Question

我想使用隐式变量和非线性求解器在系统中迭代其值，使用有限差分进行导数计算。我理解牛顿求解器需要分析导数，但非线性Gauss-Siedel似乎也没有正确迭代。为了确保我已正确编码，我在包中提供的intersect_parabola_line.py示例中测试了这种方法。

from __future__ import print_function
from openmdao.api import Component, Group, Problem, Newton, ScipyGMRES,NLGaussSeidel

class Line(Component):
    """Evaluates y = -2x + 4."""
    def __init__(self):
        super(Line, self).__init__()
        self.add_param('x', 1.0)
        self.add_output('y', 0.0)
        # User can change these.
        self.slope = -2.0
        self.intercept = 4.0

    def solve_nonlinear(self, params, unknowns, resids):
        """ y = -2x + 4 """
        x = params['x']
        m = self.slope
        b = self.intercept
        unknowns['y'] = m*x + b

class Parabola(Component):
    """Evaluates y = 3x^2 - 5"""
    def __init__(self):
        super(Parabola, self).__init__()
        self.add_param('x', 1.0)
        self.add_output('y', 0.0)
        # User can change these.
        self.a = 3.0
        self.b = 0.0
        self.c = -5.0

    def solve_nonlinear(self, params, unknowns, resids):
        """ y = 3x^2 - 5 """
        x = params['x']
        a = self.a
        b = self.b
        c = self.c
        unknowns['y'] = a*x**2 + b*x + c

class Balance(Component):
    """Evaluates the residual y1-y2"""
    def __init__(self):
        super(Balance, self).__init__()
        self.add_param('y1', 0.0)
        self.add_param('y2', 0.0)
        self.add_state('x', 5.0)

    def solve_nonlinear(self, params, unknowns, resids):
        """This component does no calculation on its own. It mainly holds the
        initial value of the state. An OpenMDAO solver outside of this
        component varies it to drive the residual to zero."""
        pass

    def apply_nonlinear(self, params, unknowns, resids):
        """ Report the residual y1-y2 """
        y1 = params['y1']
        y2 = params['y2']
        resids['x'] = y1 - y2

if __name__ == '__main__':
    top = Problem()
    root = top.root = Group()
    root.add('line', Line())
    root.add('parabola', Parabola())
    root.add('bal', Balance())

    root.connect('line.y', 'bal.y1')
    root.connect('parabola.y', 'bal.y2')
    root.connect('bal.x', 'line.x')
    root.connect('bal.x', 'parabola.x')
    root.deriv_options['type'] = 'fd'

    root.nl_solver = NLGaussSeidel() #Newton()
    root.ln_solver = ScipyGMRES()
    root.nl_solver.options['iprint'] = 2

    top.setup()

    # Positive solution
    top['bal.x'] = 7.0
    root.list_states()
    top.run()
    print('Positive Solution x=%f, line.y=%f, parabola.y=%f' % (top['bal.x'], top['line.y'], top['parabola.y']))

    # Negative solution
    top['bal.x'] = -7.0
    root.list_states()
    top.run()
    print('Negative Solution x=%f, line.y=%f, parabola.y=%f' % (top['bal.x'], top['line.y'], top['parabola.y']))

我得到的输出是：

States in model:

bal.x
Value: 7.0
Residual: 0.0

[root] NL: NLN_GS   1 | 152 1
[root] NL: NLN_GS   2 | 152 1
[root] NL: NLN_GS   2 | Converged in 2 iterations
Positive Solution x=7.000000, line.y=-10.000000, parabola.y=142.000000

States in model:

bal.x
Value: -7.0
Residual: -152.0

[root] NL: NLN_GS   1 | 124 1
[root] NL: NLN_GS   2 | 124 1
[root] NL: NLN_GS   2 | Converged in 2 iterations
Negative Solution x=-7.000000, line.y=18.000000, parabola.y=142.000000

任何提示将不胜感激。我在OSX上使用Python 2.7.13和OpenMDAO 1.7.3。

Answer 1

因此，非线性高斯赛德尔实际上无法将模型与平衡分量和隐式状态融合。你应该真的使用牛顿。为了实现这一目标，您还需要确保Newton收敛的模型也使用有限差分。在根组中设置fd时，这意味着源自该系统的派生计算会在整个系统上看到近似的fd。

要做到这一点，请尝试以下方法：

top = Problem()
root = top.root = Group()
comp1 = root.add('line', Line())
comp2 = root.add('parabola', Parabola())
comp3 = root.add('bal', Balance())

root.connect('line.y', 'bal.y1')
root.connect('parabola.y', 'bal.y2')
root.connect('bal.x', 'line.x')
root.connect('bal.x', 'parabola.x')
root.deriv_options['type'] = 'fd'
comp1.deriv_options['type'] = 'fd'
comp2.deriv_options['type'] = 'fd'
comp3.deriv_options['type'] = 'fd'

具有有限差异的OpenMDAO隐式状态

1 个答案: