# A Conflict Solving Process Based on Mapping between Physical Parameters and Engineering Parameters

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## Abstract

**:**

## 1. Introduction

- The study proposes a mapping model between physical parameters and engineering parameters, which is trained by BP neural network. The mapping model assists the designer to select engineering parameters, which improves the accuracy of the designer’s engineering parameter selection during conflict solving.
- The proposed conflict solving process can guide the designer to discover the conflicts in the design process, thus optimizing the application process of the classical TRIZ conflict matrix.

## 2. Literature Review

#### 2.1. Engineering Parameter in Conflict Matrix

#### 2.2. Artificial Neural Network

## 3. Theoretical Methods

#### 3.1. Mapping Relationship between Physical Parameters and Engineering Parameters

#### 3.2. Construction Process of the Mapping Model between Physical Parameters and Engineering Parameters

#### 3.2.1. Determination of Case Set

#### 3.2.2. Extraction of Sample Data

- (1)
- Extraction of the physical parameter set.

- (2)
- Extraction of engineering parameters.

#### 3.2.3. Coding of Sample Data

- (1)
- Coding of the physical parameter set.

- When the number of physical parameters in the physical parameter set is $n<4$, the feature codes of the ($n+1$)th to the 4th physical parameter are all set to 0. Taking the number $n=2$ as an example, the code of the physical parameter set is shown in Figure 5a.
- When the number of extracted physical parameters is $n\ge 4$, the 4th to $n$th physical parameters need to be synthesized, and the synthesized physical parameter is used as the 4th input parameter. The parameter synthesis rules are derived from the genetic idea of Bartini in the LT matrix. A new dimension L
^{n}T^{m}is obtained by multiplying the dimensions L^{n1}T^{m1}and L^{n2}T^{m2}of two physical parameters x and y. Then the physical parameter z corresponding to L^{n}T^{m}will inherit the attributes of both x and y [35,36].

- (2)
- Coding of engineering parameters.

#### 3.2.4. Training of Mapping Model

- (1)
- Determining the training method of the mapping model.

- (2)
- Determining the training algorithm for the mapping model.

- (3)
- Training the mapping model.

#### 3.3. Conflict Solving Process Based on Mapping between Physical Parameters and Engineering Parameters

**Step 1: Identifying the system problem and building the function model.**

**Step 2: Building the physical parameter logical network.**

- (1)
- According to the integrity law of technical systems [40], the system components in the function model are divided into four types: energy device, transmission device, execution device and operation control device.
- (2)
- The physical parameters of the corresponding types of components are extracted [41]. In addition, it is also necessary to consider the physical parameters corresponding to targets and super-system components that affect the system.
- (3)
- According to the $\pi $ theorem in dimensional analysis [42], the logical relationship between physical parameters is obtained. Dimensional analysis is a well-established and widely used method in the physical and engineering sciences that enables the analysis of relationships between variables, reducing the number of potential causes that need to be considered. The steps of dimensional analysis are as follows:

- (4)
- According to the logical relationship displayed by the expression $\pi $ and the interaction relationship between components, the physical parameters are connected to generate a physical parameter logical network as shown in Figure 9. The direction of the arrow points from the independent variable to the dependent variable, indicating the logical relationship between physical parameters. The solid arrow indicates a positive correlation, and the hollow arrow indicates a negative correlation.

**Step 3: Determining system conflicts.**

- (1)
- Determining the improvement goal.

- (2)
- Determining the deterioration result.

- (3)
- Determining conflicts.

**Step 4: Selecting engineering parameters through the mapping model.**

- (1)
- The physical parameter sets $P=\left({p}_{1},{p}_{2},\dots ,{p}_{n}\right)$ and ${P}^{-}=\left({p}_{1}^{-},{p}_{2}^{-},\dots ,{p}_{n}^{-}\right)$, corresponding to both conflicting parties, are determined;
- (2)
- Judging whether $P$ or ${P}^{-}$ are affected by multiple physical parameters. If it is a single physical parameter, the corresponding engineering parameters can be directly determined; otherwise, the next step can be proceeded to;
- (3)
- Judging whether $P$ or ${P}^{-}$ is related to the engineering parameters (No.24, No.35 and No.38). If it is related, it doesn’t need to be selected through the mapping model to avoid engineering parameter selection errors; otherwise, the next step can be proceeded to;
- (4)
- The physical parameter set $P$ or ${P}^{-}$ is encoded according to the LT dimension and other physical parameter characteristics;
- (5)
- The encoded physical parameter set $P$ or ${P}^{-}$ is inputted into the mapping model. Then, the corresponding engineering parameter is selected according to the mapping result.

**Step 5: Solving conflicts.**

**Step 6: Evaluating schemes.**

## 4. Case Study

#### 4.1. Case Background

#### 4.2. Case Design Process

**Step 1: Determining the problem of the bulk TCM dispenser and building its function model.**

**Step 2: Constructing the physical parameter logic network of the bulk TCM dispenser.**

**Step 3: Determining the conflict of the bulk TCM dispenser.**

- (1)
- Conflict determination process of “Unable to dispense TCM continuously”.

_{11}} and {RC

_{12}, RC

_{13}}, which correspond to “Volume limit of medicine collection space on conveyor belt” and “Acceleration by gravity, Flow limit of blanking”, respectively, where the medicine collecting space is the space formed by the conveyor belt and baffle for collecting TCM.

_{11}} and {RC

_{12}, RC

_{13}}, which are “Volume” and “Gravity, Acceleration, Mass flow”, respectively, as shown in Table 8. By sorting the physical parameters of each group in Table 8 according to the influence degree on the problem, it can be obtained that the physical parameter sets related to “Unable to dispense TCM continuously” are ${P}_{1}=\left({V}_{c}\right)$ and ${P}_{2}=\left({Q}_{o},{a}_{b},G\right)$. ${P}_{1}$ and ${P}_{2}$ are the problem’s improvement goals.

- (2)
- Conflict determination process of “TCM accumulation at outlet”.

**Step 4: Selecting engineering parameters through the mapping model.**

- (1)
- ${P}_{1}=\left({V}_{c}\right)$, ${P}_{1}^{-}=\left({V}_{F}\right)$ and ${P}_{2}^{-}=\left(\sigma \right)$ are only related to one parameter. It can be seen directly that the engineering parameters corresponding to ${P}_{1}$ and ${P}_{1}^{-}$ are No.8 Volume of stationary object, the engineering parameter corresponding to ${P}_{2}^{-}$ is No.11 Stress or pressure.
- (2)
- ${P}_{2}=\left({Q}_{o},{a}_{b},G\right)$, ${P}_{3}=\left(T,{t}_{e},{F}_{b}\right)$ and ${P}_{4}=\left({f}_{r},{l}_{r},{S}_{o}\right)$ are related to the actions of multiple parameters respectively. Direct correspondence with engineering parameters is difficult. They have no relation to the engineering parameters (No.24, No.35 and No.38).
- (3)
- ${P}_{2}$, ${P}_{3}$ and ${P}_{4}$ are encoded according to the code rules of the physical parameter set, and then inputted into the mapping model, respectively. The obtained engineering parameter mapping results are shown in Table 10. According to the mapping results, the engineering parameters corresponding to ${P}_{2}$, ${P}_{3}$ and ${P}_{4}$ are selected as No.39 Productivity, No.30 Object-affected harmful and No.25 Loss of time, respectively.

**Step 5: Solving the conflicts of the bulk TCM dispenser.**

- (1)
- Conflict solving process of “Unable to dispense TCM continuously”.

- (2)
- Conflict solving process of “TCM accumulation at outlet”.

**Step 6:**

**Evaluating schemes.**

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Training results of category ($k$) mapping model between physical parameters and engineering parameters.

**Figure A2.**Training results of sequence ($t$) mapping model between physical parameters and various engineering parameters.

## Appendix B

Scheme | Project Indicator Layer | E1 | E2 | E3 | E4 | E5 |
---|---|---|---|---|---|---|

S1 | Dispensing efficiency | 4 | 5 | 5 | 6 | 4 |

Automatic control | 6 | 5 | 6 | 6 | 6 | |

Dispensing error | 4 | 6 | 5 | 5 | 4 | |

S2 | Dispensing efficiency | 6 | 6 | 7 | 6 | 4 |

Automatic control | 7 | 5 | 7 | 5 | 5 | |

Dispensing error | 6 | 7 | 6 | 6 | 5 |

Scheme | Project Indicator Layer | E1 | E2 | E3 | E4 | E5 |
---|---|---|---|---|---|---|

S1 | Design cost | 7 | 6 | 6 | 5 | 6 |

Production cost | 6 | 5 | 4 | 5 | 4 | |

Maintenance cost | 5 | 6 | 5 | 5 | 6 | |

S2 | Design cost | 5 | 4 | 5 | 6 | 5 |

Production cost | 5 | 4 | 6 | 5 | 5 | |

Maintenance cost | 4 | 5 | 4 | 6 | 5 |

Scheme | Project Indicator Layer | E1 | E2 | E3 | E4 | E5 |
---|---|---|---|---|---|---|

S1 | Environmental protection | 5 | 6 | 7 | 5 | 5 |

Vibration and noise | 5 | 4 | 5 | 5 | 4 | |

Energy saving | 6 | 5 | 4 | 4 | 5 | |

S2 | Environmental protection | 7 | 8 | 6 | 7 | 8 |

Vibration and noise | 8 | 6 | 7 | 6 | 7 | |

Energy saving | 7 | 5 | 6 | 5 | 6 |

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**Figure 5.**(

**a**) Code of the physical parameter set when $n=2$; (

**b**) code of the physical parameter set when $n\ge 4$.

**Figure 7.**Calling module of the mapping model between physical parameters and engineering parameters.

**Figure 8.**Conflict solving process based on mapping between physical parameters and engineering parameters.

No. | Name | No. | Name | No. | Name |
---|---|---|---|---|---|

1 | Weight of moving object | 14 | Strength | 27 | Reliability |

2 | Weight of stationary object | 15 | Durability of moving object | 28 | Measurement accuracy |

3 | Length of moving object | 16 | Durability of non-moving object | 29 | Manufacturing precision |

4 | Length of stationary object | 17 | Temperature | 30 | Object-affected harmful |

5 | Area of moving object | 18 | Illumination intensity | 31 | Harmful side effect |

6 | Area of stationary object | 19 | Use of energy by moving object | 32 | Ease of manufacture |

7 | Volume of moving object | 20 | Use of energy by stationary object | 33 | Ease of operation |

8 | Volume of stationary object | 21 | Power | 34 | Ease of repair |

9 | Speed | 22 | Loss of energy | 35 | Adaptability of versatility |

10 | Force | 23 | Loss of substance | 36 | Complexity of device |

11 | Stress or pressure | 24 | Loss of information | 37 | Complexity of control |

12 | Shape | 25 | Loss of time | 38 | Level of automation |

13 | Stability of the object | 26 | Quantity of substance | 39 | Productivity |

Content | Value |
---|---|

Number | 5 |

Kendall synergy coefficient | 0.967 |

Chi square | 2557.839 |

Freedom | 529 |

Asymptotic significance | 0.000 |

Category | Engineering Parameter |
---|---|

Substance | No.1, No.2, No.14, No.23, No.26 |

Space | No.3, No.4, No.5, No.6, No.7, No.8, No.12 |

Time | No.9, No.15, No.16, No.25, No.39 |

Field | No.10, No.11, No.17, No.18, No.19, No.20, No.21, No.22 |

Structure | No.13, No.29, No.32, No.36 |

Information | No.24, No.27, No.28, No.30, No.31, No.33, No.34, No.35, No.37, No.38 |

Category | $\mathbf{Code}(\mathit{k})$ | $\mathbf{Engineering}\mathbf{Parameter}\mathbf{and}\mathbf{Its}\mathbf{Code}(\mathit{t})$ |
---|---|---|

Substance | 1 | No.1 (1), No.2 (2), No.14 (3), No.23 (4), No.26 (5) |

Space | 2 | No.3 (1), No.4 (2), No.5 (3), No.6 (4), No.7 (5), No.8 (6), No.12 (7) |

Time | 3 | No.9 (1), No.15 (2), No.16 (3), No.25 (4), No.39 (5) |

Field | 4 | No.10 (1), No.11 (2), No.17 (3), No.18 (4), No.19 (5), No.20 (6), No.21 (7), No.22 (8) |

Structure | 5 | No.13 (1), No.29 (2), No.32 (3), No.36 (4), |

Information | 6 | No.27 (1), No.28 (2), No.30 (3), No.31 (4), No.33 (5), No.34 (6), No.37 (7) |

Number | Category | Accuracy | Number | Category | Accuracy |
---|---|---|---|---|---|

1 | Substance | 95% | 4 | Field | 90% |

2 | Space | 95% | 5 | Structure | 94.7% |

3 | Time | 90% | 6 | Information | 95% |

System Composition | Component | Physical Parameters | Symbol |
---|---|---|---|

Operating control device | Single chip microcomputer | Current 1 | I_{sl} |

Energy device | Power supply device | Power, Voltage, Current 2 | P, U_{e}, I_{e} |

Transmission device | Motor I | Speed 4 | v_{m}_{1} |

Motor II | Speed 5 | v_{m}_{2} | |

Eccentric wheel | Transmission ratio 1, Speed 1, Eccentricity | i_{w}, v_{w}, d_{w} | |

Transmission assembly | Speed 7, Transmission ratio 2 | v_{da}, i_{da} | |

Execution device | Connecting rod | Length, Frequency, Shear stress | ${l}_{r},{f}_{r},\sigma $ |

Vibrating disk | Speed 2, Area 1 | v_{d}, S_{d} | |

Outlet | Speed 3, Area 2, Mass flow | v_{o}, S_{o}, Q_{o} | |

Baffle | Height | H_{g} | |

Conveyor belt | Area 3, Volume 3, Speed 6,Output flow, Output weight, Output time | S_{c}, V_{c}, v_{c}, Q_{c}, m_{c}, t_{c} | |

Weighing sensor | Accuracy, Quantity | E_{s}, N_{s} | |

Frame | Volume 1 | V_{F} | |

Medicine chest | Volume 2 | V_{m} | |

Super-system | Environment | Temperature | T |

Target | Bulk TCM | Friction, Viscosity, Pressure, Time | $F,\mu $, F_{b}, t_{e} |

No. | Dimensionless Expression | No. | Dimensionless Expression |
---|---|---|---|

1 | ${\pi}_{{v}_{o}}={v}_{o}\xb7{v}_{d}{}^{-1}{S}_{d}{}^{-1}{S}_{o}$ | 5 | ${\pi}_{{I}_{e}}={I}_{e}\xb7{P}^{-1}\xb7{U}_{e}$ |

2 | ${\pi}_{{v}_{d}}={v}_{d}\xb7{f}_{d}^{-1}\xb7{l}_{r}^{-1}$ | 6 | ${\pi}_{{v}_{da}}={v}_{da}\xb7{i}_{da}^{-1}\xb7{v}_{m2}^{-1}$ |

3 | ${\pi}_{{f}_{d}}={f}_{d}\xb7{d}_{w}\xb7{v}_{w}^{-1}$ | 7 | ${\pi}_{{m}_{c}}={m}_{c}\xb7{Q}_{c}^{-1}\xb7{t}_{c}^{-1}$ |

4 | ${\pi}_{{v}_{w}}={v}_{w}\xb7{i}_{w}^{-1}\xb7{v}_{m1}^{-1}$ | 8 | ${\pi}_{{V}_{c}}={V}_{c}\xb7{S}_{c}{}^{-1}{H}_{g}{}^{-1}$ |

No. | Root Cause | Extracted Parameters | Physical Parameter Set |
---|---|---|---|

1 | RC_{11} | Volume V_{C} | ${P}_{1}=\left({V}_{c}\right)$ |

2 | RC_{12}, RC_{13} | Gravity G, Acceleration a_{b}, Mass flow Q_{o} | ${P}_{2}=\left({Q}_{o},{a}_{b},G\right)$ |

No. | Root Cause | Extracted Parameters | Physical Parameter Set |
---|---|---|---|

1 | RC_{22}, RC_{25}, RC_{26} | Force F_{b}, Temperature T, Time t_{e} | ${P}_{3}=\left(T,{t}_{e},{F}_{b}\right)$ |

2 | RC_{21}, RC_{23}, RC_{24} | Area S_{o}, Frequency f_{r}, Length l_{r} | ${P}_{4}=\left({f}_{r},{l}_{r},{S}_{o}\right)$ |

Physical Parameter Set | ${\mathit{P}}_{2}=\left({\mathit{Q}}_{0},{\mathit{a}}_{\mathit{b}},\mathit{G}\right)$ | ${\mathit{P}}_{3}=\left(\mathit{T},{\mathit{t}}_{\mathit{e}},{\mathit{F}}_{\mathit{b}}\right)$ | ${\mathit{P}}_{4}=\left({\mathit{f}}_{\mathit{r}},{\mathit{l}}_{\mathit{r}},{\mathit{S}}_{\mathit{o}}\right)$ |
---|---|---|---|

Input code | 3-311-11-211-14-411000000 | 5-4231010114-411100000 | 0-101-11001-12001-100000 |

Mapping value | $E{p}_{4}=\left[\begin{array}{cc}3& 5\end{array}\right]$ | $E{p}_{1}=\left[\begin{array}{cc}6& 3\end{array}\right]$ | $E{p}_{2}=\left[\begin{array}{cc}3& 4\end{array}\right]$ |

Engineering parameter | No.39 Productivity | No.30 Object-affected harmful | No.25 Loss of time |

Deterioration Parameter → Improved Parameter ↓ | $\mathbf{No}.8\mathbf{Volume}\mathbf{of}\mathbf{Stationary}\mathbf{Object}({\mathit{P}}_{1}^{-})$ |
---|---|

$\mathrm{No}.8\mathrm{Volume}\mathrm{of}\mathrm{stationary}\mathrm{object}({P}_{1}$) | — |

$\mathrm{No}.39\mathrm{Productivity}({P}_{2}$) | No.35 Parameter changes, No.37 Thermal expansion, No.10 Preliminary action, No.2 Taking out |

Deterioration Parameter → Improved Parameter ↓ | $\mathbf{No}.11\mathbf{Stress}\mathbf{or}\mathbf{Pressure}\left({\mathit{P}}_{2}^{-}\right)$ |
---|---|

$\mathrm{No}.30\mathrm{Object}-\mathrm{affected}\mathrm{harmful}({P}_{3}$) | No.22 ‘Blessing in disguise’ or ‘Turn Lemons into Lemonade’, No.2 Taking out, No.37 Thermal expansion |

$\mathrm{No}.25\mathrm{Loss}\mathrm{of}\mathrm{time}({P}_{4}$) | No.37 Thermal expansion, No.36 Phase transitions, No.4 Asymmetry |

Target Layer | Comprehensive Indicator Layer (Weight Value) | Project Indicator Layer (Weight Value) |
---|---|---|

Mechanical system performance | U_{1} Service performance (0.71) | U_{11} Dispensing efficiency (0.62) |

U_{12} Automatic control (0.14) | ||

U_{13} Dispensing error (0.24) | ||

U_{2} Economic performance (0.10) | U_{21} Design cost (0.55) | |

U_{22} Production cost (0.12) | ||

U_{23} Maintenance cost (0.33) | ||

U_{3} Green performance (0.19) | U_{31} Environmental protection (0.11) | |

U_{32} Vibration and noise (0.63) | ||

U_{33} Energy saving (0.26) |

Comprehensive Indicator Layer | Prototype (S1) | New Scheme (S2) |
---|---|---|

Service performance | 4.94 | 5.85 |

Economic performance | 5.66 | 4.93 |

Green performance | 4.76 | 6.58 |

Final score | 4.98 | 5.90 |

Case | Improved Parameter | Deterioration Parameter | T1 | T2 | T3 | T4 |
---|---|---|---|---|---|---|

TCM dropping pill machine | No.29 | No.39 | 2 | 2 | 2 | 2 |

TCM pill wiping machine | No.27 | No.12 | 2 | 1 | 0 | 1 |

High-speed permanent magnet brushless DC motor | No.9 | No.30 | 2 | 1 | 2 | 1 |

New magnetic levitation rotor flowmeter | No.27 | No.26 | 2 | 2 | 1 | 2 |

Electric actuator cover | No.23 | No.14 | 2 | 1 | 2 | 1 |

Double Tourbillon Mechanical Watch | No.13 | No.36 | 1 | 2 | 1 | 2 |

Static metering method of continuous fluid | No.28 | No.9 | 2 | 2 | 2 | 2 |

Disposable anchor rod | No.12 | No.14 | 2 | 2 | 1 | 1 |

Coring device | No.11 | No.21 | 2 | 2 | 2 | 2 |

Twin screw oil and gas mixing pump | No.32 | No.30 | 1 | 0 | 1 | 1 |

Glass melting furnace | No.30 | No.16 | 1 | 1 | 0 | 2 |

Disc spring cylinder spectacle valve | No.27 | No.29 | 2 | 2 | 1 | 1 |

Hydrofining unit | No.22 | No.8 | 2 | 2 | 2 | 2 |

Mold for low pressure casting aluminum alloy wheel hub | No.39 | No.23 | 2 | 2 | 2 | 1 |

Belt conveyor of heavy calcium plant | No.13 | No.31 | 2 | 1 | 1 | 2 |

Selection accuracy | 90% | 76.7% | 66% | 70% |

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## Share and Cite

**MDPI and ACS Style**

Zhang, P.; Ma, Q.; Nie, Z.; Li, X.
A Conflict Solving Process Based on Mapping between Physical Parameters and Engineering Parameters. *Machines* **2022**, *10*, 323.
https://doi.org/10.3390/machines10050323

**AMA Style**

Zhang P, Ma Q, Nie Z, Li X.
A Conflict Solving Process Based on Mapping between Physical Parameters and Engineering Parameters. *Machines*. 2022; 10(5):323.
https://doi.org/10.3390/machines10050323

**Chicago/Turabian Style**

Zhang, Peng, Qianhao Ma, Zifeng Nie, and Xindi Li.
2022. "A Conflict Solving Process Based on Mapping between Physical Parameters and Engineering Parameters" *Machines* 10, no. 5: 323.
https://doi.org/10.3390/machines10050323