# Automated Multi-Level Dynamic System Topology Design Synthesis

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## Abstract

**:**

## 1. Introduction

#### 1.1. Automated Computational Design Synthesis Methods of Discrete System Topologies

^{®}for automated evaluation purposes, which is seen as a significant improvement.

#### 1.2. Research Contributions and Outline

- (a)
- A CDS framework to automatically formalize engineering knowledge into generic constraints. Moreover, this enables the automated generation of multi-level systems with predefined constraints;
- (b)
- The generation of multi-domain (electrical, mechanical, hydraulic, or combinations thereof) discrete system topologies. This requires a library format that specifies the domain of each component. For example, an electric machine has an electrical input and a (rotational) mechanical output. Based on these assigned domains, the constraints on the connection variables can automatically be derived;
- (c)
- The generation of topologies with different levels of expressiveness. Whereas [1,9] only declares component types and instances, this work introduces the declaration of ports and analyzes the benefits and drawbacks of this higher level of expressiveness. Furthermore, this higher level of expressiveness supports (b);
- (d)
- Further analysis of the search space: The influence of the number and degree of components vs. computational time as well as the working principle of the solving algorithm is analyzed and insights are created.

- A new computer-aided engineering (CAE) software tool has been developed, enabling the user (system engineer) to quickly set up and solve CSPs from the system to the component level, fully automated, in the field of powertrain systems.

- New electro-hydraulic actuation systems to be used in a continuously variable transmission (CVT) system (friction-based transmission type, cf. Figure 1); this is selected as a representative topology synthesis case study due to the high level of complexity and in order to demonstrate the multi-domain capabilities of the software application.

## 2. Topology Generation Methodology

- Step 1: Creation of a library;
- Step 2: Formalization of engineering knowledge;
- Step 3: Formulation and solving of a CSP;
- Step 4: Result post-processing;
- Step 5: Result analysis and classification.

#### 2.1. Step 1: Creation of a Library: Identification of Useful Components

#### 2.2. Step 2: Formalization of Engineering Knowledge: Mapping Functions to Components

- Are the components correctly physically connected? For example, are the components from different domains properly interconnected?
- Does a topology contain any unconnected components? For example, are all the ports of each component connected?
- Does the topology meet the functional requirements? For example, to power a hydraulic pump, rotational energy needs to be supplied by an engine or electric machine.

#### Constraint Classification

#### 2.3. Step 3: Formulation and Solving of a CSP: Using SWI-Prolog

**D**for every variable (components and/or connections) is 1 (present) or 0 (not present). A set of constraints

**C**completes this type of mathematical problem. These constraints are used to formalize engineering knowledge and design experience from Step 2.

#### Constraint Logic Programming over Finite Domains

#### 2.4. Step 4: Result Post-Processing: Using Filter Designs

#### Isomorphism Detection

#### 2.5. Step 5: Result Analysis and Classification

## 3. CSP Programming and Solving

#### 3.1. Arithmetic and Reification Constraints

- (1)
- These constraints use a logical equality. The truth table of logical equality is shown in Table 1. The only solution for this constraint is that A is always present.
- (2)
- In the definition of the search space, this constraint is used to force the presence of a component (1) or to prevent a connection (2) from being generated.
- (3)
- This constraint combines a sum, a logical operator, and a relational operator. This results in a constraint that limits (due to the relational operator) the presence of components A, B, and C to a maximum of two out of three.
- (4)
- This constraint uses classic negation, material implication, and an AND logic connector. This is to prevent connection CD (due to the negation) when (due to the material implication) there are connections AB and (due to the AND gate) BC. The truth table of the AND, OR, and NOT logic is shown in Table 2.
- (5)
- This constraint is the same as (4), except for the OR gate instead of the AND gate. Now, connection AC is prevented when there is a connection AB or (due to the AND gate) CD.
- (6)
- This combines the OR and AND gates from (4) and (5), respectively, to prevent connection BD.
- (7)
- This constraint combines a sum function to force the number of connections of D. For example, component D is a second-degree component, i.e., it can have two connections (two edges). To force that this component has two connections, this constraint can be added. When component D is present, then there can also exist two connections with D. However, when D is not present (D = 0), there are no connections containing D.

**Listing 1.**Examples of constraint types in Prolog code that are used to convert engineering knowledge into a constraint satisfaction problem (CSP). Note that the ‘%’ sign indicates a comment.

- Components = [A,B,C,D],
- ComponentsDomain 0..1,
- Connections = [AB,AC,AD,BC,BD,CD],
- ConnectionsDomain 0..1,
- % 0 = not present
- % 1 = present

- A #<==> 1, %(1)
- AB #<==> 0, %(2)
- sum([A,B,C], #=<, 2), %(3)
- AB #∧ BC #==> #\ CD, %(4)
- AB #∨ CD #==> #\ AC, %(5)
- (AB #∨ AD) #∧ (AC #∨ BC) #==> #\ BD, %(6)
- sum([AD,BD,CD], #=, 2*D), %(7)

#### 3.2. SWI-Prolog Solving Algorithm

#### 3.3. Improvements Implemented in the Solving Process: Reducing Computation Time

#### SAT Solvers

## 4. Automated Constraint Generation

- (1)
- The engineering level:

- (2)
- The mathematical level:

- (3)
- The logic level:

## 5. Scalability of the Method

#### 5.1. Influence of the Topology Expressiveness Level

#### 5.2. Component versus Port Expressiveness Level

#### 5.3. Search Space Definition without Constraints

^{40}, then the software overhead of starting the solving process is more dominant than the solving time. When the search space is >2

^{40}, then the solving time scales exponentially with the number of possible combinations. The influence of constraints on the solving time is considered in the next subsection.

#### 5.4. Influence of the Constraints on the Solving Process

#### 5.5. Influence of Abstraction Level Choice on Topology Generation

#### 5.6. Proposed Library Format

#### 5.7. Component Port Definition

## 6. Automated Multi-Level Topology Synthesis

#### New CAE Tool for Dynamic System Topology Synthesis

## 7. Mechatronic Actuation Systems for CVTs

#### 7.1. Problem Definition: Actuation System Design

#### 7.2. Project Setup: Session Library

_{1}and brake BR

_{1}from the CVT system. The lubrication block represents the cooling and lubrication of the clutch, brake, push belt, gears, and bearings. Please note that geometric optimization of the pulley pistons and the variation ratio optimization are outside the scope of this project. The interested reader is referred to [20].

#### 7.3. Project Setup: Project Constraints

- Prevention of a connection between the sink components;
- The looping of three or more virtual nodes is prevented;
- Prevention of two or three pumps in a parallel layout;
- No connection is allowed between sump and consumers; basically, bypassing of the pump is not allowed;
- No pumps in series connection, since this can be better replaced by a single pump;
- Only one sump may be connected to the pump in order to prevent oil recirculation.

#### 7.4. Design Space Analysis and Model-Based Evaluation

## 8. Conclusions and Recommendations

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Visualization of methodology: generation of topologies with the use of formalized component properties and engineering knowledge.

**Figure 3.**Illustration of an isomorphism topology that includes two virtual nodes (VNs) and four first-degree components (A–D). This results in 24 different possible configurations, of which 23 are isomorphous.

**Figure 5.**Two isomorphous topologies introduced by different component identifiers for multiple instances of a component.

**Figure 6.**Illustration of the first eight steps of searching with a depth-first search and backtracking. Solutions are listed in Table 3.

**Figure 7.**Visualization of the constraint: “The output of an oil pump may not indirectly, by means of two virtual nodes, be connected to the pumps input.”

**Figure 9.**CSP solving time as a function of search space size. For the ease of reading: ${2}^{12}$ s ≈ 68 min.

**Figure 10.**Schematic diagram of the multi-level topology generation process. Arbitrary example topologies are provided per system level. Related work is also indicated.

**Figure 11.**A new computer-aided engineering (CAE) tool for fully automated dynamic system topology synthesis applied to all-electric and hybrid-electric powertrain systems from the system to component level. A graphical user interface was developed for the ‘engineer’ based on the software attributes shown on the left-hand and right-hand sides, whereas the constraint programming (CP) solver and post-processor running on the software application are shown in the middle. The sequential process steps are indicated by the arrows.

**Figure 12.**Topology generation and performance results. For reasons of confidentiality, the absolute power values are not depicted. (

**a**) Histogram of the generated feasible topologies for the electro-hydraulic actuation system. (

**b**) Diagram showing the average and maximum actuation power of novel and newly synthesized on-demand CVT actuation systems simulated using theWorldwide Harmonized Light Vehicle Test Procedure (WLTP) for a passenger car.

**Table 1.**Truth table for the material implications (⇒) and logical equality (⇔). Note: # indicates a Prolog notation.

Input A | Input B | A ⇒ B | A ⇔ B |
---|---|---|---|

A $\#==>$ B | A $\#<==>$ B | ||

False | False | True | True |

True | False | False | False |

False | True | True | False |

True | True | True | True |

Input A | Input B | A AND B | A OR B | NOT A |
---|---|---|---|---|

A #∧ B | A #∨ B | #∖ A | ||

0 | 0 | False | False | True |

1 | 0 | False | True | False |

0 | 1 | False | True | |

1 | 1 | True | True |

**Table 3.**Solutions for the search algorithm example depicted in Figure 6.

Solution # | Solution # | ||
---|---|---|---|

1 | - | 11 | AC |

2 | D | 12 | ACD |

3 | C | 13 | AB |

4 | CD | 14 | ABD |

9 | A | 15 | ABC |

10 | AD | 16 | ABCD |

Expressiveness Level | ||
---|---|---|

Component | Port | |

# Component variables | 11 | 11 |

# Connection variables | 55 | 171 |

# Constraints (characters) | 2K | 11K |

# Total constraints | 26 | 168 |

Search space size | 2${}^{62}$ ≈ $5\times {10}^{18}$ | 2${}^{89}$ ≈ $6\times {10}^{26}$ |

Solving time (seconds) | 45 | 218 |

# Raw solutions | 21,536 | 102,768 |

# Post-processed solutions | 250 | 262 |

Identifier | Component | Component | Component | Number of | Energy Domain | |
---|---|---|---|---|---|---|

Type, $\mathit{\tau}$ | Name | Specification | Instances, $\sum \iota $ | Input | Output | |

A,B,C | 1 | Sump | Source | 3 | - | Hydraulic |

D,E,F | 2 | Pump | Converter | 3 | Hydraulic | Hydraulic |

G,H,I,J | 3 | VN | Virtual Node | 4 | Hydraulic | Hydraulic |

K | 4 | Primary pulley | Sink | 1 | Hydraulic | - |

L | 5 | Secondary pulley | Sink | 1 | Hydraulic | - |

M | 6 | Lubrication | Sink | 1 | Hydraulic | - |

N | 7 | Clutches | Sink | 1 | Hydraulic | - |

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**MDPI and ACS Style**

Kort, A.-J.; Wijkniet, J.; Serebrenik, A.; Hofman, T.
Automated Multi-Level Dynamic System Topology Design Synthesis. *Vehicles* **2020**, *2*, 603-624.
https://doi.org/10.3390/vehicles2040035

**AMA Style**

Kort A-J, Wijkniet J, Serebrenik A, Hofman T.
Automated Multi-Level Dynamic System Topology Design Synthesis. *Vehicles*. 2020; 2(4):603-624.
https://doi.org/10.3390/vehicles2040035

**Chicago/Turabian Style**

Kort, Aart-Jan, Jan Wijkniet, Alexander Serebrenik, and Theo Hofman.
2020. "Automated Multi-Level Dynamic System Topology Design Synthesis" *Vehicles* 2, no. 4: 603-624.
https://doi.org/10.3390/vehicles2040035