、具有整體功能和綜合行為的集合。系統(tǒng)的邊界把系統(tǒng)與系統(tǒng)的環(huán)境區(qū)分開來，環(huán)境的邊界把系統(tǒng)的環(huán)境與非系統(tǒng)集合區(qū)分開來。邊界理論、邊殼理論 從系統(tǒng)與環(huán)境相互作用角度看，系統(tǒng)是由系統(tǒng)輸入、系統(tǒng)轉(zhuǎn)換和系

2、統(tǒng)輸出組成的集合。,系統(tǒng)思考簡(jiǎn)介,就是整體考慮，綜合分析。“整體大于局部之和 ” 、 “牽一發(fā)而動(dòng)全身” 、“四兩撥千斤” 、“過猶不及” 、“圍魏救趙”、“田忌賽馬”等都是系統(tǒng)思考當(dāng)面對(duì)的系統(tǒng)比較大，內(nèi)部關(guān)系比較復(fù)雜時(shí)尤其需要，全面考慮。但這時(shí)候我們的思維往往有定勢(shì)，或者可能腦袋不夠用了。比如：應(yīng)對(duì)金融危機(jī)、房產(chǎn)泡沫的策略,第五項(xiàng)修煉第一部：全面體檢你的組織第二部：新思考、新視野第三部：四項(xiàng)核心修練第四部：進(jìn)入學(xué)習(xí)型組織

3、的時(shí)代第五部：余響,凡是值得思考的事情，沒有不是被人思考過的，我們必須做的只是試圖重新加以思考而已。 ------歌德 系統(tǒng)思考就是屬于歌德說的“教人重新思考問題”。,＋,貧困饑荒,放牧墾荒,荒漠化,土地生產(chǎn)力,＋,＋,＋,,人口,＋,惡性循環(huán)或良性循環(huán),庫(kù)存信息反饋調(diào)節(jié)過程,庫(kù)存訂貨系統(tǒng)是一個(gè)簡(jiǎn)單的反饋系統(tǒng)。從圖中可知它形成閉合的回路(或稱環(huán))，稱之為反饋回路(或環(huán))。反饋回路就是由一系列的因果與相互作用鏈組

4、成的閉合回路或者說是由信息與動(dòng)作構(gòu)成的閉合路徑。,,系統(tǒng)思考方法,表象背后的系統(tǒng)結(jié)構(gòu)—倒水之系統(tǒng)思考,系統(tǒng)思考方法,系統(tǒng)語(yǔ)言的基本組件 (Building Blocks),增強(qiáng)、平衡環(huán)路說明,系統(tǒng)思考建模原則與程序,建模原則（Anderson，1990）（1）清楚地定義各影響因子。 （2）動(dòng)態(tài)性的數(shù)據(jù)適合以時(shí)間序列的圖形趨勢(shì)顯示。 （3）避免數(shù)據(jù)冗余與負(fù)荷過重。 （4）將信息分類以層級(jí)化設(shè)計(jì)。,系統(tǒng)思考建模程序,,模擬評(píng)估

5、階段（scenario analysis）,,1、唐家山堰塞湖泄洪過程風(fēng)險(xiǎn)評(píng)估與預(yù)測(cè) --STELLA軟件建模分析,1、唐家山堰塞湖泄洪過程風(fēng)險(xiǎn)評(píng)估與預(yù)測(cè),,泄洪的流量未達(dá)到堰塞湖水位警戒水位，不會(huì)全面潰壩；但是如果降水不減少，堰塞湖的水位將在164小時(shí)后到達(dá)導(dǎo)流明渠的設(shè)計(jì)泄洪水位，應(yīng)提高施工的速度。,,2、流域水生態(tài)承載力評(píng)價(jià)---流域系統(tǒng)動(dòng)力學(xué)模型,1972 年，“羅馬俱樂部”提出了著名的《增長(zhǎng)的極限》“世界模型Ⅲ”

6、，該模型的開發(fā)是系統(tǒng)動(dòng)力學(xué)研究在大尺度生態(tài)系統(tǒng)中應(yīng)用的標(biāo)志性事件。 進(jìn)入 20 世紀(jì) 90 年代之后，面對(duì)可持續(xù)發(fā)展的概念，SD 模型在很多領(lǐng)域都得以廣泛的應(yīng)用，并開始同其它承載力研究方法進(jìn)行整合，最常見的是結(jié)合評(píng)價(jià)指標(biāo)體系。,太子河流域水生態(tài)承載力系統(tǒng)動(dòng)力學(xué)模型；贛江袁河流域水生態(tài)承載力系統(tǒng)動(dòng)力學(xué)模型太湖河網(wǎng)地區(qū)流域水生態(tài)承載力系統(tǒng)動(dòng)力學(xué)模型,,太子河流域水生態(tài)承載力系統(tǒng)動(dòng)力學(xué)模型,太子河流域系統(tǒng)動(dòng)力學(xué)模型流圖,2、流域水

7、生態(tài)承載力評(píng)價(jià)---流域系統(tǒng)動(dòng)力學(xué)模型,太子河流域水生態(tài)承載力系統(tǒng)動(dòng)力學(xué)模型,太子河流域水生態(tài)承載力計(jì)算結(jié)果,2、流域水生態(tài)承載力評(píng)價(jià)---流域系統(tǒng)動(dòng)力學(xué)模型,袁河流域系統(tǒng)動(dòng)力學(xué)模型流圖,2、流域水生態(tài)承載力評(píng)價(jià)---流域系統(tǒng)動(dòng)力學(xué)模型,贛江袁河流域水生態(tài)承載力系統(tǒng)動(dòng)力學(xué)模型,贛江袁河流域水生態(tài)承載力系統(tǒng)動(dòng)力學(xué)模型,蘆溪縣水生態(tài)承載力發(fā)展預(yù)測(cè)圖,2、流域水生態(tài)承載力評(píng)價(jià)---流域系統(tǒng)動(dòng)力學(xué)模型,3、烏梁素海流域水環(huán)境承載力仿真,運(yùn)用耦合

8、模型，對(duì)多種情景（階段新標(biāo)準(zhǔn)）進(jìn)行需求分析與評(píng)估,烏梁素海流域水環(huán)境承載力系統(tǒng)動(dòng)力學(xué)仿真模擬,,從系統(tǒng)動(dòng)力學(xué)(SD)和多目標(biāo)規(guī)劃(MOP)的基本理論出發(fā)，利用SD模型尋找出對(duì)烏梁素海流域水生態(tài)系統(tǒng)發(fā)展影響較大的敏感因素，并以敏感性因素為核心建立多目標(biāo)規(guī)劃(MOP)模型并求解；針對(duì)具 體情況設(shè)計(jì)模擬運(yùn)行方案，與決策者進(jìn)行交互，取得系統(tǒng)發(fā)展的優(yōu)化規(guī)劃方案；并對(duì)方案實(shí)施后的社會(huì)、經(jīng)濟(jì)、環(huán)境等結(jié)果進(jìn)行了預(yù)測(cè)和評(píng)價(jià)。,湖泊流域經(jīng)濟(jì)發(fā)展與湖泊

9、承載力關(guān)系研究,分期、分區(qū)的湖泊環(huán)境承載力,發(fā)展模式的合理性判別,,判別典型湖泊區(qū)域社會(huì)經(jīng)濟(jì)發(fā)展模式與湖泊環(huán)境承載力的協(xié)調(diào)性闡明湖泊承載力對(duì)流域生態(tài)環(huán)境和經(jīng)濟(jì)社會(huì)發(fā)展的制約機(jī)制,典型湖泊區(qū)域社會(huì)經(jīng)濟(jì)發(fā)展現(xiàn)狀模式,,湖泊環(huán)境承載量,,,,,,,,優(yōu)化調(diào)整,基于湖泊承載力典型湖泊流域經(jīng)濟(jì)發(fā)展模式研究,研究確定：優(yōu)先和禁止發(fā)展行業(yè)行業(yè)規(guī)模、結(jié)構(gòu)清潔發(fā)展模式,農(nóng)業(yè)產(chǎn)業(yè)最優(yōu)投入要素效率分析,主要農(nóng)產(chǎn)品生產(chǎn)發(fā)展排序,主要農(nóng)業(yè)產(chǎn)業(yè)最適規(guī)模核定

10、,技術(shù)進(jìn)步對(duì)農(nóng)業(yè)污染治理的貢獻(xiàn)度,工業(yè)結(jié)構(gòu)與污染物排放量的定量關(guān)系,環(huán)境導(dǎo)向型的工業(yè)結(jié)構(gòu)的評(píng)價(jià)體系,技術(shù)進(jìn)步對(duì)工業(yè)污染治理的貢獻(xiàn)度,基于環(huán)境友好的流域企業(yè)準(zhǔn)入標(biāo)準(zhǔn),環(huán)境導(dǎo)向的旅游容量核定,旅游行業(yè)、模式的發(fā)展排序及規(guī)模,流域環(huán)境友好旅游發(fā)展模式,生態(tài)村莊和生態(tài)社區(qū)模式構(gòu)建,環(huán)境友好型服務(wù)業(yè)模式,,,,,生態(tài)農(nóng)業(yè)發(fā)展模式,生態(tài)工業(yè)發(fā)展模式,生態(tài)旅游業(yè)發(fā)展模式,生態(tài)城鎮(zhèn)發(fā)展模式,,典型湖泊流域經(jīng)濟(jì)協(xié)調(diào)發(fā)展模式研究,根據(jù)流域總體規(guī)劃

11、的定位設(shè)計(jì)模型,,,,,,,是否滿足湖泊水環(huán)境容量約束條件？,湖泊流域最優(yōu)經(jīng)濟(jì)發(fā)展模式的確定,改變量化指標(biāo),情景設(shè)計(jì)時(shí)，涉及流域因素較多，要避免出現(xiàn)以下情況：發(fā)展模式能夠滿足容量要求，但流域經(jīng)濟(jì)和環(huán)境的綜合發(fā)展水平較低；流域經(jīng)濟(jì)和環(huán)境的綜合發(fā)展水平較高，但發(fā)展模式超過水環(huán)境容量要求；,,湖泊水資源子系統(tǒng),,人口子系統(tǒng),,經(jīng)濟(jì)子系統(tǒng),,湖泊水質(zhì)量子系統(tǒng),首先，滿足湖泊水環(huán)境容量要求；其次，評(píng)估滿足湖泊水環(huán)境容量要求的發(fā)展模式，擇優(yōu)選

12、取。,,社會(huì)進(jìn)程,,,,入湖污染負(fù)荷,湖泊水環(huán)境容量,,,,,2010,2015,2020,2025,SD模型輸出,A.SD建模方法,,SD模型建模步驟,,利用Vensim PLE（Ventana Simulation Environment Personal Learning Edition）軟件來完成系統(tǒng)建模過程，直觀的給出流域環(huán)境與人口、社會(huì)經(jīng)濟(jì)發(fā)展水平、水資源和水質(zhì)量之間的關(guān)系；定量的分析在現(xiàn)有社會(huì)經(jīng)濟(jì)條件下，水環(huán)境承載力在

13、未來時(shí)段的動(dòng)態(tài)發(fā)展變化 。,（1）模型構(gòu)建,建模流程系統(tǒng)邊界確定系統(tǒng)結(jié)構(gòu)分析及變量確定系統(tǒng)因果關(guān)系分析系統(tǒng)模型構(gòu)建（流圖及方程）模型有效性檢驗(yàn),B.SD模型系統(tǒng)結(jié)構(gòu),,湖泊流域生態(tài)與經(jīng)濟(jì)系統(tǒng)耦合模型,,流域人口子系統(tǒng),B.SD模型系統(tǒng)結(jié)構(gòu),,流域農(nóng)林子系統(tǒng),B.SD模型系統(tǒng)結(jié)構(gòu),,流域工業(yè)子系統(tǒng),B.SD模型系統(tǒng)結(jié)構(gòu),,湖泊水平衡子系統(tǒng),,B.SD模型系統(tǒng)結(jié)構(gòu),,湖泊污染物平衡子系統(tǒng),,B.SD模型系統(tǒng)結(jié)構(gòu),,流域水平衡子系

14、統(tǒng),,B.SD模型系統(tǒng)結(jié)構(gòu),C. 多目標(biāo)規(guī)劃模型（MOP）,,目標(biāo)函數(shù)： max(∑收益-∑成本),1 種植業(yè)子系統(tǒng)2. 畜牧業(yè)子系統(tǒng)3. 工業(yè)子系統(tǒng)4. 農(nóng)村生活子系統(tǒng)5. 城鎮(zhèn)生活子系統(tǒng),,收益：,,成本：,,收益：,成本：,,,收益：,成本：,,,成本：,成本：0,C. 多目標(biāo)規(guī)劃模型（MOP）,,約束條件：,1 種植業(yè)子系統(tǒng)2. 畜牧業(yè)子系統(tǒng)3. 工業(yè)子系統(tǒng)4. 農(nóng)村生活子

15、系統(tǒng)5. 城鎮(zhèn)生活子系統(tǒng),,,,,,,1.1 糧食產(chǎn)量約束 1.2 種植面積約束 1.3 種植水量約束,2.1 最低養(yǎng)殖量約束2.2 畜牧業(yè)水量約束,3.1 工業(yè)水量約束3.2 工業(yè)產(chǎn)值約束,4.1 生活用水量約束,5.1 烏梁素海水量平衡5.2 烏梁素海水質(zhì)約束： 考慮TN、TP、COD、氨氮、鹽度約束,,,湖泊水環(huán)境承載力指標(biāo)體系,人口及社會(huì)經(jīng)濟(jì)發(fā)展水平,水資源稟賦及開發(fā)利用水平,環(huán)境容量與污染負(fù)荷水平,環(huán)

16、境保護(hù)與治理水平,生態(tài)系統(tǒng)功能水平,7個(gè),6個(gè),10個(gè),6個(gè),7個(gè),量化指標(biāo)36個(gè),評(píng)估指標(biāo)13個(gè)：用于評(píng)估湖泊水環(huán)境對(duì)經(jīng)濟(jì)發(fā)展模式的承載度,量化指標(biāo)也稱為約束性指標(biāo)，是建模時(shí)需要考慮的因素。 在考慮特殊湖泊流域時(shí)，可以適當(dāng)增加量化指標(biāo)。,（2）評(píng)價(jià)指標(biāo)體系構(gòu)建,共6個(gè),共7個(gè),共6個(gè),共7個(gè),共10個(gè),確定流域內(nèi)點(diǎn)源及非點(diǎn)源的入湖負(fù)荷時(shí)，要進(jìn)行詳細(xì)的源解析，并且要考慮污染源時(shí)空布局、降雨量、河流水文等因素。,評(píng)估指標(biāo)：流域最優(yōu)經(jīng)濟(jì)

17、發(fā)展模式評(píng)估指標(biāo),人均GDP,工業(yè)萬元GDP需水量,萬元GDP污水排放量,萬元GDP污水處理量,水資源供需比,人均水資源可供量,COD環(huán)境容量比入湖負(fù)荷,TN環(huán)境容量比入湖負(fù)荷,TP環(huán)境容量比入湖負(fù)荷,農(nóng)業(yè)萬元GDP需水量,工業(yè)GDP增長(zhǎng)率,流域生態(tài)環(huán)境需水量,城市化水平,部分評(píng)估指標(biāo)來源于量化指標(biāo)； 部分評(píng)估指標(biāo)是綜合多個(gè)量化指標(biāo)后產(chǎn)生的指標(biāo)； 評(píng)估指標(biāo)可根據(jù)湖泊流域的特征適當(dāng)增刪指標(biāo)，但指標(biāo)要有實(shí)際的意義。,,c. 湖泊水環(huán)境承

18、載度計(jì)算：,Cj ——第j個(gè)方案對(duì)應(yīng)的湖泊水環(huán)境承載度；Xi ——無量綱化后的第i個(gè)指標(biāo)值；Wi ——第i個(gè)指標(biāo)的權(quán)重。,,,,以承載度最大的方案優(yōu)化湖泊流域經(jīng)濟(jì)發(fā)展模式,a. 指標(biāo)無量綱化處理：極值處理法,b. 指標(biāo)權(quán)重賦值：層次分析法（偏重政策導(dǎo)向）,,,,,,,,烏梁素海綠色流域建設(shè)與污染綜合治理,生態(tài)需水,產(chǎn)業(yè)政策與結(jié)構(gòu)調(diào)整減排,生態(tài)水核算,農(nóng)業(yè)產(chǎn)業(yè)調(diào)整與布局,工業(yè)產(chǎn)業(yè)結(jié)構(gòu)調(diào)整與布局,水生態(tài)產(chǎn)業(yè)構(gòu)建方案,補(bǔ)水方案,配套工程

19、,污染源工程治理與控制,低污染水凈化處理系統(tǒng),城鎮(zhèn)生活污染控制,農(nóng)村面源污染系統(tǒng)控制,畜禽養(yǎng)殖污染治理,工業(yè)園區(qū)廢水處理與回用控制,排干污染水處理系統(tǒng),河口濕地修復(fù)方案,農(nóng)田排水濕地凈化方案,水土流失防治,林業(yè)建設(shè),庫(kù)塘濕地修復(fù),物理化學(xué)措施,湖濱帶構(gòu)建,環(huán)湖帶景觀帶構(gòu)建,截滲溝建設(shè),環(huán)湖公路修建,湖泊水體生境改善方案,底泥疏浚與處理處置及資源化,網(wǎng)格水道工程,植物平衡收割與資源化工程,生物多樣性保護(hù),生態(tài)補(bǔ)水,,（3）方案制定與情景

20、分析（四大類方案）,內(nèi)源污染治理與生境改善,清水產(chǎn)流機(jī)制修復(fù)與排干水凈化,污染源系統(tǒng)控制,,,,,,,,,,,,情景1：村落生活污水-畜禽-垃圾系統(tǒng)治理工程的實(shí)施 情景2：在情景1基礎(chǔ)上，增加農(nóng)田污染徑流系統(tǒng)治理工程（含產(chǎn)業(yè)結(jié)構(gòu)的調(diào)整）情景3：在情景2基礎(chǔ)上，增加入湖河流污染控制與生態(tài)修復(fù)工程的實(shí)施,4、水資源永續(xù)管理系統(tǒng)動(dòng)力決策支持系統(tǒng),策略面 : 供給面與需求面策略之?dāng)M定。財(cái)務(wù)面 : 針對(duì)策略面所擬定的策略，進(jìn)行財(cái)務(wù)成本效益分

21、析。水量面 : 計(jì)算于預(yù)先擬定之供給面與需求面策略下，系統(tǒng)整體的供水量。水質(zhì)面 : 計(jì)算在系統(tǒng)的供水量給定下，水庫(kù)與河川的水質(zhì)狀況。指標(biāo)面 : 藉由指標(biāo)的設(shè)計(jì)來反應(yīng)水量面、水質(zhì)面與財(cái)務(wù)面的沖擊。,4-1水量系統(tǒng)動(dòng)力模型建置,,4-2人工湖系統(tǒng)動(dòng)力模型,4-3廢污水再利用系統(tǒng)動(dòng)力模型,,4-4自來水管線更換系統(tǒng)動(dòng)力學(xué)模型,4-5凈水場(chǎng)擴(kuò)充系統(tǒng)動(dòng)態(tài)模型,4-6 跨流域供水動(dòng)力學(xué)模型,4-7 農(nóng)業(yè)用水系統(tǒng)動(dòng)力學(xué)模型,4-8 水價(jià)調(diào)整系統(tǒng)

22、動(dòng)力模型,,,4-9整體水量和水質(zhì)問題整合之系統(tǒng)動(dòng)力流圖,4-10 生活污染之系統(tǒng)動(dòng)力學(xué)模型,4-11 畜牧污染之系統(tǒng)動(dòng)力學(xué)模型,4-12工業(yè)污染之系統(tǒng)動(dòng)力學(xué)模型,4-13旅游污染之系統(tǒng)動(dòng)力模型,4-14 水庫(kù)富營(yíng)養(yǎng)化與淤積系統(tǒng)動(dòng)力模型,4-15 GIS與Vensim間數(shù)據(jù)轉(zhuǎn)換示意圖,4-16 可持續(xù)利用評(píng)價(jià)指標(biāo)體系構(gòu)建,4-17 系統(tǒng)架構(gòu)畫面窗口,4-18 水量面策略情境仿真操作窗口,4-19 水量面策略模擬結(jié)果展示,4-20 水

23、質(zhì)面河川污染策略情境仿真及結(jié)果展示窗口,參數(shù)調(diào)整,結(jié)果輸出,4-21 水質(zhì)面水庫(kù)富營(yíng)養(yǎng)化與淤積策略情境仿真及結(jié)果展示窗口,系統(tǒng)動(dòng)力學(xué)解決問題的主要步驟,系統(tǒng)動(dòng)力學(xué)解決問題的主要步驟,大體可分為五步首先要用系統(tǒng)動(dòng)力學(xué)的理論、原理和方法對(duì)研究對(duì)象進(jìn)行系統(tǒng)分析其次進(jìn)行系統(tǒng)的結(jié)構(gòu)分析，劃分系統(tǒng)層次與子塊，確定總體的與局部的反饋機(jī)制第三步建立數(shù)學(xué)的、規(guī)范的模型第四步以系統(tǒng)動(dòng)力學(xué)理論為指導(dǎo)藉助模型進(jìn)行模擬與政策分析，可進(jìn)一步剖析系統(tǒng)得到更

24、多的信息，發(fā)現(xiàn)新的問題然后反過來再修改模型第五步檢驗(yàn)評(píng)估模型,系統(tǒng)動(dòng)力學(xué)解決問題的主要步驟—系統(tǒng)分析,系統(tǒng)分析是用系統(tǒng)動(dòng)力學(xué)解決問題的第一步，其主要任務(wù)在于分析問題，剖析要因。調(diào)查收集有關(guān)系統(tǒng)的情況與統(tǒng)計(jì)數(shù)據(jù)了解用戶提出的要求、目的與明確所要解決的問題分析系統(tǒng)的基本問題與主要問題，基本矛盾與主要矛盾，變量與主要變量初步劃定系統(tǒng)的界限，并確定內(nèi)生變量，外生變量，輸入量確定系統(tǒng)行為的參考模式,系統(tǒng)動(dòng)力學(xué)解決問題的主要步驟—系統(tǒng)的

25、結(jié)構(gòu)分析,這一步主要任務(wù)在于處理系統(tǒng)信息，分析系統(tǒng)的反饋機(jī)制。分析系統(tǒng)總體的與局部的反饋機(jī)制劃分系統(tǒng)的層次與子塊分析系統(tǒng)的變量、變量間關(guān)系，定義變量(包括常數(shù))，確定變量的種類及主要變量確定回路及回路間的反饋耦合關(guān)系；初步確定系統(tǒng)的主回路及它們的性質(zhì)；分析主回路隨時(shí)間轉(zhuǎn)移的可能性,系統(tǒng)動(dòng)力學(xué)解決問題的主要步驟—建立數(shù)學(xué)的規(guī)范模型,建立數(shù)學(xué)的規(guī)范模型建立L，R，A，C諸方程確定與估計(jì)參數(shù)給所有N方程，C方程與表函數(shù)賦值,系統(tǒng)

26、動(dòng)力學(xué)解決問題的主要步驟—模型模擬與政策分析,模型模擬與政策分析以系統(tǒng)動(dòng)力學(xué)的理論為指導(dǎo)進(jìn)行模型模擬與政策分析，更深入地剖析系統(tǒng)尋找解決問題的決策，并盡可能付之實(shí)施，取得實(shí)踐結(jié)果，獲取更豐富的信息，發(fā)現(xiàn)新的矛盾與問題修改模型，包括結(jié)構(gòu)與參數(shù)的修改。,系統(tǒng)動(dòng)力學(xué)解決問題的主要步驟—模型的檢驗(yàn)與評(píng)估,模型的檢驗(yàn)與評(píng)估這一步驟的內(nèi)容并不都是放在最后一齊來做的，其中相當(dāng)一部分內(nèi)容是在上述其他步驟中分散進(jìn)行的,系統(tǒng)動(dòng)力學(xué)解決問題的主要步驟

27、,系統(tǒng)動(dòng)力學(xué)解決問題的主要步驟,系統(tǒng)動(dòng)力學(xué)的建模工具 – VenSim,www.vensim.com,,Vensim 運(yùn)用 ––– 創(chuàng)建水平變量,,Vensim 運(yùn)用 –––創(chuàng)建速率變量,,Vensim 運(yùn)用 ––– 創(chuàng)建因果關(guān)系,,Vensim 運(yùn)用 ––– 創(chuàng)建方程式,,Vensim 運(yùn)用 ––– 創(chuàng)建變量的副本,,Vensim 運(yùn)用 ––– 刪除圖元,,Vensim 運(yùn)用 ––– 創(chuàng)建常數(shù)、其他變量,,Vensim 運(yùn)用 –––

28、創(chuàng)建常數(shù)、其他變量,,,,,,Vensim 運(yùn)用 ––– 創(chuàng)建注釋,,Vensim 運(yùn)用 ––– 字體,,Vensim 運(yùn)用 ––– 字體顏色,,Vensim 運(yùn)用 ––– 邊框顏色,,Vensim 運(yùn)用 ––– 邊框樣式,,Vensim 運(yùn)用 ––– 文字位置,,Vensim 運(yùn)用 ––– 箭線顏色,,Vensim 運(yùn)用 ––– 箭線形式與粗細(xì),,Vensim 運(yùn)用 ––– 箭線極性,,Vensim 運(yùn)用 ––– 文字置后,,Vens

29、im 運(yùn)用 ––– 結(jié)構(gòu)分析工具 Tree Diagram Causes,,Vensim 運(yùn)用 ––– 結(jié)構(gòu)分析工具 Tree Diagram Causes,,Vensim 運(yùn)用 ––– 結(jié)構(gòu)分析工具 Tree Diagram Uses,,Vensim 運(yùn)用 ––– 結(jié)構(gòu)分析工具 Tree Diagram Uses,,Vensim 運(yùn)用 ––– 結(jié)構(gòu)分析工具 Document,,Vensim 運(yùn)用 ––– 結(jié)構(gòu)分析工具 Document

30、,,Vensim 運(yùn)用 ––– 結(jié)構(gòu)分析工具 Loops,,Vensim 運(yùn)用 ––– 結(jié)構(gòu)分析工具 Loops,,,,Vensim 運(yùn)用 ––– 結(jié)構(gòu)分析工具 Units Check,,Vensim 運(yùn)用 ––– 數(shù)據(jù)集分析工具 Strip Graph Causes,,Vensim 運(yùn)用 ––– 數(shù)據(jù)集分析工具 Strip Graph,,Vensim 運(yùn)用 ––– 數(shù)據(jù)集分析工具 Strip Graph Uses,,Vensim 運(yùn)用

31、 ––– 數(shù)據(jù)集分析工具 Table,,Vensim 運(yùn)用 ––– 數(shù)據(jù)集分析工具 Runs Compare,,Vensim 運(yùn)用 ––– 數(shù)據(jù)集分析工具 Runs Compare,,,Vensim 運(yùn)用 ––– Custom Graph,Custom graphs allow you to customize the content of a graph, to show exactly the variables, runs, an

32、d style of graph you want.,Vensim 運(yùn)用 ––– Custom Graph,Custom graphs allow you to customize the content of a graph, to show exactly the variables, runs, and style of graph you want.,,Vensim 運(yùn)用 ––– Custom Graph,Custom grap

33、hs allow you to customize the content of a graph, to show exactly the variables, runs, and style of graph you want.,Vensim 運(yùn)用 ––– Custom Graph,Custom graphs allow you to customize the content of a graph, to show exactly

34、the variables, runs, and style of graph you want.,Vensim 運(yùn)用 ––– Custom Graph,Custom graphs allow you to customize the content of a graph, to show exactly the variables, runs, and style of graph you want.,Building a Simul

35、ation Model Using Vensim,Vensim ConventionsThe Population ModelWriting FormulasChecking for Model Syntax and Units ErrorsSimulating the ModelModel Analysis,Vensim Naming Conventions,Levels have initial letters capit

36、alized PopulationRates and auxiliaries are all lower case birthsConstants and Lookup Tables are all capitals AVERAGE LIFETIME,The Population Model (rabbit),FINAL TIME: 52TIME STEP: 0.25Units: weeks,Writing Formula

37、s,AVERAGE LIFETIME = 25Units: weekBIRTH RATE = 0.04Units: 1/weekbirths = Population * BIRTH RATEUnits: rabbits/weekdeaths = Population / AVERAGE LIFETIMEUnits: rabbits/weekPopulation = INTEG(births-deaths,500

38、)Units: rabbits,Writing Formulas,INTEG (rate, initial value) Returns the integral of the rate. The rate is numerically integrated. The initial value is the value of the variable that is being integrated, at the star

39、t of the simulation. Restrictions: INTEG must directly follow the equal sign. It signals Vensim that the variable on the left-hand side of the equation is a Level or State variable.INTEG ( unit / time, unit ) -->

40、 unit The units of the integral must be the same as the units of the initial condition. The rate must have the same units, divided by the units of TIME_STEP. ExamplesValidL = INTEG( R, 0.0 )L = INTEG(A, B )Inva

41、lidL = A + INTEG( R, 0.0 ) L = INTEG( B, 0.0 ) + 1 L = 2.0 * INTEG( R, 0.0 ) + 1.0INTEG must follow the equal sign, and it cannot be part of a more complex mathematical expression. These formulations are made

42、 valid by defining an auxiliary variable to perform the indicated operations， e.g.L = INTEG( R, 0.0 )aux = A + L,Checking for Model Syntax and Units Errors,,,Simulating the Model,Model Analysis ––– Strip Graph and Tabl

43、e,Population appears unchanging from 500 rabbits ? equilibrium,Model Analysis ––– Unconstrained Growth,Changes of birth rate from 0.04 to 0.08 can generate unconstrained growth. This is one

44、of the simplest possible dynamic behaviors, also known as exponential growth.,,,rabbit2,,Model Analysis ––– Unconstrained Growth,Model Analysis ––– Unconstrained Growth,,,,,,Model Analysis ––– Exponential Decay,Changes o

45、f AVERAGE LIFETIME from 25 to 10 can generate exponential decay in the population. This is one of the simplest possible dynamic behaviors, also known as exponential decay.,,,rabbit3,,Model Analysis ––– Exponential Decay

46、,Model Analysis ––– Exponential Decay,,,,,,Nonlinear Relationships,The population model presented in the previous is a simple model that uses only multiplication and division in its formulas. While addition, subtractio

47、n, multiplication and division are the most common components of formulas, sometimes it is necessary to capture different types of relationships. Vensim PLE has a number of functions such as EXP (exponential) and LN (na

48、tural logarithm) that can be helpful. Most of the time, however, it is more convenient to make up functions with customized properties.The development of Lookup Tables is a means of capturing nonlinear relationships.,

49、Nonlinear Relationships ––– Rabbits Limited By Food Resource,Let’s examine a simulation model of growth in a rabbit population until it hits a resource constraint, in this case a fixed land area resulting in a fixed food

50、 supply. Rabbits can multiply as long as sufficient food is available; when the rabbit population approaches the constraint (carrying capacity), the population is limited by an increase in rabbit deaths (from insufficie

51、nt food). The relationship between the carrying capacity and rabbit deaths is described by a nonlinear Lookup Table.,,FINAL TIME: 10TIME STEP: 0.125Units for Time: Year,Nonlinear Relationships ––– Rabbits Limited By

52、Food Resource,Nonlinear Relationships ––– Rabbits Limited By Food Resource,INITIAL RABBIT POPULATION = 100Units: RabbitRABBIT BIRTH RATE = 1.1Units: 1/YearAVERAGE RABBIT LIFE = 2Units: Yearrabbit births = Rabbit Po

53、pulation * RABBIT BIRTH RATEUnits: Rabbit/Yearrabbit deaths = (Rabbit Population / AVERAGE RABBIT LIFE) * effect of crowding on deathsUnits: Rabbit/YearRabbit Population = INTEG(rabbit births–rabbit deaths, INITIAL R

54、ABBIT POPULATION)Units: Rabbit,Nonlinear Relationships ––– Rabbits Limited By Food Resource,Now you will define the carrying capacity. A certain area of grassland exists and each rabbit requires an amount of grass to l

55、ive on. Dividing the area of grassland by the area of grass required per rabbit gives the number of rabbits that can live on that land.AREA OF GRASSLAND = 20000Units: square yardsGRASS REQUIRED PER RABBIT = 10Units:

56、 square yards/Rabbitcarrying capacity = AREA OF GRASSLAND / GRASS REQUIRED PER RABBITUnits: RabbitRabbit crowding is defined as the rabbit population divided by carrying capacity. This model will expect the numerical

57、 value to fall within the range from 0 (if no rabbits exist) to 2 (when rabbit population is double the carrying capacity). rabbit crowding = Rabbit Population / carrying capacityUnits: dmnlThe amount of rabbit crowd

58、ing will affect the death rate of rabbits: higher crowding implies a higher death rate. To change the death rate based on rabbit crowding, you will use a graphical Lookup Table.,Nonlinear Relationships ––– The Effect of

59、 Crowding on Deaths,In the formulation of this model we have said that the more crowded it is, the more rabbits will die. In thinking about this it seems likely that a little bit of crowding will not make to much differ

60、ence, whereas a lot of crowding would. Extending this to an extreme, if the rabbits were so crowded that they were squishing each other we would not expect them to live for more than a few moments. While you could try

61、to find a function that has this property, the Lookup Table provides an easier solution. A Lookup Table is an arbitrary function, one that you define as a table or graph, that describes a relationship between an input

62、and an output. The Lookup Table for this model allows us to describe how rabbit deaths change when the rabbit population exceeds the carrying capacity. An intermediate concept, effect of crowding on deaths, will rela

63、te the rabbit crowding to rabbits deaths through the Lookup Table. The effect of crowding on deaths will take the input values from the variable rabbit crowding and convert them to output values by using the Lookup Tabl

64、e.,Nonlinear Relationships ––– The Effect of Crowding on Deaths,Nonlinear Relationships ––– The Effect of Crowding on Deaths,Nonlinear Relationships ––– The Effect of Crowding on Deaths,This graph, in words, says that as

65、 the input (rabbit crowding) moves from 0, output rises slowly, but as rabbit crowding gets higher, output rises faster and faster. The effect of crowding on deaths is more rapid at higher levels of rabbit crowding, jus

66、t as we discussed earlier. The graph has been normalized to go through the 1,1 point. Another way to think of this is that AVERAGE RABBIT LIFE is the rabbit life that would be average when population is at the carryin

67、g capacity for the ecosystem.,Rabbits Limited By Food Resource ––– Equations list,AREA OF GRASSLAND = 20000Units: square yardsAVERAGE RABBIT LIFE = 2Units: Yearcarrying capacity = AREA OF GRASSLAND / GRASS REQUIRED P

68、ER RABBITUnits: Rabbiteffect of crowding on deaths = EFFECT OF CROWDING ON DEATHS LOOKUP(rabbit crowding)Units: DmnlEFFECT OF CROWDING ON DEATHS LOOKUP ([(0,0)-(10,10)],(0,0.5),(1,1),(1.5,2),(2,5),(2.5,10))Units: D

69、mnlGRASS REQUIRED PER RABBIT = 10Units: square yards/RabbitINITIAL RABBIT POPULATION = 100Units: RabbitRABBIT BIRTH RATE = 1.1Units: 1/Yearrabbit births = Rabbit Population * RABBIT BIRTH RATEUnits: Rabbit/Yearr

70、abbit crowding = Rabbit Population / carrying capacityUnits: Dmnlrabbit deaths = (Rabbit Population / AVERAGE RABBIT LIFE) * effect of crowding on deathsUnits: Rabbit/YearRabbit Population = INTEG(rabbit births-rabbi