带有非线性方程组约束的最小二乘法问题

denny2651

大家好！

我要做的是通过最小二乘法，来从一组非线性方程组中确定5个常数(c,n,d_0,d_1,d_2)。
具体的目标函数就是下面程序里的SSRE_total,它的含义就是实验值和理论值之间的平方差，实验数据已经通过constant定义成矩阵。
有的压力是实验测出来的，再通过下面的程序算出来这些压力（计算值），具体计算就是基于连续性方程和假定的一个压力与流量，面积的关系式v=c*deltaP^n*A. A有三种值，分别就是d_0,d_1,d_2.

下面是我稍微改动以后的1stopt程序，constant定义的就是那些原始数据，每个数组有98个原始数据。

我要处理的问题很简单，一个有6个房间的一层建筑，已知其中5个房间的供气流量和与周围环境的压差读数，需要通过假设一个leakage function，以及利用质量守恒，来估算每个房间每个裂缝的等效面积。

公式呢，最关键是质量守恒：
v_1a_star+v_31_star+v_1=0;
v_2a_star+v_32_star+v_2=0;
v_3swa_star+v_3nda_star+v_3nwa_star+v_3=v_31_star+v_32_star+v_34_star+v_35_star+v_36_star;
v_4a_star+v_34_star+v_4=0;
v_5la_star+v_5ra_star+v_35_star+v_5=0;
v_36_star+v_6a_star=0;

（v_1，v_2，v_3，v_4，v_5已知）
以及流过每个房间缝隙的流量与压差，面积的一个关系，就是leakage function：比如：
v_36=c*deltap_36^n*A_36，其他的类同。
这里我假定A_36=d_2
其他的还有另两种面积，分别为d_0和d_1，加上c和n，总共是5个，需要通过最小化目标函数SSRE_total得到这5个参数。

程序的其他部分，比如那些if， else if之类的，都只是为了判断一个房间两侧压力不同时，如何把压差给计算成正值而不是负值。还有那些各种压力之间的转换，就是考虑到压力测量点和裂缝开口处的外界风压不同，需要转换转换“基准值”而已，最终基准都转换到了以大气压为准。
v_36_star和v_36的区别就是压差不同决定了在上述的质量守恒里，是不是加个"-"号，这样就使得不管两侧压力大小如何，上述的质量守恒方程形式，符号，总是对的。

整个求解的思路就是如此，这里就是通过求解质量守恒，求解出一组“计算压差值”，再与“实验压差值”比较，就是那个目标函数SSRE_total，最小化以后，希望能确定c,n,d_1,d_2,d_3这5个参数。

我的想法是：把所有的那些连续性方程（质量守恒）作为conststr，要最优化的函数就是实验值和计算值的加总平方差。可是程序提示我说：d_0,d_1,d-2没出现在minfunction里，所以无法继续。
不知道大家有什么好的方法可以解决这个问题的么？谢谢！

我写的1stopt程序如下：

Title "98GA";
Parameter d_0[-1,1],d_1[-1,1],d_2[-1,1],c[0,1],n[0.6,1];

Var i: integer;
   
constant v_1(1:98)=[0.1153844,0.1158121,0.1178574,0.1166648,0.1188816,0.1159457,0.1156278,0.0087406,0.0085242,0.0142083,0.0144683,0.0084271,0.0082189,0.0104373,0.0142343,0.0161085,0.0197801,0.0159115,0.0182092,0.0157571,0.0153241,0,0,0,0,0,0,0,0.00196,0.00614,0.00425,0.00603,0.00868,0.00945,0.00745,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.2527864,0.2517426,0.2516711,0.2534295,0.2550065,0.2562049,0.2548979,0.3454,0.3380018,0.3416196,0.3334365,0.3390023,0.3390162,0.3380664,0,0.1092943,0.1076042,0.1116846,0.1095734,0.1092915,0.1116004,0.1329509,0.088851,0.0882887,0.0906466,0.0904273,0.0875922,0.0903747,0.0876433,0,0,0,0,0,0,0,0,0,0,0,0,0];
constant v_2(1:98)=[0.2133417,0.2103198,0.2095807,0.2120369,0.2108637,0.2137315,0.2109991,0.1340609,0.1317221,0.133674,0.1342319,0.1345542,0.1325076,0.1350571,0.1361732,0.1312187,0.1356421,0.1346505,0.1348923,0.1336443,0.1360058,0.0858698,0.0873808,0.087218,0.0849354,0.0859586,0.0873737,0.0859237,0.13665,0.14224,0.13649,0.1382,0.1371,0.13655,0.13745,0.03038,0.02833,0.02538,0.03303,0.03211,0.03339,0.03275,0,0,0,0,0,0,0,0.0390855,0.0367367,0.0356808,0.0314771,0.0391902,0.0377648,0.0342635,0.3736501,0.3731486,0.3661831,0.3761752,0.3666716,0.3647163,0.3714868,0.3649604,0.3674707,0.3660102,0.3594999,0.3677742,0.3601322,0.3623103,0,0.2409467,0.2438006,0.2428114,0.2403277,0.2442072,0.2498713,0.2677871,0.1769558,0.1772381,0.1760419,0.179562,0.1773469,0.1752758,0.181166,0,0,0,0,0,0,0,0,0,0,0,0,0];
constant v_3(1:98)=[0.7221251,0.7259809,0.7267369,0.7294272,0.7278451,0.7239058,0.7304886,0.5301189,0.537017,0.5398716,0.5326701,0.5395808,0.5391522,0.5367918,0.4861219,0.4846957,0.4935833,0.4834967,0.4866834,0.4908041,0.4943802,0.2727893,0.2800386,0.2761293,0.2819132,0.2824784,0.2788911,0.2782705,0.504,0.5083,0.50759,0.50708,0.50123,0.50363,0.50369,0.12046,0.12138,0.12111,0.12199,0.12447,0.11977,0.11913,0.0138239,0.0120498,0.0105262,0.0105828,0.0106506,0.0147947,0.0127723,0.1081574,0.1042881,0.1046241,0.1042237,0.1069839,0.1053004,0.1031196,1.4512736,1.4433179,1.4347395,1.4463796,1.4497334,1.4520597,1.4492068,1.2784507,1.2810703,1.2857849,1.274607,1.2920066,1.3040017,1.2838664,0,0.8566462,0.8424237,0.8451893,0.8559388,0.8521533,0.8821638,0.9190127,0.6639221,0.6608206,0.6598218,0.6532031,0.6599321,0.6659473,0.663368,0,0,0,0,0,0,0,0,0,0,0,0,0];
constant v_4(1:98)=[0.2012605,0.1998017,0.2024108,0.1995538,0.1970432,0.1994111,0.1963843,0.1191281,0.1157285,0.1158678,0.1175557,0.1157836,0.1180433,0.1140255,0.104545,0.1028086,0.1040736,0.1050054,0.1016123,0.1022974,0.1034741,0.0997631,0.098541,0.097212,0.0981,0.0980098,0.0946237,0.0981608,0.14434,0.14226,0.14318,0.14303,0.14157,0.14067,0.1443,0.1195,0.11639,0.11961,0.11915,0.11646,0.11634,0.1149,0.1000356,0.100196,0.099435,0.1004066,0.1000497,0.1000268,0.0998315,0.1089901,0.1102022,0.1083704,0.1083934,0.1073327,0.1092583,0.1066581,0.3483768,0.3499204,0.3485267,0.3556563,0.3497143,0.3473895,0.3491127,0.3253524,0.3268419,0.3261791,0.3245969,0.3291956,0.331477,0.3296025,0.05235,0.2526176,0.2499491,0.2499554,0.2506434,0.2498008,0.2537176,0.2646943,0.2108972,0.210728,0.2131858,0.2097585,0.2124072,0.2116428,0.2116725,0.1111799,0.111503,0.1098932,0.1108202,0.1116581,0.1118944,0.1117458,0.04399,0.04303,0.04487,0.04313,0.04647,0.04382];
constant v_5(1:98)=[0.3183537,0.3180397,0.3175429,0.317154,0.3151392,0.3190725,0.317859,0.2281595,0.2266698,0.2272368,0.228295,0.2263697,0.2240111,0.2277053,0.1979112,0.1967879,0.1979944,0.1968427,0.1898825,0.1942099,0.1910417,0.1925118,0.1908942,0.195142,0.1931634,0.1921338,0.1893105,0.1891088,0.25905,0.26091,0.26038,0.25859,0.25515,0.25772,0.25903,0.13238,0.12979,0.13349,0.125,0.12531,0.12507,0.12817,0.0968879,0.0964823,0.0968204,0.0996116,0.0975158,0.096635,0.0972286,0.1798021,0.1768756,0.1769846,0.1767325,0.177118,0.1765921,0.1761528,0.6829881,0.6811701,0.6827532,0.6829214,0.6768484,0.6873106,0.6859397,0.3565438,0.3514279,0.3475938,0.3442464,0.3402677,0.3366773,0.3300396,0.0713,0.5119989,0.515914,0.5138058,0.5123597,0.5091259,0.5225556,0.5396783,0.4136771,0.4144844,0.413779,0.4152861,0.4167888,0.4118164,0.4127404,0.1835098,0.1816511,0.1821079,0.1820693,0.1819781,0.1792573,0.1789363,0.05299,0.05191,0.05146,0.04812,0.04784,0.04576];

constant p_1wa(1:98)=[-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-2.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3];
constant p_2wa(1:98)=[1,1,1,1,1,1,1,0,0,0,0,0,0,0,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0,0,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,3.8,1,1,1,1,1,1];
constant p_3nda(1:98)=[-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,0,0,0,0,0,0,0,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,0,0,0,0,0,0,0,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,0,0,0,0,0,0,0,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.1,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-2.9,-0.1,-0.1,-0.1,-0.1,-0.1,-0.1];
constant p_3nwa(1:98)=[-0.8,-0.8,-0.8,-0.8,-0.8,-0.8,-0.8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.8,-0.8,-0.8,-0.8,-0.8,-0.8,-0.8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.8,-0.8,-0.8,-0.8,-0.8,-0.8,-0.8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.8,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-8.4,-0.8,-0.8,-0.8,-0.8,-0.8,-0.8];
constant p_3swa(1:98)=[-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2];
constant p_4wa(1:98)=[-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.2,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-1.1,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2];
constant p_5lwa(1:98)=[-0.6,-0.6,-0.6,-0.6,-0.6,-0.6,-0.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.6,-0.6,-0.6,-0.6,-0.6,-0.6,-0.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.6,-0.6,-0.6,-0.6,-0.6,-0.6,-0.6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.6,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-2.2,-0.6,-0.6,-0.6,-0.6,-0.6,-0.6];
constant p_5rwa(1:98)=[-0.8,-0.8,-0.8,-0.8,-0.8,-0.8,-0.8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.8,-0.8,-0.8,-0.8,-0.8,-0.8,-0.8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.8,-0.8,-0.8,-0.8,-0.8,-0.8,-0.8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-1.8,-0.8,-0.8,-0.8,-0.8,-0.8,-0.8];
constant p_6sda(1:98)=[-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.3,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-1.5,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3];

constant p_1a(1:98)=[-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.5,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-2,-0.5,-0.5,-0.5,-0.5,-0.5,-0.5];
constant p_2a(1:98)=[-0.9,-0.9,-0.9,-0.9,-0.9,-0.9,-0.9,0,0,0,0,0,0,0,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0,0,0,0,0,0,0,-0.9,-0.9,-0.9,-0.9,-0.9,-0.9,-0.9,0.1,0.1,0.1,0.1,0.1,0.1,0.1,0,0,0,0,0,0,0,-0.9,-0.9,-0.9,-0.9,-0.9,-0.9,-0.9,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.9,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-1.7,-0.9,-0.9,-0.9,-0.9,-0.9,-0.9];
constant p_3sa(1:98)=[-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.2,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2];
constant p_4a(1:98)=[-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.2,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-1.9,-0.2,-0.2,-0.2,-0.2,-0.2,-0.2];
constant p_5a(1:98)=[0.2,0.2,0.2,0.2,0.2,0.2,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.2,0.2,0.2,0.2,0.2,0.2,0.2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,0.2,0.2,0.2,0.2,0.2,0.2];

constant deltap_1a_exp(1:98)=[49.64,49.48,49.45,49.29,49.49,49.19,49.09,24.5,24.5,24.42,24.4,24.32,24.28,24.32,24.75,24.56,24.6,24.22,24.48,24.36,24.64,15.25,15.44,15.53,15.41,15.5,15.57,15.47,25.1,24.64,24.88,25.03,25.07,24.89,25.03,10.27,9.97,9.97,10.07,10,10.01,9.95,3.69,3.74,3.77,3.76,3.77,3.73,3.74,13.93,13.88,13.94,13.9,13.94,13.88,13.79,147.16,147.01,147.17,147.07,147.05,147.09,146.97,140.39,140.34,140.43,140.27,140.54,140.39,140.46,3.58,67.92,68.22,67.85,67.8,67.31,69.47,74.69,54.2,54.09,54.09,54.13,54.04,54.2,54.26,15.47,15.46,15.53,15.49,15.5,15.55,15.54,3.88,3.72,3.61,3.66,3.72,3.71];
constant deltap_2a_exp(1:98)=[47.78,47.32,47.49,47.18,47.55,46.89,47.21,22.86,22.85,22.77,22.77,22.76,22.67,22.7,23.31,22.95,22.71,22.59,22.59,22.96,23.63,13.56,13.72,13.77,13.68,13.75,13.85,13.8,23.41,23.1,23.44,23.34,23.61,23.25,23.27,8.09,8.18,8.41,7.86,7.57,7.68,7.99,1.72,1.75,1.74,1.73,1.72,1.65,1.63,12.02,12.03,12.06,11.96,12.02,11.99,11.87,145.91,145.75,145.88,145.59,145.6,145.63,145.47,139.39,139.34,139.42,139.32,139.45,139.38,139.45,3.25,67.17,67.55,67.02,66.86,66.4,68.6,73.68,53.34,53.29,53.37,53.47,53.41,53.41,53.54,15.45,15.4,15.46,15.47,15.38,15.46,15.4,3.48,3.36,3.33,3.23,3.07,3.33];
constant deltap_4a_exp(1:98)=[49.32,49.39,49.35,49.53,48.97,49.27,49.36,26.06,26.01,25.96,25.95,25.92,25.89,25.89,25.75,25.76,25.91,25.52,25.58,25.6,25.72,16.5,16.57,16.54,16.53,16.52,16.44,16.46,25.37,25.64,25.42,25.82,25.51,25.7,25.78,11.1,11.25,11.15,11.12,11.14,11,11.11,4.66,4.66,4.65,4.67,4.64,4.61,4.62,14.8,14.76,14.82,14.8,14.76,14.77,14.73,152.91,152.94,153.03,152.85,152.85,152.75,152.74,145.79,145.92,146,145.91,145.9,145.88,145.93,3.55,70.1,70.39,70.19,70.06,69.7,72.1,77.23,56.02,56.02,56.08,55.99,56.06,56.15,56.15,15.82,15.78,15.79,15.74,15.76,15.69,15.68,3.23,3.4,3.25,3.13,3.43,3.21];
constant deltap_5a_exp(1:98)=[47.8,47.86,47.93,47.91,47.6,47.75,47.79,24.4,24.38,24.31,24.34,24.31,24.27,24.31,24.16,24.13,24.05,23.94,23.94,23.96,24.12,15.14,15.25,15.17,15.18,15.18,15.12,15.14,23.44,23.82,23.64,23.97,23.58,23.79,23.88,10.13,9.83,9.86,9.9,9.75,9.9,9.76,3.73,3.73,3.75,3.73,3.72,3.75,3.69,13.48,13.45,13.49,13.47,13.42,13.49,13.44,146.04,146.05,146.14,145.98,145.97,145.99,145.93,107.36,107.41,107.44,107.34,107.42,107.34,107.33,2.96,64.88,65.16,65.02,64.83,64.49,66.76,71.39,52.07,52.07,52.12,52.06,52.12,52.18,52.22,14.93,14.87,14.86,14.82,14.82,14.76,14.74,2.72,2.91,2.79,2.74,3.06,2.78];
constant deltap_6a_exp(1:98)=[32.46,32.66,32.51,32.4,32.33,32.3,32.08,14.83,14.82,14.84,14.77,14.64,14.69,14.59,14.68,14.79,14.66,14.7,14.76,15.08,14.81,9.43,9.44,9.39,9.45,9.54,9.53,9.46,16.33,16.06,16.28,16.21,15.96,16.06,16.07,6.6,6.47,6.43,6.62,6.58,6.79,6.77,2.71,2.72,2.73,2.69,2.75,2.68,2.68,9.13,9.17,9.21,9.17,9.19,9.22,9.15,128.83,128.8,128.92,128.89,128.92,128.89,128.82,136.28,136.39,136.45,136.42,136.39,136.42,136.44,3.66,50.55,50.96,50.39,50.25,50.19,51.84,55.61,41.17,41.12,41.25,41.4,41.29,41.26,41.44,12.21,12.3,12.22,12.3,12.26,12.4,12.27,3.71,3.71,3.71,3.76,3.61,3.85];
constant deltap_3ndagauge_exp(1:98)=[59.99,59.27,61.54,59.59,61.65,60.72,60.54,23.77,23.64,23.72,23.55,23.58,23.53,23.45,26.28,25.9,25.82,25.79,25.91,25.75,25.91,16.08,16,16.04,15.9,15.92,16.1,15.93,43.1,43.75,43.09,42.94,45.95,42.68,44.91,12.69,12.88,12.3,12.31,12.23,12.43,12.62,4.16,4.18,4.13,4.1,4.11,4.06,4.03,14.52,14.42,14.44,14.39,14.4,14.44,14.37,151.45,151.4,151.56,151.39,151.37,151.32,151.15,144.28,144.41,144.5,144.42,144.45,144.56,144.5,19.22,70.87,71.17,70.97,70.91,70.51,72.8,77.74,57.31,57.34,57.41,57.42,57.42,57.44,57.51,18.52,18.54,18.52,18.48,18.47,18.52,18.51,19.14,18.24,19.85,18.6,19.42,19.06];
constant deltap_3nwagauge_exp(1:98)=[60.7,60.93,60.4,60.54,59.83,61.11,60.31,27.44,27.43,27.43,27.39,27.34,27.28,27.32,27.98,27.96,28.27,27.81,27.89,27.5,28.48,18.63,18.7,18.74,18.62,18.68,18.69,18.66,39.04,38.54,38.25,39.25,41.11,39.56,38.94,13.2,12.94,13.27,12.82,12.85,12.84,12.71,6.06,6.08,6.06,6.12,6.04,5.99,5.98,16.66,16.71,16.72,16.7,16.69,16.76,16.66,154.31,154.3,154.4,154.23,154.17,154.25,154.14,147.55,147.56,147.69,147.64,147.7,147.76,147.69,17.12,73.23,73.55,73.31,73.14,72.73,75.12,80.11,59.68,59.7,59.74,59.74,59.71,59.77,59.79,20.76,20.78,20.8,20.72,20.7,20.7,20.69,17.19,16.96,17.93,17.41,17.29,14.86];
constant deltap_3swagauge_exp(1:98)=[47.98,48.05,47.87,47.84,47.97,47.68,47.66,23.24,23.22,23.26,23.17,23.06,23.12,23.08,22.65,22.51,22.68,22.3,22.66,22.52,22.71,13.21,13.28,13.22,13.23,13.32,13.34,13.26,23.19,23,23.14,23.14,23.17,23.05,23.22,8.42,8.24,8.21,8.06,8.15,8.12,8.29,2.08,2.11,2.09,2.04,2.14,2.04,2.07,12.21,12.25,12.29,12.27,12.29,12.3,12.23,146.71,146.6,146.77,146.75,146.79,146.72,146.63,139.69,139.77,139.79,139.66,139.8,139.74,139.74,2.54,66.54,67.05,66.38,66.17,65.98,68.19,73.13,52.74,52.71,52.87,53.02,52.93,52.98,53.17,13.85,13.93,13.84,13.87,13.81,13.98,13.88,2.51,2.51,2.42,2.61,2.32,2.57];

conststr
for i:=1 to 98 do

p_1=deltap_1a+p_1a;
p_2=deltap_2a+p_2a;

p_4=deltap_4a+p_4a;
p_5=deltap_5a+p_5a;
p_6=deltap_6a+p_6sda;

if p_3_ave<p_3nda then deltap_3nda:=p_3nda-p_3_ave;
else if p_3_ave=p_3nda then deltap_3nda:=0;
else if p_3_ave>p_3nda then deltap_3nda:=p_3_ave-p_3nda;

if p_3_ave<p_3nwa then deltap_3nwa:=p_3nwa-p_3_ave;
else if p_3_ave=p_3nwa then deltap_3nwa:=0;
else if p_3_ave>p_3nwa then deltap_3nwa:=p_3_ave-p_3nwa;

if p_3_ave<p_3swa then deltap_3swa:=p_3swa-p_3_ave;
else if p_3_ave=p_3swa then deltap_3swa:=0;
else if p_3_ave>p_3swa then deltap_3swa:=p_3_ave-p_3swa;

if p_1<p_1wa then deltap_1wa:=p_1wa-p_1;
else if p_1=p_1wa then deltap_1wa:=0;
else if p_1>p_1wa then deltap_1wa:=p_1-p_1wa;

if p_2<p_2wa then deltap_2wa:=p_2wa-p_2;
else if p_2=p_2wa then deltap_2wa:=0;
else if p_2>p_2wa then deltap_2wa:=p_2-p_2wa;

if p_4<p_4wa then deltap_4wa:=p_4wa-p_4;
else if p_4=p_4wa then deltap_4wa:=0;
else if p_4>p_4wa then deltap_4wa:=p_4-p_4wa;

if p_5<p_5lwa then deltap_5lwa:=p_5lwa-p_5;
else if p_5=p_5lwa then deltap_5lwa:=0;
else if p_5>p_5lwa then deltap_5lwa:=p_5-p_5lwa;

if p_5<p_5rwa then deltap_5rwa:=p_5rwa-p_5;
else if p_5=p_5rwa then deltap_5rwa:=0;
else if p_5>p_5rwa then deltap_5rwa:=p_5-p_5rwa;

if p_3_ave<p_1 then deltap_31:=p_1-p_3_ave;
else if p_3_ave=p_1 then deltap_31:=0;
else if p_3_ave>p_1 then deltap_31:=p_3_ave-p_1;

if p_3_ave<p_2 then deltap_32:=p_2-p_3_ave;
else if p_3_ave=p_2 then deltap_32:=0;
else if p_3_ave>p_2 then deltap_32:=p_3_ave-p_2;

if p_3_ave<p_4 then deltap_34:=p_4-p_3_ave;
else if p_3_ave=p_4 then deltap_34:=0;
else if p_3_ave>p_4 then deltap_34:=p_3_ave-p_4;

if p_3_ave<p_5 then deltap_35:=p_5-p_3_ave;
else if p_3_ave=p_5 then deltap_35:=0;
else if p_3_ave>p_5 then deltap_35:=p_3_ave-p_5;

if p_3_ave<p_6 then deltap_36:=p_6-p_3_ave;
else if p_3_ave=p_6 then deltap_36:=0;
else if p_3_ave>p_6 then deltap_36:=p_3_ave-p_6;

v_1a=c*abs(deltap_1wa)^n*d_0;
v_2a=c*abs(deltap_2wa)^n*d_0;
v_3swa=c*abs(deltap_3swa)^n*d_0;
v_3nda=c*abs(deltap_3nda)^n*d_1;
v_3nwa=c*abs(deltap_3nwa)^n*d_0;
v_4a=c*abs(deltap_4wa)^n*d_0;
v_5la=c*abs(deltap_5lwa)^n*d_0;
v_5ra=c*abs(deltap_5rwa)^n*d_0;
v_6a=c*abs(deltap_6a)^n*d_1;

v_31=c*abs(deltap_31)^n*d_2;
v_32=c*abs(deltap_32)^n*d_2;
v_34=c*abs(deltap_34)^n*d_2;
v_35=c*abs(deltap_35)^n*d_2;
v_36=c*abs(deltap_36)^n*d_2;

if p_1<p_1wa then v_1a_star:=v_1a;
else if p_1=p_1wa then v_1a_star:=0;
else if p_1>p_1wa then v_1a_star:=-v_1a;

if p_2<p_2wa then v_2a_star:=v_2a;
else if p_2=p_2wa then v_2a_star:=0;
else if p_2>p_2wa then v_2a_star:=-v_2a;

if p_3_ave<p_3nda then v_3nda_star:=v_3nda;
else if p_3_ave=p_3nda then v_3nda_star:=0;
else if p_3_ave>p_3nda then v_3nda_star:=-v_3nda;

if p_3_ave<p_3nwa then v_3nwa_star:=v_3nwa;
else if p_3_ave=p_3nwa then v_3nwa_star:=0;
else if p_3_ave>p_3nwa then v_3nwa_star:=-v_3nwa;

if p_3_ave<p_3swa then v_3swa_star:=v_3swa;
else if p_3_ave=p_3swa then v_3swa_star:=0;
else if p_3_ave>p_3swa then v_3swa_star:=-v_3swa;

if p_4<p_4wa then v_4a_star:=v_4a;
else if p_4=p_4wa then v_4a_star:=0;
else if p_4>p_4wa then v_4a_star:=-v_4a;

if p_5<p_5lwa then v_5la_star:=v_5la;
else if p_5=p_5lwa then v_5la_star:=0;
else if p_5>p_5lwa then v_5la_star:=-v_5la;

if p_5<p_5rwa then v_5ra_star:=v_5ra;
else if p_5=p_5rwa then v_5ra_star:=0;
else if p_5>p_5rwa then v_5ra_star:=-v_5ra;

if p_6<p_6sda then v_6a_star:=v_6a;
else if p_6=p_6sda then v_6a_star:=0;
else if p_6>p_6sda then v_6a_star:=-v_6a;

if p_1<p_3_ave then v_31_star:=v_31;
else if p_1=p_3_ave then v_31_star:=0;
else if p_1>p_3_ave then v_31_star:=-v_31;

if p_2<p_3_ave then v_32_star:=v_32;
else if p_2=p_3_ave then v_32_star:=0;
else if p_2>p_3_ave then v_32_star:=-v_32;

if p_4<p_3_ave then v_34_star:=v_34;
else if p_4=p_3_ave then v_34_star:=0;
else if p_4>p_3_ave then v_34_star:=-v_34;

if p_5<p_3_ave then v_35_star:=v_35;
else if p_5=p_3_ave then v_35_star:=0;
else if p_5>p_3_ave then v_35_star:=-v_35;

if p_6<p_3_ave then v_36_star:=v_36;
else if p_6=p_3_ave then v_36_star:=0;
else if p_6>p_3_ave then v_36_star:=-v_36;


{These 6 equations are airflow mass conservation for unbalanced dilution ventilation system only}
v_1a_star+v_31_star+v_1=0;
v_2a_star+v_32_star+v_2=0;
v_3swa_star+v_3nda_star+v_3nwa_star+v_3=v_31_star+v_32_star+v_34_star+v_35_star+v_36_star;
v_4a_star+v_34_star+v_4=0;
v_5la_star+v_5ra_star+v_35_star+v_5=0;
v_36_star+v_6a_star=0;

SSRE_1a=sum(i=0:97)((deltap_1a_exp-deltap_1a)^2/deltap_1a_exp^2);
SSRE_2a=sum(i=0:97)((deltap_2a_exp-deltap_2a)^2/deltap_2a_exp^2);
SSRE_4a=sum(i=0:97)((deltap_4a_exp-deltap_4a)^2/deltap_4a_exp^2);
SSRE_5a=sum(i=0:97)((deltap_5a_exp-deltap_5a)^2/deltap_5a_exp^2);
SSRE_6a=sum(i=0:97)((deltap_6a_exp-deltap_6a)^2/deltap_6a_exp^2);
SSRE_3nda=sum(i=0:97)((deltap_3ndagauge_exp-deltap_3nda)^2/deltap_3ndagauge_exp^2);
SSRE_3nwa=sum(i=0:97)((deltap_3nwagauge_exp-deltap_3nwa)^2/deltap_3nwagauge_exp^2);
SSRE_3swa=sum(i=0:97)((deltap_3swagauge_exp-deltap_3swa)^2/deltap_3swagauge_exp^2);

SSRE_total=SSRE_1a+SSRE_2a+SSRE_4a+SSRE_5a+SSRE_6a+SSRE_3nda+SSRE_3nwa+SSRE_3swa;

minfunction SSRE_total;