Inverse design

WISDEM/examples/09_floating/IEA-15-240-RWT_VolturnUS-S.yaml

@@ -690,6 +690,8 @@ components:
               joint2: col3_lower_pontoon
               outer_shape: *pontlow_out
               internal_structure: *pontlow_int
+        transition_piece_mass: 100.e3
+        transition_piece_cost: 300.e3
     mooring:
         nodes:
             - name: line1_anchor

WISDEM/examples/16_inverse_design/analysis_options.yaml

@@ -0,0 +1,50 @@
+general:
+    folder_output: outputs
+    fname_output: refturb_output
+
+design_variables:
+    floating:
+        joints:
+            flag: True
+            z_coordinate:
+                - names: [spar_keel]
+                  lower_bound: -40.0
+                  upper_bound: -15.0
+                - names: [spar_freeboard]
+                  lower_bound: -40.0
+                  upper_bound: -15.0
+        members:
+            flag: True
+            groups:
+                - names: [spar]
+                  ballast:
+                      lower_bound: 1.0
+                      upper_bound: 1e4
+
+    mooring:
+        line_length:
+            flag: True
+            lower_bound: 100.0
+            upper_bound: 1000.0
+
+merit_figure: inverse_design
+
+inverse_design:
+    floatingse.platform_mass:
+        ref_value: 6.e6
+        units: kg
+    floatingse.mooring_mass:
+        ref_value: 4.5e5
+        units: kg
+    floatingse.system_structural_center_of_mass:
+        ref_value: [0., -60.]
+        indices: [1, 2]
+        units: m
+
+driver:
+    optimization:
+        flag: True         # Flag to enable optimization
+        tol: 1.e-4          # Optimality tolerance
+        solver: SLSQP       # Optimization solver. Other options are 'SLSQP' - 'CONMIN'
+        step_size: 1.e-6    # Step size for finite differencing
+        form: forward       # Finite differencing mode, either forward or central

WISDEM/examples/16_inverse_design/inverse_spar_design.py

@@ -0,0 +1,16 @@
+import os
+import sys
+import time
+
+from wisdem.commonse.mpi_tools import MPI
+from wisdem.glue_code.runWISDEM import run_wisdem
+
+## File management
+run_dir = os.path.dirname(os.path.realpath(__file__)) + os.sep
+wisdem_examples = os.path.dirname(os.path.dirname(run_dir))
+fname_wt_input_oc3 = os.path.join(wisdem_examples, "09_floating", "nrel5mw-spar_oc3.yaml")
+fname_modeling_options = os.path.join(wisdem_examples, "09_floating", "modeling_options_noRNA.yaml")
+fname_analysis_options = run_dir + os.sep + "analysis_options.yaml"
+
+
+wt_opt, modeling_options, opt_options = run_wisdem(fname_wt_input_oc3, fname_modeling_options, fname_analysis_options)

WISDEM/wisdem/floatingse/floating_frame.py

@@ -58,6 +58,12 @@ def setup(self):
             self.add_input(f"member{k}:Pz", np.zeros(MEMMAX), units="N/m")
             self.add_input(f"member{k}:qdyn", np.zeros(MEMMAX), units="Pa")
 
+        self.add_input("transition_node", np.zeros(3), units="m")
+        self.add_input("transition_piece_mass", 0.0, units="kg")
+        self.add_input("transition_piece_cost", 0.0, units="USD")
+
+        self.add_output("transition_piece_I", np.zeros(6), units="kg*m**2")
+
         self.add_output("platform_nodes", NULL * np.ones((NNODES_MAX, 3)), units="m")
         self.add_output("platform_Fnode", NULL * np.ones((NNODES_MAX, 3)), units="N")
         self.add_output("platform_Rnode", NULL * np.ones(NNODES_MAX), units="m")
@@ -85,12 +91,12 @@ def setup(self):
         self.add_discrete_output("platform_elem_memid", [-1] * NELEM_MAX)
         self.add_output("platform_displacement", 0.0, units="m**3")
         self.add_output("platform_center_of_buoyancy", np.zeros(3), units="m")
-        self.add_output("platform_center_of_mass", np.zeros(3), units="m")
+        self.add_output("platform_hull_center_of_mass", np.zeros(3), units="m")
         self.add_output("platform_centroid", np.zeros(3), units="m")
         self.add_output("platform_ballast_mass", 0.0, units="kg")
         self.add_output("platform_hull_mass", 0.0, units="kg")
         self.add_output("platform_mass", 0.0, units="kg")
-        self.add_output("platform_I_total", np.zeros(6), units="kg*m**2")
+        self.add_output("platform_I_hull", np.zeros(6), units="kg*m**2")
         self.add_output("platform_cost", 0.0, units="USD")
         self.add_output("platform_Awater", 0.0, units="m**2")
         self.add_output("platform_Iwater", 0.0, units="m**4")
@@ -157,7 +163,9 @@ def set_node_props(self, inputs, outputs):
         n_member = opt["floating"]["members"]["n_members"]
 
         # Number of valid nodes
-        nnode = np.where(outputs["platform_nodes"][:, 0] == NULL)[0][0]
+        node_platform = outputs["platform_nodes"]
+        nnode = np.where(node_platform[:, 0] == NULL)[0][0]
+        node_platform = node_platform[:nnode, :]
 
         # Find greatest radius of all members at node intersections
         Rnode = np.zeros(nnode)
@@ -175,6 +183,13 @@ def set_node_props(self, inputs, outputs):
             iglob = self.node_mem2glob[(k, icb)]
             Fnode[iglob, 2] += inputs[f"member{k}:buoyancy_force"]
 
+        # Get transition piece inertial properties
+        itrans_platform = util.closest_node(node_platform, inputs["transition_node"])
+        m_trans = float(inputs["transition_piece_mass"])
+        r_trans = Rnode[itrans_platform]
+        I_trans = m_trans * r_trans ** 2.0 * np.r_[0.5, 0.5, 1.0, np.zeros(3)]
+        outputs["transition_piece_I"] = I_trans
+
         # Store outputs
         outputs["platform_Rnode"] = NULL * np.ones(NNODES_MAX)
         outputs["platform_Rnode"][:nnode] = Rnode
@@ -265,13 +280,21 @@ def set_element_props(self, inputs, outputs, discrete_inputs, discrete_outputs):
             cg_plat += imass * inputs[f"member{k}:center_of_mass"]
             cb_plat += ivol * inputs[f"member{k}:center_of_buoyancy"]
 
+        # Add transition piece
+        m_trans = inputs["transition_piece_mass"]
+        cg_trans = inputs["transition_node"]
+        I_trans = util.assembleI(outputs["transition_piece_I"])
+        mass += m_trans
+        cost += inputs["transition_piece_cost"]
+        cg_plat += m_trans * cg_trans
+
         # Finalize outputs
         cg_plat /= mass
         cb_plat /= volume
 
         # With CG known, loop back through to compute platform I
         unit_z = np.array([0.0, 0.0, 1.0])
-        I_total = np.zeros((3, 3))
+        I_hull = np.zeros((3, 3))
         for k in range(n_member):
             xyz_k = inputs[f"member{k}:nodes_xyz"]
             inodes = np.where(xyz_k[:, 0] == NULL)[0][0]
@@ -287,10 +310,14 @@ def set_element_props(self, inputs, outputs, discrete_inputs, discrete_outputs):
 
             # Rotate member inertia tensor
             I_k = util.assembleI(inputs[f"member{k}:I_total"])
-            I_k2 = T @ I_k @ T.T
+            I_k_rot = T @ I_k @ T.T
 
             # Now do parallel axis theorem
-            I_total += np.array(I_k2) + imass * (np.dot(R, R) * np.eye(3) - np.outer(R, R))
+            I_hull += np.array(I_k_rot) + imass * (np.dot(R, R) * np.eye(3) - np.outer(R, R))
+
+        # Add in transition piece
+        R = cg_plat - cg_trans
+        I_hull += I_trans + m_trans * (np.dot(R, R) * np.eye(3) - np.outer(R, R))
 
         # Store outputs
         nelem = elem_A.size
@@ -340,9 +367,9 @@ def set_element_props(self, inputs, outputs, discrete_inputs, discrete_outputs):
         outputs["platform_hull_mass"] = mass - m_ball
         outputs["platform_cost"] = cost
         outputs["platform_displacement"] = volume
-        outputs["platform_center_of_mass"] = cg_plat
+        outputs["platform_hull_center_of_mass"] = cg_plat
         outputs["platform_center_of_buoyancy"] = cb_plat
-        outputs["platform_I_total"] = util.unassembleI(I_total)
+        outputs["platform_I_hull"] = util.unassembleI(I_hull)
         outputs["platform_Awater"] = Awater
         outputs["platform_Iwater"] = Iwater
         outputs["platform_added_mass"] = m_added
@@ -357,7 +384,8 @@ def setup(self):
 
     def compute(self, inputs, outputs):
         transition_node = inputs["transition_node"]
-        tower_top_node = transition_node
+        tower_top_node = 0  #previous code altered the original definition of transition_node
+        tower_top_node += transition_node
         tower_top_node[2] += float(inputs["tower_height"])
         outputs["tower_top_node"] = tower_top_node
 
@@ -395,8 +423,9 @@ def setup(self):
         self.add_input("platform_elem_Pz1", NULL * np.ones(NELEM_MAX), units="N/m")
         self.add_input("platform_elem_Pz2", NULL * np.ones(NELEM_MAX), units="N/m")
         self.add_input("platform_elem_qdyn", NULL * np.ones(NELEM_MAX), units="Pa")
-        self.add_input("platform_center_of_mass", np.zeros(3), units="m")
+        self.add_input("platform_hull_center_of_mass", np.zeros(3), units="m")
         self.add_input("platform_mass", 0.0, units="kg")
+        self.add_input("platform_I_hull", np.zeros(6), units="kg*m**2")
         self.add_input("platform_displacement", 0.0, units="m**3")
 
         self.add_input("tower_nodes", NULL * np.ones((MEMMAX, 3)), units="m")
@@ -433,7 +462,6 @@ def setup(self):
         self.add_input("rho_water", 0.0, units="kg/m**3")
         self.add_input("tower_top_node", np.zeros(3), units="m")
         self.add_input("transition_node", np.zeros(3), units="m")
-        self.add_input("transition_piece_mass", 0.0, units="kg")
         self.add_input("rna_mass", 0.0, units="kg")
         self.add_input("rna_cg", np.zeros(3), units="m")
         self.add_input("mooring_neutral_load", np.zeros((n_attach, 3)), units="N")
@@ -478,7 +506,8 @@ def setup(self):
         self.add_output("constr_variable_margin", val=0.0)
         self.add_output("member_variable_volume", val=np.zeros(n_member), units="m**3")
         self.add_output("member_variable_height", val=np.zeros(n_member))
-        self.add_output("transition_piece_I", np.zeros(6), units="kg*m**2")
+        self.add_output("platform_total_center_of_mass", np.zeros(3), units="m")
+        self.add_output("platform_I_total", np.zeros(6), units="kg*m**2")
 
     def compute(self, inputs, outputs):
         # Combine nodes
@@ -576,17 +605,17 @@ def compute(self, inputs, outputs):
 
         # Mass summaries
         m_platform = inputs["platform_mass"]
+        cg_platform = inputs["platform_hull_center_of_mass"]
+        I_platform = util.assembleI(inputs["platform_I_hull"])
         m_tower = inputs["tower_mass"]
         m_rna = inputs["rna_mass"]
-        m_trans = inputs["transition_piece_mass"]
-        m_sys = m_platform + m_tower + m_rna + m_trans
+        m_sys = m_platform + m_tower + m_rna
         outputs["system_structural_mass"] = m_sys
 
         outputs["system_structural_center_of_mass"] = (
-            m_platform * inputs["platform_center_of_mass"]
+            m_platform * cg_platform
             + m_tower * inputs["tower_center_of_mass"]
             + m_rna * (inputs["rna_cg"] + inputs["tower_top_node"])
-            + m_trans * inputs["transition_node"]
         ) / m_sys
 
         # Balance out variable ballast
@@ -600,6 +629,7 @@ def compute(self, inputs, outputs):
         outputs["constr_variable_margin"] = V_variable / capacity_sum
         V_variable_member = V_variable * capacity / capacity_sum
         outputs["member_variable_volume"] = V_variable_member
+        m_variable_member = V_variable_member * rho_water
 
         # Now find the CG of the variable mass assigned to each member
         n_member = capacity.size
@@ -632,11 +662,51 @@ def compute(self, inputs, outputs):
             m_sys * outputs["system_structural_center_of_mass"] + m_variable * cg_variable
         ) / (m_sys + m_variable)
 
-        # Transition piece properties
-        m_trans = float(inputs["transition_piece_mass"])
-        r_trans = inputs["platform_Rnode"][itrans_platform]
-        I_trans = m_trans * r_trans ** 2.0 * np.r_[0.5, 0.5, 1.0, np.zeros(3)]
-        outputs["transition_piece_I"] = I_trans
+        # Compute the total cg for the platform and the variable ballast together using a weighted sum approach
+        cg_plat_total = (m_variable * cg_variable + m_platform * cg_platform) / (m_variable + m_platform)
+        outputs["platform_total_center_of_mass"] = cg_plat_total
+
+        # Now loop again to compute variable I
+        unit_z = np.array([0.0, 0.0, 1.0])
+        I_variable = np.zeros((3, 3))
+        for k in range(n_member):
+            if V_variable_member[k] == 0.0:
+                continue
+
+            xyz = inputs[f"member{k}:nodes_xyz"]
+            inodes = np.where(xyz[:, 0] == NULL)[0][0]
+            xyz = xyz[:inodes, :]
+            vec_k = xyz[-1, :] - xyz[0, :]
+
+            ds = outputs["member_variable_height"][k]
+
+            # Compute I aligned with member
+            h_k = ds * np.sqrt(np.sum(vec_k ** 2))
+            if h_k == 0.0:
+                continue
+            r_k = np.sqrt(V_variable_member[k] / h_k / np.pi)
+            I_k = (
+                m_variable_member[k] * np.r_[(3 * r_k ** 2 + h_k ** 2) / 12.0 * np.ones(2), 0.5 * r_k ** 2, np.ones(3)]
+            )
+
+            # Rotate I to global c.s.
+            T = util.rotate_align_vectors(vec_k, unit_z)
+            I_k_rot = T @ util.assembleI(I_k) @ T.T
+
+            # Now do parallel axis theorem
+            R = cg_variable - cg_variable_member[k, :]
+            I_variable += np.array(I_k_rot) + m_variable_member[k] * (np.dot(R, R) * np.eye(3) - np.outer(R, R))
+
+        # Find platform I with variable contribution
+        I_total = np.zeros((3, 3))
+
+        # Compute the full moment of inertia for the platform and variable ballast
+        R = cg_plat_total - cg_platform
+        I_total += I_platform + m_platform * (np.dot(R, R) * np.eye(3) - np.outer(R, R))
+
+        R = cg_plat_total - cg_variable
+        I_total += I_variable + m_variable * (np.dot(R, R) * np.eye(3) - np.outer(R, R))
+        outputs["platform_I_total"] = util.unassembleI(I_total)
 
 
 class FrameAnalysis(om.ExplicitComponent):
@@ -648,7 +718,7 @@ def setup(self):
         n_attach = opt["mooring"]["n_attach"]
 
         self.add_input("platform_mass", 0.0, units="kg")
-        self.add_input("platform_center_of_mass", np.zeros(3), units="m")
+        self.add_input("platform_hull_center_of_mass", np.zeros(3), units="m")
         self.add_input("platform_added_mass", np.zeros(6), units="kg")
         self.add_input("platform_center_of_buoyancy", np.zeros(3), units="m")
         self.add_input("platform_displacement", 0.0, units="m**3")
@@ -818,8 +888,9 @@ def compute(self, inputs, outputs):
             m_trans = float(inputs["transition_piece_mass"])
             if frame == "tower":
                 m_trans += float(inputs["platform_mass"]) + inputs["platform_added_mass"][0] + m_variable
-                cg_trans = inputs["transition_node"] - inputs["platform_center_of_mass"]
+                cg_trans = inputs["transition_node"] - inputs["platform_hull_center_of_mass"]
                 I_trans[:3] += inputs["platform_added_mass"][3:]
+
             else:
                 m_trans += m_variable
                 cg_trans = np.zeros(3)

WISDEM/wisdem/glue_code/gc_PoseOptimization.py

@@ -432,8 +432,8 @@ def set_objective(self, wt_opt):
             else:
                 wt_opt.model.add_objective("floatingse.tower_mass", ref=1e6)
 
-        elif self.opt["merit_figure"] == "mononpile_mass":
-            wt_opt.model.add_objective("towerse.mononpile_mass", ref=1e6)
+        elif self.opt["merit_figure"] == "monopile_mass":
+            wt_opt.model.add_objective("towerse.monopile_mass", ref=1e6)
 
         elif self.opt["merit_figure"] == "structural_mass":
             if not self.modeling["flags"]["floating"]:
@@ -470,6 +470,10 @@ def set_objective(self, wt_opt):
                 wt_opt.model.add_objective("rotorse.rp.powercurve.Cp_regII", ref=-1.0)
             else:
                 wt_opt.model.add_objective("rotorse.ccblade.CP", ref=-1.0)
+
+        elif self.opt["merit_figure"] == "inverse_design":
+            wt_opt.model.add_objective("inverse_design.objective")
+
         else:
             raise ValueError("The merit figure " + self.opt["merit_figure"] + " is unknown or not supported.")
 

WISDEM/wisdem/glue_code/gc_WT_DataStruc.py

@@ -1,9 +1,10 @@
 import copy
 
 import numpy as np
+from scipy.interpolate import PchipInterpolator, interp1d
+
 import openmdao.api as om
 import wisdem.moorpy.MoorProps as mp
-from scipy.interpolate import PchipInterpolator, interp1d
 from wisdem.commonse.utilities import arc_length, arc_length_deriv
 from wisdem.rotorse.parametrize_rotor import ParametrizeBladeAero, ParametrizeBladeStruct
 from wisdem.rotorse.geometry_tools.geometry import remap2grid, trailing_edge_smoothing
@@ -2128,6 +2129,8 @@ def setup(self):
         jivc = self.add_subsystem("joints", om.IndepVarComp(), promotes=["*"])
         jivc.add_output("location_in", val=np.zeros((n_joints, 3)), units="m")
         jivc.add_output("transition_node", val=np.zeros(3), units="m")
+        jivc.add_output("transition_piece_mass", val=0.0, units="kg", desc="point mass of transition piece")
+        jivc.add_output("transition_piece_cost", val=0.0, units="USD", desc="cost of transition piece")
 
         # Additions for optimizing individual nodes or multiple nodes concurrently
         self.add_subsystem("nodedv", NodeDVs(options=floating_init_options["joints"]), promotes=["*"])

WISDEM/wisdem/glue_code/gc_WT_InitModel.py

@@ -922,7 +922,8 @@ def assign_floating_values(wt_opt, modeling_options, floating):
     else:
         itrans = modeling_options["floating"]["transition_joint"]
     wt_opt["floating.transition_node"] = wt_opt["floating.location_in"][itrans, :]
-
+    wt_opt["floating.transition_piece_mass"] = floating["transition_piece_mass"]
+    wt_opt["floating.transition_piece_cost"] = floating["transition_piece_cost"]
     # Make sure IVCs are initialized too
     for k, linked_node_dict in enumerate(modeling_options["floating"]["joints"]["design_variable_data"]):
         idx = linked_node_dict["indices"]
@@ -1139,7 +1140,7 @@ def assign_environment_values(wt_opt, environment, offshore, blade_flag):
     wt_opt["env.G_soil"] = environment["soil_shear_modulus"]
     wt_opt["env.nu_soil"] = environment["soil_poisson"]
     if blade_flag:
-        wt_opt['rotorse.wt_class.V_mean_overwrite'] = environment['V_mean']
+        wt_opt["rotorse.wt_class.V_mean_overwrite"] = environment["V_mean"]
 
     return wt_opt