一
import pandas as pd import numpy as np #初始化参数 D_0=70 theta=120 alpha=1.5 d=200 d=d*np.sin(np.radians(90-theta/2))/np.sin(np.radians(90-alpha+theta/2)) distances=np.array([-800,-600,-400,-200,0,200,400,600,800]) D=D_0-distances*np.tan(np.radians(alpha)) print(D) W=D*np.sin(np.radians(theta/2))*(1/np.sin(np.radians((180-theta)/2+alpha))+1/np.sin(np.radians((180-theta)/2-alpha))) print(W) n=1-d/W print(n) #创建DataFrame用于保存结果 df=pd.DataFrame({'测线距中心点处的距离/m':distances}) df['海水深度/m']=D df['覆盖宽度/m']=W df['与前一条测线的覆盖率/%']=n #将DataFrame保存为Excel文件 path=r'C:\Users\Administrator\Desktop\大学\数学建模\2023国B\result1.xlsx' df.to_excel(path,index=False)
二
import pandas as pd import numpy as np def get_width(B): #初始化参数 D_0 = 120 #海底深度（单位：m） alpha=1.5 #坡度（单位：度） D=D_0-distances*np.tan(np.radians(alpha))*np.cos(np.radians(180-B)) theta=120 #换能器的开角（单位：度） alpha=np.arctan(abs(np.sin(np.radians(B)))*np.tan(np.radians(alpha)))*180/np.pi print(D) W=D*np.sin(np.radians(theta/2))*(1/np.sin(np.radians((180-theta)/2+alpha))+1/np.sin(np.radians((180-theta)/2-alpha))) print(W) return W distances=np.array([0,0.3,0.6,0.9,1.2,1.5,1.8,2.1]) distances=distances*1852 print(distances) angel=[0,45,90,135,180,225,270,315] W=[] for i in angel: W.append(get_width(i)) #将DataFrame保存为Excel文件 path=r'C:\Users\Administrator\Desktop\大学\数学建模\2023国B\result2.xlsx' pd.DataFrame(W).to_excel(path,index=False)
三
1、
import pandas as pd import numpy as np import matplotlib.pyplot as plt plt.rcParams['font.sans-serif']=['SimHei'] #显示中文 def get_width(B,D_0): #初始化参数 alpha=1.5 #坡度 D=D_0 theta=120 alpha=np.arctan(abs(np.sin(np.radians(B)))*np.tan(np.radians(alpha)))*180/np.pi print(D) W = D * np.sin(np.radians(theta / 2)) * ( 1 / np.sin(np.radians((180 - theta) / 2 + alpha)) + 1 / np.sin(np.radians((180 - theta) / 2 - alpha))) print(W) return W angle=np.linspace(0,360,360) W=[] for i in angle: W.append(get_width(i,150)) print(W) plt.plot(angle,W) plt.scatter(90,W[89],color='r') plt.scatter(270,W[269],color='r') plt.text(90,W[89],'({},{})'.format(90,W[89])) plt.text(270,W[269],'({},{})'.format(270,W[269])) angle=np.linspace(0,360,360) W=[] for i in angle: W.append(get_width(i,149.5)) print(W) plt.plot(angle,W) plt.scatter(90,W[89],color='r') plt.scatter(270,W[269],color='r') plt.text(90,W[89],'({},{})'.format(90,W[89])) plt.text(270,W[269],'({},{})'.format(270,W[269])) plt.xlabel("不同角度") plt.ylabel("覆盖宽度") plt.show()
2、
import pandas as pd import numpy as np import matplotlib.pyplot as plt plt.rcParams['font.sans-serif']=['SimHei'] #显示中文 def sin(a): return np.sin(np.radians(a)) def cos(a): return np.cos(np.radians(a)) def tan(a): return np.tan(np.radians(a)) angle=np.linspace(0,360,360) low=110-2*2852*np.tan(np.radians(1.5)) high=110+2*2852*np.tan(np.radians(1.5)) alpha=1.5#坡度 theta=120 #换能器的开角 n=np.linspace(0.1,0.2,100) cnt=[] for i in n: x=sin(theta/2)*cos(alpha)*high/(sin(90-theta/2-alpha)+sin(alpha)*sin(theta/2)) x=high-x*tan(alpha) print(x) ans=[] ans.append(x) A = sin(90 - theta / 2 + alpha) B = sin(90 - theta / 2 - alpha) C=sin(theta/2)/A-1/tan(alpha) D=i*sin(theta/2)*(1/A+1/B)-sin(theta/2)/B-1/tan(alpha) while True: x=x*C/D if x<low: break ans.append(x) #print(len(ans)) cnt.append(len(ans)) #print(ans[-1]) n=np.array(n) print(n) print(cnt) plt.plot(n,cnt,color='r') plt.xlabel("不同重复率") plt.ylabel("测线总数") plt.show()
3、
import pandas as pd import numpy as np import matplotlib.pyplot as plt plt.rcParams['font.sans-serif']=['SimHei'] #显示中文 def sin(a): return np.sin(np.radians(a)) def cos(a): return np.cos(np.radians(a)) def tan(a): return np.tan(np.radians(a)) angle=np.linspace(0,360,360) low=110-2*2852*np.tan(np.radians(1.5)) high=110+2*2852*np.tan(np.radians(1.5)) alpha=1.5#坡度 theta=120 #换能器的开角 n=0.1 cnt=[] x = sin(theta / 2) * cos(alpha) * high / (sin(90 - theta / 2 - alpha) + sin(alpha) * sin(theta / 2)) x = high - x * tan(alpha) print(x) ans = [] ans.append(x) A = sin(90 - theta / 2 + alpha) B = sin(90 - theta / 2 - alpha) C = sin(theta / 2) / A - 1 / tan(alpha) D = n * sin(theta / 2) * (1 / A + 1 / B) - sin(theta / 2) / B - 1 / tan(alpha) while True: x = x * C / D if x < low: break ans.append(x) #print(len(ans)) #print(ans[-1]) index=np.arange(len(ans)) ans=np.array(ans) dis=[] for i in range(len(ans)-1): dis.append((ans[i]-ans[i+1])/tan(alpha)) for i in range(len(dis)-1): dis[i+1]+=dis[i] #plt.scatter(index,ans,color='g') #plt.xlabel("测线编号") #plt.ylabel("水深") #plt.show() print(dis) dis.insert(0,0) dis=np.array(dis)/1852 y=np.zeros(len(dis)) #plt.scatter(dis,y,marker='x',s=10) plt.xlabel("各测线得到水平位置") plt.ylim(-1.2,1.2) plt.yticks(alpha=0) plt.tick_params(axis='y',width=0) y=np.linspace(-1,1,10000) for i in range(len(dis)-1): x=np.full((1,10000),dis[i]) plt.scatter(x,y,s=0.0001,color='c') tx=np.linspace(dis[i],dis[i+1],1000) if i%2==0: ty=1 else: ty=-1 ty=np.full((1,1000),ty) plt.scatter(tx,ty,s=0.0001,color='c') x=np.full((1,10000),dis[-1]) plt.scatter(x,y,x=0.0001,color='c') plt.show() path=r'C:\Users\Administrator\Desktop\大学\数学建模\2023国B\距离.xlsx' pd.DataFrame(dis).to_excel(path) path = r'C:\Users\Administrator\Desktop\大学\数学建模\2023国B\距离.xlsx' pd.DataFrame(ans).to_excel(path)
4、
import pandas as pd import numpy as np import matplotlib.pyplot as plt plt.rcParams['font.sans-serif']=['SimHei'] #显示中文 def sin(a): return np.sin(np.radians(a)) def cos(a): return np.cos(np.radians(a)) def tan(a): return np.tan(np.radians(a)) def get_Wleft(D): return D*sin(theta/2)/sin(90-theta/2-alpha) def get_WRight(D): return D*sin(theta/2)/sin(90-theta/2+alpha) angle=np.linspace(0,360,360) low=110-2*2852*np.tan(np.radians(1.5)) high=110+2*2852*np.tan(np.radians(1.5)) alpha=1.5#坡度 theta=120 #换能器的开角 n=0.1 cnt=[] x = sin(theta / 2) * cos(alpha) * high / (sin(90 - theta / 2 - alpha) + sin(alpha) * sin(theta / 2)) x = high - x * tan(alpha) print(x) ans = [] ans.append(x) while True: high=x-(get_WRight(x)-(get_WRight(x)+get_Wleft(x))*n)*sin(alpha) x=sin(theta/2)*cos(alpha)*high/(sin(90-theta/2-alpha)+sin(alpha)*sin(theta/2)) x=high-x*tan(alpha) if x < low: break ans.append(x) print(ans) print(len(ans)) print(ans[-1]) index=np.array(len(ans)) plt.scatter(index,ans,color='g') plt.xlabel("测线编号") plt.ylabel("水深") plt.show() #path = r'C:\Users\Administrator\Desktop\大学\数学建模\2023国B\水深.xlsx' #pd.DataFrame(ans).to_excel(path)
5、
import pandas as pd import numpy as np import matplotlib.pyplot as plt def sin(a): return np.sin(np.radians(a)) def cos(a): return np.cos(np.radians(a)) def tan(a): return np.tan(np.radians(a)) def get_Wleft(D): return D*sin(theta/2)/sin(90-theta/2-alpha) angle=90 alpha=np.linspace(0.5,10,100) theta=np.linspace(90,150,100) x_d=70 w=[] for i in alpha: for j in theta: w.append(x_d*sin(j/2)*(1/sin(90-j/2-i)+1/sin(90-j/2+i))) print(w) w=np.array(w).reshape(100,100) alpha,theta=np.meshgrid(alpha,theta) #创建三位图形对象和坐标轴 fig=plt.figure() ax=fig.add_subplot(111,projection='3d') #绘制三维图形 ax.plot_surface(alpha,theta,w,cmap='viridis') #设置坐标轴标签 ax.set_xlabel('alpha') ax.set_ylabel('theta') ax.set_zlabel('w') #显示图形 plt.show()
