Development of Washing Machine Dehydration Unbalance Control Specifications Through Bayesian Optimization

Featured Application

Optimization of control parameters for home appliances.

Abstract

Optimizing control specifications to prevent unbalance during the dehydration process in washing machine development is a complex task that consumes significant time and resources. Traditional methods involve expert engineers conducting various experiments and data analyses to develop optimal control specifications. However, these approaches are time-consuming and struggle to optimize diverse performance factors simultaneously. Additionally, the quality of the results heavily depends on the engineers’ experience and capabilities, making it challenging to maintain consistent quality. To overcome these limitations, a new data-driven approach is proposed. This study proposes a methodology that uses Bayesian Optimization to predict the unbalance during the dehydration process and derive optimal control specifications to minimize it. Bayesian Optimization builds a predictive model based on collected data and uses an acquisition function for efficient exploration to find the optimal solution. Through this method, we automated the optimization of unbalance prevention control specifications. Applying the proposed methodology to an actual washing machine model achieved performance equivalent to that derived by expert engineers. Specifically, we succeeded in maintaining the maximum vibration during the dehydration process below the target level and reducing the time to reach high-speed rotation (RPM) ranges. The main contribution of this study is the rapid derivation of machine learning-based optimized control specifications with minimal human intervention and small-scale experiments by building a test automation system within the home appliance development process. This approach shortened the development period and improved quality consistency.

1. Introduction

Washing machines are essential home appliances in modern households, and their performance and efficiency directly affect consumer satisfaction. Specifically, the dehydration performance of a washing machine significantly influences the washing time, energy consumption, and product’s durability and reliability. Dehydration performance is closely related to various factors such as power consumption, dehydration time, moisture content difference before and after washing, and vibration. These factors are interrelated, forming trade-offs in which improving one aspect may degrade another. With recent stringent energy efficiency regulations and consumer preferences for reduced vibration, washing machine manufacturers are continually striving to shorten the time to reach high-speed dehydration. This effort aims to reduce overall washing time and improve energy efficiency while minimizing vibration during the dehydration process. However, achieving these goals simultaneously is a technically challenging task. In particular, the unbalance occurring during the dehydration process is a major cause of vibration and noise, which can compromise the product’s safety and reliability.

The unbalance phenomenon in washing machines originates from the uneven distribution of laundry and dynamically changes depending on the type, amount, and placement of clothes. When unbalance occurs, the degree of unbalance is calculated by measuring the difference in angular velocity at each rotational position of the motor; this value is called the unbalance (UB) value. If the motor continues to accelerate while unbalance is detected, vibration increases rapidly. To prevent this, the motor stops rotating when the UB value exceeds specific thresholds during operation. These thresholds are specified in the Unbalance Table (UBT)—the dehydration control specification—and the dehydration performance is determined according to the UBT values set for each dehydration stage. Therefore, developing optimal dehydration unbalance prevention control specifications under various conditions requires numerous repetitive experiments and specialized data analysis, relying heavily on the experience and intuition of expert engineers. This dependence leads to prolonged development processes, increased costs, and variability in development quality based on the engineer’s expertise. Automating and streamlining the development of control specifications is essential to address these issues. Methodologies that utilize artificial intelligence techniques are required to derive optimal control specifications from small amounts of data, enhancing the consistency and reliability of the development process.

This study introduces Bayesian Optimization (BO) techniques to automatically develop unbalance prevention control specifications during the washing machine dehydration process. BO is a machine learning method that efficiently finds the optimal value of a target function in high-dimensional spaces. It is particularly suitable for optimizing functions with high evaluation costs. The method builds a probabilistic model of the unknown objective function based on current observational data, estimates the function, and determines the next exploration point through an acquisition function. This approach helps to reach the optimal value with a minimal number of experiments. With minimal human intervention, we built a test automation system called GAUS (Global Auto UB-table Tuning System), automating the entire process from experimental data collection and model training to optimal specification derivation. The main contribution of this study is the proposal of an efficient machine learning-based optimization methodology for developing unbalance prevention control specifications in washing machine dehydration. By automating the control specification development process—previously reliant on extensive experimental data or expert engineers’ experience—we reduced the development period and cost and enhanced the consistency of the development quality.

2. Related Work

Traditionally, engineers have developed and refined dehydration control specifications through repeated experiments and analyses. This approach, based on long-accumulated expertise within companies, involves engineers repeatedly testing and manually adjusting the control specifications.

Each time a parameter in the UB Table changes, the engineer edits and compiles the control code, downloads it to the MCU (Microcontroller Unit), and then manually runs tests and analyzes the results. If the experimental results fail to meet the target performance (vibration or unbalance criteria), they readjust the parameters and repeat.

Although this method is standard practice in the industry, it is labor-intensive and time-consuming, making it a natural benchmark for comparison with the automated BO approach. The engineer-driven manual process was highly inefficient for applying new parameters proposed by the BO algorithm, as BO generates a new candidate UB Table at every iteration. Applying these parameters manually in the absence of automation significantly slowed down the experimental loop.

Research has been conducted through various approaches in previous years to enhance the efficiency and safety of the dehydration process in washing machines. Studies have focused on developing active balancing mechanisms to suppress vibrations due to unbalance [1,2,3], designing suspension structures [4,5], dynamic modeling [6,7], and applying control algorithms.

Various control algorithm approaches have been explored to enhance dehydration performance in washing machines. Martiniello [8], Yorukoglu and Altug [9,10], and Su [11] proposed algorithms for measuring and evaluating the magnitude of unbalance caused by fixed loads or for estimating the position of unbalance. Yalcin and Erol [12] introduced a semi-active vibration control method that adjusts the maximum force generated by suspension elements, thereby enhancing the dynamic stability of front-loading washing machines. Joko and Honda [13] developed a dynamic model combining mechanical and stochastic algorithms to improve vibration suppression efficiency. However, their reliance on simplified two-dimensional models and single-variable unbalance limited the applicability of their approach to real-world spin performance. Shimizu [14] employed reinforcement learning to optimize spin speed by incrementally adjusting the rotation speed during dehydration to minimize unbalance. In and Kang [15] first proposed a dehydration simulator through Monte Carlo simulation based on experiments estimating the tub’s vibrations. They suggested control factors that minimize the dehydration time and vibrations using the simulator.

Despite these studies, significant variations and uncertainty remain in the maximum vibration levels and entry times during repeated dehydration experiments, even under identical conditions. Overcoming these issues requires optimizing the dehydration algorithm. Existing washing machines use algorithms that stop and retry if the vibration value exceeds a threshold during the rotation cycle. Determining algorithms under various load conditions requires substantial effort because there is a trade-off between the total vibration and dehydration time. With advancements in artificial intelligence technology, prediction control methods based on recurrent neural networks (RNNs) have recently been used to solve the dehydration unbalance problem. However, they require large amounts of training data and additional technology to determine active control factors.

Conversely, BO has been utilized across engineering disciplines for variable optimization. It effectively performs repeated search processes for global optimization and black-box problems by efficiently finding optimal solutions using previous search results [16,17,18]. Recent studies have used BO in various contexts based on these characteristics. For example, Fu [19] combined BO with Long Short-Term Memory (LSTM) to propose a model that predicts rock bursts in underground coal mines, enhancing safety. Choi and Park [20] applied BO to thermal runaway diagnosis in lithium-ion batteries, improving the performance of data-driven models. Wright [21] utilized BO to solve the race-tracking problem in resin transfer molding processes, significantly enhancing efficiency. These studies demonstrate the efficiency and robustness of BO in various engineering problems, providing practical solutions even with small datasets and high evaluation costs [22,23].

The UB Table for the dehydration cycle is defined in a time-series manner (i.e., different rotational speeds in sequence, with the low-speed stage affecting the high-speed stage’s vibration). Because RNNs (recurrent neural networks) store past state information, they are suited to analyzing such sequential data.

Early in our research, we attempted an automated UB Table tuning method by combining RNN (for time-series modeling) with a classification model (Random Forest). However, the RNN required over 5000 experimental data sets to achieve sufficient accuracy—rendering it impractical in a real manufacturing setting due to the long training time and large data needs. Nevertheless, since an RNN is typically considered a standard approach for time-series data, we selected it as a comparison target.

Current studies have remained at the laboratory and simulation level, with limitations in their direct application to actual washing machine development. Practical development requires tuning dehydration control factors to meet target dehydration performance with a minimal number of tests under various load conditions. BO is helpful in situations where evaluation costs are high, or optimization efficiency is crucial, as it enables efficient exploration even in high-dimensional nonlinear functions. Unlike methods that rely on repeated experiments and analysis by expert engineers, BO can derive optimal control parameters even with small amounts of experimental data, enabling stable and efficient dehydration control. Therefore, this paper proposes a method that leverages the advantages of BO to overcome the limitations of existing control specification development methods and explore optimal dehydration control parameters.

3. Method: Unbalance Prevention Control in Dehydration Based on BO

In this study, we propose a control specification development method based on BO to solve the unbalance problem that may occur during the dehydration process with a minimal number of tests. The two essential components of the BO method are the surrogate model and the acquisition function. First, the surrogate model probabilistically estimates the values and variances of the unknown objective function. Then, the acquisition function is used to find the optimal input value $x_{i+1}$ that is most likely to improve the currently obtained optimal solution. This value is utilized to verify whether it is optimal in the next iteration, $i+1$.

The optimization process of the control specifications based on BO consists of three steps shown in Figure 1. The first step is the preparation of the UBT dataset, where data is collected and preprocessed to define it for use in the machine learning model. The unbalance prevention control specifications, called UBT values, are defined as Input Parameters, and the test results—such as tub vibration (fail count, mean, and standard deviation) and dehydration entry time (fail count, mean, and standard deviation)—are defined as Output Parameters. Based on the Output Parameters, we define a dehydration performance indicator called the Dehydration Score (DS). Using these Input Parameters, Output Parameters, and DS values, we construct a Data and Score Matrix to enable effective learning by the machine learning model.

The second step involves using a Gaussian Process (GP)-based surrogate model to predict the DS function values and generate predictable UBT values even in untested regions. By estimating the DS values based on the GP, we build a probabilistic predictive model from the existing training data and predict regions where the UBT values are likely optimal. The prediction range is expressed as the mean and $\pm 2\sigma$ (standard deviation), indicating uncertainty. Moreover, the acquisition function predicts the optimal input value at the current score and generates new UBT, deriving UBT values where the maximum DS is expected. This process is performed iteratively and designed to generate improved UBT values in each iteration compared to the previous ones.

In the final step, verification tests are conducted on the washing machine using the new UBT values. For each UBT, more than 10 verification tests are performed to confirm the consistency and reliability of the scores. Based on these results, we evaluate the final performance of the UBT values by calculating the DS function and verifying whether actual improvement has been achieved. If the DS meets the set criteria, we adopt the UBT as the optimal unbalance prevention control specification. If further enhancement is needed, we add the new UBT and its DS value to the Data and Score Matrix to update the surrogate model, and then repeat the optimization process.

3.1. Preparation of the UBT Dataset

We analyzed and preprocessed the UBT Dataset, as shown in Figure 1a, to prepare it for use in the BO algorithm. The goal of preprocessing is to collect data and transform it into a format suitable for BO. To this end, we collected the Input Parameters, which are the unbalance prevention control specifications (UBT values), and considered each UBT value as an instance to conduct multiple experiments. The experimental results for each instance were measured as Output Parameters and evaluated by calculating the DS.

The preprocessing of the UBT Dataset is divided into three main steps. First, we collect data and define and extract the relevant features. Second, we process the collected data to make it suitable for BO. Lastly, we construct the Data and Score Matrix based on the collected data to prepare it as input for optimization.

3.1.1. Collection of the UBT Dataset: Feature Definition

By analyzing the UBT dataset, we defined features for imbalance prevention control specifications and prepared a dataset to extract these features for machine learning applications.

The Input Parameters, $x_i$, required for the experiment, ${[Slope}_{Step1},{RPM}_{Step1},{Table}_{Step1},\dots , {Slope}_{StepN},{RPM}_{StepN},{Table}_{StepN}{]}_i$, form a 34-dimensional vector. This vector is composed of UBT values for each dehydration stage from Step 1 to Step N, which are the control specifications to prevent imbalance.

Multiple experiments were conducted by considering each UBT value as the i-th instance. The Output Parameters measured from these experiments, [Time Max, Time Mean, Time Std, Vibration Max, Vibration Mean, Vibration Std, Tmeout Fail Count, Vibration Max Fail Count]_i, are indicators related to entry time and vibration, consisting of an 8-dimensional vector composed of failure counts, maximum values, mean values, and standard deviations.

3.1.2. Refinement of the UBT Dataset

After extracting important variables from the collected UBT Dataset, we refine it to be suitable for data analysis. Using the Pandas and NumPy frameworks, we remove unnecessary data or noise and supplement missing values through data cleansing. Each Input Parameter (UBT control specification) and Output Parameter (test result value) is clearly defined and then converted into a form usable for BO learning through standardization, vectorization, and normalization.

3.1.3. Composition of the Data and Score Matrix and Definition of the DS

The preprocessed data is organized into a multidimensional matrix called the Data and Score Matrix, which includes the UBT values according to each experimental condition, experimental results, and Dehydration Score (DS) values. In this matrix, each row represents an instance of the dehydration unbalance prevention control specification (UBT), and the DS is calculated through multiple experimental results for each instance. This enables a performance comparison based on the DS. The UBT and DS values are visually compared using color intensity to represent their magnitudes. Darker colors indicate higher values and better performance, while lighter colors correspond to lower values and poorer performance. This matrix is essential in the BO process as it is used to track the performance of each UBT through iterative experiments and select the optimal control specification.

The Data and Score Matrix was constructed for each input value based on the results collected from repeated experiments for each instance shown in Figure 1a: UBT Dataset.

$$Data \& Score Matrix=\left[\left[x_1,{f_{DS}(x}_1)\right],\left[x_2,{f_{DS}(x}_2)\right],\dots ,\left[x_t,{f_{DS}(x}_t)\right]\right],$$

(1)

To compute the value of the objective function, we selected the DS, which reflects the entry time and vibration amount. The DS function ${f_{DS}(x}_i)$ takes the Output Parameters as input to calculate the performance metric and is defined as follows. This function is used as the key performance metric for optimization in the subsequent BO algorithm.

$${Max f}_{DS}\left(x_i\right)= \Phi \left(Z_t\right)\times \Phi \left(Z_v\right)\times 100,\Phi \sim N\left(\mu , {\sigma }^2\right),$$

(2)

$$\begin{gathered} Subject to Time Fail Count=0 \\ Max TV Fail Count=0 \end{gathered}$$

(3)

$$Z_t= {\displaystyle \frac{(T_t-{\mu }_t )}{{\sigma }_t}}, Z_v={\displaystyle \frac{(T_v-{\mu }_v )}{{\sigma }_v}},$$

(4)

Here, $\Phi$ is the cumulative distribution function (CDF) of the standard normal distribution. We compute the satisfaction levels of both entry time and vibration via the cumulative distribution function ($\Phi$). Since $\Phi$ produces values between 0 and 1, we multiply it by 100 to express the results as percentages, enabling easier interpretation and comparison without affecting the optimization goal. $T_t$ is the threshold for entry time, ${\mu }_t$ is the mean of entry times, ${\sigma }_t$ is the standard deviation of entry times, $T_v$ is the threshold for vibration value, ${\mu }_v$ is the mean of vibration values, and ${\sigma }_v$ is the standard deviation of vibration values.

When setting the thresholds for entry time ($T_t$) and vibration ($T_v$), we referred to product testing regulations, consumer requirements, and internal safety criteria. Specifically, the entry time threshold was chosen based on the goal that the user’s laundry cycle should finish within a certain time frame, while the vibration threshold was established to comply with the product’s mechanical stability needs, noise regulations, and the company’s internal testing standards.

The DS is calculated by considering the thresholds, means, and standard deviations of dehydration entry time and tub vibration amount, assuming they follow a normal distribution. To calculate the probability of meeting the pass criteria, we use the Z values $Z_t$ for entry time and $Z_v$ for vibration amount, applying the cumulative normal distribution function $\Phi$. The constraints are that the number of times the dehydration entry time and maximum vibration value exceed the maximum allowable value must be zero. This means achieving stable results without dehydration test specification failures in more than 10 repeated tests while satisfying the target performance.

3.2. Application of the Surrogate Model

Figure 2 shows the overall flow of the BO process, explaining how the surrogate model predicts performance based on each UBT and the experimental data and how the acquisition function gradually searches for the optimal unbalance prevention control specification UBT based on the performance scores.

The surrogate model predicting the distribution of the control specifications uses a non-parametric method called the GP to estimate the unknown objective function (performance of the unbalance prevention control specification). The GP predicts both the mean and uncertainty (variance) of the DS through the given experimental data, enabling a performance estimation of the UBT regions not yet explored in the experimental space. As more observation data is accumulated, the uncertainty of the estimation decreases, and the likelihood of finding the optimal UBT increases.

Figure 2a: Make Regression Model visualizes the surrogate model, showing the performance prediction modeling of unbalance using the GP. In this figure, the predicted distribution of the DS for each UBT value and the uncertainty range for that score can be visually confirmed. The predicted mean values are represented by a red curve, indicating the expected performance of the corresponding UBT values. The training data is shown as blue dots, representing the score distribution obtained from actual experiments applying the UBT values. The predicted uncertainty range is shown as a gray-shaded area of $\pm 2\sigma$, indicating the confidence interval of the predicted values. Regions where the predicted DS mean values (red curve) are high indicate control specifications with excellent performance. In contrast, regions with larger gray shading represent areas where the confidence in performance prediction is low and high uncertainty.

When estimating the predicted DS function value $f_{DS}$, for a given Input Parameters UBT x, the GP-based predictive modeling is expressed as follows: [18]

$$f_{DS}\left(x\right) ~ GP({\mu }_{DS}\left(x\right),k_{DS}\left(x,x^{\prime }\right)),$$

(5)

Here, ${\mu }_{DS}\left(x\right)$ is the mean function, and $k_{DS}\left(x,x^{\prime }\right)$ is the covariance function (kernel function).

Given observed data $D={\left\{\left(x_i,{f(x}_i)\right)\right\}}_{i=1}^N$ the predictive distribution of the predicted function value $f_{DS}^{i+1}$ for a new input $x^{*}$ is calculated as follows: [18]

$$p\left(f_{DS}^{i+1}|x_{i+1},D\right)=N\left({\mu }_{DS}\left(x_{i+1}\right),{\sigma }_{DS}^2\left(x_{i+1}\right)\right),$$

(6)

Here, D is the set of observed data; $x_{i+1}$ is the new input value to be predicted, and $f_{DS}^{i+1}$ represents the DS for the new input value. ${\sigma }_{DS}^2\left(x_{i+1}\right)$ indicates the variance representing the uncertainty of the prediction.

3.3. Application of the Acquisition Function

Using the surrogate model’s predicted values, the acquisition function proposes UBT values for the unbalance prevention control specification, aiming to discover the maximum DS in untested regions. In this study, we used Expected Improvement (EI) as the acquisition function. As the experiment progresses, we recommend the UBT for the unbalance control specification through the EI method, experimentally verify whether it meets the target value, and perform the optimization.

Figure 2b: Suggest Candidate Sampling is the sampling process used to select candidate input values for the next stage in the BO process, with the aim being to select input value candidates likely to maximize the objective function value. We generated candidate values using a uniform distribution sampling method, and these candidate values were used as inputs for the acquisition function.

EI is an acquisition function that balances exploration and exploitation. Exploitation acts to improve performance further in regions already known to perform well, while exploration seeks new possibilities in regions not yet explored. EI predicts the probability and degree of improvement over the current best observed performance to suggest the optimization direction. EI is calculated using the predicted mean performance ${\mu }_{DS}\left(x\right)$ and standard deviation ${\sigma }_{DS}\left(x\right)$ for input value x. Here, ${\mu }_{DS}\left(x\right)$ represents the predicted performance and ${\sigma }_{DS}\left(x\right)$ represents the uncertainty of that prediction. EI combines these two values to evaluate the potential for performance improvement at that point. Additionally, EI measures the potential for improvement at a given point by comparing the current best observed performance, $f_{DS}\left(x^{+}\right)$ with predicted outcomes. A greater difference suggests a higher likelihood that exploring that point will lead to better performance, guiding the optimization process efficiently.

Figure 2c: Suggest Possible Maximum shows the process of deriving a new UBT using the acquisition function and calculating the score based on it. This process aims to generate a new UBT (unbalance prevention control specification), evaluate its performance, and derive the optimal control specification. The acquisition function predicts the optimal control parameters based on existing data to generate a new UBT. The various colored rectangles displayed on the washing machine model represent the UBT derived through the acquisition function, with each color indicating specific ranges of control values. This visualizes the control specifications that minimize unbalance. The newly calculated DS is based on key test results such as entry time and vibration amount, and we can confirm that the performance has improved compared to previous table values. Figure 2c: Suggest Possible Maximum visually shows the new UBT and the corresponding DS matrix, highlighting instances where a high DS has achieved optimal performance.

The EI formula is as follows: [18]

$$EI\left(x\right)=\left\{\begin{array}{cc}\left({\mu }_{DS}\left(x\right)-f_{DS}\left(x^{+}\right)-\xi \right) \Phi \left(Z_{DS}\right)+{\sigma }_{DS}\left(x\right) \phi \left(Z_{DS}\right),& \sigma \left(x\right)>0\\ 0,& \sigma \left(x\right)=0\end{array}\right.$$

(7)

where

$$Z_{Dehy Score}=\left\{\begin{array}{cc}{\displaystyle \frac{{\mu }_{DS}\left(x\right)-f_{DS}\left(x^{+}\right)-\xi }{{\sigma }_{DS}\left(x\right)}},& \sigma \left(x\right)>0\\ 0,& \sigma \left(x\right)=0\end{array}\right.$$

(8)

Here, ${\mu }_{DS}\left(x\right)$ is the predicted mean performance at input $x$; ${\sigma }_{DS}\left(x\right)$ is the standard deviation of that prediction, representing the uncertainty. $f_{DS}\left(x^{+}\right)$ is the current best observed performance value, and ξ is a parameter that adjusts the degree of exploration; larger values promote exploration.

$\Phi \left(Z_{DS}\right)$ is the cumulative distribution function (CDF) of the standard normal distribution of the DS, and $\phi \left(Z_{DS}\right)$ is the probability density function (PDF) of the standard normal distribution. $Z_{Dehy Score}$ is a standardized indicator that considers both the mean and standard deviation of the performance improvement potential of the DS.

Based on this value, EI calculates the potential for improvement at the experimental points, suggesting the optimization direction. A larger $\Phi \left(Z_{DS}\right)$ means greater uncertainty in the prediction at that point, promoting exploration.

Conversely, a larger ${\mu }_{DS}\left(x\right)-f_{DS}\left(x^{+}\right)$ value indicates that the expected performance at that point is higher than the current best performance, strengthening exploitation. In calculating EI, the added parameter $\xi$ adjusts the degree of exploration, promoting exploration and broader experimentation. This parameter controls the extent to which the exploration region is widened, and by adjusting the size of $\xi$, the focus of the optimization can be controlled. A large $\xi$ value enhances exploration to search more in unknown regions, while a small $\xi$ value strengthens exploitation to focus on regions that have already shown high performance.

As the experiment progresses, the UBT is updated through EI by reflecting the predicted performance and uncertainty for each experimental point. This process balances exploration and exploitation to find the optimal control specification. Based on this, the BO continuously derives the optimal control specification, ultimately achieving the optimal performance for unbalance prevention in the dehydration control specifications.

3.4. Dehydration Unbalance Control Specification Automation Process

Figure 3 illustrates the entire process of applying the BO algorithm to the automation of the dehydration unbalance control specification. This process was designed to find the optimal control specification with minimal experiments through iterative optimization.

In this experiment, we performed multiple washing machine dehydration tests for each new UBT candidate $x_{i+1}$ and evaluated the resulting DS, $f_{DS}\left(x_{i+1}\right)$. This value was added to the existing UBT data and score matrix to be utilized in the next optimization stage.

For modeling performance evaluation, the newly generated UBT was input into the test automation system to automatically update the washing machine control program. The performance of the control specification was then verified through actual dehydration tests.

The optimization starts by forming a dataset and collecting initial observation data as pairs of input and function values. Then, the BO algorithm constructs a surrogate model, which predicts the DS and incorporates uncertainty. Through the acquisition function, the candidate solution with the highest possibility of improving the current optimal value is selected, and the objective function value for that input is obtained through actual experiments. This process is repeated until the optimal condition is satisfied. As the observation data increases, the prediction accuracy of the surrogate model improves, gradually deriving the optimal control specification.

3.5. Construction of GAUS (Global Auto UB-Table Tuning System)

To automatically optimize the unbalance prevention control specifications in the washing machine dehydration process, we developed GAUS, which automates vibration control experiments, manages data, and optimizes control specifications using artificial intelligence.

GAUS consists of three main components: the vibration measurement and test automation system, the test information management system, and the UBT tuning automation system, as illustrated in Figure 4.

The first component, the vibration measurement and test automation system, measures in real-time the vibrations generated during the actual washing machine dehydration process and automatically conducts experiments to verify the effectiveness of the control specifications (UB Table). In traditional practice, an engineer would manually modify the UB Table, compile the updated code, and download it to the washing machine. However, with GAUS, changes to the UB Table can be immediately reflected in the washing machine via the Micom Write program. This automated Micom Write program takes the standardized table of UB parameters and transmits them to the washing machine’s MCU (Microcontroller Unit) through serial communication. The actual process is designed so that an automatic script runs upon a simple button click in the Micom Write software.

Various vibration sensors are installed at multiple points on the tub and cabinet of the washing machine, collecting vibration data from different axes. At the same time, the washing machine’s internal device data (time, RPM, UB values, stage information, and internal sensor readings) and external vibration data are automatically logged as test data. Both the machine’s internal data and the collected vibration data are transmitted via the vibration measurement system to the test information management system. This data is then utilized by the UB Table Tuning automation system to update the control specifications.

Thus, the test automation system reflects the control specification changes made by the UB Table Tuning automation system onto the washing machine’s control MCU and carries out tests of the washing machine’s dehydration performance. By automating the experimental process—no manual intervention required—the system significantly accelerates the optimization of unbalance prevention control specifications.

The second component, the test information management system, provides remote management of actual UB tests in the field, including test planning and UB Table registration, monitoring of test progress, and storage of test results. It also manages databases for ongoing tests, vibration measurement results, and test log data, as well as scheduling and running repeated tests indefinitely.

This test information management system manages all test data within the system, systematically collecting any data generated during the testing process. As a central data repository, it oversees data flow between the vibration measurement/test automation system and the UB Table Tuning automation system. It stores the large volume of test data, and based on that data, supplies what the optimization algorithm needs to improve the control specifications. It also forwards improved UB Table proposals generated during testing to other systems, thereby providing integrated data management and system-to-system data linkage.

The third component, the machine learning-based UB Table Tuning automation system, serves as the “brain” that creates and fine-tunes an optimized UB Table for unbalance prevention control. It uses the data provided by the test information management system, along with the test results collected by the vibration measurement/test automation system, and automatically adjusts the control specifications through a BO algorithm. By continuously exploring the optimal UB Table via a data-driven algorithm, the system can reduce vibration and maximize control performance. Once the improved UB Table control specification is generated, it is delivered to the test information management system so that additional experiments can be performed and evaluated.

From a data flow perspective, in GAUS system, the vibration data collected by the vibration measurement and test automation system is sent to the test information management system, which then relays it to the UB Table Tuning automation system to carry out the optimization process. The test information management system, in turn, stores large volumes of data and, based on it, produces UB Table improvement proposals. These proposals are then transmitted back to the vibration measurement and test automation system, realizing data linkage between the systems. Such an automated system reduces the time and cost of experimental work, and also improves the consistency and accuracy of experimental results.

GAUS system plays a vital role in optimizing the unbalance prevention control specifications of the washing machine’s dehydration process, maximizing efficiency by leveraging machine learning for control specification adjustments and experiment automation. Through this system, testing speed and accuracy are enhanced, and the level of human involvement in the control specification optimization process is minimized, producing more consistent outcomes.

4. Experiment

In this experiment, we applied the unbalance prevention control specifications developed through BO to an actual front-loading washing machine and verified the target performance through repeated experiments.

Figure 5 shows the types of clothing used in the experiment. The Light Load condition consists of a small load of jeans; although the load weight is small, the unbalance is significant, making dehydration entry difficult. The Medium Load condition is about 40% of the rated capacity, comprising winter jackets and towels. Due to the high moisture content of winter jackets, the imbalance is large, and as water drains during dehydration, an unbalanced distribution occurs, making dehydration entry unfavorable. The Heavy Load condition is about 60% of the rated capacity with various garments like shirts and underwear. In this case, the weight of the load, imbalance, and moisture content are all substantial, increasing the possibility that the imbalance distribution may change during dehydration.

4.1. Verification Experiment of the DS Using BO

The BO DS verification experiment was conducted under Medium Load conditions over a total of 10 iterations, with 17 repeated tests per iteration. Through this, we conducted a total of 170 tests and were able to optimize the UBT control specifications for a single load condition. In the optimization process, the DS value was used as the objective function, and constraints were set so that the Time Fail Count and Max Vibration (Max Tub Vibration) Fail Count were zero. Finally, the ninth UBT condition was selected as the control specification. This method could be applied to other load conditions in the same way to develop UBT control specifications. Although some variability existed in the results for each load condition, we were able to optimize the UBT control specifications within a maximum of 400 tests.

Figure 6 shows the changes in the maximum and average entry time, which is the dehydration entry time, according to the test iterations in the BO optimization test results. The entry time should be minimized because a shorter time can reduce the overall washing cycle time. The X-axis represents the test stages (Initial, 1st, 2nd, ..., 9th), and the Y-axis indicates the entry time in seconds (s).

Entry Time Max is shown as a solid line. Starting from a very high value in the initial stage, it showed significant volatility—decreasing rapidly at the beginning, then increasing, and finally converging while the overall volatility significantly decreased. Entry Time Avg is represented by a dotted line. The average entry time started at a low level in the initial stage and maintained a relatively constant value afterward. Although there was a slight increase in the fourth test, it gradually decreased, maintaining a generally stable trend without significant fluctuations.

This result confirms that while the Entry Time Max performance can change rapidly in the early stages of the BO optimization, it decreases with repeated test iterations. The average value of the entry time showed a stable decreasing trend according to the test iterations.

Figure 7 shows the changes in the maximum and average Max Vibration according to the test iterations in the BO optimization test results. Max Vibration is the vibration value of the washing tub, which should be minimized as it adversely affects noise and product reliability. However, it is in a trade-off relationship with the entry time.

Max Vibration Max is shown as a solid line. The maximum value of Max Vibration showed a decreasing trend in the initial stages, then increased sharply in the fifth test, and decreased again towards the end. This result indicates that, while the Max Vibration Max performance may exhibit volatility during BO optimization, it successfully meets the DS target value in the end.

The average value of Max Vibration did not show any significant changes according to the test iterations.

By the ninth BO test iteration, the Entry Time Max and Max Vibration Max values had decreased to satisfactory levels. This result indicates that a dehydration control specification that satisfies the dehydration time and maximum vibration was set. It is evident from the fourth and fifth tests that the Entry Time Max and Max Vibration Max have a clear trade-off relationship.

Figure 8 visualizes the optimization process of the UBT control specifications that satisfy the objective function and constraints through repeated test iterations. The X-axis represents the test iterations (Initial to 9th iteration), and the Y-axis shows the DS performance indicator and the constraints counts for Time Fail Count and Max Vibration Fail Count. In this experiment, one DS and two constraints were used to measure the optimization of the control specifications.

The DS, represented by a black solid line with circular markers, serves as a comprehensive performance evaluation indicator that takes both the entry time ($Z_t$) and vibration magnitude ($Z_v$) into account. The DS value showed significant fluctuations until midway through the tests but tended to meet the DS target value by the end. These results demonstrate that the performance underwent significant changes during the optimization process but eventually found the optimal value and terminated. Convergence of the DS to 1 means the probability of satisfying the entry time and vibration amount performance targets is nearly 1. Time Fail Count (blue dotted line) and Max Vibration Fail Count (orange dotted line) represent the counts of exceeding the allowable criteria in the entry time and maximum vibration, respectively. As the test iterations progressed, the Fail Counts initially showed somewhat high counts but eventually satisfied the constraints by reducing them to zero in the ninth iteration.

At the ninth iteration, with the DS value converging close to 1 and the Time Fail Count and Max Vibration Fail Count satisfying the constraints of zero counts, we were able to select the optimized UBT. This result means that through the iterative optimization process, we secured stable dehydration performance without exceeding the vibration and entry time specifications while simultaneously satisfying the target performance for the entry time and vibration amount.

4.2. Expert Engineer vs. BO Experiment

4.2.1. Verification of the Test Procedure and Data Organization Method

In this experiment, we compared the dehydration performance of an engineer’s manual method and the BO-based automation system using a front-loading washing machine. Three load conditions—Light, Medium, and Heavy—known for their difficulty in meeting the acceptance test criteria, were selected as comparison targets. For each load condition, more than 30 repeated tests were conducted. The performance comparison items for the test were the entry time and Max Vibration, and statistical values were calculated based on these. The calculated statistical values are expressed as the average, maximum, Z-values, etc., and the counts of exceeding the criteria were also checked. Additionally, for visualization, box plots and individual test values represented as dots were used to visually compare the results for each load condition.

4.2.2. Verification of the Test Results and Box Plots

A comparison between the engineer’s manual method and the BO-based automated approach revealed no statistically significant differences in entry time or vibration level between the two methods when more than 30 repeated tests were conducted under the same samples and load conditions. Notably, even under challenging load conditions where it is difficult to pass the acceptance test, the BO method showed results similar to the engineer’s manual development method.

Figure 9 shows box plots comparing the entry times for each load condition using the engineer’s method and the BO method. When comparing entry times across the three load conditions, the BO method significantly reduced the entry time under the Light Load compared to the engineer’s method. For the Medium and Heavy Loads, there were no significant differences in the entry time between the two methods.

Figure 10 is a box plot comparing the Max Vibration when using the engineer’s method and the BO method for each load condition.

For the Light Load, the BO method did not have any effect on reducing the vibration compared to the engineer’s method. For the Medium and Heavy Loads, there was almost no difference in the vibration between the two methods. This result suggests that the effect of the vibration optimization varies depending on each load condition, indicating the need to adjust the optimization method to suit specific load states.

4.2.3. Verification Test Results Table

Table 1. Verification test results of the entry time and Max Vibration (engineer vs. BO).

Load Type	Output Parameter			Engineer						BO				T-Test	(Two-Sided)
		Test Trials	Average	Max	St.Dev.	Z-Value	Fail Count	Test Trials	Average	Max	St.Dev.	Z-Value	Fail Count	T-Statistics	p-Value
Light Load	Entry Time [s]	51	551	1873	434	0.9	8	53	279	1348	257	2.9	1	3.865	0.0002
	Vibration [mm]		6.4	12.1	2.3	1.6	3		7.4	10.4	2.1	1.2	3	−2.475	0.0150
Medium Load	Entry Time [s]	32	233	652	162	4.6	0	35	229	677	161	4.7	0	0.135	0.8932
	Vibration [mm]		6.4	9.9	2.2	1.7	0		6.0	8.6	1.2	3.3	0	0.929	0.3578
Heavy Load	Entry Time [s]	49	240	768	150	5.0	0	31	289	834	217	3.1	0	−1.015	0.3150
	Vibration [mm]		4.9	10.4	1.6	3.6	1		4.7	7.9	1.5	3.6	0	0.284	0.7768

summarizes the test results for the entry time and Max Vibration, comparing the results of the engineer’s settings and the BO settings for the three load conditions. The table shows key performance indicators including the average (Average), maximum value (Max), standard deviation (St.Dev.), Z-value, fail count (i.e., the number of times the existing criteria were exceeded), and T-Test (two-sided) results (T-Statistics and p-value).

Under the Light Load condition, BO significantly improved performance compared to the engineer’s settings. The average entry time was reduced from 551 to 279 s, and the maximum entry time decreased from 1873 to 1348 s. Additionally, the average vibration amount increased from 6.4 mm to 7.4 mm. According to the T-Test, these differences were statistically significant (T-Statistics = 3.865, p = 0.0002 for entry time, and T-Statistics = −2.475, p = 0.0150 for Vibration).

In the Medium Load condition, BO yielded a slight decrease in entry time from 233 to 229 s, with no significant difference, and the vibration amount remained similar (from an average of 6.4 to 6.0). The T-Test (T-Statistics = −1.015, p = 0.3150 for entry time; T-Statistics = 0.284, p = 0.7768 for Vibration) found no statistically significant difference, suggesting a trade-off may exist between faster entry time and lower vibration. The T-Test results (T-Statistics = 0.135, p = 0.8932 for entry time; T-Statistics = 0.929, p = 0.3578 for Vibration) indicate no statistically significant difference compared to the engineer’s approach.

For the Heavy Load condition, the average entry time increased slightly from 240 to 269 s when using BO, but the vibration amount decreased from an average of 4.9 to 4.7. The T-Test (T-Statistics = −1.015, p = 0.3150 for entry time; T-Statistics = 0.284, p = 0.7768 for Vibration) found no statistically significant difference, suggesting a trade-off may exist between faster entry time and lower vibration.

BO demonstrated dehydration performance at a level comparable to the engineer in terms of entry time and vibration under Medium and Heavy Load conditions. However, under the Light Load condition, BO showed statistically significant superiority in entry time but significant inferiority in vibration, resulting in conflicting outcomes. This suggests that adjusting $T_t$ (the threshold for entry time) and $T_v$ (the threshold for vibration value) according to the load conditions is necessary to balance and optimize performance. The experimental results confirmed that the BO-based automation system (GAUS) achieved unbalance prevention control specifications equivalent to those of the engineer and met the dehydration performance test criteria, demonstrating its applicability to product development.

4.2.4. The Effectiveness of the BO-Based Automation System (GAUS)

As a result of applying GAUS, as shown in

Table 2. The effectiveness of the BO-based automation system (Engineer vs. GAUS).

Category	Engineer	GAUS
Automation	Manual	BO-based Tuning Automation
Development Period	3 months (Minor development standard)	1 month (Minor development standard)
Development Quality	-	Equivalent to Engineer level
Development Workforce	1 person required.8 h per day for testing and analysis	Unmanned possible. 24 h per day for testing and analysis
Tuning Scope	Entry time, vibration level perspective, selective tuning	Entry time, vibration level perspective, full-range UB Table Tuning

, we cut the development period (previously ~3 months for minor optimizations) down to ~1 month, a reduction exceeding 60%, while achieving dehydration performance equivalent to that of a seasoned engineer’s manual tuning. The daily labor burden also dropped, as GAUS can operate 24 h a day in an automated manner, whereas an engineer must manually test for about 8 h per day. Thus, we have quantitatively demonstrated that the BO-based GAUS approach outperforms or at least matches the manual process while saving significant time and labor costs.

4.3. RNN vs. BO Experiment

Comparing the BO technique with the previously applied RNN method, the BO showed equal or better performance in terms of the entry time and maximum vibration. The RNN method required more than 5000 tests to train in advance for predicting the vibration performance, making it difficult to apply in practice. The RNN model built a predictive model based on the initial UB values of dehydration and generated the optimal UBT through it. In contrast, the BO method could derive control specifications at a level equivalent to the RNN with a maximum of 500 tests. In terms of the number of tests, the BO method is considered more suitable for automating the control specifications of washing machines compared to the RNN method. For this experiment, the vibration threshold, $T_v$ was reduced to 70% of its original value to meet the stricter vibration requirements under conditions requiring minimal vibration.

Figure 11 shows the entry time verification results for the RNN and BO, comparing the entry times in the Light and Medium Load conditions. In the Light Load condition, the RNN method resulted in entry times that were, on average, higher than those achieved by the BO method, and exhibited a wider distribution. In contrast, the BO method recorded relatively shorter entry times, with the data distribution concentrated at lower values. For the Medium Load condition, the BO method demonstrated faster and more stable entry times compared to the RNN. This result indicates that the BO method had faster and more stable entry times in both the Light and Medium Load conditions when compared to the RNN.

This result demonstrates that the BO had faster and more stable entry times compared to the RNN in the Light and Medium loads.

Figure 12 shows the Max Vibration verification results for the RNN and BO, comparing the maximum vibration values for the Light and Medium Load conditions. Under the Light Load condition, the RNN method showed higher maximum vibration values and a wider distribution compared to the BO method. The BO method had relatively lower vibration values and a narrower distribution, indicating greater stability. In the Medium Load condition, the BO method exhibited lower maximum vibration values and a narrower distribution compared to the RNN, with less variation in vibration values. This result indicates that BO exhibited a more stable vibration control performance compared to the RNN.

Table 3. Verification test results of the entry time and Max Vibration (RNN vs. BO).

Load Type	Output Parameter			RNN						BO				T-Test	(Two-Sided)
		Test Trials	Average	Max	St.Dev.	Z-Value	Fail Count	Test Trials	Average	Max	St.Dev.	Z-Value	Fail Count	T-Statistics	p-Value
Light Load	Entry Time [s]	100	174	501	105	7	8	32	77	245	60	14	0	6.488	4.1 × 10−9
	Vibration [mm]		10.8	17.7	3.8	1.9	3		6.7	9.1	1.3	8.7	0	9.191	8.3 × 10−16
Medium Load	Entry Time [s]	85	332	1033	201	3	0	31	211	559	152	5	0	3.040	0.0029
	Vibration [mm]		12.0	17.9	3.9	1.6	0		11.4	16.5	2.5	2.6	0	0.907	0.3673

compares the RNN and BO in the Light and Medium Load conditions. The main comparison items are the entry time and vibration amount, consisting of the average, maximum values, whether the criteria were exceeded, Z-values, and the number of tests.

For the Light Load condition, the BO method achieved an average entry time of 77 s with a maximum of 245 s, and vibration amounts averaging 6.7 mm with a maximum of 9.1 mm. In comparison, the RNN method had an average entry time of 174 s with a maximum of 501 s, and vibration amounts averaging 10.8 mm with a maximum of 17.7 mm. The T-Test results (Two-Sided) showed statistically significant differences in both entry time (T-Statistic: 6.488, p-value: 4.1 × 10⁻⁹) and vibration (T-Statistic: 9.191, p-value: 8.3 × 10⁻¹⁶).

In the Medium Load condition, the BO method resulted in an average entry time of 211 s with a maximum of 559 s, and vibration amounts averaging 11.4 mm with a maximum of 16.5 mm. The RNN method, on the other hand, produced an average Entry Time of 332 s with a maximum of 1033 s, and vibration amounts averaging 12.0 mm with a maximum of 17.9 mm. The T-Test results showed statistically significant differences in entry time (T-Statistic: 3.040, p-value: 0.0029), while the difference in vibration was not significant (T-Statistic: 0.907, p-value: 0.3673).

These test results confirm that the BO showed a more efficient and stable performance compared to the RNN in terms of the entry time and vibration amount.

5. Discussion

In this study, we proposed a method for developing control specifications that effectively solve the imbalance problem occurring during the washing machine dehydration process by utilizing BO. Control specification development using BO was carried out in three steps. First, we constructed a UBT dataset, defined input and Output Parameters, and calculated the dehydration performance metric DS. Second, we used a surrogate model based on a GP to predict DS even in unknown regions and generated optimal UBT values through the acquisition function. Finally, we applied the new UBT values to actual washing machines to perform validation tests and confirmed whether performance was improved. In this process, GAUS system automated the processes from experimental planning of the washing machine dehydration process to data measurement, management, and imbalance prevention control specification development using BO, thereby enhancing experimental efficiency and dehydration performance.

As a result of experiments using the BO method, we were able to optimize the UBT control specifications under load conditions. As the number of test iterations progressed, the dehydration entry time (entry time) and maximum vibration amount (Max Vibration) decreased steadily, and the DS reached 1, confirming that the target performance was satisfied. Moreover, when compared with the manual method of professional engineers under various load conditions, the BO method showed equal or better performance in terms of entry time and vibration amount. Compared to the existing RNN-based method, the BO method could derive control specifications of equal level with significantly fewer test iterations. The RNN model requires more than 5000 tests to build a predictive model, making it less practical, whereas the BO method achieved optimization with up to 500 tests. This implies that the BO method is more suitable for the automation of washing machine control specifications.

Future research needs to improve the parts that require empirical decisions, such as hyperparameter tuning and the initial value setting of the BO method. Methods for performance improvement according to the type of laundry load are also necessary. Because these factors can significantly impact performance, additional research is required to optimize them. Furthermore, to further enhance the search efficiency of the methodology developed in this study, research is needed to narrow down the search range where the optimal solution is likely to occur by applying appropriate classification methods (e.g., Decision Trees). Such techniques can increase sample efficiency in BO and solve the exploration–exploitation balance problem.

Moreover, the impact of data quality variability on BO performance has not yet been sufficiently addressed, and we plan to analyze this in greater depth in future research. For example, we plan to design scenarios where data quality is progressively degraded, or specific segments are deliberately excluded, to experimentally assess the robustness of BO in identifying optimal values under such conditions.

6. Conclusions

This study presented a BO methodology capable of deriving optimal values for vibration levels and entry times in washing machine dehydration imbalance control with minimal explorations. Experimental verification under various load conditions of a front-loader washing machine confirmed that it showed performance equal to that of experienced engineers’ manual results. This study showed that it is possible to enhance product development competitiveness by reducing the consumption of resources such as cost, time, and manpower required for washing machine control specification development. By automating repetitive development tasks, we provided an environment where engineers could focus on high-value-added tasks and were able to shorten the development period. In particular, we confirmed that the BO-based active learning method is a practical alternative for efficiently deriving optimal design plans while developing control specifications.

As a result of applying GAUS, the automation of UB Table testing and tuning reduced the UBT tuning development period by more than 60%, achieving dehydration performance at a level equivalent to that of engineers’ manual work.

Although we applied our BO approach to a specific washing machine model to successfully tune dehydration control specifications, additional verification is needed for generalization to other models or manufacturing processes. Nevertheless, the approach we propose—defining a UB Table search range and an objective function to find the optimal value—suggests the following potential for broader application:

First, the same principle (i.e., defining the objective function and adjusting the search range) can be extended to other washing machine functions, such as washing, rinsing, drying, or even other appliance control parameters.

Second, by resetting performance targets (e.g., energy consumption, total cycle time) for each function, we can implement a BO approach to optimize them.

A promising future direction involves applying the BO algorithm to various stages of home appliance development to meet distinct functional performance targets. Successfully demonstrating that the approach optimizes not only dehydration performance but also other tasks will confirm that the BO algorithm verified in this study is sufficiently general for broader parameter-tuning scenarios.