Application of RBF model in the relationship between organisational innovation and organisational performance of HEM enterprises

High-end equipment manufacturing (HEM) enterprises are the high-end part of the high-tech industry and traditional equipment manufacturing industry, which integrates multi-disciplinary and multi-field high technology. The development of HEM enterprises plays an important role in leading and promoting industrial transformation and upgrading. Therefore, in recent years, our country has vigorously supported and developed HEM enterprises [1]. HEM enterprises have always faced high technical requirements in the market and fast updates and iteration. Therefore, enterprises focused most of their attention on technological innovation, while ignoring organisational innovation. However, with the continuous expansion of scale and production capacity, the previous management model has been difficult to meet the current needs of enterprises. Many enterprises urgently need to use organisational innovation to change the status quo of business operations and improve organisational efficiency and innovation. Although organisational innovation is a risky activity [2], numerous studies have demonstrated that the effect of organisational innovation on performance is positive. For example, Robinson believes that organisational innovation promotes improvements in product quality and market share, and enhances performance [3]. Similarly, OECD points out that organisational innovation improves performance by reducing transaction costs, improving employee satisfaction (and labour productivity), obtaining non-tradable assets or reducing supply costs [4]. Some scholars also believe that organisational innovation indirectly improves organisational performance (OP) through intermediary variables such as organisational learning [5], organisational capabilities [6] and technological innovation [7]. In short, organisational innovation and OP are inextricably linked, and different scholars have chosen different aspects for research.

At present, the definition of organisational innovation is not completely unified. Scholars have defined organisational innovation according to research needs: Damanpour defines organisational innovation as a new approach to devise strategy and structure, modify management processes and administrative systems, motivate and reward employees, and achieve organisational adaptation and change [8]. Mazzanti believes organisational innovation is an activity that breaks conventions. The innovation process is accompanied by changes in organisational structure, power modes, norms, business models, relationships, etc. [9]. Armbruster considers that organisational innovation is the application of new management and work ideas in the organisation and divides it into two categories: process innovation and structural innovation [10]. From the definition, we can see that organisational innovation is a concept involving multiple dimensions. Kotter and Cohen believe that strategy, structure, culture and processes are very important parts of organisational innovation [11]. Perri proposed that organisational innovation consists of two parts: internal innovation and external innovation. Internal innovation includes innovation in organisational structure and organisational model, while external innovation includes innovation in inter-organisational relationships [12]. Zhang Meili summarised the ten elements of organisational innovation involved in previous research results, namely strategy, process, relationship, institution, market, structure, service, culture, learning and personnel, and divided them into four types of organisational innovation [13].

Based on previous studies, this paper believes that organisational innovation is to adapt to the external environment and the application of new management methods within the organisation. Our research mainly focuses on organisational elements related to internal management at the organisational level. Among the ten elements summarised by Zhang Meili, we extracted the five elements that fit the scope of this article, namely structure, strategy, culture, process and institution. Therefore, the organisational innovation studied in this article specifically includes strategic innovation, structural innovation, process renewal, cultural innovation and institutional innovation. Strategic innovation refers to the organisation's new approach to strategic positioning and business models to gain competitive advantage and create value [14]. Structural innovation refers to activities that change the way of organisation coordination, communication and contact, and the distribution of organisational responsibilities and obligations [15]. Process innovation refers to the new approach to operating procedures, methods and rule systems in production and management activities [16]. Cultural innovation is an activity that promotes or reshapes organisational culture [17]. Institutional innovation refers to a new approach to forming relevant management systems within an organisation.

Organisational innovation is a complex process involving a series of organisational elements which do not exist independently but interact with each other. The relationship between organisational innovation and OP is also difficult to express in a simple linear relationship and is more like a complex system. Organisational innovation is the input, OP is the output, and the process of organisational innovation on performance is an unknown function. Therefore, this article attempts to introduce a neural network model that further explores the functional relationship between organisational innovation and OP. Among the many neural network models, the Radial Basis Function (RBF) is a feedforward network with strong approximation ability and fast convergence. It is very suitable for scenarios with small data levels. So, this paper introduces the RBF model to fit the effect of organisational innovation on OP and attempts to establish a model to obtain a more accurate relationship between the two so as to take more targeted innovation activities.

RBF network is a kind of feedforward neural network and, generally, can be divided into three layers: input layer, hidden layer and output layer [18]. The RBF network structure is shown in Figure 1. When the RBF network fits the process of the system, first, the low-dimensional data samples are mapped into the high-dimensional space through the RBF so that it has the possibility of linear fitting; then, the linear approximation method is used to train the network structure. This allows the RBF network to approximate any nonlinear function and has a faster convergence speed [19].

Fig. 1

The sample mapping process can be abstracted as distorting an originally flat data space R in a higher-dimensional Euclidean space into R’. This distorted data expression can be calculated by the data difference in the Euclidean space. In this paper, the spatial mathematical expression after interpolation calculation is denoted as G, which can be calculated in the following form: (1-1) G(xi)=di G({x_i}) = {d_i}

Among them, i is the number of central points of the RBF settlement and d is the projection of the sample point on the R’ plane. Mathematical expressions for calculating curved surfaces can be used in the following ways: (1-2) G(X)=∑i=1nωiφ(x−xi) G(X) = \sum\limits_{i = 1}^n {\omega _i}\varphi \left( {x - {x_i}} \right)

Among them, x − x_i is the norm of the centre of the sample point and ω is the weight of the radial basis network.

Combining Eqs (1-1) and (1-2), the following form can be obtained: (1-3) ∑i=1Nωiφ(x−xi)=di \sum\limits_{i = 1}^N {\omega _i}\varphi \left( {x - {x_i}} \right) = {d_i}

Let φ_ij = x_i − x_j, and the form of the formula (1-3) can be organised as: (1-4) [φ11φ12⋯φ15φ21φ22⋯φ25⋯⋯⋯⋯φ51φ52⋯φ55][ω1ω2⋯ω5]=[d1d2…d5] \left[ {\matrix{ {{\varphi _{11}}} & {{\varphi _{12}}} & \cdots & {{\varphi _{15}}} \cr {{\varphi _{21}}} & {{\varphi _{22}}} & \cdots & {{\varphi _{25}}} \cr \cdots & \cdots & \cdots & \cdots \cr {{\varphi _{51}}} & {{\varphi _{52}}} & \cdots & {{\varphi _{55}}} \cr } } \right]\left[ {\matrix{ {{\omega _1}} \cr {{\omega _2}} \cr \cdots \cr {{\omega _5}} \cr } } \right] = \left[ {\matrix{ {{d_1}} \cr {{d_2}} \cr \ldots \cr {{d_5}} \cr } } \right]

Let Ω = [ω₁ ω₂·… ω_n]^T and D = [d₁ d₂ … d_n]^T, then Eq. (1-4) can be expressed as Eq. (1-5) (1-5) Φ⋅Ω=D \Phi \cdot \Omega = {\rm{D}}

Among them, Ω shows the weight of the output layer of the RBF network and D is the target response vector. D is the prior condition given when calculating the surface. In this paper, the Gauss function is selected [20], and its specific form is shown in the formula (1-6). (1-6) φ(r)=exp(−r22δ2) \varphi (r) = \exp \left( { - {{{r^2}} \over {2{\delta ^2}}}} \right)

After determining D and Φ, the weights of the radial basis network can be solved according to the formula shown in Eq. (1-7) to determine the weights of the output layer of the RBF network. (1-7) Ω=Φ−1⋅D \Omega = {\Phi ^{ - 1}} \cdot D

Currently, for HEM enterprises, competition in the external market is becoming increasingly fierce. The importance of organisational innovation has become increasingly prominent. In this situation, this article uses the RBF model to study the relationship between organisational innovation and OP, and attempts to clarify the important role of organisational innovation on OP. The results show that all dimensions of organisational innovation have a positive effect on performance. Arranged in descending order of the degree of influence on OP, the results are strategic innovation, structural innovation, process innovation, cultural innovation and institutional innovation.

Based on the research results, suggestions are made for HEM enterprises to organise innovation activities. First, take strategic innovations at the right time, regularly evaluate the external market environment, accurately position its own resources and capabilities, maintain a keen sense of the market, seize market opportunities and make full use of corporate resources. Second, according to the actual management needs of the organisation, appropriately reduce the organisational hierarchy, delegate decision-making power and fully release the staff's enthusiasm; at the same time, increase the management width, strengthen communication and exchanges between departments and thereby improve work efficiency. Third, streamlining the management process and removing complicated and redundant processes will not only help improve the work efficiency of each department and reduce management costs but also shorten the overall product cycle and improve product quality. Fourth, establish an innovative culture and vigorously promote the importance of innovation and the enterprise's innovation-oriented values in ideology; encourage innovation, tolerate failure in behaviour and provide employees with more learning and training opportunities so that employees have more inspiration and knowledge accumulation, and then it is easier to generate good ideas. Fifth, improve the incentive mechanism and internal intellectual property system, and give material and spiritual rewards to employees who have achieved important innovations in their work. While stimulating employees’ enthusiasm for innovation, these rewards also set an example for other employees. At the same time, the property rights system protects the innovation achievements and interests of employees.